Finite Group Databasebeta

← #11910468

Subgroups — #11910468

Order 1152.

1958 conjugacy classes of subgroups.

The subgroup lattice has 1129 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596143C211yesmaximal, characteristic, complemented
2C3×#5684C211yesmaximal, characteristic, complemented
3C3×#5680C211yesmaximal, characteristic, complemented
4#10595416C212yesmaximal, complemented
5#10595367C212yesmaximal, complemented
6#10595260C212yesmaximal, complemented
7#10595187C212yesmaximal, complemented
8#10594239C212yesmaximal, complemented
9#10594169C212yesmaximal, complemented
10#10594131C212yesmaximal, complemented
11#10594098C212yesmaximal, complemented
12#10594086C212yesmaximal, complemented
13#10594044C212yesmaximal, complemented
14#10594042C212yesmaximal, complemented
15#10594029C212yesmaximal, complemented
16#10593952C211yesmaximal, characteristic, complemented
17#10593921C211yesmaximal, characteristic, complemented
18#10593874C211yesmaximal, characteristic, complemented
19#10593868C211yesmaximal, characteristic, complemented
20#87094—31nomaximal
21#86132—31nomaximal
22C32×#124C2211yescharacteristic
23#64153C2212yes—
24#64144C2212yes—
25#64088C2212yes—
26#64088C2212yes—
27#64087C2212yes—
28#64087C2212yes—
29#64079C2211yescharacteristic
30#64079C2211yescharacteristic
31C3×#946C2212yes—
32C3×#946C2211yescharacteristic
33C3×Q8×Dic3C2211yescharacteristic
34C3×#939C2212yes—
35C3×#938C2211yescharacteristic
36C3×D4×Dic3C2211yescharacteristic
37C3×#886C2212yes—
38C3×#884C2212yes—
39C3×#883C2212yes—
40C3×#883C2212yes—
41C3×#67⋊C4C2212yes—
42C3×#879C2212yes—
43C3×#878C2212yes—
44C3×#877C2212yes—
45C3×#875C2211yescharacteristic
46C3×C42×D3C2211yescharacteristic
47C3×#870C2211yescharacteristic
48C3×#870C2211yescharacteristic
49#63982C2212yes—
50#63980C2212yes—
51Dic3×#67C2212yes—
52Dic3×#67C2212yes—
53#63970C2212yes—
54#63969C2212yes—
55#63964C2212yes—
56#63964C2212yes—
57#63962C2212yes—
58#63961C2212yes—
59#63959C2212yes—
60#63959C2212yes—
61#63959C2212yes—
62#63956C2212yes—
63#63955C2212yes—
64C2×Dic32C2212yes—
65#63919C2212yes—
66#63918C2211yescharacteristic
67#63918C2211yescharacteristic
68#63913C2212yes—
69#63908C2211yescharacteristic
70#63905C2212yes—
71#63905C2212yes—
72#63899C2212yes—
73#63899C2212yes—
74#63893C2212yes—
75Dic3×D12C2211yescharacteristic
76#63884C2212yes—
77#63879C2212yes—
78#63877C2212yes—
79#63877C2212yes—
80C4×D3×Dic3C2212yes—
81#63862C2212yes—
82#63862C2212yes—
83#63861C2212yes—
84#63859C2212yes—
85#63858C2212yes—
86#63858C2212yes—
87#63857C2212yes—
88#63856C2211yescharacteristic
89#63851C2212yes—
90#63851C2212yes—
91#63851C2212yes—
92#63847C2212yes—
93#63847C2212yes—
94#63847C2212yes—
95#63846C2212yes—
96#63846C2212yes—
97#63846C2212yes—
98#63845C2212yes—
99#63845C2212yes—
100#63844C2212yes—
101Dic3×Dic6C2211yescharacteristic
