Finite Group Databasebeta

← #28328947

Subgroups — #28328947

Order 13568.

2960 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811692C211yesmaximal, characteristic, complemented
2C2×#16811691C211yesmaximal, characteristic, complemented
3#20291246C213yesmaximal, complemented
4#20291242C213yesmaximal, complemented
5#20291239C213yesmaximal, complemented
6#20291231C213yesmaximal, complemented
7#20291230C211yesmaximal, characteristic, complemented
8#20291220C211yesmaximal, characteristic, complemented
9Q8×C22⋊#6157C211yesmaximal, characteristic, complemented
10#20291203C213yesmaximal, complemented
11#20291202C213yesmaximal, complemented
12#124×#6157C213yesmaximal, complemented
13#20291172C213yesmaximal, complemented
14C4×Q8×#6157C211yesmaximal, characteristic, complemented
15#548×D53C211yesmaximal, characteristic
16#16811692—28no—
17#16811691—28no—
18C2×Q8×#6157C2211yescharacteristic
19C2×Q8×#6157C2213yes—
20C2×Q8×#6157C2211yescharacteristic
21C2×Q8×#6157C2213yes—
22C2×Q8×#6157C2211yescharacteristic
23C2×Q8×#6157C2211yescharacteristic
24C2×D4×#6157C2213yes—
25C2×D4×#6157C2213yes—
26C2×#13133296C2213yes—
27C2×#13133296C2213yes—
28C2×#13133296C2213yes—
29C22×C4⋊#6157C2213yes—
30(C2×#6157)⋊Q8C2213yes—
31(C2×#6157)⋊Q8C2213yes—
32#16811575C2213yes—
33#16811575C2213yes—
34#16811575C2213yes—
35#16811575C2213yes—
36#16811574C2213yes—
37#16811574C2213yes—
38#16811574C2213yes—
39#16811574C2213yes—
40#16811573C2211yescharacteristic
41#16811573C2213yes—
42#16811573C2213yes—
43#16811573C2213yes—
44#16811573C2216yes—
45#16811573C2216yes—
46#16811572C2216yes—
47#16811571C2216yes—
48#16811570C2216yes—
49#16811567C2213yes—
50#16811565C2213yes—
51#16811565C2213yes—
52C4⋊C4×#6157C2213yes—
53C4⋊C4×#6157C2213yes—
54C4×C4⋊#6157C2213yes—
55C4×C4⋊#6157C2213yes—
56C22⋊C4×#6157C2216yes—
57C22⋊C4×#6157C2216yes—
58C4×C22⋊#6157C2213yes—
59C4×C22⋊#6157C2213yes—
60C42×#6157C2213yes—
61C2×#41×D53C2211yescharacteristic
62C22×Q8×D53C2211yescharacteristic
63#16811285C411yescharacteristic, complemented
64#16811284C411yescharacteristic, complemented
65#16811283C413yescomplemented
66#16811282C413yescomplemented
67#16811281C413yescomplemented
68#16811280C411yescharacteristic, complemented
69#16811279C413yescomplemented
70#124×D53C2213yes—
71C22⋊Q8×D53C2213yes—
72#121×D53C2213yes—
73C4×Q8×D53C2211yescharacteristic
74C4×D4×D53C2213yes—
75C53×#548C411yescharacteristic, complemented
76C23×#6157C2316yes—
77Q8×#6157—24no—
78Q8×#6157—24no—
79Q8×#6157—24no—
80Q8×#6157—212no—
81Q8×#6157—212no—
82Q8×#6157D418yescomplemented
83D4×#6157—212no—
84D4×#6157—212no—
