Finite Group Databasebeta

← #28293121

Subgroups — #28293121

Order 13568.

7102 conjugacy classes of subgroups.

The subgroup lattice has 1562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288574C214yesmaximal, complemented
2#20288571C214yesmaximal, complemented
3#20288570C214yesmaximal, complemented
4#20288562C214yesmaximal, complemented
5#20288561C214yesmaximal, complemented
6#20288557C214yesmaximal, complemented
7#20288436C211yesmaximal, characteristic, complemented
8#20288435C211yesmaximal, characteristic, complemented
9#20288434C211yesmaximal, characteristic, complemented
10#20288429C214yesmaximal, complemented
11#20288426C214yesmaximal, complemented
12#20288421C212yesmaximal, complemented
13#20288419C214yesmaximal, complemented
14#20288418C212yesmaximal, complemented
15#20288415C214yesmaximal, complemented
16#20288126C214yesmaximal, complemented
17#20288125C214yesmaximal, complemented
18#20288119C211yesmaximal, characteristic, complemented
19#20288045C212yesmaximal, complemented
20#20288043C211yesmaximal, characteristic, complemented
21C2×#16811103C211yesmaximal, characteristic, complemented
22#520×D53C212yesmaximal, complemented
23C53×#3493C211yesmaximal, characteristic, complemented
24C22×#11719945C2211yescharacteristic
25C2×#41×D53C2212yes—
26#16811357C2218yescomplemented
27#16811356C2214yescomplemented
28#16811355C2214yescomplemented
29#16811355C2218yescomplemented
30#16811350C2214yescomplemented
31#16811349C2214yescomplemented
32#16811347C2214yescomplemented
33#16811345C2214yescomplemented
34#16811344C2214yescomplemented
35#16811342C2214yescomplemented
36#16811341C2218yescomplemented
37#16811341C2214yescomplemented
38#16811340C2218yescomplemented
39#16811340C2218yescomplemented
40#16811339C2214yescomplemented
41#16811337C2214yescomplemented
42#16811336C2214yescomplemented
43#16811335C2218yescomplemented
44#16811333C2214yescomplemented
45#16811332C2214yescomplemented
46#16811331C2214yescomplemented
47#16811330C2214yescomplemented
48#16811329C2214yescomplemented
49#16811328C2214yescomplemented
50#16811326C2214yescomplemented
51#16811325C2214yescomplemented
52#16811325C2214yescomplemented
53#16811324C2218yescomplemented
54#16811323C2214yescomplemented
55#16811319C2214yescomplemented
56#16811317C2214yescomplemented
57#16811317C2214yescomplemented
58#16811316C2218yescomplemented
59#16811315C2214yescomplemented
60#16811315C2214yescomplemented
61#16811314C2214yescomplemented
62#16811313C2214yescomplemented
63#16811312C2214yescomplemented
64#16811312C2214yescomplemented
65#16811311C2214yescomplemented
66#16811309C2218yescomplemented
67#16811306C2218yescomplemented
68#16811291C2218yescomplemented
69#16811278C2214yescomplemented
70#16811277C2214yescomplemented
71#16811274C2214yescomplemented
72#16811273C2214yescomplemented
73#16811271C2218yescomplemented
74#16811254C2211yescharacteristic, complemented
75#16811253C2214yescomplemented
76#16811251C2212yescomplemented
77#16811250C2214yescomplemented
78#16811248C2214yes—
79#16811221C2218yescomplemented
80#16811217C2218yescomplemented
81#16811216C2218yescomplemented
82#16811215C2218yescomplemented
83#16811214C2218yescomplemented
84#16811214C2218yescomplemented
85#16811213C2214yescomplemented
86#16811212C2218yescomplemented
87#16811211C2214yescomplemented
88#16811210C2214yescomplemented
89#16811207C2218yescomplemented
90#16811207C2218yescomplemented
91#16811205C2218yescomplemented
92#16811204C2211yescharacteristic
93#16811203C2212yes—
94#16811203C2212yes—
95#16811202C2212yes—
96#16811202C2212yes—
97#16811201C2212yes—
98#16811196C2214yescomplemented
99#16811196C2212yescomplemented
100#16811196C2212yescomplemented
101#16811195C2214yescomplemented
102#16811189C2214yescomplemented
103#16811189C2212yescomplemented
104#16811189C2212yescomplemented
105#16811188C2214yescomplemented
106#16811184C2214yes—
107#16811183C2214yes—
108#16811181C2214yes—
109#16811179C2214yescomplemented
110#16811178C2214yescomplemented
111#16811175C2214yescomplemented
112#16811170C2214yes—
113#16811170C2214yes—
114#16811168C2214yes—
115#16811160C2218yescomplemented
116#16811159C2214yescomplemented
117#16811157C2214yescomplemented
118#16811156C2218yescomplemented
119#16811154C2214yescomplemented
120#16811152C2218yescomplemented
121#16811151C2218yescomplemented
122#16811136C2214yescomplemented
123#16811135C2212yescomplemented
124#16811135C2218yescomplemented
125#16811134C2212yescomplemented
126#16811133C2214yescomplemented
127#16811133C2218yescomplemented
128#16811132C2214yescomplemented
129#16811132C2214yescomplemented
130#16811132C2218yescomplemented
131#16811132C2218yescomplemented
132#16811131C2218yescomplemented
133#16811130C2212yescomplemented
134#16811129C2218yescomplemented
135#16811106C2212yescomplemented
