Finite Group Databasebeta

← #28293286

Subgroups — #28293286

Order 13568.

10986 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811458C211yesmaximal, characteristic, complemented
2C2×2−1+4×D53C211yesmaximal, characteristic, complemented
3#20288507C213yesmaximal, complemented
4#20288505C213yesmaximal, complemented
5#20288503C211yesmaximal, characteristic, complemented
6#20288500C211yesmaximal, characteristic, complemented
7#20288497C213yesmaximal, complemented
8#20288496C211yesmaximal, characteristic, complemented
9#20288495C213yesmaximal, complemented
10#20288394C214yesmaximal, complemented
11#20288386C2112yesmaximal, complemented
12#20288361C214yesmaximal, complemented
13#20288352C2112yesmaximal, complemented
14#20288046C213yesmaximal, complemented
15#20288042C213yesmaximal, complemented
16C2×#16811193C213yesmaximal, complemented
17#536×D53C213yesmaximal, complemented
18#20287914C211yesmaximal, characteristic, complemented
19C53×#3500C211yesmaximal, characteristic, complemented
20#16811458—216no—
21C2×#13133265C2212yescomplemented
22C2×#13133265C2213yescomplemented
23C2×#13133264C2212yes—
24C2×#13133264C2216yescomplemented
25C2×#13133264C2213yescomplemented
26C2×#13133264C2211yescharacteristic, complemented
27C2×#13133264C2213yescomplemented
28C2×#13133264C2211yescharacteristic, complemented
292−1+4×D53—216no—
30C2×#13133262C2216yes—
31C2×#13133262C2213yescomplemented
32C22×#11719947C2213yes—
33C22×#11719947C2216yescomplemented
34C2×#41×D53C2213yes—
35C2×#41×D53C2211yescharacteristic
36C2×#41×D53C2213yescomplemented
37C2×#41×D53C2216yescomplemented
38C2×#41×D53C2212yescomplemented
39C22×Q8×D53C2213yescomplemented
40C22×Q8×D53C2212yescomplemented
41Q8×D212C2214yescomplemented
42D4×Dic106C22112yescomplemented
43Q8×C22⋊D53C2214yescomplemented
44#16811286C22112yescomplemented
45#16811281C22112yescomplemented
46#16811280C2214yescomplemented
47#16811279C22112yescomplemented
48#16811278C22112yescomplemented
49#16811277C22112yescomplemented
50#16811275C22112yescomplemented
51#16811273C22124yescomplemented
52#16811272C22112yescomplemented
53#16811271C22124yescomplemented
54#16811270C22112yescomplemented
55#16811267C22112yescomplemented
56#16811266C22112yescomplemented
57#16811263C22124yescomplemented
58#16811260C22124yescomplemented
59#16811202C22112yescomplemented
60#16811200C22112yescomplemented
61#16811199C2213yescomplemented
62#16811199C2213yescomplemented
63#16811198C2213yescomplemented
64#16811198C2213yescomplemented
65#16811197C2213yescomplemented
66#16811196C22112yescomplemented
67#16811195C22112yescomplemented
68#16811194C2213yescomplemented
69#16811194C2213yescomplemented
70#16811193C2216yescomplemented
71#16811193C2213yescomplemented
72#16811193C22112yescomplemented
73#16811193C22112yescomplemented
74#16811193C2216yescomplemented
75#16811193C2216yescomplemented
76#16811193C2213yescomplemented
77#16811191C2211yescharacteristic, complemented
78#16811191C2213yescomplemented
79#16811190C2213yescomplemented
80#16811186C2213yescomplemented
81#16811186C2213yescomplemented
82#16811183C22112yescomplemented
83#16811181C22112yescomplemented
84#16811173C2213yescomplemented
85#16811172C2216yescomplemented
86#16811171C2216yescomplemented
87#16811169C2213yescomplemented
88#16811169C2213yescomplemented
89C2×#13133217C2213yescomplemented
90C2×#13133215C2213yescomplemented
91C4⋊Q8×D53C2216yescomplemented
92C2×#13133204C2213yescomplemented
93#124×D53C2216yescomplemented
94#16811133C22112yescomplemented
95#16811132C22112yescomplemented
96#16811132C22112yescomplemented
97#16811129C22112yescomplemented
98C2×#13133199C22112yescomplemented
99#123×D53C22112yescomplemented
100C2×#13133194C22112yescomplemented