102#63841C2211yescharacteristic
103#63841C2211yescharacteristic
104#63840C2212yes—
105#63839C2212yes—
106#63837C2212yes—
107#63837C2212yes—
108#63837C2212yes—
109C3×#562—31no—
110C3×#529—31no—
111#5712—32no—
112#5712—32no—
113#5699—31no—
114#5688—31no—
115C3⋊#564—31no—
116C3⋊#564—31no—
117#5684D311yescharacteristic, complemented
118#5680—31no—
119#5680D311yescharacteristic, complemented
120#5672—31no—
121#5672—31no—
122#5672—31no—
123#5672—61no—
124#5667—32no—
125#5651—32no—
126#5651—32no—
127#5651—32no—
128#5649—32no—
129#5649—32no—
130#5646—32no—
131#5646—32no—
132#5646—32no—
133#5622—32no—
134#5622—32no—
135#5621—32no—
136#5621—32no—
137#5621—32no—
138#5600—32no—
139#5600—32no—
140#5578—32no—
141#5557—32no—
142#5538—32no—
143#5538—32no—
144#5528—32no—
145#5517—32no—
146#5479—31no—
147#5470—31no—
148C2×C32×Q8C2311yescharacteristic
149C2×C32×D4C2311yescharacteristic
150C22×C3⋊Dic3C2312yes—
151C2×#634C2312yes—
152C2×C3×#67C2312yes—
153C2×C3×#67C2312yes—
154C2×C3×#67C2312yes—
155C22×C3×Dic3C2312yes—
156C22×C3×Dic3C2312yes—
157C2×C3×D12C2311yescharacteristic
158C2×C3×C4×D3C2311yescharacteristic
159C2×C3×C4×D3C2311yescharacteristic
160C2×C3×C4×D3C2312yes—
161C2×C3×C4×D3C2311yescharacteristic
162C2×C3×Dic6C2311yescharacteristic
163C2×#627C2312yes—
164C2×#627C2312yes—
165C2×#627C2312yes—
166C2×#625C2312yes—
167C2×D3×Dic3C2312yes—
168C2×D3×Dic3C2312yes—
169C32×C22⋊C4C2312yes—
170C32×C22⋊C4C2312yes—
171C32×C42C2311yescharacteristic
172#3757C2312yes—
173#3757C2312yes—
174#3757C2312yes—
175C4⋊(C3⋊Dic3)C2311yescharacteristic
176C4⋊(C3⋊Dic3)C2311yescharacteristic
177C4⋊(C3⋊Dic3)C2311yescharacteristic
178C4⋊(C3⋊Dic3)C2311yescharacteristic
179#3750C2312yes—
180#3750C2312yes—
181#3750C2312yes—
182#3750C2312yes—
183#3750C2312yes—
184#3750C2312yes—
185C4×C3⋊Dic3C2312yes—
186C3×#217C2312yes—
187C3×#217C2312yes—
188C3×#217C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×(C2×D3)⋊C4C2312yes—
193C3×C4⋊Dic3C2312yes—
194C3×C4⋊Dic3C2312yes—
195C3×C4⋊Dic3C2311yescharacteristic
196C3×C4⋊Dic3C2311yescharacteristic
197C3×C4⋊Dic3C2311yescharacteristic
198C3×C4⋊Dic3C2311yescharacteristic
199C3×Dic3⋊C4C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×Dic3⋊C4C2312yes—
202C3×Dic3⋊C4C2312yes—
203C3×Dic3⋊C4C2312yes—
204C3×Dic3⋊C4C2312yes—
205C3×C4×Dic3C2311yescharacteristic
206C3×C4×Dic3C2312yes—
207C3×C4×Dic3C2311yescharacteristic
208C3×C4×Dic3C2311yescharacteristic
209#3724C2312yes—
210#3724C2312yes—
211#3724C2312yes—
212#3724C2312yes—
213Dic3⋊Dic3C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221(C2×D3)⋊Dic3C2312yes—
222(C2×D3)⋊Dic3C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229Dic32C2312yes—
230Dic32C2312yes—
231Dic32C2312yes—
232Dic32C2312yes—
233Dic32C2312yes—
234Dic32C2312yes—
235#3531—91noSylow
236C3×#126—32no—
237C3×#125—31no—