85#13133296—212no—
86#13133296—212no—
87#13133296—212no—
88C2×C4⋊#6157—212no—
89C2×C4⋊#6157C2313yes—
90C2×C4⋊#6157C2313yes—
91C2×C4⋊#6157C2313yes—
92C2×C4⋊#6157C2313yes—
93C2×C4⋊#6157C2313yes—
94C2×C4⋊#6157C2313yes—
95C2×C4⋊#6157C2311yescharacteristic
96C2×C4⋊#6157C2313yes—
97C2×C4⋊#6157C2313yes—
98C2×C4⋊#6157C2313yes—
99C2×C22⋊#6157C2311yescharacteristic
100C2×C22⋊#6157C2313yes—
101C2×C22⋊#6157C2313yes—
102C2×C22⋊#6157C2313yes—
103C2×C22⋊#6157C2313yes—
104C2×C22⋊#6157C2311yescharacteristic
105C2×C22⋊#6157C2313yes—
106C2×C22⋊#6157C2313yes—
107C2×C22⋊#6157C2316yes—
108C2×C4×#6157C2311yescharacteristic
109C2×C4×#6157C2313yes—
110C2×C4×#6157C2313yes—
111C2×C4×#6157C2313yes—
112C2×C4×#6157C2316yes—
113C2×C4×#6157C2313yes—
114C2×C4×#6157C2313yes—
115C2×C4×#6157C2313yes—
116C2×C4×#6157C2313yes—
117(C2×#6157)⋊C4C2311yescharacteristic
118(C2×#6157)⋊C4C2313yes—
119(C2×#6157)⋊C4C2313yes—
120(C2×#6157)⋊C4C2313yes—
121(C2×#6157)⋊C4C2313yes—
122(C2×#6157)⋊C4C2316yes—
123(C2×#6157)⋊C4C2316yes—
124(C2×#6157)⋊C4C2311yescharacteristic
125(C2×#6157)⋊C4C2316yes—
126C2×#11719949C2×C411yescharacteristic
127C2×#11719945C2×C413yes—
128C2×#11719947C2×C413yes—
129#41×D53—24no—
130#41×D53—24no—
131C22×Dic106C2×C413yescomplemented
132C2×Q8×D53—24no—
133C2×Q8×D53—24no—
134C2×Q8×D53C2×C411yescharacteristic, complemented
135C2×Q8×D53C2×C413yescomplemented
136C2×Q8×D53C2313yes—
137C2×Q8×D53C2311yescharacteristic
138C2×D4×D53C2313yes—
139C2×D4×D53C2313yes—
140C22×C4×D53C2313yes—
141C22×C4×D53C2313yes—
142#13133206C2×C413yescomplemented
143#13133205C2×C413yescomplemented
144#13133204C2×C413yescomplemented
145#13133203C2×C416yescomplemented
146#13133203C2×C416yescomplemented
147#13133197C2×C413yescomplemented
148#13133196C2×C413yescomplemented
149#13133195C2×C416yescomplemented
150#13133194C2×C416yescomplemented
151#13133193C2×C413yescomplemented
152#13133192C2×C413yescomplemented
153#13133191C2×C413yescomplemented
154#13133190C2×C416yescomplemented
155#13133189C2×C416yescomplemented
156#13133188C2×C413yescomplemented
157Q8×Dic53C2×C411yescharacteristic, complemented
158C4×Dic106C2×C413yescomplemented
159#13133182C2×C413yescomplemented
160C4×D212C2×C413yescomplemented
161D4×Dic53C2×C413yescomplemented
162#13133179C2×C413yescomplemented
163C4×C22⋊D53C2×C413yescomplemented
164C4×C22⋊D53C2×C413yescomplemented
165#13133177C2×C413yescomplemented
166#13133177C2×C413yescomplemented
167C4⋊C4×D53C2313yes—
168C4⋊C4×D53C2313yes—
169C22⋊C4×D53C2313yes—
170C22⋊C4×D53C2316yes—
171C22⋊C4×D53C2311yescharacteristic
172C42×D53C2313yes—
173C2×#41×C53C2×C411yescharacteristic