101C22⋊Q8×D53C22112yescomplemented
102#16811105C2212yescomplemented
103#16811102C2216yescomplemented
104#16811099C2212yescomplemented
105#16811095C2216yescomplemented
106#41×Dic53C2211yescharacteristic, complemented
107C4×#11719945C2213yescomplemented
108#16811091C2213yescomplemented
109C2×#13133174C2213yescomplemented
110#117×D53C2213yescomplemented
111C2×2−1+4×C53C2211yescharacteristic, complemented
112C2×H(5,𝔽2)×C53C2211yescharacteristic, complemented
113C53×#548C2214yescomplemented
114C53×#546C22112yescomplemented
115C53×#536C2213yescomplemented
116C53×#535C2213yescomplemented
117C53×#532C2213yescomplemented
118C2×#124×C53C2213yescomplemented
119C4×#41×C53C2211yescharacteristic, complemented
120#13133265—216no—
121#13133265—224no—
122#13133264—28no—
123#13133264—28no—
124#13133264—216no—
125#13133264—248no—
126#13133264—224no—
127#13133264—224no—
128#13133262—248no—
129#13133262—224no—
130C2×#11719949C2316yes—
131C2×#11719949C2313yes—
132C2×#11719949C2311yescharacteristic
133C2×#11719949C2311yescharacteristic
134C2×#11719945C2316yes—
135C2×#11719945C23112yes—
136C2×#11719945C2316yes—
137C2×#11719945C2316yes—
138C2×#11719945C2316yes—
139C2×#11719945C2313yes—
140C2×#11719945C2313yes—
141C2×#11719945C2313yes—
142C2×#11719947—248no—
143C2×#11719947—224no—
144C2×#11719947C2316yes—
145C2×#11719947C23112yes—
146C2×#11719947C2316yes—
147C2×#11719947C23112yes—
148C2×#11719947C2316yes—
149C2×#11719947C2316yes—
150C2×#11719947C2316yes—
151C2×#11719947C2313yes—
152C2×#11719947C2316yes—
153C2×#11719947C2313yes—
154C2×#11719947C2316yes—
155C2×#11719947C2316yes—
156C2×#11719947C2313yes—
157#41×D53—216no—
158#41×D53—248no—
159#41×D53—224no—
160#41×D53—224no—
161#41×D53D4116yescomplemented
162C22×Dic106C2316yes—
163C22×Dic106C2316yes—
164C22×Dic106C2316yes—
165C22×Dic106C2313yes—
166C22×Dic106C2313yes—
167C2×Q8×D53—216no—
168C2×Q8×D53—224no—
169C2×Q8×D53C2312yes—
170C2×Q8×D53C2316yes—
171C2×Q8×D53C2312yes—
172C2×Q8×D53C2316yes—
173C2×Q8×D53C2316yes—
174C2×Q8×D53C2313yes—
175C2×Q8×D53C2313yes—
176C2×Q8×D53C2316yes—
177C2×Q8×D53C2311yescharacteristic
178C22×C22⋊D53C2316yes—
179C22×C22⋊D53C23112yes—
180C2×D4×D53C2316yes—
181C2×D4×D53C2316yes—
182C2×D4×D53C2313yes—
183C2×D4×D53C2316yes—
184C2×D4×D53C2311yescharacteristic
185C2×D4×D53C2313yes—
186C23×Dic53C2316yes—
187C22×C4×D53C2316yes—
188C22×C4×D53C2316yes—
189C22×C4×D53C2316yes—
190C22×C4×D53C2313yes—
191#13133217C23112yes—
192#13133217C2316yes—
193#13133217C2313yes—
194#13133216C23124yes—
195#13133215C23112yes—
196#13133215C2313yes—
197#13133215C2316yes—
198#13133215C2313yes—
199#13133214C2311yescharacteristic
200#13133213C2311yescharacteristic
201#13133213C2313yes—
202#13133206C2313yes—
203#13133206C2311yescharacteristic
204#13133205C2313yes—
205#13133205C2313yes—
206#13133204C23112yes—
207#13133204C2316yes—
208#13133204C2313yes—
209#13133204C2313yes—
210#13133203C23124yes—
211#13133202C23112yes—
212#13133202C23112yes—
213#13133201C23112yes—
214#13133201C23112yes—
215#13133200C23112yes—
216#13133199C23124yes—
217#13133199C23124yes—
218#13133199C23112yes—
219#13133199C23124yes—
220#13133199C23112yes—
221#13133198C23112yes—
222#13133198C23112yes—
223#13133197C23112yes—
224#13133197C23112yes—
225#13133196C23112yes—
226#13133196C23112yes—
227#13133195C23112yes—
228#13133195C23112yes—
229#13133194C23124yes—
230#13133194C23112yes—
231#13133194C23124yes—
232#13133194C23124yes—
233#13133194C23112yes—
234#13133193C23112yes—
235#13133191C23112yes—
236#13133190C23124yes—
237#13133190C23112yes—
238#13133190C2314yes—
239#13133189C23112yes—
240#13133189C23112yes—
241#13133189C23112yes—
242#13133189C23112yes—
243#13133188C23112yes—
244#13133188C23124yes—
245#13133187C23112yes—