238C3×#125—31no—
239C3×#124—21no—
240C3×#124—31no—
241C3×#124C2×D311yescharacteristic
242C3×#124C2×D311yescharacteristic
243C3×#123—32no—
244C3×#123—32no—
245C3×#123—32no—
246C3×C22⋊Q8—32no—
247C3×C22⋊Q8—31no—
248C3×C22⋊Q8—32no—
249C3×#121—32no—
250C3×#121—31no—
251C3×#121—32no—
252C3×C4×Q8—31no—
253C3×C4×D4—31no—
254C3×C4×D4—32no—
255C3×#117—32no—
256C2×C3×C42—31no—
257#946—31no—
258#946C2×D311yescharacteristic
259#946C2×D312yes—
260Q8×Dic3—31no—
261Q8×Dic3C2×D311yescharacteristic
262#944—32no—
263#944—32no—
264#944—32no—
265#944—62no—
266#939—32no—
267#939—32no—
268#939—32no—
269#939C2×D312yes—
270#938—32no—
271#938—31no—
272#938C2×D311yescharacteristic
273#936—32no—
274#936—32no—
275#936—32no—
276#935—32no—
277#935—32no—
278#935—32no—
279#935—32no—
280#935—32no—
281#935—32no—
282#935—62no—
283D4×Dic3—32no—
284D4×Dic3—32no—
285D4×Dic3—31no—
286D4×Dic3C2×D311yescharacteristic
287#930—31no—
288#929—32no—
289#929—32no—
290#929—32no—
291C4×#67—32no—
292C4×#67—32no—
293C4×#67—32no—
294#926—32no—
295#926—31no—
296#926—31no—
297#924—31no—
298#924—32no—
299#924—32no—
300#924—32no—
301#924—32no—
302#924—32no—
303#924—32no—
304C2×C4×Dic3—32no—
305C2×C4×Dic3—32no—
306C2×C4×Dic3—32no—
307#898—32no—
308#898—32no—
309#898—32no—
310#898—32no—
311#898—32no—
312#897—32no—
313#897—32no—
314#896—32no—
315#896—32no—
316#896—32no—
317#896—32no—
318#896—32no—
319#894—32no—
320#892—31no—
321#892—31no—
322#890—32no—
323#890—32no—
324#890—32no—
325#890—32no—
326#890—32no—
327#889—32no—
328#889—32no—
329#889—32no—
330#889—32no—
331#889—32no—
332#889—32no—
333#889—32no—
334#889—32no—
335#889—32no—
336#889—32no—
337#889—32no—
338#888—32no—
339#888—32no—
340#888—32no—
341#888—32no—
342#888—32no—
343#888—31no—
344#888—31no—
345#887—32no—
346#887—32no—
347#887—32no—
348#887—32no—
349#886—32no—
350#886C2×D312yes—
351#885—32no—
352#885—32no—
353#885—32no—
354#885—32no—
355#885—32no—
356#884C2×D312yes—
357#883—32no—
358#883—32no—
359#883—32no—
360#883C2×D312yes—
361#883C2×D312yes—
362#67⋊C4—32no—
363#67⋊C4C2×D312yes—
364#879—32no—
365#879—32no—
366#879—32no—
367#879—32no—
368#879—32no—
369#879—32no—
370#879—32no—
371#879—32no—
372#879—32no—
373#879—32no—
374#879—32no—
375#879—32no—
376#879—62no—
377#879—62no—
378#879C2×D312yes—
379#878—32no—
380#878—32no—
381#878—32no—
382#878—32no—
383#878—32no—
384#878—32no—
385#878—32no—
386#878—32no—
387#878—32no—
388#878—32no—
389#878—32no—
390#878—62no—
391#878—62no—
392#878C2×D312yes—
393#877—32no—
394#877—32no—
395#877—32no—
396#877C2×D312yes—
397#876—32no—
398#875C2×D311yescharacteristic
399C4×D12—31no—
400#872—32no—
401#872—32no—
402C42×D3—32no—
403C42×D3C2×D311yescharacteristic
404#870—31no—
405#870—31no—
406#870—31no—
407#870—31no—
408#870—61no—
409#870—61no—
410#870C2×D311yescharacteristic
411#870C2×D311yescharacteristic
412#869—31no—