174C22×Q8×C53C2×C411yescharacteristic, complemented
175#124×C53C2×C413yescomplemented
176C22⋊Q8×C53C2×C413yescomplemented
177#121×C53C2×C413yescomplemented
178C4×Q8×C53C2×C411yescharacteristic, complemented
179C4×D4×C53C2×C413yescomplemented
180C23×D53C2413yes—
181C23×D53C2411yescharacteristic
182C22×#6157—212no—
183C22×#6157—46no—
184C22×#6157—46no—
185C22×#6157C2413yes—
186C22×#6157C2413yes—
187C22×#6157C2413yes—
188C22×#6157C2411yescharacteristic
189C22×#6157C2411yescharacteristic
190C22×#6157C2413yes—
191C22×#6157C2411yescharacteristic
192C22×#6157C2411yescharacteristic
193#41×C53—24no—
194C2×Q8×C53—24no—
195C2×Q8×C53C22×C413yes—
196C2×Q8×C53C22×C411yescharacteristic
197C2×D4×C53C22×C413yes—
198C2×D4×C53C22×C413yes—
199C22×C4×C53C22×C413yes—
200C22×C4×C53C22×C413yes—
201C2×C22⋊D53C22×C416yes—
202C2×C22⋊D53C22×C413yes—
203C2×C22⋊D53C22×C413yes—
204C22×Dic53C22×C413yes—
205C22×Dic53C22×C413yes—
206#11719949—24no—
207Q8×D53—24no—
208Q8×D53—26no—
209Q8×D53—26no—
210Q8×D53—212no—
211Q8×D53C2×D414yes—
212Q8×D53#4114yes—
213#11719947—212no—
214D4×D53—26no—
215D4×D53—26no—
216D4×D53—43no—
217D4×D53—43no—
218#11719945—212no—
219C2×D212C22×C413yes—
220C2×D212C22×C413yes—
221C2×C4×D53—26no—
222C2×C4×D53—26no—
223C2×C4×D53—26no—
224C2×C4×D53—26no—
225C2×C4×D53C22×C413yes—
226C2×C4×D53C22×C413yes—
227C2×C4×D53C22×C413yes—
228C2×C4×D53C22×C413yes—
229C2×C4×D53C2411yescharacteristic
230C2×C4×D53C2413yes—
231C2×C4×D53C2413yes—
232C2×C4×D53C2411yescharacteristic
233C2×C4×D53C2413yes—
234C2×Dic106—212no—
235C2×Dic106C22×C416yes—
236C2×Dic106C22×C413yes—
237C2×Dic106C22×C413yes—
238C22⋊#6157—26no—
239C22⋊#6157—22no—
240C22⋊#6157—26no—
241C22⋊#6157—26no—
242C22⋊#6157—22no—
243C22⋊#6157—26no—
244C22⋊#6157—46no—
245C22⋊#6157—43no—
246C22⋊#6157—43no—
247C4⋊#6157—26no—
248C4⋊#6157—22no—
249C4⋊#6157—26no—
250C4⋊#6157—26no—
251C4⋊#6157—26no—
252C4⋊#6157—26no—
253C4⋊#6157—26no—
254C4⋊#6157—43no—
255C4⋊#6157—43no—
256C4⋊#6157C2×D4112yes—
257C4×#6157—212no—
258C4×#6157—22no—
259C4×#6157—26no—
260C4×#6157—26no—
261C4×#6157—26no—
262C4×#6157—43no—
263C4×#6157—43no—
264C4×#6157—43no—
265C4×#6157C2×D4112yes—
266C4⋊C4×C53C22×C413yes—
267C4⋊C4×C53C22×C413yes—
268C22⋊C4×C53C22×C411yescharacteristic
269C22⋊C4×C53C22×C413yes—
270C22⋊C4×C53C22×C416yes—
271C42×C53C22×C413yes—
272C22⋊Dic53C22×C411yescharacteristic
273C22⋊Dic53C22×C413yes—
274C22⋊Dic53C22×C416yes—
275#11719921C22×C411yescharacteristic
276#11719921C22×C413yes—
277#11719921C22×C411yescharacteristic
278#11719921C22×C413yes—
279#11719921C22×C416yes—
280#11719921C22×C416yes—
281C4⋊Dic53C22×C413yes—