246#13133187C2314yes—
247#13133186C23112yes—
248#13133185C23112yes—
249#13133185C23112yes—
250Q8×Dic53C2312yes—
251C4×Dic106C2316yes—
252#13133182C2316yes—
253C4×D212C2316yes—
254C4×D212C23112yes—
255D4×Dic53C2316yes—
256D4×Dic53C23124yes—
257#13133179C2316yes—
258C4×C22⋊D53C23112yes—
259C4×C22⋊D53C23112yes—
260C4×C22⋊D53C23112yes—
261#13133177C23112yes—
262#13133177C23124yes—
263#13133176C2313yes—
264#13133175C2316yes—
265#13133174C2313yes—
266#13133174C2311yescharacteristic
267#13133174C2313yes—
268#13133174C2313yes—
269#13133174C2316yes—
270#13133174C2316yes—
271#13133173C2316yes—
272C2×C4⋊Dic53C23112yes—
273C2×#11719919C23112yes—
274C2×#11719919C2316yes—
275C4⋊C4×D53C23124yes—
276C4⋊C4×D53C2316yes—
277C2×C22⋊Dic53C23112yes—
278C2×#11719921C2316yes—
279C22⋊C4×D53C23124yes—
280C22⋊C4×D53C2316yes—
281C2×C4×Dic53C2313yes—
282C42×D53C2316yes—
2832−1+4×C53—28no—
284H(5,𝔽2)×C53—28no—
285C2×#41×C53C2316yes—
286C2×#41×C53C2312yes—
287C2×#41×C53C2313yes—
288C2×#41×C53C2313yes—
289C2×#41×C53C2311yescharacteristic
290C22×Q8×C53C2312yes—
291C22×Q8×C53C2313yes—
292C22×D4×C53C2316yes—
293C22×D4×C53C2313yes—
294C4⋊Q8×C53C2313yes—
295#127×C53C2313yes—
296#124×C53C23112yes—
297#124×C53C2313yes—
298#124×C53C2316yes—
299#124×C53C2311yescharacteristic
300#123×C53C23112yes—
301C22⋊Q8×C53C23112yes—
302#121×C53C23112yes—
303#121×C53C23112yes—
304#120×C53C23112yes—
305C4×Q8×C53C2312yes—
306C4×D4×C53C2316yes—
307C4×D4×C53C23112yes—
308#117×C53C2313yes—
309C2×C22⋊C4×C53C23112yes—
310C2×C42×C53C2313yes—
311C24×C53C2416yes—
312C23×D53C2416yes—
313C23×D53C2412yes—
314C23×D53C2413yes—
315#41×C53—28no—
316#41×C53—224no—
317#41×C53—212no—
318#41×C53—212no—
319#41×C53C2×D418yes—
320C2×Q8×C53—28no—
321C2×Q8×C53—212no—
322C2×Q8×C53C2416yes—
323C2×Q8×C53C2413yes—
324C2×Q8×C53C2411yescharacteristic
325C2×Q8×C53C2411yescharacteristic
326C2×D4×C53—224no—
327C2×D4×C53—212no—
328C2×D4×C53C2416yes—
329C2×D4×C53C2416yes—
330C2×D4×C53C2416yes—
331C2×D4×C53C2413yes—
332C2×D4×C53C2411yescharacteristic
333C2×D4×C53C24112yes—
334C2×D4×C53C2413yes—
335C22×C4×C53C2416yes—
336C22×C4×C53C2416yes—
337C22×C4×C53C2416yes—
338C22×C4×C53C2416yes—
339C22×C4×C53C2413yes—
340C2×C22⋊D53—224no—
341C2×C22⋊D53—248no—
342C2×C22⋊D53C2416yes—
343C2×C22⋊D53C2416yes—
344C2×C22⋊D53C2416yes—
345C2×C22⋊D53C24112yes—
346C2×C22⋊D53C2412yes—
347C2×C22⋊D53C2416yes—
348C2×C22⋊D53C2416yes—
349C2×C22⋊D53C24112yes—
350C2×C22⋊D53C2414yes—
351C2×C22⋊D53C2416yes—
352C22×Dic53—224no—
353C22×Dic53C2416yes—
354C22×Dic53C2416yes—
355C22×Dic53C24112yes—
356C22×Dic53C2416yes—
357C22×Dic53C2416yes—
358C22×Dic53C2416yes—
359C22×Dic53C2413yes—
360#11719949—224no—
361#11719949—24no—
362#11719949—212no—
363#11719949C2×D418yes—
364Q8×D53—28no—
365Q8×D53—28no—
366Q8×D53—224no—
367Q8×D53—212no—
368Q8×D53—224no—
369Q8×D53—224no—
370Q8×D53—212no—
371Q8×D53—224no—
372Q8×D53C2×D418yes—
373#11719947—224no—
374#11719947—224no—
375#11719947—248no—
376#11719947—248no—
377#11719947—224no—
378#11719947—224no—
379#11719947—224no—
380#11719947—212no—
381#11719947—212no—
382#11719947—224no—
383#11719947—224no—
384#11719947—224no—
385#11719947C2×D4124yes—
386D4×D53—224no—
387D4×D53—224no—
388D4×D53—224no—
389D4×D53—24no—
390D4×D53—212no—
391D4×D53C2×D4124yes—
392#11719945—212no—
393#11719945—212no—
394#11719945—248no—
395#11719945—224no—
396#11719945—224no—
397#11719945—224no—
398#11719945—224no—
399#11719945C2×D4124yes—
400C2×D212C2416yes—
401C2×D212C2412yes—
402C2×D212C2411yescharacteristic
403C2×D212C2411yescharacteristic
404C2×D212C2414yes—
405C2×D212C2413yes—
406C2×C4×D53—224no—
407C2×C4×D53—224no—
408C2×C4×D53—224no—
409C2×C4×D53C2×D4124yes—
410C2×C4×D53C24112yes—
411C2×C4×D53C2416yes—