136#16811105C2214yescomplemented
137#16811104C2214yescomplemented
138#16811104C2212yescomplemented
139#16811103C2214yescomplemented
140#16811103C2214yescomplemented
141#16811103C2214yescomplemented
142#16811103C2214yescomplemented
143#16811103C2212yescomplemented
144#16811103C2214yescomplemented
145#16811102C2218yescomplemented
146#16811102C2214yescomplemented
147C2×C4×Dic106C2212yescomplemented
148C4×Q8×D53C2214yescomplemented
149C2×C4×D212C2212yes—
150C2×#13133177C2212yes—
151C2×#13133177C2212yescomplemented
152C4×D4×D53C2218yes—
153C4×D4×D53C2214yescomplemented
154C2×#13133175C2211yescharacteristic
155C2×#13133175C2211yescharacteristic, complemented
156#117×D53C2212yes—
157#117×D53C2214yescomplemented
158C22×C4⋊Dic53C2211yescharacteristic, complemented
159C2×C4⋊C4×D53C2211yescharacteristic
160C2×C4⋊C4×D53C2214yescomplemented
161C2×C4⋊C4×D53C2211yescharacteristic, complemented
162C53×#556C2214yescomplemented
163C53×#555C2214yescomplemented
164C53×#553C2214yescomplemented
165C53×#552C2214yescomplemented
166C53×#544C2211yescharacteristic, complemented
167C53×#538C2214yescomplemented
168C53×#537C2211yescharacteristic
169C53×#529C2214yescomplemented
170C53×#525C2212yescomplemented
171C53×#520C2212yescomplemented
172C2×#117×C53C2211yescharacteristic, complemented
173C2×#11719949C2312yes—
174C2×#11719945—28no—
175C2×#11719945C2312yes—
176C2×#11719945C2312yes—
177C2×#11719945C2312yes—
178C2×#11719945C2312yes—
179C2×#11719945C2312yes—
180C2×#11719945C2314yes—
181C2×#11719945C2318yes—
182C2×#11719947C2312yes—
183C2×#11719947C2314yes—
184C2×#11719947C2318yes—
185#41×D53—216no—
186C22×Dic106C2311yescharacteristic
187C2×Q8×D53C2312yes—
188C22×D212C2311yescharacteristic
189C22×C22⋊D53C2311yescharacteristic
190C22×C22⋊D53C2311yescharacteristic
191C2×D4×D53C2314yes—
192C2×D4×D53C2312yes—
193C23×Dic53C2312yes—
194C22×C4×D53C2314yes—
195C22×C4×D53C2311yescharacteristic
196C22×C4×D53C2312yes—
197C22×C4×D53C2318yes—
198C22×C4×D53C2312yes—
199C22×C4×D53C2311yescharacteristic
200#13133217C2314yes—
201#13133216C2314yes—
202#13133216C2314yes—
203#13133216C2314yes—
204#13133216C2314yes—
205#13133216C2314yes—
206#13133216C2314yes—
207#13133215C2314yes—
208#13133213C2314yes—
209#13133213C2314yes—
210#13133213C2314yes—
211#13133212C2318yes—
212#13133212C2318yes—
213#13133212C2318yes—
214#13133212C2318yes—
215#13133211C2318yes—
216#13133211C2318yes—
217#13133210C2318yes—
218#13133210C2318yes—
219#13133210C2318yes—
220#13133210C2318yes—
221#13133209C2318yes—
222#13133209C2314yes—
223#13133209C2314yes—
224#13133208C2318yes—
225#13133208C2314yes—
226#13133208C2314yes—
227#13133208C2314yes—
228#13133208C2314yes—
229#13133207C2318yes—
230#13133207C2318yes—
231#13133207C2318yes—
232#13133206C2318yes—
233#13133206C2314yes—
234#13133205C2314yes—
235#13133204C2314yes—
236#13133203C2318yes—
237#13133203C2318yes—
238#13133203C2314yes—
239#13133203C2314yes—
240#13133203C2314yes—
241#13133203C2318yes—
242#13133203C2314yes—
243#13133202C2318yes—
244#13133202C2318yes—
245#13133202C2314yes—
246#13133202C2314yes—
247#13133202C2318yes—
248#13133201C2318yes—
249#13133201C2318yes—
250#13133201C2318yes—
251#13133201C2314yes—
252#13133200C2318yes—
253#13133200C2314yes—
254#13133199C2318yes—
255#13133199C2318yes—
256#13133199C2318yes—
257#13133199C2318yes—
258#13133199C2314yes—
259#13133199C2314yes—
260#13133199C2318yes—
261#13133198C2318yes—
262#13133198C2314yes—
263#13133197C2318yes—
264#13133197C2312yes—
265#13133197C2314yes—
266#13133197C2312yes—
267#13133197C2318yes—
268#13133196C2318yes—
269#13133196C2312yes—
270#13133196C2314yes—
271#13133196C2312yes—
272#13133196C2314yes—
273#13133195C2318yes—
274#13133195C2318yes—
275#13133195C2314yes—
276#13133195C2314yes—
277#13133195C2318yes—
278#13133195C2318yes—
279#13133194C2318yes—
280#13133194C2318yes—
281#13133194C2314yes—
282#13133194C2314yes—
283#13133194C2318yes—
284#13133193C2312yes—
285#13133193C2314yes—
286#13133193C2312yes—
287#13133193C2318yes—
288#13133192C2312yes—
289#13133192C2318yes—
290#13133192C2312yes—
291#13133192C2314yes—
292#13133192C2314yes—
293#13133192C2314yes—
294#13133191C2314yes—
295#13133191C2312yes—
296#13133191C2312yes—
297#13133191C2314yes—
298#13133190C2314yes—
299#13133190C2318yes—
300#13133190C2318yes—
301#13133190C2314yes—
302#13133190C2314yes—
303#13133190C2314yes—
304#13133190C2314yes—
305#13133190C2314yes—
306#13133189C2314yes—
307#13133189C2318yes—
308#13133189C2318yes—
309#13133189C2314yes—
310#13133189C2318yes—
311#13133188C2314yes—
312#13133188C2312yes—
313#13133188C2312yes—
314#13133188C2314yes—
315#13133188C2314yes—
316#13133187C2318yes—
317#13133187C2314yes—
318#13133187C2314yes—
319#13133187C2314yes—
320#13133186C2314yes—
321#13133185C2314yes—
322#13133185C2314yes—
323#13133185C2318yes—
324#13133185C2314yes—