282C4⋊Dic53C22×C413yes—
283#11719919C22×C413yes—
284#11719919C22×C413yes—
285#11719919C22×C416yes—
286C4×Dic53C22×C413yes—
287C4×Dic53C22×C413yes—
288C4×Dic53C22×C413yes—
289C23×C53C23×C411yescharacteristic
290C23×C53C23×C413yes—
291C22×D53—21no—
292C22×D53—23no—
293C22×D53—21no—
294C22×D53—23no—
295C22×D53—23no—
296C22×D53—21no—
297C22×D53—21no—
298C22×D53—23no—
299C22×D53—23no—
300C22×D53—21no—
301C22×D53—21no—
302C22×D53—23no—
303C22×D53C23×C411yescharacteristic
304C22×D53C23×C413yes—
305C22×D53C2511yescharacteristic
306C2×#6157—21no—
307C2×#6157—21no—
308C2×#6157—21no—
309C2×#6157—21no—
310C2×#6157—23no—
311C2×#6157—23no—
312C2×#6157—23no—
313C2×#6157—21no—
314C2×#6157—21no—
315C2×#6157—23no—
316C2×#6157—23no—
317C2×#6157—23no—
318C2×#6157—21no—
319C2×#6157—23no—
320C2×#6157—23no—
321C2×#6157—21no—
322C2×#6157—21no—
323C2×#6157—23no—
324C2×#6157—23no—
325C2×#6157—21no—
326C2×#6157—23no—
327C2×#6157—812no—
328C2×#6157C22×D416yes—
329C2×#6157C22×D412yes—
330C2×#61572−1+412yes—
331Q8×C53—26no—
332Q8×C53C4×D414yes—
333D4×C53—26no—
334D4×C53—43no—
335C2×C4×C53—26no—
336C2×C4×C53—26no—
337C2×C4×C53C23×C413yes—
338C2×C4×C53C23×C411yescharacteristic
339C2×C4×C53C23×C413yes—
340C2×C4×C53C23×C411yescharacteristic
341C2×C4×C53C23×C413yes—
342C22⋊D53—212no—
343C22⋊D53—43no—
344C22⋊D53—43no—
345C2×Dic53—26no—
346C2×Dic53—26no—
347C2×Dic53C23×C413yes—
348C2×Dic53C23×C411yescharacteristic
349C2×Dic53C23×C413yes—
350C2×Dic53C23×C411yescharacteristic
351C2×Dic53C23×C413yes—
352D212—26no—
353D212—43no—
354C4×D53—23no—
355C4×D53—21no—
356C4×D53—21no—
357C4×D53—23no—
358C4×D53—21no—
359C4×D53—21no—
360C4×D53—23no—
361C4×D53—23no—
362C4×D53—26no—
363C4×D53—26no—
364C4×D53—26no—
365C4×D53—26no—
366C4×D53C22×D416yes—
367C4×D53C2×#4116yes—
368Dic106—26no—
369Dic106—212no—
370Dic106C4×D4112yes—
371#34312—531nomaximal, Sylow
372C22×C53—21no—
373C22×C53—23no—
374C22×C53—21no—
375C22×C53—23no—
376C22×C53—21no—
377C22×C53—23no—
378C22×C53C24×C411yescharacteristic
379C2×D53—21no—
380C2×D53—23no—
381C2×D53—21no—
382C2×D53—23no—
383C2×D53—21no—
384C2×D53—23no—
385C2×D53—41no—
386C2×D53—43no—
387C2×D53—43no—
388C2×D53—41no—
389C2×D53—41no—
390C2×D53—43no—
391C2×D53—41no—
392C2×D53—43no—
393C2×D53C23×D411yescharacteristic
394C2×D53C22×#4111yescharacteristic
395C2×D53C2×2−1+411yescharacteristic
396C2×D53#58511yescharacteristic
397C2×D53#58511yescharacteristic
398C2×D53#58511yescharacteristic
399#6157—22no—
400#6157—26no—
401#6157—22no—
402#6157—43no—
403#6157—41no—
404#6157—41no—
405#6157—43no—
406#6157—43no—
407C4×C53—23no—
408C4×C53—21no—