412C2×C4×D53C2416yes—
413C2×C4×D53C2416yes—
414C2×C4×D53C2416yes—
415C2×C4×D53C2412yes—
416C2×C4×D53C2416yes—
417C2×C4×D53C24112yes—
418C2×C4×D53C2413yes—
419C2×C4×D53C2413yes—
420C2×C4×D53C2411yescharacteristic
421C2×C4×D53C2413yes—
422C2×Dic106—212no—
423C2×Dic106—212no—
424C2×Dic106—224no—
425C2×Dic106—224no—
426C2×Dic106—224no—
427C2×Dic106C2416yes—
428C2×Dic106C24112yes—
429C2×Dic106C2416yes—
430C2×Dic106C2416yes—
431C2×Dic106C2416yes—
432C2×Dic106C2413yes—
433C2×Dic106C2413yes—
434C2×Dic106C2413yes—
435C4⋊C4×C53C2416yes—
436C4⋊C4×C53C24112yes—
437C22⋊C4×C53C24112yes—
438C22⋊C4×C53C24124yes—
439C22⋊C4×C53C2416yes—
440C22⋊C4×C53C2414yes—
441C42×C53C2411yescharacteristic
442C42×C53C2413yes—
443C42×C53C2416yes—
444C22⋊Dic53C24124yes—
445C22⋊Dic53C2416yes—
446C22⋊Dic53C24112yes—
447C22⋊Dic53C24112yes—
448#11719921C2416yes—
449#11719921C24112yes—
450#11719921C24112yes—
451#11719921C2412yes—
452#11719921C2416yes—
453#11719921C2416yes—
454#11719921C24112yes—
455#11719921C2414yes—
456C4⋊Dic53C24124yes—
457C4⋊Dic53C2416yes—
458C4⋊Dic53C24112yes—
459#11719919C2416yes—
460#11719919C24112yes—
461#11719919C24124yes—
462#11719919C2412yes—
463#11719919C24112yes—
464#11719919C2416yes—
465#11719919C2416yes—
466C4×Dic53C2413yes—
467C4×Dic53C24112yes—
468C4×Dic53C2411yescharacteristic
469C4×Dic53C2416yes—
470C23×C53—212no—
471C23×C53—412no—
472C23×C53C2512yes—
473C23×C53C2516yes—
474C23×C53C2513yes—
475C22×D53—24no—
476C22×D53—212no—
477C22×D53—46no—
478C22×D53—44no—
479C22×D53—412no—
480C22×D53C22×D4112yes—
481C22×D53C2512yes—
482C22×D53C2512yes—
483C22×D53C2513yes—
484C22×D53C2511yescharacteristic
485Q8×C53—26no—
486Q8×C53—212no—
487Q8×C53—22no—
488Q8×C53C22×D414yes—
489D4×C53—212no—
490D4×C53—212no—
491D4×C53—26no—
492D4×C53—212no—
493D4×C53—22no—
494D4×C53—412no—
495D4×C53C22×D4112yes—
496C2×C4×C53—212no—
497C2×C4×C53—212no—
498C2×C4×C53—212no—
499C2×C4×C53—46no—
500C2×C4×C53C22×D4112yes—
501C2×C4×C53C2512yes—
502C2×C4×C53C2516yes—
503C2×C4×C53C2516yes—
504C2×C4×C53C2512yes—
505C2×C4×C53C2511yescharacteristic
506C2×C4×C53C2513yes—
507C22⋊D53—212no—
508C22⋊D53—212no—
509C22⋊D53—212no—
510C22⋊D53—212no—
511C22⋊D53—224no—
512C22⋊D53—24no—
513C22⋊D53—212no—
514C22⋊D53—412no—
515C22⋊D53—44no—
516C22⋊D53C22×D4124yes—
517C2×Dic53—212no—
518C2×Dic53—212no—
519C2×Dic53—212no—
520C2×Dic53—224no—
521C2×Dic53—212no—
522C2×Dic53—46no—
523C2×Dic53C22×D4112yes—
524C2×Dic53C2516yes—
525C2×Dic53C2516yes—
526C2×Dic53C2516yes—
527C2×Dic53C2512yes—
528C2×Dic53C2513yes—
529C2×Dic53C2511yescharacteristic
530D212—24no—
531D212—212no—
532D212—22no—
533D212—22no—
534D212—44no—
535D212C22×D4112yes—
536C4×D53—212no—
537C4×D53—212no—
538C4×D53—224no—
539C4×D53—212no—
540C4×D53—212no—
541C4×D53—24no—
542C4×D53—212no—
543C4×D53—412no—
544C4×D53C22×D4112yes—
545C4×D53C22×D4112yes—
546C4×D53C22×D414yes—
547C4×D53C22×D4112yes—
548Dic106—26no—
549Dic106—212no—
550Dic106—26no—
551Dic106—212no—
552Dic106—212no—
553Dic106—224no—
554Dic106—212no—
555Dic106C22×D4112yes—
556#62859—531nomaximal, Sylow
557C22×C53—26no—
558C22×C53—22no—
559C22×C53—26no—
560C22×C53—24no—
561C22×C53—212no—
562C22×C53—812no—
563C22×C53C23×D416yes—
564C22×C53C2611yescharacteristic
565C2×D53—26no—
566C2×D53—22no—
567C2×D53—22no—
568C2×D53—22no—
569C2×D53—24no—
570C2×D53—24no—
571C2×D53—412no—
572C2×D53—48no—
573C2×D53—812no—
574C2×D53C23×D412yes—
575C2×D53C23×D416yes—
576C4×C53—22no—
577C4×C53—26no—
578C4×C53—26no—
579C4×C53—22no—
580C4×C53C23×D412yes—
581C4×C53C23×D416yes—
582Dic53—26no—
583Dic53—26no—
584Dic53—26no—
585Dic53—22no—
586Dic53C23×D416yes—
587Dic53C23×D412yes—
588C2×#585—531no—
589C22×2−1+4—531no—
590#3500—531no—
591#3500—533no—
592#3500—533no—