413#869—31no—
414C4×Dic6—31no—
415C4×Dic6—32no—
416C4×Dic6—32no—
417C4×Dic6—32no—
418C4×Dic6—32no—
419C23×C32C2412yes—
420C22×C3×D3C2411yescharacteristic
421C22×C3×D3C2412yes—
422C32×Q8—41no—
423C32×D4—41no—
424C2×C32×C4C2411yescharacteristic
425C2×C32×C4C2412yes—
426C2×C32×C4C2411yescharacteristic
427C2×C32×C4C2411yescharacteristic
428C2×C3⋊Dic3—42no—
429C2×C3⋊Dic3C2412yes—
430C2×C3⋊Dic3C2412yes—
431C2×C3⋊Dic3C2412yes—
432C2×C3⋊Dic3C2412yes—
433#634—42no—
434C3×#67—42no—
435C3×#67—42no—
436C3×#67—42no—
437C2×C3×Dic3—24no—
438C2×C3×Dic3—42no—
439C2×C3×Dic3C2412yes—
440C2×C3×Dic3C2412yes—
441C2×C3×Dic3C2412yes—
442C2×C3×Dic3C2412yes—
443C2×C3×Dic3C2412yes—
444C2×C3×Dic3C2411yescharacteristic
445C2×C3×Dic3C2411yescharacteristic
446C2×C3×Dic3C2411yescharacteristic
447C3×D12—41no—
448C3×C4×D3—22no—
449C3×C4×D3—41no—
450C3×C4×D3—41no—
451C3×C4×D3—42no—
452C3×Dic6—41no—
453#627—42no—
454#627—42no—
455#627—42no—
456#625—42no—
457D3×Dic3—24no—
458D3×Dic3—42no—
459#564—91no—
460#563—92no—
461#563—92no—
462#563—92no—
463#563—92no—
464#563—91no—
465#563—91no—
466#562—31no—
467#562—92no—
468#562—92no—
469#533—91no—
470#533—92no—
471#533—92no—
472#529—31no—
473#529—91no—
474#529—92no—
475#529—92no—
476#529—92no—
477#529—92no—
478C2×C3×Q8—21no—
479C2×C3×Q8—31no—
480C2×C3×Q8C22×D311yescharacteristic
481C2×C3×Q8C22×D311yescharacteristic
482C2×C3×D4—21no—
483C2×C3×D4—32no—
484C2×C3×D4—32no—
485C2×C3×D4—32no—
486C2×C3×D4—31no—
487C2×C3×D4C22×D311yescharacteristic
488C2×C3×D4C22×D311yescharacteristic
489C22×C3×C4—32no—
490C22×C3×C4—32no—
491C22×C3×C4—31no—
492C22×C3×C4—32no—
493C22×C3×C4—31no—
494C22×C3×C4—31no—
495C2×#67—32no—
496C2×#67—32no—
497C2×#67C22×D312yes—
498C2×#67C22×D312yes—
499C2×#67C22×D312yes—
500C22×Dic3—32no—
501C22×Dic3—32no—
502C22×Dic3—32no—
503C22×Dic3—32no—
504C22×Dic3—62no—
505C22×Dic3C22×D312yes—
506C22×Dic3C22×D312yes—
507C2×D12C22×D311yescharacteristic
508C2×C4×D3—32no—
509C2×C4×D3—32no—
510C2×C4×D3C22×D311yescharacteristic
511C2×C4×D3C22×D312yes—
512C2×C4×D3C22×D311yescharacteristic
513C2×C4×D3C22×D311yescharacteristic
514C2×Dic6—32no—
515C2×Dic6—32no—
516C2×Dic6—32no—
517C2×Dic6—32no—
518C2×Dic6—32no—
519C2×Dic6—32no—
520C2×Dic6—32no—
521C2×Dic6—32no—
522C2×Dic6—62no—
523C2×Dic6C22×D311yescharacteristic
524C3×C4⋊C4—32no—
525C3×C4⋊C4—32no—
526C3×C4⋊C4—32no—
527C3×C4⋊C4—32no—
528C3×C4⋊C4—31no—
529C3×C4⋊C4—31no—
530C3×C4⋊C4—32no—
531C3×C4⋊C4—32no—
532C3×C4⋊C4—32no—
533C3×C4⋊C4—31no—
534C3×C4⋊C4—31no—
535C3×C4⋊C4—32no—
536C3×C22⋊C4—22no—
537C3×C22⋊C4—22no—
538C3×C22⋊C4—32no—
539C3×C22⋊C4—32no—
540C3×C22⋊C4—32no—
541C3×C22⋊C4—32no—
542C3×C22⋊C4—32no—
543C3×C22⋊C4—32no—
544C3×C22⋊C4—32no—
545C3×C22⋊C4C22×D312yes—
546C3×C22⋊C4C22×D312yes—
547C3×C22⋊C4C22×D312yes—
548C3×C22⋊C4C22×D312yes—
549C3×C42—21no—
550C3×C42—31no—
551C3×C42—32no—
552C3×C42—31no—