409C4×C53—23no—
410C4×C53—21no—
411C4×C53C2×C4×D416yes—
412Dic53—23no—
413Dic53—21no—
414Dic53—23no—
415Dic53—21no—
416Dic53C2×C4×D416yes—
417C2×#548—531no—
418C2×#520—531no—
419C2×#519—531no—
420#2367—533no—
421#2363—533no—
422#2360—533no—
423#2352—533no—
424#2351—531no—
425#2341—531no—
426Q8×C22⋊C4—531no—
427#2324—533no—
428#2323—533no—
429C4×#124—533no—
430#2293—533no—
431C42×Q8—531no—
432C2×C53—43no—
433C2×C53—41no—
434C2×C53C22×C4×D411yescharacteristic
435C2×C53#342811yescharacteristic
436C2×C53C4×2−1+411yescharacteristic
437D53—41no—
438D53—43no—
439D53#349711yescharacteristic
440D53#350011yescharacteristic
441D53#351611yescharacteristic
442D53#352411yescharacteristic
443C22×#41—531no—
444C23×Q8—531no—
445#548—531no—
446#548—531no—
447#548—533no—
448#548—533no—
449#548—533no—
450#548—531no—
451#548—533no—
452#548#615711yescharacteristic, complemented
453C2×#124—533no—
454C2×C22⋊Q8—533no—
455C2×#121—533no—
456#520—1068no—
457#519—1068no—
458C2×C4×Q8—531no—
459C2×C4×Q8—531no—
460C2×C4×Q8—533no—
461C2×C4×Q8—531no—
462C2×C4×Q8—531no—
463C2×C4×Q8—531no—
464C2×C4×Q8—533no—
465C2×C4×D4—533no—
466C2×C4×D4—533no—
467C2×C4×D4—533no—
468C2×#117—533no—
469C2×#117—533no—
470C2×#117—533no—
471C22×C4⋊C4—533no—
472#391—533no—
473#391—533no—
474#390—533no—
475#390—533no—
476#390—533no—
477#390—533no—
478#389—533no—
479#389—533no—
480#389—533no—
481#389—533no—
482#388—536no—
483#388—536no—
484#388—533no—
485#388—533no—
486#388—531no—
487#388—533no—
488#387—536no—
489#386—536no—
490#385—536no—
491#382—533no—
492#380—533no—
493#380—533no—
494C4×C4⋊C4—533no—
495C4×C4⋊C4—533no—
496C4×C4⋊C4—533no—
497C4×C4⋊C4—533no—
498C4×C22⋊C4—533no—
499C4×C22⋊C4—533no—
500C4×C22⋊C4—536no—
501C4×C22⋊C4—536no—
502C43—533no—
503C53#3431211yescharacteristic, complemented, Sylow
504C2×#41—531no—
505C2×#41—533no—
506C2×#41—533no—
507C2×#41—1064no—
508C2×#41—1064no—
509C2×#41C2×#615711yescharacteristic
510C22×Q8—531no—
511C22×Q8—533no—
512C22×Q8—533no—
513C22×Q8—531no—
514C22×Q8—533no—
515C22×Q8—1064no—
516C22×Q8—1064no—
517C22×Q8C2×#615711yescharacteristic, complemented
518C22×D4—533no—
519C22×D4—533no—
520C23×C4—533no—
521C23×C4—533no—
522C23×C4—536no—
523#124—533no—
524#124—533no—
525#124—536no—
526#124—536no—
527#124—533no—
528#124C2×#615713yescomplemented
529C22⋊Q8—533no—
530C22⋊Q8—533no—
531C22⋊Q8—536no—
532C22⋊Q8—533no—
533C22⋊Q8—536no—
534C22⋊Q8C2×#615713yescomplemented
535#121—533no—
536#121—536no—
537#121—533no—
538#121—533no—
539#121—536no—
540#121C2×#615713yescomplemented
541C4×Q8—538no—
542C4×Q8—531no—
543C4×Q8—533no—
544C4×Q8—533no—