593#3500D5311yescharacteristic, complemented
594#3499—531no—
595#3499—533no—
596#3499—533no—
597#3499—531no—
598#3489—534no—
599#3489—5312no—
600#3486—534no—
601#3485—5312no—
602#3449—533no—
603#3449—533no—
604C2×#536—533no—
605C2×#536—533no—
606#3428—531no—
607C2×C53—26no—
608C2×C53—42no—
609C2×C53—46no—
610C2×C53C24×D411yescharacteristic
611C2×C532−1+612yes—
612D53—22no—
613D53—26no—
614D53—42no—
615D53—42no—
616#585—10616no—
617C2×2−1+4—536no—
618C2×2−1+4—533no—
619C2×2−1+4—531no—
620C2×2−1+4—532no—
621C2×2−1+4—533no—
622C2×2−1+4—531no—
623C2×2−1+4—532no—
624C2×2−1+4—533no—
625C2×2−1+4—10616no—
626C2×2−1+4C2×D5311yescharacteristic, complemented
627C2×H(5,𝔽2)—536no—
628C2×H(5,𝔽2)—533no—
629C2×H(5,𝔽2)C2×D5311yescharacteristic, complemented
630C22×#41—531no—
631C22×#41—533no—
632C22×#41—536no—
633C22×#41—533no—
634C22×#41—532no—
635C22×#41—533no—
636C22×#41—536no—
637C23×Q8—533no—
638C23×Q8—532no—
639D4×Q8—534no—
640D4×Q8—5312no—
641D4×Q8—534no—
642D4×Q8—5312no—
643#548—534no—
644#548—5312no—
645#548—5312no—
646#548C2×D5314yescomplemented
647#547—5312no—
648#547—5324no—
649#547—5312no—
650#547—5324no—
651#547—5312no—
652#547—5312no—
653#546—5312no—
654#546—5312no—
655#546—5312no—
656#546—5324no—
657#546—5324no—
658#546C2×D53112yescomplemented
659#537—5312no—
660#537—5312no—
661#536—533no—
662#536—533no—
663#536—533no—
664#536—533no—
665#536—533no—
666#536—536no—
667#536—533no—
668#536—5312no—
669#536—5312no—
670#536—536no—
671#536—536no—
672#536—533no—
673#536—5312no—
674#536—5312no—
675#536—533no—
676#536—533no—
677#536C2×D5313yescomplemented
678#535—533no—
679#535—533no—
680#535—533no—
681#535—531no—
682#535—533no—
683#535C2×D5313yescomplemented
684#534—5312no—
685#534—5312no—
686#532—533no—
687#532—533no—
688#532—536no—
689#532—536no—
690#532—533no—
691#532C2×D5313yescomplemented
692C2×C4⋊Q8—533no—
693C2×C4⋊Q8—536no—
694C2×C4⋊Q8—533no—
695C2×#124—533no—
696C2×#124—536no—
697C2×#124C2×D5313yescomplemented
698#525—5312no—
699#525—5312no—
700#525—5312no—
701#525—5312no—
702C2×#123—5312no—
703C2×#123—5312no—
704C2×C22⋊Q8—5312no—
705C2×C22⋊Q8—5312no—
706#520—532no—
707#520—536no—
708#519—532no—
709#518—536no—
710C4×#41—531no—
711C4×#41—533no—
712C4×#41—533no—
713C4×#41C2×D5311yescharacteristic, complemented
714C2×#117—533no—
715C2×#117—533no—
716C53#6285911yescharacteristic, complemented, Sylow
7172−1+4—28no—
7182−1+4—10616no—
7192−1+4—10624no—
7202−1+4—10616no—
7212−1+4—10648no—
7222−1+4—10624no—
7232−1+4—10624no—
7242−1+4—1068no—
7252−1+4—1068no—
726H(5,𝔽2)—28no—
727H(5,𝔽2)—10648no—
728H(5,𝔽2)—10624no—
729C2×#41—5316no—
730C2×#41—531no—
731C2×#41—533no—
732C2×#41—531no—
733C2×#41—536no—
734C2×#41—533no—
735C2×#41—536no—
736C2×#41—536no—
737C2×#41—533no—
738C2×#41—536no—
739C2×#41—533no—
740C2×#41—536no—
741C2×#41—536no—
742C2×#41—536no—
743C2×#41—5312no—
744C2×#41—536no—
745C2×#41—5312no—
746C2×#41—536no—
747C2×#41—533no—
748C2×#41—536no—
749C2×#41—536no—
750C2×#41—533no—
751C2×#41—533no—
752C2×#41—536no—
753C2×#41—5312no—
754C2×#41—536no—
755C2×#41—10624no—
756C2×#41—10624no—
757C2×#41—10624no—
758C2×#41—10648no—
759C2×#41—10648no—
760C2×#41—10616no—
761C2×#41C22×D5313yes—
762C2×#41C22×D5313yes—
763C2×#41C22×D5316yes—
764C2×#41C22×D5312yes—
765C2×#41C22×D5311yescharacteristic
766C22×Q8—531no—
767C22×Q8—536no—
768C22×Q8—536no—
769C22×Q8—533no—
770C22×Q8—533no—
771C22×Q8—536no—
772C22×Q8—536no—
773C22×Q8—532no—
774C22×Q8—532no—
775C22×Q8—536no—
776C22×Q8—533no—
777C22×Q8—533no—
778C22×Q8—536no—
779C22×Q8—536no—
780C22×Q8—10624no—
781C22×Q8—10616no—
782C22×Q8C22×D5313yes—
783C22×Q8C22×D5312yes—
784C22×D4—533no—
785C22×D4—536no—
786C22×D4—5312no—
787C22×D4—536no—
788C22×D4—533no—
789C22×D4—536no—
790C22×D4—531no—