553C3×C42—31no—
554C3×C42C22×D311yescharacteristic
555C3×C42C22×D311yescharacteristic
556#217—32no—
557#217—32no—
558#217—32no—
559#217—32no—
560#217—32no—
561#217—32no—
562#217—32no—
563#217—32no—
564#217—32no—
565#217—32no—
566#217—32no—
567#217—32no—
568#217—32no—
569#217—32no—
570#217—62no—
571#217—62no—
572#217—62no—
573#217C22×D312yes—
574#217C22×D312yes—
575#217C22×D312yes—
576(C2×D3)⋊C4—32no—
577(C2×D3)⋊C4—32no—
578(C2×D3)⋊C4—32no—
579(C2×D3)⋊C4—32no—
580(C2×D3)⋊C4—32no—
581(C2×D3)⋊C4—32no—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4C22×D312yes—
585(C2×D3)⋊C4C22×D312yes—
586(C2×D3)⋊C4C22×D312yes—
587(C2×D3)⋊C4C22×D312yes—
588C4⋊Dic3—31no—
589C4⋊Dic3—31no—
590C4⋊Dic3—31no—
591C4⋊Dic3—31no—
592C4⋊Dic3—31no—
593C4⋊Dic3—31no—
594C4⋊Dic3—31no—
595C4⋊Dic3—31no—
596C4⋊Dic3—32no—
597C4⋊Dic3—32no—
598C4⋊Dic3—32no—
599C4⋊Dic3—32no—
600C4⋊Dic3—32no—
601C4⋊Dic3—32no—
602C4⋊Dic3—32no—
603C4⋊Dic3—32no—
604C4⋊Dic3—61no—
605C4⋊Dic3—61no—
606C4⋊Dic3—61no—
607C4⋊Dic3—61no—
608C4⋊Dic3C22×D312yes—
609C4⋊Dic3C22×D311yescharacteristic
610C4⋊Dic3C22×D311yescharacteristic
611C4⋊Dic3C22×D311yescharacteristic
612C4⋊Dic3C22×D311yescharacteristic
613C4⋊Dic3C22×D312yes—
614Dic3⋊C4—32no—
615Dic3⋊C4—32no—
616Dic3⋊C4—32no—
617Dic3⋊C4—32no—
618Dic3⋊C4—32no—
619Dic3⋊C4—32no—
620Dic3⋊C4—32no—
621Dic3⋊C4—32no—
622Dic3⋊C4—32no—
623Dic3⋊C4—32no—
624Dic3⋊C4—32no—
625Dic3⋊C4—32no—
626Dic3⋊C4—32no—
627Dic3⋊C4—32no—
628Dic3⋊C4—32no—
629Dic3⋊C4—32no—
630Dic3⋊C4—32no—
631Dic3⋊C4—32no—
632Dic3⋊C4—32no—
633Dic3⋊C4—32no—
634Dic3⋊C4—32no—
635Dic3⋊C4—32no—
636Dic3⋊C4—32no—
637Dic3⋊C4—32no—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—62no—
643Dic3⋊C4—62no—
644Dic3⋊C4—62no—
645Dic3⋊C4—62no—
646Dic3⋊C4—62no—
647Dic3⋊C4—62no—
648Dic3⋊C4C22×D312yes—
649Dic3⋊C4C22×D312yes—
650Dic3⋊C4C22×D312yes—
651Dic3⋊C4C22×D312yes—
652Dic3⋊C4C22×D312yes—
653Dic3⋊C4C22×D312yes—
654C4×Dic3—32no—
655C4×Dic3—32no—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3—32no—
659C4×Dic3—32no—
660C4×Dic3—32no—
661C4×Dic3—32no—
662C4×Dic3—32no—
663C4×Dic3—32no—
664C4×Dic3—32no—
665C4×Dic3—32no—
666C4×Dic3—32no—
667C4×Dic3—32no—
668C4×Dic3—62no—
669C4×Dic3C22×D311yescharacteristic
670C4×Dic3C22×D311yescharacteristic
671C4×Dic3C22×D311yescharacteristic
672C4×Dic3C22×D312yes—
673C22×C32—22no—
674C22×C32—22no—
675C22×C32—22no—
676C22×C32C2511yescharacteristic
677C2×C3×D3—22no—
678C2×C3×D3—21no—
679C2×C3×D3—22no—
680C2×C3×D3—21no—
681C2×C3×D3—22no—
682C2×C3×D3—21no—
683C32×C4—21no—
684C32×C4—21no—
685C32×C4—22no—
686C32×C4—21no—
687C3⋊Dic3—22no—
688C3⋊Dic3—22no—
689C3⋊Dic3—22no—
690C3⋊Dic3—22no—
691C3×Dic3—22no—
692C3×Dic3—22no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—22no—
696C3×Dic3—22no—
697C3×Dic3—22no—
698C3×Dic32−1+412yes—
699C4⋊Q8—91no—
700C4⋊Q8—91no—
701C4⋊Q8—92no—
702C4⋊Q8—92no—