545C4×Q8—10612no—
546C4×Q8—10612no—
547C4×Q8—1064no—
548C4×Q8—1064no—
549C4×Q8—1064no—
550C4×Q8C2×#615711yescharacteristic, complemented
551C4×D4—533no—
552C4×D4—533no—
553C4×D4—533no—
554C4×D4—533no—
555C4×D4—533no—
556C4×D4—533no—
557C4×D4—533no—
558C4×D4—10612no—
559C4×D4—10612no—
560C4×D4C2×#615713yescomplemented
561#117—10612no—
562#117—10612no—
563#117—10612no—
564C2×C4⋊C4—533no—
565C2×C4⋊C4—533no—
566C2×C4⋊C4—533no—
567C2×C4⋊C4—533no—
568C2×C4⋊C4—533no—
569C2×C4⋊C4—531no—
570C2×C4⋊C4—533no—
571C2×C4⋊C4—533no—
572C2×C4⋊C4—533no—
573C2×C4⋊C4—533no—
574C2×C4⋊C4—533no—
575C2×C4⋊C4—533no—
576C2×C4⋊C4—10612no—
577C2×C22⋊C4—531no—
578C2×C22⋊C4—533no—
579C2×C22⋊C4—536no—
580C2×C22⋊C4—533no—
581C2×C22⋊C4—531no—
582C2×C22⋊C4—533no—
583C2×C22⋊C4—533no—
584C2×C22⋊C4—531no—
585C2×C22⋊C4—533no—
586C2×C22⋊C4—533no—
587C2×C22⋊C4—536no—
588C2×C22⋊C4—533no—
589C2×C42—533no—
590C2×C42—533no—
591C2×C42—533no—
592C2×C42—536no—
593C2×C42—533no—
594C2×C42—533no—
595C2×C42—531no—
596C2×C42—533no—
597C2×C42—533no—
598C2×C42—533no—
599#95—531no—
600#95—533no—
601#95—533no—
602#95—533no—
603#95—536no—
604#95—536no—
605#95—533no—
606#95—536no—
607#95—531no—
608C24—533no—
609C24—531no—
610#41—24no—
611#41—10612no—
612#41—10612no—
613#41—1064no—
614C2×Q8—24no—
615C2×Q8—534no—
616C2×Q8—534no—
617C2×Q8—533no—
618C2×Q8—536no—
619C2×Q8—533no—
620C2×Q8—10612no—
621C2×Q8—1066no—
622C2×Q8—1066no—
623C2×Q8—10612no—
624C2×Q8—1064no—
625C2×Q8C22×#615713yes—
626C2×Q8C22×#615711yescharacteristic
627C2×D4—536no—
628C2×D4—533no—
629C2×D4—533no—
630C2×D4—533no—
631C2×D4—533no—
632C2×D4—1066no—
633C2×D4—1066no—
634C2×D4—2123no—
635C2×D4—2123no—
636C2×D4C22×#615713yes—
637C2×D4C22×#615713yes—
638C22×C4—533no—
639C22×C4—531no—
640C22×C4—533no—
641C22×C4—531no—
642C22×C4—533no—
643C22×C4—533no—
644C22×C4—533no—
645C22×C4—533no—
646C22×C4—533no—
647C22×C4—533no—
648C22×C4—531no—
649C22×C4—533no—
650C22×C4—533no—
651C22×C4—531no—
652C22×C4—533no—
653C22×C4—533no—
654C22×C4—531no—
655C22×C4—533no—
656C22×C4—531no—
657C22×C4—1066no—
658C22×C4—1066no—
659C22×C4—1066no—
660C22×C4—1066no—
661C22×C4—10612no—
662C22×C4—2126no—
663C22×C4—2126no—
664C22×C4C22×#615713yes—
665C22×C4C22×#615713yes—
666C4⋊C4—5312no—
667C4⋊C4—533no—
668C4⋊C4—533no—
669C4⋊C4—533no—
670C4⋊C4—536no—
671C4⋊C4—533no—
672C4⋊C4—1066no—
673C4⋊C4—1066no—
674C4⋊C4—1062no—
675C4⋊C4—1066no—
676C4⋊C4—1066no—
677C4⋊C4—1066no—
678C4⋊C4—1066no—
679C4⋊C4—2123no—
680C4⋊C4—2123no—
681C4⋊C4C22×#615713yes—
682C4⋊C4C22×#615713yes—
683C22⋊C4—531no—
684C22⋊C4—533no—
685C22⋊C4—536no—
686C22⋊C4—531no—
687C22⋊C4—531no—