791C22×D4—536no—
792C22×D4C22×D5313yes—
793C22×D4C22×D5316yes—
794C23×C4—533no—
795C23×C4—536no—
796C23×C4—536no—
797C23×C4—536no—
798C23×C4—536no—
799C4⋊Q8—533no—
800C4⋊Q8—533no—
801C4⋊Q8—536no—
802C4⋊Q8—5312no—
803C4⋊Q8—5324no—
804C4⋊Q8—536no—
805C4⋊Q8—533no—
806C4⋊Q8—5312no—
807C4⋊Q8C22×D5313yes—
808#127—531no—
809#127—533no—
810#127—531no—
811#127C22×D5313yes—
812#124—533no—
813#124—531no—
814#124—533no—
815#124—536no—
816#124—5312no—
817#124—533no—
818#124—5324no—
819#124—533no—
820#124—533no—
821#124C22×D5316yes—
822#124C22×D5313yes—
823#124C22×D53112yes—
824#124C22×D5311yescharacteristic
825#123—5312no—
826#123—5312no—
827#123—5312no—
828#123—5312no—
829#123—5312no—
830#123—5324no—
831#123—5312no—
832#123—5324no—
833#123—5324no—
834#123—5312no—
835#123—5312no—
836#123—5312no—
837#123C22×D53112yes—
838C22⋊Q8—5312no—
839C22⋊Q8—5312no—
840C22⋊Q8—5312no—
841C22⋊Q8—5312no—
842C22⋊Q8—5312no—
843C22⋊Q8—5312no—
844C22⋊Q8—5312no—
845C22⋊Q8—5324no—
846C22⋊Q8—5312no—
847C22⋊Q8—5324no—
848C22⋊Q8—5324no—
849C22⋊Q8—5312no—
850C22⋊Q8C22×D53112yes—
851#121—5312no—
852#121—5312no—
853#121—5312no—
854#121—5324no—
855#121—5312no—
856#121—5312no—
857#121—5312no—
858#121—534no—
859#121—5312no—
860#121—5324no—
861#121C22×D53112yes—
862#121C22×D53112yes—
863#120—5312no—
864#120—5312no—
865#120—5312no—
866#120—534no—
867#120—5312no—
868#120C22×D53112yes—
869C4×Q8—532no—
870C4×Q8—536no—
871C4×Q8—536no—
872C4×Q8C22×D5312yes—
873C4×D4—536no—
874C4×D4—5324no—
875C4×D4—5312no—
876C4×D4—5312no—
877C4×D4—5312no—
878C4×D4—536no—
879C4×D4—5312no—
880C4×D4—5324no—
881C4×D4—536no—
882C4×D4—5312no—
883C4×D4C22×D5316yes—
884C4×D4C22×D53112yes—
885#117—533no—
886#117—536no—
887#117—536no—
888#117—533no—
889#117—531no—
890#117—533no—
891#117—533no—
892#117—536no—
893#117—536no—
894#117C22×D5313yes—
895C2×C4⋊C4—536no—
896C2×C4⋊C4—5312no—
897C2×C4⋊C4—5312no—
898C2×C4⋊C4—536no—
899C2×C4⋊C4—5324no—
900C2×C22⋊C4—5312no—
901C2×C22⋊C4—536no—
902C2×C22⋊C4—536no—
903C2×C22⋊C4—5324no—
904C2×C22⋊C4C22×D53112yes—
905C2×C42—533no—
906C2×C42—536no—
907C2×C42C22×D5313yes—
908C24—533no—
909C24—536no—
910C24—532no—
911C24C23×D5316yes—
912#41—28no—
913#41—224no—
914#41—212no—
915#41—212no—
916#41—538no—
917#41—5324no—
918#41—5324no—
919#41—10624no—
920#41—10624no—
921#41—10624no—
922#41—10648no—
923#41—10624no—
924#41—10624no—
925#41—10612no—
926#41—10624no—
927#41—10624no—
928#41—10624no—
929#41—10624no—
930#41—10612no—
931#41—1064no—
932#41—10612no—
933#41—10648no—
934#41—10648no—
935#41—10624no—
936#41—10624no—
937#41—10624no—
938#41—10624no—
939#41—10612no—
940#41—10612no—
941#41D4×D5318yes—
942C2×Q8—28no—
943C2×Q8—212no—
944C2×Q8—538no—
945C2×Q8—533no—
946C2×Q8—536no—
947C2×Q8—5312no—
948C2×Q8—536no—
949C2×Q8—536no—
950C2×Q8—536no—
951C2×Q8—533no—
952C2×Q8—533no—
953C2×Q8—10624no—
954C2×Q8—10624no—
955C2×Q8—10624no—
956C2×Q8—10612no—
957C2×Q8—10624no—
958C2×Q8—10624no—
959C2×Q8—10624no—
960C2×Q8—10612no—
961C2×Q8—10624no—
962C2×Q8—1068no—
963C2×Q8—1068no—
964C2×Q8—10612no—
965C2×Q8—10612no—
966C2×Q8C23×D5316yes—
967C2×Q8C23×D5313yes—
968C2×Q8C23×D5311yescharacteristic
969C2×Q8C23×D5311yescharacteristic
970C2×D4—224no—
971C2×D4—212no—
972C2×D4—536no—
973C2×D4—5324no—
974C2×D4—536no—
975C2×D4—536no—
976C2×D4—536no—
977C2×D4—532no—
978C2×D4—5312no—
979C2×D4—536no—
980C2×D4—536no—
981C2×D4—534no—
982C2×D4—5312no—
983C2×D4—533no—
984C2×D4—536no—
985C2×D4—532no—
986C2×D4—531no—
987C2×D4—531no—
988C2×D4—534no—
989C2×D4—1064no—
990C2×D4—10612no—
991C2×D4—10624no—
992C2×D4—10624no—
993C2×D4—10624no—
994C2×D4—10648no—
995C2×D4—10624no—
996C2×D4C23×D5316yes—
997C2×D4C23×D5316yes—
998C2×D4C23×D5316yes—
999C2×D4C23×D5313yes—
1000C2×D4C23×D5311yescharacteristic