703C4⋊Q8—92no—
704C4⋊Q8—92no—
705#126—32no—
706#126—92no—
707#126—92no—
708#126—92no—
709#126—92no—
710#126—92no—
711#126—92no—
712#126—92no—
713#126—92no—
714#126—92no—
715#125—31no—
716#125—31no—
717#125—92no—
718#125—92no—
719#125—92no—
720#125—92no—
721#125—92no—
722#125—92no—
723#125—92no—
724#125—92no—
725#125—91no—
726#125—91no—
727#124—31no—
728#124—92no—
729#124—92no—
730#124—92no—
731#124—92no—
732#124D3211yescharacteristic
733#123—32no—
734#123—32no—
735#123—32no—
736#123—92no—
737#123—92no—
738#123—92no—
739#123—92no—
740#123—92no—
741#123—92no—
742#123—92no—
743C22⋊Q8—31no—
744C22⋊Q8—32no—
745C22⋊Q8—32no—
746C22⋊Q8—92no—
747C22⋊Q8—92no—
748C22⋊Q8—92no—
749C22⋊Q8—92no—
750C22⋊Q8—92no—
751C22⋊Q8—92no—
752C22⋊Q8—92no—
753C22⋊Q8—92no—
754C22⋊Q8—92no—
755C22⋊Q8—92no—
756C22⋊Q8—91no—
757C22⋊Q8—92no—
758C22⋊Q8—92no—
759#121—31no—
760#121—32no—
761#121—32no—
762#121—91no—
763#121—92no—
764#121—92no—
765C4×Q8—31no—
766C4×Q8—92no—
767C4×Q8—92no—
768C4×Q8—92no—
769C4×Q8—92no—
770C4×Q8—91no—
771C4×D4—31no—
772C4×D4—32no—
773C4×D4—91no—
774C4×D4—92no—
775C4×D4—92no—
776C4×D4—92no—
777#117—32no—
778#117—92no—
779#117—92no—
780#117—92no—
781#117—91no—
782#117—91no—
783C2×C42—31no—
784C2×C42—92no—
785C2×C42—92no—
786C23×C3—22no—
787C23×C3—31no—
788C23×C3—32no—
789C23×C3C23×D312yes—
790C23×C3C23×D312yes—
791C22×D3C23×D311yescharacteristic
792C22×D3C23×D312yes—
793C3×Q8—41no—
794C3×Q8—41no—
795C3×Q8—81no—
796C3×Q8—121no—
797C3×D4—41no—
798C3×D4—41no—
799C3×D4—81no—
800C3×D4—121no—
801C3×D4—122no—
802C3×D4—122no—
803C3×D4—122no—
804C2×C3×C4—22no—
805C2×C3×C4—21no—
806C2×C3×C4—21no—
807C2×C3×C4—21no—
808C2×C3×C4—31no—
809C2×C3×C4—32no—
810C2×C3×C4—32no—
811C2×C3×C4—32no—
812C2×C3×C4—32no—
813C2×C3×C4—32no—
814C2×C3×C4—31no—
815C2×C3×C4—31no—
816C2×C3×C4—62no—
817C2×C3×C4—64no—
818C2×C3×C4—122no—
819C2×C3×C4—121no—
820C2×C3×C4—121no—
821C2×C3×C4—122no—
822C2×C3×C4C23×D312yes—
823C2×C3×C4C23×D312yes—
824C2×C3×C4C23×D311yescharacteristic
825C2×C3×C4C23×D311yescharacteristic
826C2×C3×C4C23×D311yescharacteristic
827C2×C3×C4C23×D311yescharacteristic
828C2×C3×C4C23×D311yescharacteristic
829C2×C3×C4C23×D311yescharacteristic
830#67—42no—
831#67—42no—
832#67—42no—
833#67—122no—
834#67—122no—
835C2×Dic3—24no—
836C2×Dic3—32no—
837C2×Dic3—32no—
838C2×Dic3—32no—
839C2×Dic3—32no—
840C2×Dic3—32no—
841C2×Dic3—32no—
842C2×Dic3—32no—
843C2×Dic3—32no—
844C2×Dic3—42no—
845C2×Dic3—62no—
846C2×Dic3—62no—
847C2×Dic3—62no—
848C2×Dic3—62no—
849C2×Dic3—64no—
850C2×Dic3—122no—
851C2×Dic3—122no—
852C2×Dic3—122no—
853C2×Dic3—242no—
854C2×Dic3C23×D312yes—
855C2×Dic3C23×D312yes—
856C2×Dic3C23×D312yes—
857C2×Dic3C23×D312yes—
858C2×Dic3C23×D312yes—
859C2×Dic3C23×D311yescharacteristic
860C2×Dic3C23×D311yescharacteristic
861C2×Dic3C23×D311yescharacteristic
862D12—41no—
863C4×D3—22no—