688C22⋊C4—533no—
689C22⋊C4—533no—
690C22⋊C4—536no—
691C22⋊C4—536no—
692C22⋊C4—1062no—
693C22⋊C4—1066no—
694C22⋊C4—1062no—
695C22⋊C4—1066no—
696C22⋊C4—1066no—
697C22⋊C4—1066no—
698C22⋊C4—2123no—
699C22⋊C4—2126no—
700C22⋊C4—2123no—
701C22⋊C4C22×#615711yescharacteristic
702C22⋊C4C22×#615713yes—
703C22⋊C4C22×#615716yes—
704C42—5312no—
705C42—533no—
706C42—533no—
707C42—533no—
708C42—1062no—
709C42—1066no—
710C42—1066no—
711C42—10612no—
712C42—1066no—
713C42—2123no—
714C42—2123no—
715C42—2123no—
716C42C22×#615713yes—
717C23—531no—
718C23—533no—
719C23—531no—
720C23—1061no—
721C23—1063no—
722C23—1061no—
723C23—1063no—
724C23—1061no—
725C23—1063no—
726C23—1063no—
727C23—1061no—
728C23—1063no—
729C23—1063no—
730C23—1061no—
731C23—1061no—
732C23C23×#615713yes—
733C23C23×#615711yescharacteristic
734Q8—26no—
735Q8—5312no—
736Q8—10612no—
737Q8—1066no—
738Q8D4×#615714yes—
739D4—26no—
740D4—43no—
741D4—10612no—
742D4—1066no—
743D4—2123no—
744D4—2123no—
745D4—2123no—
746C2×C4—26no—
747C2×C4—26no—
748C2×C4—533no—
749C2×C4—536no—
750C2×C4—536no—
751C2×C4—532no—
752C2×C4—536no—
753C2×C4—532no—
754C2×C4—531no—
755C2×C4—533no—
756C2×C4—533no—
757C2×C4—531no—
758C2×C4—1066no—
759C2×C4—1066no—
760C2×C4—1063no—
761C2×C4—1061no—
762C2×C4—1061no—
763C2×C4—1063no—
764C2×C4—1063no—
765C2×C4—1061no—
766C2×C4—1061no—
767C2×C4—1063no—
768C2×C4—1066no—
769C2×C4—1066no—
770C2×C4—1061no—
771C2×C4—1061no—
772C2×C4—1061no—
773C2×C4—1061no—
774C2×C4—1063no—
775C2×C4—1063no—
776C2×C4—1066no—
777C2×C4—1066no—
778C2×C4—1061no—
779C2×C4—1063no—
780C2×C4—1061no—
781C2×C4—1063no—
782C2×C4—1063no—
783C2×C4—1063no—
784C2×C4—1063no—
785C2×C4—1061no—
786C2×C4—1063no—
787C2×C4—1061no—
788C2×C4—1063no—
789C2×C4—1063no—
790C2×C4—1061no—
791C2×C4—1061no—
792C2×C4—1063no—
793C2×C4—42412no—
794C2×C4C23×#615711yescharacteristic
795C2×C4C23×#615713yes—
796C2×C4C23×#615713yes—
797C2×C4C23×#615711yescharacteristic
798C2×C4C23×#615713yes—
799C22—21no—
800C22—23no—
801C22—21no—
802C22—23no—
803C22—21no—
804C22—23no—
805C22—531no—
806C22—531no—
807C22—531no—
808C22—531no—
809C22—531no—
810C22—531no—
811C22—1061no—
812C22—1063no—
813C22—1061no—
814C22—1063no—
815C22—1063no—
816C22—1061no—
817C22—2123no—
818C22—2121no—
819C22—2121no—
820C22—2123no—
821C22—2121no—
822C22—2123no—
823C22—2121no—
824C22—2123no—
825C22C24×#615711yescharacteristic
826C4—21no—
827C4—23no—
828C4—23no—
829C4—21no—
830C4—536no—
831C4—1066no—
832C4—1062no—
833C4—1062no—
834C4—1061no—
835C4—1063no—
836C4—1063no—
837C4—1061no—
838C4—2123no—
839C4—2121no—
840C4—2121no—
841C4—2123no—
842C4—2123no—