325Q8×Dic53C2314yes—
326Q8×Dic53C2314yes—
327Q8×Dic53C2314yes—
328C4×Dic106C2314yes—
329C4×Dic106C2314yes—
330C4×Dic106C2314yes—
331C4×Dic106C2314yes—
332C4×Dic106C2318yes—
333C4×Dic106C2314yes—
334C4×Dic106C2314yes—
335#13133182C2318yes—
336#13133182C2314yes—
337#13133182C2318yes—
338#13133182C2314yes—
339#13133182C2314yes—
340C4×D212C2314yes—
341C4×D212C2314yes—
342C4×D212C2314yes—
343C4×D212C2318yes—
344C4×D212C2314yes—
345C4×D212C2318yes—
346C4×D212C2318yes—
347C4×D212C2318yes—
348D4×Dic53C2314yes—
349D4×Dic53C2314yes—
350D4×Dic53C2318yes—
351D4×Dic53C2314yes—
352D4×Dic53C2318yes—
353#13133179C2314yes—
354#13133179C2314yes—
355#13133179C2314yes—
356#13133179C2318yes—
357C4×C22⋊D53C2314yes—
358C4×C22⋊D53C2314yes—
359C4×C22⋊D53C2318yes—
360C4×C22⋊D53C2318yes—
361C4×C22⋊D53C2314yes—
362C4×C22⋊D53C2314yes—
363C4×C22⋊D53C2318yes—
364C4×C22⋊D53C2318yes—
365#13133177C2318yes—
366#13133177C2318yes—
367#13133177C2318yes—
368#13133177C2318yes—
369#13133177C2318yes—
370#13133177C2318yes—
371#13133177C2318yes—
372#13133177C2318yes—
373#13133177C2318yes—
374#13133176C2314yes—
375#13133176C2312yes—
376#13133175C2318yes—
377#13133175C2314yes—
378#13133175C2314yes—
379#13133175C2314yes—
380#13133175C2314yes—
381#13133175C2312yes—
382#13133175C2312yes—
383#13133175C2314yes—
384#13133175C2314yes—
385#13133174C2318yes—
386#13133174C2318yes—
387#13133174C2318yes—
388#13133174C2314yes—
389#13133173C2318yes—
390#13133173C2318yes—
391#13133173C2318yes—
392#13133173C2314yes—
393C2×C4⋊Dic53C2314yes—
394C2×C4⋊Dic53C2314yes—
395C2×C4⋊Dic53C2314yes—
396C2×C4⋊Dic53C2311yescharacteristic
397C2×C4⋊Dic53C2311yescharacteristic
398C2×C4⋊Dic53C2312yes—
399C2×#11719919C2318yes—
400C2×#11719919C2312yes—
401C2×#11719919C2312yes—
402C4⋊C4×D53C2318yes—
403C4⋊C4×D53C2314yes—
404C4⋊C4×D53C2314yes—
405C4⋊C4×D53C2314yes—
406C4⋊C4×D53C2314yes—
407C4⋊C4×D53C2314yes—
408C4⋊C4×D53C2314yes—
409C4⋊C4×D53C2312yes—
410C4⋊C4×D53C2318yes—
411C4⋊C4×D53C2312yes—
412C2×#11719921C2312yes—
413C2×#11719921C2312yes—
414C22⋊C4×D53C2314yes—
415C22⋊C4×D53C2318yes—
416C2×C4×Dic53C2312yes—
417C2×C4×Dic53C2312yes—
418C42×D53C2314yes—
419C42×D53C2318yes—
420C2×#41×C53C2312yes—
421C23×C4×C53C2311yescharacteristic
422C4⋊Q8×C53C2314yes—
423#126×C53C2318yes—
424#126×C53C2318yes—
425#125×C53C2314yes—
426#125×C53C2314yes—
427#124×C53C2314yes—
428#124×C53C2318yes—
429#123×C53C2318yes—
430#123×C53C2314yes—
431C22⋊Q8×C53C2312yes—
432C22⋊Q8×C53C2312yes—
433C22⋊Q8×C53C2314yes—
434C22⋊Q8×C53C2314yes—
435#121×C53C2312yes—
436#121×C53C2318yes—
437#121×C53C2312yes—
438#121×C53C2314yes—
439#121×C53C2314yes—
440#120×C53C2314yes—
441C4×Q8×C53C2314yes—
442C4×Q8×C53C2314yes—
443C4×D4×C53C2314yes—
444C4×D4×C53C2314yes—
445C4×D4×C53C2318yes—
446C4×D4×C53C2314yes—
447C4×D4×C53C2314yes—
448#117×C53C2314yes—
449#117×C53C2314yes—
450#117×C53C2312yes—
451#117×C53C2314yes—
452#117×C53C2318yes—
453C2×C4⋊C4×C53C2314yes—
454C2×C4⋊C4×C53C2311yescharacteristic
455C2×C4⋊C4×C53C2311yescharacteristic
456C2×C22⋊C4×C53C2312yes—
457C2×C42×C53C2312yes—
458C24×C53C2411yescharacteristic
459C23×D53C2414yes—
460C23×D53C2411yescharacteristic
461C23×D53C2411yescharacteristic
462#41×C53—28no—
463C2×Q8×C53C2412yes—
464C2×Q8×C53C2414yes—
465C2×D4×C53C2414yes—
466C2×D4×C53C2412yes—
467C2×D4×C53C2414yes—
468C2×D4×C53C2414yes—
469C2×D4×C53C2414yes—
470C22×C4×C53—24no—
471C22×C4×C53C2411yescharacteristic
472C22×C4×C53C2414yes—
473C22×C4×C53C2412yes—
474C22×C4×C53C2412yes—
475C22×C4×C53C2412yes—
476C22×C4×C53C2412yes—
477C22×C4×C53C2418yes—
478C22×C4×C53C2411yescharacteristic
479C2×C22⋊D53—24no—
480C2×C22⋊D53—24no—
481C2×C22⋊D53C2412yes—
482C2×C22⋊D53C2412yes—
483C2×C22⋊D53C2412yes—
484C2×C22⋊D53C2412yes—
485C2×C22⋊D53C2414yes—
486C2×C22⋊D53C2414yes—
487C2×C22⋊D53C2414yes—
488C2×C22⋊D53C2414yes—
489C2×C22⋊D53C2418yes—
490C2×C22⋊D53C2414yes—
491C2×C22⋊D53C2414yes—
492C2×C22⋊D53C2414yes—
493C22×Dic53—82no—
494C22×Dic53C2411yescharacteristic
495C22×Dic53C2414yes—
496C22×Dic53C2412yes—
497C22×Dic53C2412yes—
498C22×Dic53C2418yes—
499C22×Dic53C2418yes—
500C22×Dic53C2411yescharacteristic
501#11719949—28no—
502Q8×D53—28no—
503#11719947—216no—
504#11719947—28no—
505#11719947—88no—
506D4×D53—216no—
507D4×D53—28no—
508#11719945—28no—
509#11719945—216no—
510#11719945—28no—
511#11719945—28no—
512#11719945—28no—
513#11719945—28no—
514#11719945—88no—
515C2×D212—24no—
516C2×D212C2414yes—
517C2×D212C2412yes—
518C2×D212C2412yes—
519C2×D212C2412yes—
520C2×D212C2414yes—
521C2×D212C2414yes—
522C2×D212C2414yes—
523C2×C4×D53—24no—
524C2×C4×D53—216no—
525C2×C4×D53—82no—
526C2×C4×D53—88no—
527C2×C4×D53—82no—
528C2×C4×D53#4118yescomplemented
529C2×C4×D53C2414yes—
530C2×C4×D53C2414yes—
531C2×C4×D53C2414yes—
532C2×C4×D53C2412yes—
533C2×C4×D53C2412yes—
534C2×C4×D53C2414yes—
535C2×C4×D53C2418yes—