864C4×D3—41no—
865C4×D3—41no—
866C4×D3—42no—
867C4×D3—64no—
868C4×D3—122no—
869Dic6—41no—
870Dic6—122no—
871Dic6—122no—
872Dic6—122no—
873Dic6—122no—
874Dic6—122no—
875Dic6—122no—
876Dic6—122no—
877Dic6—122no—
878Dic6—242no—
879C2×C32—42no—
880C2×C32C2×2−1+411yescharacteristic
881C2×C32#58511yescharacteristic
882C2×C32#58511yescharacteristic
883C3×D3—42no—
884C3×D3—41no—
885C2×Q8—31no—
886C2×Q8—92no—
887C2×Q8—92no—
888C2×Q8—92no—
889C2×Q8—92no—
890C2×Q8C2×D3211yescharacteristic
891C2×D4—32no—
892C2×D4—32no—
893C2×D4—32no—
894C2×D4—31no—
895C2×D4—92no—
896C2×D4C2×D3211yescharacteristic
897C22×C4—32no—
898C22×C4—32no—
899C22×C4—31no—
900C22×C4—31no—
901C22×C4—31no—
902C22×C4—32no—
903C22×C4—92no—
904C22×C4—92no—
905C22×C4—92no—
906C4⋊C4—32no—
907C4⋊C4—32no—
908C4⋊C4—31no—
909C4⋊C4—31no—
910C4⋊C4—31no—
911C4⋊C4—32no—
912C4⋊C4—31no—
913C4⋊C4—32no—
914C4⋊C4—32no—
915C4⋊C4—32no—
916C4⋊C4—32no—
917C4⋊C4—32no—
918C4⋊C4—92no—
919C4⋊C4—92no—
920C4⋊C4—92no—
921C4⋊C4—92no—
922C4⋊C4—92no—
923C4⋊C4—92no—
924C4⋊C4—92no—
925C4⋊C4—92no—
926C4⋊C4—92no—
927C4⋊C4—92no—
928C4⋊C4—92no—
929C4⋊C4—92no—
930C4⋊C4—92no—
931C4⋊C4—91no—
932C4⋊C4—91no—
933C4⋊C4—92no—
934C4⋊C4—92no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—92no—
938C4⋊C4—92no—
939C4⋊C4—92no—
940C22⋊C4—32no—
941C22⋊C4—32no—
942C22⋊C4—32no—
943C22⋊C4—32no—
944C22⋊C4—32no—
945C22⋊C4—32no—
946C22⋊C4—32no—
947C22⋊C4—92no—
948C22⋊C4—92no—
949C22⋊C4—92no—
950C22⋊C4—92no—
951C22⋊C4—92no—
952C22⋊C4—92no—
953C22⋊C4—92no—
954C22⋊C4—92no—
955C22⋊C4—92no—
956C22⋊C4—92no—
957C22⋊C4—92no—
958C22⋊C4C2×D3212yes—
959C22⋊C4C2×D3212yes—
960C42—31no—
961C42—31no—
962C42—31no—
963C42—32no—
964C42—92no—
965C42—92no—
966C42—92no—
967C42—92no—
968C42—92no—
969C42—92no—
970C42—92no—
971C42C2×D3211yescharacteristic
972C22×C3—22no—
973C22×C3—22no—
974C22×C3—22no—
975C22×C3—22no—
976C22×C3—22no—
977C22×C3—22no—
978C22×C3—21no—
979C22×C3—42no—
980C22×C3—42no—
981C22×C3—42no—
982C22×C3—62no—
983C22×C3—62no—
984C22×C3—62no—
985C22×C3—61no—
986C22×C3—61no—
987C22×C3—61no—
988C22×C3C24×D311yescharacteristic
989C22×C3C24×D311yescharacteristic
990C2×D3—21no—
991C2×D3—21no—
992C2×D3—21no—
993C2×D3—22no—
994C2×D3—22no—
995C2×D3—22no—
996C3×C4—21no—
997C3×C4—22no—
998C3×C4—21no—
999C3×C4—21no—
1000C3×C4—21no—
1001C3×C4—22no—
1002C3×C4—21no—
1003C3×C4—21no—
1004C3×C4—32no—
1005C3×C4—42no—
1006C3×C4—41no—
1007C3×C4—41no—
1008C3×C4—41no—
1009C3×C4—62no—
1010C3×C4—62no—
1011C3×C4—62no—
1012C3×C4—61no—
1013C3×C4—61no—
1014C3×C4—62no—
1015C3×C4—62no—
1016Dic3—22no—
1017Dic3—21no—
1018Dic3—21no—
1019Dic3—22no—
1020Dic3—22no—
1021Dic3—22no—
1022Dic3—22no—
1023Dic3—62no—
1024Dic3—62no—
1025Dic3—62no—
1026Dic3—62no—
1027Dic3—62no—
1028Dic3—62no—
1029Dic3—62no—
1030Dic3—62no—
1031Dic3—122no—
1032Dic3—122no—
1033Dic3—122no—
1034Dic3—122no—