1001C2×D4C23×D53112yes—
1002C2×D4C23×D5313yes—
1003C22×C4—533no—
1004C22×C4—5324no—
1005C22×C4—533no—
1006C22×C4—533no—
1007C22×C4—533no—
1008C22×C4—531no—
1009C22×C4—536no—
1010C22×C4—536no—
1011C22×C4—536no—
1012C22×C4—5312no—
1013C22×C4—536no—
1014C22×C4—536no—
1015C22×C4—5312no—
1016C22×C4—536no—
1017C22×C4—536no—
1018C22×C4—536no—
1019C22×C4—536no—
1020C22×C4—532no—
1021C22×C4—536no—
1022C22×C4—5312no—
1023C22×C4—10624no—
1024C22×C4—10624no—
1025C22×C4—10624no—
1026C22×C4—10624no—
1027C22×C4C23×D5316yes—
1028C22×C4C23×D5316yes—
1029C22×C4C23×D5316yes—
1030C22×C4C23×D5316yes—
1031C22×C4C23×D5313yes—
1032C4⋊C4—536no—
1033C4⋊C4—532no—
1034C4⋊C4—5312no—
1035C4⋊C4—5312no—
1036C4⋊C4—5324no—
1037C4⋊C4—5324no—
1038C4⋊C4—5312no—
1039C4⋊C4—536no—
1040C4⋊C4—536no—
1041C4⋊C4—536no—
1042C4⋊C4C23×D53112yes—
1043C4⋊C4C23×D5316yes—
1044C22⋊C4—5312no—
1045C22⋊C4—5324no—
1046C22⋊C4—536no—
1047C22⋊C4—5312no—
1048C22⋊C4—536no—
1049C22⋊C4—532no—
1050C22⋊C4—5312no—
1051C22⋊C4—5312no—
1052C22⋊C4—536no—
1053C22⋊C4—536no—
1054C22⋊C4—534no—
1055C22⋊C4—5312no—
1056C22⋊C4C23×D53124yes—
1057C22⋊C4C23×D5316yes—
1058C22⋊C4C23×D53112yes—
1059C22⋊C4C23×D5314yes—
1060C42—531no—
1061C42—533no—
1062C42—5312no—
1063C42—536no—
1064C42C23×D5313yes—
1065C42C23×D5311yescharacteristic
1066C42C23×D5316yes—
1067C23—212no—
1068C23—412no—
1069C23—531no—
1070C23—533no—
1071C23—5312no—
1072C23—532no—
1073C23—532no—
1074C23—10612no—
1075C23—1064no—
1076C23—21212no—
1077C23—2126no—
1078C23—2124no—
1079C23C24×D5316yes—
1080C23C24×D5312yes—
1081C23C24×D5313yes—
1082Q8—212no—
1083Q8—26no—
1084Q8—22no—
1085Q8—5312no—
1086Q8—10612no—
1087Q8—10624no—
1088Q8—10612no—
1089Q8—10612no—
1090Q8—1066no—
1091Q8—10612no—
1092Q8—1066no—
1093Q8C2×D4×D5314yes—
1094D4—212no—
1095D4—212no—
1096D4—212no—
1097D4—26no—
1098D4—22no—
1099D4—412no—
1100D4—5324no—
1101D4—5312no—
1102D4—1064no—
1103D4—10612no—
1104D4—10612no—
1105D4—1064no—
1106D4—10612no—
1107D4—10624no—
1108D4—10612no—
1109D4—10612no—
1110D4—10612no—
1111D4—1062no—
1112D4—1062no—
1113D4—2124no—
1114D4—2124no—
1115D4—21212no—
1116D4C2×D4×D53112yes—
1117C2×C4—212no—
1118C2×C4—212no—
1119C2×C4—212no—
1120C2×C4—46no—
1121C2×C4—5312no—
1122C2×C4—533no—
1123C2×C4—531no—
1124C2×C4—534no—
1125C2×C4—5312no—
1126C2×C4—5312no—
1127C2×C4—5312no—
1128C2×C4—536no—
1129C2×C4—532no—
1130C2×C4—536no—
1131C2×C4—536no—
1132C2×C4—1064no—
1133C2×C4—10612no—
1134C2×C4—10612no—
1135C2×C4—10612no—
1136C2×C4—10624no—
1137C2×C4—10612no—
1138C2×C4—10624no—
1139C2×C4—10612no—
1140C2×C4—10612no—
1141C2×C4—10612no—
1142C2×C4—10612no—
1143C2×C4—10612no—
1144C2×C4—21212no—
1145C2×C4—2126no—
1146C2×C4C2×D4×D53112yes—
1147C2×C4C24×D5316yes—
1148C2×C4C24×D5312yes—
1149C2×C4C24×D5316yes—
1150C2×C4C24×D5312yes—
1151C2×C4C24×D5311yescharacteristic
1152C2×C4C24×D5313yes—
1153C22—26no—
1154C22—22no—
1155C22—26no—
1156C22—24no—
1157C22—212no—
1158C22—812no—
1159C22—532no—
1160C22—536no—
1161C22—1066no—
1162C22—1062no—
1163C22—1062no—
1164C22—1062no—
1165C22—1064no—
1166C22—1064no—
1167C22—42412no—
1168C22—21212no—
1169C22—2128no—
1170C22C22×D4×D5316yes—
1171C22C25×D5311yescharacteristic
1172C4—22no—
1173C4—26no—
1174C4—22no—
1175C4—26no—
1176C4—532no—
1177C4—536no—
1178C4—1066no—
1179C4—1066no—
1180C4—1066no—
1181C4—1062no—
1182C4C22×D4×D5316yes—
1183C4C22×D4×D5312yes—
1184C2—26no—
1185C2—46no—
1186C2—42no—
1187C2—1066no—
1188C2—1062no—
1189C2—2122no—
1190C2—2122no—
1191C2C23×D4×D5311yescharacteristic
1192C2#2028952812yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3500C2
hypercenter#3500D53
hypocenterC53#62859
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. C2×#16811458C2semidirect
2. C2×2−1+4×D53C2semidirect