536C2×C4×D53C2414yes—
537C2×C4×D53C2418yes—
538C2×C4×D53C2418yes—
539C2×C4×D53C2418yes—
540C2×C4×D53C2412yes—
541C2×C4×D53C2412yes—
542C2×Dic106—24no—
543C2×Dic106C2412yes—
544C2×Dic106C2414yes—
545C2×Dic106C2411yescharacteristic
546C2×Dic106C2411yescharacteristic
547C2×Dic106C2411yescharacteristic
548C2×Dic106C2411yescharacteristic
549C2×Dic106C2414yes—
550C2×Dic106C2418yes—
551C4⋊C4×C53C2414yes—
552C4⋊C4×C53C2412yes—
553C4⋊C4×C53C2414yes—
554C4⋊C4×C53C2418yes—
555C4⋊C4×C53C2412yes—
556C4⋊C4×C53C2414yes—
557C4⋊C4×C53C2418yes—
558C4⋊C4×C53C2414yes—
559C4⋊C4×C53C2414yes—
560C4⋊C4×C53C2414yes—
561C22⋊C4×C53C2418yes—
562C22⋊C4×C53C2414yes—
563C22⋊C4×C53C2414yes—
564C22⋊C4×C53C2418yes—
565C22⋊C4×C53C2418yes—
566C22⋊C4×C53C2414yes—
567C22⋊C4×C53C2414yes—
568C22⋊C4×C53C2414yes—
569C42×C53C2414yes—
570C42×C53C2414yes—
571C42×C53C2418yes—
572C42×C53C2414yes—
573C22⋊Dic53C2414yes—
574C22⋊Dic53C2418yes—
575C22⋊Dic53C2414yes—
576C22⋊Dic53C2414yes—
577C22⋊Dic53C2414yes—
578C22⋊Dic53C2418yes—
579C22⋊Dic53C2414yes—
580#11719921C2414yes—
581#11719921C2418yes—
582#11719921C2414yes—
583#11719921C2418yes—
584#11719921C2418yes—
585#11719921C2418yes—
586#11719921C2414yes—
587#11719921C2414yes—
588#11719921C2414yes—
589#11719921C2418yes—
590#11719921C2414yes—
591#11719921C2418yes—
592#11719921C2414yes—
593#11719921C2414yes—
594#11719921C2414yes—
595#11719921C2414yes—
596C4⋊Dic53C2414yes—
597C4⋊Dic53C2412yes—
598C4⋊Dic53C2414yes—
599C4⋊Dic53C2418yes—
600C4⋊Dic53C2412yes—
601C4⋊Dic53C2414yes—
602C4⋊Dic53C2414yes—
603C4⋊Dic53C2414yes—
604C4⋊Dic53C2418yes—
605C4⋊Dic53C2414yes—
606C4⋊Dic53C2414yes—
607C4⋊Dic53C2414yes—
608#11719919C2414yes—
609#11719919C2414yes—
610#11719919C2414yes—
611#11719919C2414yes—
612#11719919C2414yes—
613#11719919C2418yes—
614#11719919C2418yes—
615#11719919C2414yes—
616#11719919C2414yes—
617#11719919C2418yes—
618#11719919C2418yes—
619#11719919C2418yes—
620#11719919C2414yes—
621#11719919C2418yes—
622#11719919C2414yes—
623#11719919C2414yes—
624C4×Dic53C2418yes—
625C4×Dic53C2418yes—
626C4×Dic53C2418yes—
627C4×Dic53C2414yes—
628C4×Dic53C2414yes—
629C4×Dic53C2414yes—
630C4×Dic53C2414yes—
631C4×Dic53C2414yes—
632C4×Dic53C2414yes—
633C4×Dic53C2414yes—
634C23×C53—22no—
635C23×C53—41no—
636C23×C53—41no—
637C23×C53C2512yes—
638C23×C53C2514yes—
639C23×C53C2511yescharacteristic
640C22×D53—22no—
641C22×D53—28no—
642C22×D53—41no—
643C22×D53—44no—
644C22×D53—41no—
645C22×D53—41no—
646C22×D53—44no—
647C22×D53—41no—
648C22×D53C2×#4114yes—
649C22×D53C2512yes—
650C22×D53C2514yes—
651C22×D53C2512yes—
652Q8×C53—24no—
653Q8×C53—44no—
654D4×C53—28no—
655D4×C53—24no—
656D4×C53—44no—
657D4×C53—44no—
658D4×C53—44no—
659C2×C4×C53—22no—
660C2×C4×C53—28no—
661C2×C4×C53—24no—
662C2×C4×C53—24no—
663C2×C4×C53—42no—
664C2×C4×C53—48no—
665C2×C4×C53—42no—
666C2×C4×C53C2×#4114yes—
667C2×C4×C53C2514yes—
668C2×C4×C53C2511yescharacteristic
669C2×C4×C53C2511yescharacteristic
670C2×C4×C53C2514yes—
671C2×C4×C53C2514yes—
672C2×C4×C53C2514yes—
673C2×C4×C53C2514yes—
674C2×C4×C53C2512yes—
675C22⋊D53—28no—
676C22⋊D53—24no—
677C22⋊D53—24no—
678C22⋊D53—28no—
679C22⋊D53—24no—
680C22⋊D53—24no—
681C22⋊D53—28no—
682C22⋊D53—44no—
683C22⋊D53—48no—
684C22⋊D53—44no—
685C22⋊D53—44no—
686C22⋊D53—44no—
687C2×Dic53—22no—
688C2×Dic53—28no—
689C2×Dic53—48no—
690C2×Dic53—42no—
691C2×Dic53—42no—
692C2×Dic53—48no—
693C2×Dic53C2×#4114yes—
694C2×Dic53C2514yes—
695C2×Dic53C2514yes—
696C2×Dic53C2514yes—
697C2×Dic53C2511yescharacteristic
698C2×Dic53C2511yescharacteristic
699C2×Dic53C2514yes—
700C2×Dic53C2514yes—
701C2×Dic53C2511yescharacteristic
702C2×Dic53C2511yescharacteristic
703D212—24no—
704D212—24no—
705D212—28no—
706D212—24no—
707D212—44no—
708D212—44no—
709D212—44no—
710C4×D53—28no—
711C4×D53—24no—
712C4×D53—24no—
713C4×D53—28no—
714C4×D53—28no—
715C4×D53—44no—
716C4×D53—48no—
717C4×D53—48no—
718C4×D53—48no—
719C4×D53—48no—
720C4×D53—44no—
721C4×D53C2×#4118yes—
722C4×D53C2×#4118yes—
723Dic106—24no—
724Dic106—22no—
725Dic106—22no—
726Dic106—22no—
727Dic106—22no—
728Dic106—28no—
729Dic106—44no—
730Dic106—48no—
731#62845—531nomaximal, Sylow
732C22×C53—21no—
733C22×C53—21no—
734C22×C53—24no—
735C22×C53—22no—
736C22×C53—22no—
737C22×C53—24no—
738C22×C53—22no—
739C22×C53—24no—
740C22×C53—44no—
741C22×C53C22×#4112yes—
742C22×C53C2611yescharacteristic
743C2×D53—22no—
744C2×D53—22no—
745C2×D53—22no—
746C2×D53—24no—
747C2×D53—22no—
748C2×D53—24no—
749C2×D53—24no—
750C2×D53—22no—
751C2×D53—44no—
752C2×D53—416no—
753C2×D53—44no—
754C2×D53C22×#4114yes—
755C4×C53—21no—
756C4×C53—21no—
757C4×C53—24no—
758C4×C53—24no—
759C4×C53—24no—
760C4×C53—24no—
761C4×C53—24no—
762C4×C53C22×#4114yes—
763Dic53—24no—
764Dic53—21no—
765Dic53—21no—
766Dic53—24no—
767Dic53—24no—
768Dic53—24no—
769Dic53—24no—
770Dic53C22×#4112yes—
771Dic53C22×#4112yes—