1035Dic3#101012yes—
1036C32#353111yescharacteristic, complemented, Sylow
1037C23—32no—
1038C23—31no—
1039C23C22×D3212yes—
1040Q8—41no—
1041Q8—121no—
1042Q8—362no—
1043Q8—362no—
1044Q8—362no—
1045Q8—362no—
1046D4—41no—
1047D4—121no—
1048D4—122no—
1049D4—122no—
1050D4—122no—
1051D4—362no—
1052C2×C4—31no—
1053C2×C4—31no—
1054C2×C4—31no—
1055C2×C4—32no—
1056C2×C4—32no—
1057C2×C4—32no—
1058C2×C4—32no—
1059C2×C4—32no—
1060C2×C4—62no—
1061C2×C4—64no—
1062C2×C4—92no—
1063C2×C4—92no—
1064C2×C4—92no—
1065C2×C4—92no—
1066C2×C4—121no—
1067C2×C4—122no—
1068C2×C4—121no—
1069C2×C4—122no—
1070C2×C4—184no—
1071C2×C4—362no—
1072C2×C4—362no—
1073C2×C4C22×D3212yes—
1074C2×C4C22×D3211yescharacteristic
1075C2×C4C22×D3211yescharacteristic
1076C2×C4C22×D3211yescharacteristic
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—21no—
1080C2×C3—42no—
1081C2×C3—42no—
1082C2×C3—82no—
1083C2×C3—121no—
1084C2×C3—122no—
1085C2×C3C2×#101011yescharacteristic
1086C2×C3#596411yescharacteristic
1087C2×C3#596411yescharacteristic
1088C2×C3#596611yescharacteristic
1089C2×C3#596611yescharacteristic
1090C2×C3D3×2−1+411yescharacteristic
1091D3—42no—
1092D3—41no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—62no—
1097C22—61no—
1098C22—61no—
1099C22—62no—
1100C22—61no—
1101C22—62no—
1102C22C23×D3211yescharacteristic
1103C4—21no—
1104C4—22no—
1105C4—21no—
1106C4—21no—
1107C4—32no—
1108C4—62no—
1109C4—61no—
1110C4—62no—
1111C4—62no—
1112C4—62no—
1113C4—61no—
1114C4—62no—
1115C4—182no—
1116C4—182no—
1117C4—182no—
1118C4—182no—
1119C3—21no—
1120C3#8613211yescharacteristic, complemented
1121C3#8709411yescharacteristic, complemented
1122C2—42no—
1123C2—122no—
1124C2—121no—
1125C2#1059667811yescharacteristic
1126C2D3×#101011yescharacteristic
1127C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#124C22
hypercenter#124D32
hypocenterC32#3531
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #10596143C2semidirect
2. C3×#5684C2semidirect
3. C3×#5680C2semidirect
4. #10595416C2semidirect
5. #10595367C2semidirect
6. #10595260C2semidirect
7. #10595187C2semidirect
8. #10594239C2semidirect
9. #10594169C2semidirect
10. #10594131C2semidirect
11. #10594098C2semidirect
12. #10594086C2semidirect
13. #10594044C2semidirect
14. #10594042C2semidirect
15. #10594029C2semidirect
16. #10593952C2semidirect
17. #10593921C2semidirect
18. #10593874C2semidirect
19. #10593868C2semidirect
117. #5684D3semidirect
119. #5680D3semidirect
1036. C32#3531semidirect
1120. C3#86132semidirect
1121. C3#87094semidirect

Maximal subgroups

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

subgroupindex
#105961432
C3×#56842
C3×#56802
#105954162
#105953672
#105952602
#105951872
#105942392
#105941692
#105941312
#105940982
#105940862
#105940442
#105940422
#105940292
#105939522
#105939212
#105938742
#105938682
#870943
#861323