843C4C2×D4×#615716yes—
844C2—41no—
845C2—43no—
846C2—531no—
847C2—531no—
848C2—531no—
849C2—531no—
850C2—2121no—
851C2—2123no—
852C2C22×D4×#615711yescharacteristic
853C2#2029169511yescharacteristic
854C22−1+4×#615711yescharacteristic
subgroupG/H
center, FrattiniC22C24×#6157
commutator, socleC22×C53C24×C4
FittingC53×#548C4
prime radical#548×D53C2
cosocleC22×D53C25
hypercenter#548#6157
hypocenterC53#34312
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#16811692C2semidirect
2. C2×#16811691C2semidirect
3. #20291246C2semidirect
4. #20291242C2semidirect
5. #20291239C2semidirect
6. #20291231C2semidirect
7. #20291230C2semidirect
8. #20291220C2semidirect
9. Q8×C22⋊#6157C2semidirect
10. #20291203C2semidirect
11. #20291202C2semidirect
12. #124×#6157C2semidirect
13. #20291172C2semidirect
14. C4×Q8×#6157C2semidirect
63. #16811285C4semidirect
64. #16811284C4semidirect
65. #16811283C4semidirect
66. #16811282C4semidirect
67. #16811281C4semidirect
68. #16811280C4semidirect
69. #16811279C4semidirect
75. C53×#548C4semidirect
82. Q8×#6157D4semidirect
131. C22×Dic106C2×C4semidirect
134. C2×Q8×D53C2×C4semidirect
135. C2×Q8×D53C2×C4semidirect
142. #13133206C2×C4semidirect
143. #13133205C2×C4semidirect
144. #13133204C2×C4semidirect
145. #13133203C2×C4semidirect
146. #13133203C2×C4semidirect
147. #13133197C2×C4semidirect
148. #13133196C2×C4semidirect
149. #13133195C2×C4semidirect
150. #13133194C2×C4semidirect
151. #13133193C2×C4semidirect
152. #13133192C2×C4semidirect
153. #13133191C2×C4semidirect
154. #13133190C2×C4semidirect
155. #13133189C2×C4semidirect
156. #13133188C2×C4semidirect
157. Q8×Dic53C2×C4semidirect
158. C4×Dic106C2×C4semidirect
159. #13133182C2×C4semidirect
160. C4×D212C2×C4semidirect
161. D4×Dic53C2×C4semidirect
162. #13133179C2×C4semidirect
163. C4×C22⋊D53C2×C4semidirect
164. C4×C22⋊D53C2×C4semidirect
165. #13133177C2×C4semidirect
166. #13133177C2×C4semidirect
174. C22×Q8×C53C2×C4semidirect
175. #124×C53C2×C4semidirect
176. C22⋊Q8×C53C2×C4semidirect
177. #121×C53C2×C4semidirect
178. C4×Q8×C53C2×C4semidirect
179. C4×D4×C53C2×C4semidirect
452. #548#6157semidirect
503. C53#34312semidirect
517. C22×Q8C2×#6157semidirect
528. #124C2×#6157semidirect
534. C22⋊Q8C2×#6157semidirect
540. #121C2×#6157semidirect
550. C4×Q8C2×#6157semidirect
560. C4×D4C2×#6157semidirect

Maximal subgroups

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

subgroupindex
C2×#168116922
C2×#168116912
#202912462
#202912422
#202912392
#202912312
#202912302
#202912202
Q8×C22⋊#61572
#202912032
#202912022
#124×#61572
#202911722
C4×Q8×#61572
#548×D532
#3431253