772#3507—534no—
773#3507—534no—
774#3507—534no—
775#3506—534no—
776#3506—534no—
777#3506—534no—
778#3493—534no—
779#3493—534no—
780#3493—531no—
781#3493—531no—
782#3493—531no—
783#3493D5311yescharacteristic, complemented
784#3492—534no—
785#3492—534no—
786#3492—532no—
787#3492—532no—
788#3459—534no—
789#3459—534no—
790#3458—531no—
791#3449—531no—
792#3449—532no—
793C2×#520—532no—
794C2×#520—531no—
795C2×C53—22no—
796C2×C53—44no—
797C2×C53—42no—
798C2×C53C23×#4111yescharacteristic
799C2×C53H(7,𝔽2)11yescharacteristic
800C2×C532−1+611yescharacteristic
801D53—24no—
802D53—42no—
803D53—44no—
804C22×#41—532no—
805C22×#41—531no—
806#559—538no—
807#559—534no—
808#559—538no—
809#559—534no—
810#557—534no—
811#557—534no—
812#556—534no—
813#556—538no—
814#556—538no—
815#556—534no—
816#556—534no—
817#556—534no—
818#556—534no—
819#556—538no—
820#556C2×D5314yescomplemented
821#555—534no—
822#555—538no—
823#555—534no—
824#555—534no—
825#555C2×D5314yescomplemented
826#554—534no—
827#554—534no—
828#554—534no—
829#554—534no—
830#554—534no—
831#554—534no—
832#553—538no—
833#553—534no—
834#553—538no—
835#553—534no—
836#553—534no—
837#553—534no—
838#553—534no—
839#553—534no—
840#553—534no—
841#553C2×D5314yescomplemented
842#552—538no—
843#552—534no—
844#552—534no—
845#552—534no—
846#552—534no—
847#552—534no—
848#552—538no—
849#552—534no—
850#552—534no—
851#552C2×D5314yescomplemented
852#550—538no—
853#547—538no—
854#547—534no—
855#547—534no—
856#547—534no—
857#547—534no—
858#544—534no—
859#544—534no—
860#544—532no—
861#544—531no—
862#544C2×D5311yescharacteristic, complemented
863#543—534no—
864#539—538no—
865#539—538no—
866#539—538no—
867#539—538no—
868#539—538no—
869#539—538no—
870#538—538no—
871#538—538no—
872#538—538no—
873#538—534no—
874#538—538no—
875#538—534no—
876#538—534no—
877#538C2×D5314yescomplemented
878#537—532no—
879#537—532no—
880#537—532no—
881#537—532no—
882#537—532no—
883#537—531no—
884#537C2×D5311yescharacteristic
885#536—534no—
886#536—534no—
887#536—532no—
888#536—532no—
889#535—534no—
890#535—532no—
891#535—532no—
892#535—534no—
893#534—534no—
894#534—534no—
895#534—534no—
896#533—534no—
897#533—534no—
898#533—534no—
899#532—534no—
900#532—534no—
901#532—534no—
902#529—538no—
903#529—538no—
904#529—534no—
905#529—534no—
906#529—538no—
907#529—538no—
908#529—534no—
909#529C2×D5314yescomplemented
910#525—532no—
911#525—532no—
912#525—538no—
913#525—534no—
914#525—534no—
915#525—538no—
916#525—538no—
917#525—534no—
918#525—534no—
919#525—538no—
920#525—538no—
921#525—532no—
922#525—538no—
923#525C2×D5312yescomplemented
924#520—532no—
925#520—534no—
926#520—534no—
927#520—538no—
928#520—532no—
929#520—534no—
930#520—534no—
931#520—534no—
932#520—534no—
933#520—534no—
934#520—532no—
935#520—534no—
936#520C2×D5312yescomplemented
937C2×C4×Q8—534no—
938C2×C4×Q8—532no—
939C2×C4×D4—538no—
940C2×C4×D4—534no—
941C2×C4×D4—532no—
942C2×C4×D4—532no—
943C2×C4×D4—532no—
944C2×#117—532no—
945C2×#117—534no—
946C2×#117—531no—
947C2×#117—531no—
948C2×#117C2×D5311yescharacteristic, complemented
949C22×C4⋊C4—531no—
950C22×C4⋊C4—531no—
951C22×C4⋊C4—531no—
952C22×C4⋊C4—534no—
953C53#6284511yescharacteristic, complemented, Sylow
954C2×#41—532no—
955C2×#41—532no—
956C2×#41—534no—
957C2×#41—538no—
958C2×#41—532no—
959C2×#41—532no—
960C2×#41—532no—
961C2×#41—532no—
962C2×#41—532no—
963C2×#41—534no—
964C2×#41—538no—
965C2×#41—1068no—
966C2×#41—10616no—
967C2×#41C22×D5312yes—
968C22×Q8—532no—
969C22×Q8—531no—
970C22×D4—531no—
971C22×D4—531no—
972C22×D4—534no—
973C22×D4—532no—
974C22×D4—531no—
975C23×C4—531no—
976C23×C4—532no—
977C23×C4—534no—
978C23×C4—531no—
979C23×C4—532no—
980C23×C4—532no—
981C23×C4—538no—
982C23×C4C22×D5311yescharacteristic
983C4⋊Q8—534no—
984C4⋊Q8—534no—
985C4⋊Q8—534no—
986C4⋊Q8—534no—
987C4⋊Q8—534no—
988C4⋊Q8—534no—
989C4⋊Q8—534no—
990C4⋊Q8—534no—
991C4⋊Q8C22×D5314yes—
992#127—534no—
993#127—534no—
994#127—534no—
995#126—538no—
996#126—538no—
997#126—538no—
998#126—538no—
999#126—538no—
1000#126—538no—
1001#126—538no—
1002#126—538no—
1003#126—538no—
1004#126—538no—
1005#126C22×D5318yes—
1006#126C22×D5318yes—
1007#125—538no—
1008#125—538no—
1009#125—534no—
1010#125—534no—
1011#125—538no—
1012#125—538no—
1013#125—534no—
1014#125—534no—
1015#125—538no—
1016#125—534no—
1017#125—534no—
1018#125C22×D5314yes—
1019#125C22×D5314yes—
1020#124—534no—
1021#124—538no—
1022#124—534no—
1023#124—538no—
1024#124—538no—
1025#124—534no—
1026#124—534no—
1027#124—534no—
1028#124—538no—
1029#124—534no—
1030#124—534no—
1031#124C22×D5318yes—
1032#124C22×D5314yes—
1033#123—534no—
1034#123—538no—
1035#123—534no—
1036#123—538no—
1037#123—538no—
1038#123—534no—
1039#123—534no—
1040#123—538no—
1041#123—538no—
1042#123—534no—
1043#123—534no—
1044#123—538no—
1045#123—534no—