3. #20288507C2semidirect
4. #20288505C2semidirect
5. #20288503C2semidirect
6. #20288500C2semidirect
7. #20288497C2semidirect
8. #20288496C2semidirect
9. #20288495C2semidirect
10. #20288394C2semidirect
11. #20288386C2semidirect
12. #20288361C2semidirect
13. #20288352C2semidirect
14. #20288046C2semidirect
15. #20288042C2semidirect
16. C2×#16811193C2semidirect
17. #536×D53C2semidirect
18. #20287914C2semidirect
19. C53×#3500C2semidirect
21. C2×#13133265C22semidirect
22. C2×#13133265C22semidirect
24. C2×#13133264C22semidirect
25. C2×#13133264C22semidirect
26. C2×#13133264C22semidirect
27. C2×#13133264C22semidirect
28. C2×#13133264C22semidirect
31. C2×#13133262C22semidirect
33. C22×#11719947C22semidirect
36. C2×#41×D53C22semidirect
37. C2×#41×D53C22semidirect
38. C2×#41×D53C22semidirect
39. C22×Q8×D53C22semidirect
40. C22×Q8×D53C22semidirect
41. Q8×D212C22semidirect
42. D4×Dic106C22semidirect
43. Q8×C22⋊D53C22semidirect
44. #16811286C22semidirect
45. #16811281C22semidirect
46. #16811280C22semidirect
47. #16811279C22semidirect
48. #16811278C22semidirect
49. #16811277C22semidirect
50. #16811275C22semidirect
51. #16811273C22semidirect
52. #16811272C22semidirect
53. #16811271C22semidirect
54. #16811270C22semidirect
55. #16811267C22semidirect
56. #16811266C22semidirect
57. #16811263C22semidirect
58. #16811260C22semidirect
59. #16811202C22semidirect
60. #16811200C22semidirect
61. #16811199C22semidirect
62. #16811199C22semidirect
63. #16811198C22semidirect
64. #16811198C22semidirect
65. #16811197C22semidirect
66. #16811196C22semidirect
67. #16811195C22semidirect
68. #16811194C22semidirect
69. #16811194C22semidirect
70. #16811193C22semidirect
71. #16811193C22semidirect
72. #16811193C22semidirect
73. #16811193C22semidirect
74. #16811193C22semidirect
75. #16811193C22semidirect
76. #16811193C22semidirect
77. #16811191C22semidirect
78. #16811191C22semidirect
79. #16811190C22semidirect
80. #16811186C22semidirect
81. #16811186C22semidirect
82. #16811183C22semidirect
83. #16811181C22semidirect
84. #16811173C22semidirect
85. #16811172C22semidirect
86. #16811171C22semidirect
87. #16811169C22semidirect
88. #16811169C22semidirect
89. C2×#13133217C22semidirect
90. C2×#13133215C22semidirect
91. C4⋊Q8×D53C22semidirect
92. C2×#13133204C22semidirect
93. #124×D53C22semidirect
94. #16811133C22semidirect
95. #16811132C22semidirect
96. #16811132C22semidirect
97. #16811129C22semidirect
98. C2×#13133199C22semidirect
99. #123×D53C22semidirect
100. C2×#13133194C22semidirect
101. C22⋊Q8×D53C22semidirect
102. #16811105C22semidirect
103. #16811102C22semidirect
104. #16811099C22semidirect
105. #16811095C22semidirect
106. #41×Dic53C22semidirect
107. C4×#11719945C22semidirect
108. #16811091C22semidirect
109. C2×#13133174C22semidirect
110. #117×D53C22semidirect
111. C2×2−1+4×C53C22semidirect
112. C2×H(5,𝔽2)×C53C22semidirect
113. C53×#548C22semidirect
114. C53×#546C22semidirect
115. C53×#536C22semidirect
116. C53×#535C22semidirect
117. C53×#532C22semidirect
118. C2×#124×C53C22semidirect
119. C4×#41×C53C22semidirect
161. #41×D53D4semidirect
593. #3500D53semidirect
626. C2×2−1+4C2×D53semidirect
629. C2×H(5,𝔽2)C2×D53semidirect
646. #548C2×D53semidirect
658. #546C2×D53semidirect
677. #536C2×D53semidirect
683. #535C2×D53semidirect
691. #532C2×D53semidirect
697. C2×#124C2×D53semidirect
713. C4×#41C2×D53semidirect
716. C53#62859semidirect

Maximal subgroups

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

subgroupindex
C2×#168114582
C2×2−1+4×D532
#202885072
#202885052
#202885032
#202885002
#202884972
#202884962
#202884952
#202883942
#202883862
#202883612
#202883522
#202880462
#202880422
C2×#168111932
#536×D532
#202879142
C53×#35002
#6285953