1046#123—538no—
1047#123—538no—
1048#123—538no—
1049#123—538no—
1050#123—538no—
1051#123—538no—
1052#123—538no—
1053#123C22×D5318yes—
1054#123C22×D5314yes—
1055C22⋊Q8—532no—
1056C22⋊Q8—534no—
1057C22⋊Q8—532no—
1058C22⋊Q8—538no—
1059C22⋊Q8—532no—
1060C22⋊Q8—534no—
1061C22⋊Q8—532no—
1062C22⋊Q8—538no—
1063C22⋊Q8—534no—
1064C22⋊Q8—538no—
1065C22⋊Q8—538no—
1066C22⋊Q8—534no—
1067C22⋊Q8—532no—
1068C22⋊Q8—534no—
1069C22⋊Q8—532no—
1070C22⋊Q8—534no—
1071C22⋊Q8—538no—
1072C22⋊Q8—538no—
1073C22⋊Q8—538no—
1074C22⋊Q8—538no—
1075C22⋊Q8—538no—
1076C22⋊Q8—534no—
1077C22⋊Q8—534no—
1078C22⋊Q8—538no—
1079C22⋊Q8—538no—
1080C22⋊Q8C22×D5314yes—
1081C22⋊Q8C22×D5312yes—
1082C22⋊Q8C22×D5312yes—
1083C22⋊Q8C22×D5314yes—
1084#121—534no—
1085#121—538no—
1086#121—532no—
1087#121—534no—
1088#121—534no—
1089#121—532no—
1090#121—534no—
1091#121—538no—
1092#121—538no—
1093#121—534no—
1094#121—532no—
1095#121—534no—
1096#121—532no—
1097#121—534no—
1098#121—534no—
1099#121—532no—
1100#121—532no—
1101#121—534no—
1102#121—538no—
1103#121—534no—
1104#121—534no—
1105#121—534no—
1106#121—534no—
1107#121—534no—
1108#121—538no—
1109#121—538no—
1110#121—534no—
1111#121—534no—
1112#121C22×D5314yes—
1113#121C22×D5318yes—
1114#121C22×D5312yes—
1115#121C22×D5312yes—
1116#121C22×D5314yes—
1117#120—534no—
1118#120—534no—
1119#120—534no—
1120#120—538no—
1121#120—534no—
1122#120—534no—
1123#120—538no—
1124#120—534no—
1125#120—534no—
1126#120C22×D5314yes—
1127C4×Q8—534no—
1128C4×Q8—534no—
1129C4×Q8—534no—
1130C4×Q8—534no—
1131C4×Q8—538no—
1132C4×Q8—534no—
1133C4×Q8—538no—
1134C4×Q8—534no—
1135C4×Q8—534no—
1136C4×Q8—534no—
1137C4×Q8—534no—
1138C4×Q8—538no—
1139C4×Q8—534no—
1140C4×Q8—534no—
1141C4×Q8—534no—
1142C4×Q8C22×D5314yes—
1143C4×Q8C22×D5314yes—
1144C4×D4—538no—
1145C4×D4—534no—
1146C4×D4—534no—
1147C4×D4—538no—
1148C4×D4—534no—
1149C4×D4—538no—
1150C4×D4—538no—
1151C4×D4—538no—
1152C4×D4—538no—
1153C4×D4—534no—
1154C4×D4—534no—
1155C4×D4—534no—
1156C4×D4—534no—
1157C4×D4—538no—
1158C4×D4—534no—
1159C4×D4—534no—
1160C4×D4—534no—
1161C4×D4—538no—
1162C4×D4—538no—
1163C4×D4—538no—
1164C4×D4—538no—
1165C4×D4—538no—
1166C4×D4—538no—
1167C4×D4—538no—
1168C4×D4—538no—
1169C4×D4—538no—
1170C4×D4—538no—
1171C4×D4—538no—
1172C4×D4—538no—
1173C4×D4—534no—
1174C4×D4—538no—
1175C4×D4—534no—
1176C4×D4—534no—
1177C4×D4—534no—
1178C4×D4C22×D5318yes—
1179C4×D4C22×D5314yes—
1180C4×D4C22×D5314yes—
1181C4×D4C22×D5314yes—
1182C4×D4C22×D5314yes—
1183#117—532no—
1184#117—534no—
1185#117—534no—
1186#117—532no—
1187#117—534no—
1188#117—532no—
1189#117—534no—
1190#117—534no—
1191#117—534no—
1192#117—534no—
1193#117—538no—
1194#117—534no—
1195#117—538no—
1196#117—538no—
1197#117—538no—
1198#117—534no—
1199#117—538no—
1200#117—538no—
1201#117—538no—
1202#117C22×D5312yes—
1203#117C22×D5314yes—
1204#117C22×D5314yes—
1205#117C22×D5314yes—
1206#117C22×D5318yes—
1207C2×C4⋊C4—531no—
1208C2×C4⋊C4—531no—
1209C2×C4⋊C4—532no—
1210C2×C4⋊C4—532no—
1211C2×C4⋊C4—532no—
1212C2×C4⋊C4—538no—
1213C2×C4⋊C4—534no—
1214C2×C4⋊C4—534no—
1215C2×C4⋊C4—534no—
1216C2×C4⋊C4—534no—
1217C2×C4⋊C4—532no—
1218C2×C4⋊C4—534no—
1219C2×C4⋊C4—538no—
1220C2×C4⋊C4—538no—
1221C2×C4⋊C4—534no—
1222C2×C4⋊C4—534no—
1223C2×C4⋊C4—534no—
1224C2×C4⋊C4—534no—
1225C2×C4⋊C4—532no—
1226C2×C4⋊C4C22×D5311yescharacteristic
1227C2×C4⋊C4C22×D5314yes—
1228C2×C4⋊C4C22×D5311yescharacteristic
1229C2×C22⋊C4—532no—
1230C2×C22⋊C4—532no—
1231C2×C22⋊C4—534no—
1232C2×C22⋊C4—538no—
1233C2×C22⋊C4C22×D5312yes—
1234C2×C42—532no—
1235C2×C42—532no—
1236C2×C42—538no—
1237C2×C42—534no—
1238C2×C42C22×D5312yes—
1239C24—531no—
1240C24—534no—
1241C24—531no—
1242C24C23×D5311yescharacteristic
1243#41—28no—
1244#41—1068no—
1245#41—1068no—
1246#41—1068no—
1247#41—1068no—
1248#41—10616no—
1249#41—10616no—
1250#41—1068no—
1251#41—1068no—
1252#41—1068no—
1253#41—4248no—
1254#41—4248no—
1255C2×Q8—531no—
1256C2×Q8—531no—
1257C2×Q8—532no—
1258C2×Q8—534no—
1259C2×Q8—531no—
1260C2×Q8—531no—
1261C2×Q8—534no—
1262C2×Q8—538no—
1263C2×Q8—1064no—
1264C2×Q8—1068no—
1265C2×Q8C23×D5312yes—
1266C2×Q8C23×D5314yes—
1267C2×D4—534no—
1268C2×D4—532no—
1269C2×D4—532no—
1270C2×D4—534no—
1271C2×D4—532no—
1272C2×D4—534no—
1273C2×D4—532no—
1274C2×D4—534no—
1275C2×D4—534no—
1276C2×D4—538no—
1277C2×D4—534no—
1278C2×D4—534no—
1279C2×D4—534no—
1280C2×D4—532no—
1281C2×D4—532no—
1282C2×D4—532no—
1283C2×D4—534no—
1284C2×D4—534no—
1285C2×D4—534no—
1286C2×D4—1064no—
1287C2×D4—1068no—
1288C2×D4—1064no—
1289C2×D4—10616no—
1290C2×D4—1064no—
1291C2×D4C23×D5314yes—
1292C2×D4C23×D5312yes—
1293C2×D4C23×D5314yes—
1294C2×D4C23×D5314yes—
1295C2×D4C23×D5314yes—
1296C22×C4—24no—
1297C22×C4—531no—
1298C22×C4—538no—
1299C22×C4—532no—
1300C22×C4—532no—
1301C22×C4—531no—
1302C22×C4—534no—
1303C22×C4—532no—
1304C22×C4—532no—
1305C22×C4—538no—
1306C22×C4—538no—
1307C22×C4—534no—
1308C22×C4—534no—
1309C22×C4—532no—
1310C22×C4—534no—
1311C22×C4—532no—
1312C22×C4—534no—
1313C22×C4—538no—
1314C22×C4—534no—
1315C22×C4—538no—
1316C22×C4—538no—
1317C22×C4—538no—
1318C22×C4—10616no—
1319C22×C4—1064no—
1320C22×C4—4242no—
1321C22×C4—4242no—
1322C22×C4—4248no—
1323C22×C4—4242no—
1324C22×C4C23×D5311yescharacteristic
1325C22×C4C23×D5312yes—
1326C22×C4C23×D5312yes—
1327C22×C4C23×D5314yes—
1328C22×C4C23×D5312yes—
1329C22×C4C23×D5312yes—
1330C22×C4C23×D5318yes—
1331C22×C4C23×D5311yescharacteristic
1332C4⋊C4—534no—
1333C4⋊C4—534no—
1334C4⋊C4—534no—
1335C4⋊C4—534no—
1336C4⋊C4—532no—
1337C4⋊C4—534no—
1338C4⋊C4—538no—
1339C4⋊C4—534no—
1340C4⋊C4—534no—
1341C4⋊C4—538no—
1342C4⋊C4—538no—
1343C4⋊C4—534no—
1344C4⋊C4—534no—
1345C4⋊C4—534no—
1346C4⋊C4—532no—
1347C4⋊C4—534no—
1348C4⋊C4—538no—
1349C4⋊C4—534no—
1350C4⋊C4—534no—
1351C4⋊C4—538no—
1352C4⋊C4—538no—
1353C4⋊C4—538no—
1354C4⋊C4—534no—
1355C4⋊C4—538no—
1356C4⋊C4—534no—
1357C4⋊C4—534no—
1358C4⋊C4—534no—
1359C4⋊C4—534no—
1360C4⋊C4C23×D5314yes—
1361C4⋊C4C23×D5312yes—
1362C4⋊C4C23×D5318yes—
1363C4⋊C4C23×D5312yes—
1364C4⋊C4C23×D5314yes—
1365C4⋊C4C23×D5318yes—
1366C4⋊C4C23×D5314yes—
1367C4⋊C4C23×D5314yes—
1368C4⋊C4C23×D5314yes—
1369C4⋊C4C23×D5314yes—
1370C22⋊C4—534no—
1371C22⋊C4—538no—
1372C22⋊C4—534no—
1373C22⋊C4—534no—
1374C22⋊C4—534no—
1375C22⋊C4—538no—
1376C22⋊C4—534no—
1377C22⋊C4—534no—
1378C22⋊C4—538no—
1379C22⋊C4—534no—
1380C22⋊C4—538no—
1381C22⋊C4—538no—
1382C22⋊C4—538no—
1383C22⋊C4—534no—
1384C22⋊C4—534no—
1385C22⋊C4—538no—
1386C22⋊C4—534no—
1387C22⋊C4—534no—
1388C22⋊C4—534no—
1389C22⋊C4—534no—
1390C22⋊C4—534no—
1391C22⋊C4—538no—
1392C22⋊C4—534no—
1393C22⋊C4C23×D5314yes—
1394C22⋊C4C23×D5318yes—
1395C22⋊C4C23×D5318yes—
1396C22⋊C4C23×D5314yes—
1397C22⋊C4C23×D5318yes—
1398C22⋊C4C23×D5314yes—
1399C22⋊C4C23×D5314yes—
1400C22⋊C4C23×D5314yes—
1401C42—538no—
1402C42—538no—
1403C42—534no—
1404C42—534no—
1405C42—538no—
1406C42—534no—
1407C42—534no—
1408C42—534no—
1409C42—534no—
1410C42—534no—
1411C42C23×D5318yes—
1412C42C23×D5314yes—
1413C42C23×D5314yes—
1414C42C23×D5314yes—
1415C23—22no—
1416C23—41no—
1417C23—41no—
1418C23—532no—
1419C23—534no—
1420C23—534no—
1421C23—532no—
1422C23—1068no—
1423C23—1062no—
1424C23—2121no—
1425C23—2121no—
1426C23—2124no—
1427C23—2121no—
1428C23—2121no—
1429C23—2124no—
1430C23C24×D5314yes—
1431C23C24×D5312yes—
1432C23C24×D5311yescharacteristic
1433Q8—24no—
1434Q8—44no—
1435Q8—1062no—
1436Q8—1062no—
1437Q8—1062no—
1438Q8—1062no—
1439Q8—1068no—
1440Q8—1064no—
1441Q8—2124no—
1442Q8—2128no—
1443D4—28no—
1444D4—24no—
1445D4—44no—
1446D4—44no—
1447D4—44no—
1448D4—1064no—
1449D4—1064no—
1450D4—1068no—
1451D4—1064no—
1452D4—1064no—
1453D4—1068no—
1454D4—1064no—
1455D4—1064no—
1456D4—1068no—
1457D4—1068no—
1458D4—1064no—
1459D4—2124no—
1460D4—2124no—
1461D4—2124no—
1462D4—2124no—
1463D4—2124no—
1464D4—2124no—
1465D4—2128no—
1466D4—2124no—
1467C2×C4—22no—
1468C2×C4—24no—
1469C2×C4—24no—
1470C2×C4—28no—
1471C2×C4—42no—
1472C2×C4—48no—
1473C2×C4—42no—
1474C2×C4—534no—
1475C2×C4—531no—
1476C2×C4—531no—
1477C2×C4—538no—
1478C2×C4—538no—
1479C2×C4—534no—
1480C2×C4—534no—
1481C2×C4—531no—
1482C2×C4—534no—
1483C2×C4—531no—
1484C2×C4—534no—
1485C2×C4—534no—
1486C2×C4—1068no—
1487C2×C4—1068no—
1488C2×C4—1068no—
1489C2×C4—1062no—
1490C2×C4—1068no—
1491C2×C4—1064no—
1492C2×C4—1064no—
1493C2×C4—2124no—
1494C2×C4—2128no—
1495C2×C4—2124no—
1496C2×C4—2128no—
1497C2×C4—2128no—
1498C2×C4—2128no—
1499C2×C4—2122no—
1500C2×C4—2122no—
1501C2×C4—2128no—
1502C2×C4—2128no—
1503C2×C4#41×D5314yes—
1504C2×C4C24×D5314yes—
1505C2×C4C24×D5314yes—
1506C2×C4C24×D5314yes—
1507C2×C4C24×D5314yes—
1508C2×C4C24×D5314yes—
1509C2×C4C24×D5311yescharacteristic
1510C2×C4C24×D5311yescharacteristic
1511C2×C4C24×D5312yes—
1512C22—21no—
1513C22—21no—
1514C22—22no—
1515C22—24no—
1516C22—24no—
1517C22—22no—
1518C22—24no—
1519C22—22no—
1520C22—44no—
1521C22—534no—
1522C22—1062no—
1523C22—1062no—
1524C22—1064no—
1525C22—1062no—
1526C22—1062no—
1527C22—1064no—
1528C22—1064no—
1529C22—1062no—
1530C22—2124no—
1531C22—2124no—
1532C22—21216no—
1533C22C2×#41×D5312yes—
1534C22C25×D5311yescharacteristic
1535C4—21no—
1536C4—21no—
1537C4—24no—
1538C4—24no—
1539C4—24no—
1540C4—24no—
1541C4—24no—
1542C4—532no—
1543C4—532no—
1544C4—1064no—
1545C4—1061no—
1546C4—1061no—
1547C4—1064no—
1548C4—1064no—
1549C4—1064no—
1550C4—1064no—
1551C4C2×#41×D5314yes—
1552C2—22no—
1553C2—42no—
1554C2—44no—
1555C2—1064no—
1556C2—2122no—
1557C2—2124no—
1558C2C22×#41×D5311yescharacteristic
1559C2#2028952611yescharacteristic
1560C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3493C2
hypercenter#3493D53
hypocenterC53#62845
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3493

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20288574C2semidirect
2. #20288571C2semidirect
3. #20288570C2semidirect
4. #20288562C2semidirect
5. #20288561C2semidirect
6. #20288557C2semidirect
7. #20288436C2semidirect
8. #20288435C2semidirect
9. #20288434C2semidirect
10. #20288429C2semidirect
11. #20288426C2semidirect
12. #20288421C2semidirect
13. #20288419C2semidirect
14. #20288418C2semidirect
15. #20288415C2semidirect
16. #20288126C2semidirect
17. #20288125C2semidirect
18. #20288119C2semidirect
19. #20288045C2semidirect
20. #20288043C2semidirect
21. C2×#16811103C2semidirect
22. #520×D53C2semidirect
23. C53×#3493C2semidirect
26. #16811357C22semidirect
27. #16811356C22semidirect
28. #16811355C22semidirect
29. #16811355C22semidirect
30. #16811350C22semidirect
31. #16811349C22semidirect
32. #16811347C22semidirect
33. #16811345C22semidirect
34. #16811344C22semidirect
35. #16811342C22semidirect
36. #16811341C22semidirect
37. #16811341C22semidirect
38. #16811340C22semidirect
39. #16811340C22semidirect
40. #16811339C22semidirect
41. #16811337C22semidirect
42. #16811336C22semidirect
43. #16811335C22semidirect
44. #16811333C22semidirect
45. #16811332C22semidirect
46. #16811331C22semidirect
47. #16811330C22semidirect
48. #16811329C22semidirect
49. #16811328C22semidirect
50. #16811326C22semidirect
51. #16811325C22semidirect
52. #16811325C22semidirect
53. #16811324C22semidirect
54. #16811323C22semidirect
55. #16811319C22semidirect
56. #16811317C22semidirect
57. #16811317C22semidirect
58. #16811316C22semidirect
59. #16811315C22semidirect
60. #16811315C22semidirect
61. #16811314C22semidirect
62. #16811313C22semidirect
63. #16811312C22semidirect
64. #16811312C22semidirect
65. #16811311C22semidirect
66. #16811309C22semidirect
67. #16811306C22semidirect
68. #16811291C22semidirect
69. #16811278C22semidirect
70. #16811277C22semidirect
71. #16811274C22semidirect
72. #16811273C22semidirect
73. #16811271C22semidirect
74. #16811254C22semidirect
75. #16811253C22semidirect
76. #16811251C22semidirect
77. #16811250C22semidirect
79. #16811221C22semidirect
80. #16811217C22semidirect
81. #16811216C22semidirect
82. #16811215C22semidirect
83. #16811214C22semidirect
84. #16811214C22semidirect
85. #16811213C22semidirect
86. #16811212C22semidirect
87. #16811211C22semidirect
88. #16811210C22semidirect
89. #16811207C22semidirect
90. #16811207C22semidirect
91. #16811205C22semidirect
98. #16811196C22semidirect
99. #16811196C22semidirect
100. #16811196C22semidirect
101. #16811195C22semidirect
102. #16811189C22semidirect
103. #16811189C22semidirect
104. #16811189C22semidirect
105. #16811188C22semidirect
109. #16811179C22semidirect
110. #16811178C22semidirect
111. #16811175C22semidirect
115. #16811160C22semidirect
116. #16811159C22semidirect
117. #16811157C22semidirect
118. #16811156C22semidirect
119. #16811154C22semidirect
120. #16811152C22semidirect
121. #16811151C22semidirect
122. #16811136C22semidirect
123. #16811135C22semidirect
124. #16811135C22semidirect
125. #16811134C22semidirect
126. #16811133C22semidirect
127. #16811133C22semidirect
128. #16811132C22semidirect
129. #16811132C22semidirect
130. #16811132C22semidirect
131. #16811132C22semidirect
132. #16811131C22semidirect
133. #16811130C22semidirect
134. #16811129C22semidirect
135. #16811106C22semidirect
136. #16811105C22semidirect
137. #16811104C22semidirect
138. #16811104C22semidirect
139. #16811103C22semidirect
140. #16811103C22semidirect
141. #16811103C22semidirect
142. #16811103C22semidirect
143. #16811103C22semidirect
144. #16811103C22semidirect
145. #16811102C22semidirect
146. #16811102C22semidirect
147. C2×C4×Dic106C22semidirect
148. C4×Q8×D53C22semidirect
151. C2×#13133177C22semidirect
153. C4×D4×D53C22semidirect
155. C2×#13133175C22semidirect
157. #117×D53C22semidirect
158. C22×C4⋊Dic53C22semidirect
160. C2×C4⋊C4×D53C22semidirect
161. C2×C4⋊C4×D53C22semidirect
162. C53×#556C22semidirect
163. C53×#555C22semidirect
164. C53×#553C22semidirect
165. C53×#552C22semidirect
166. C53×#544C22semidirect
167. C53×#538C22semidirect
169. C53×#529C22semidirect
170. C53×#525C22semidirect
171. C53×#520C22semidirect
172. C2×#117×C53C22semidirect
528. C2×C4×D53#41semidirect
783. #3493D53semidirect
820. #556C2×D53semidirect
825. #555C2×D53semidirect
841. #553C2×D53semidirect
851. #552C2×D53semidirect
862. #544C2×D53semidirect
877. #538C2×D53semidirect
909. #529C2×D53semidirect
923. #525C2×D53semidirect
936. #520C2×D53semidirect
948. C2×#117C2×D53semidirect
953. C53#62845semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202885742
#202885712
#202885702
#202885622
#202885612
#202885572
#202884362
#202884352
#202884342
#202884292
#202884262
#202884212
#202884192
#202884182
#202884152
#202881262
#202881252
#202881192
#202880452
#202880432
C2×#168111032
#520×D532
C53×#34932
#6284553