Finite Group Databasebeta

← #11909941

Subgroups — #11909941

Order 1152.

2101 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic
2C3×#5470C211yesmaximal, characteristic, complemented
3C2×C3×C4×Dic6C211yesmaximal, characteristic, complemented
4#10594955C212yesmaximal
5#10594825C212yesmaximal, complemented
6#10594808C212yesmaximal, complemented
7#10594807C214yesmaximal, complemented
8#10594803C212yesmaximal, complemented
9#10593903C211yesmaximal, characteristic, complemented
10#10593883C212yesmaximal, complemented
11#10593865C211yesmaximal, characteristic, complemented
12#10593864C211yesmaximal, characteristic, complemented
13#10593861C211yesmaximal, characteristic, complemented
14#10593851C212yesmaximal, complemented
15#10593850C212yesmaximal, complemented
16#10593849C214yesmaximal, complemented
17#10593848C212yesmaximal, complemented
18#86266—31nomaximal
19#85804—31nomaximal
20C22×C3×Dic6C2211yescharacteristic
21C2×#3797C2212yes—
22C2×C32×C42C2211yescharacteristic
23#64139C2211yescharacteristic
24#64138C2212yes—
25C4×#638C2212yes—
26#64133C2211yescharacteristic
27#64085C2212yes—
28#64084C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30#64081C2212yes—
31#64079C2211yescharacteristic
32C4×#634C2211yescharacteristic
33C3×#926C2212yes—
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C3×#924C2212yes—
36C3×#924C2212yes—
37C2×C3×Dic3⋊C4C2212yes—
38C2×C3×C4×Dic3C2212yes—
39C3×#870C2212yes—
40C3×#869C2211yescharacteristic
41C3×#869C2211yescharacteristic
42C3×C4×Dic6C2211yescharacteristic
43C3×C4×Dic6C2212yes—
44C3×C4×Dic6C2212yes—
45C3×C4×Dic6C2212yes—
46C3×C4×Dic6C2212yes—
47C3×C4×Dic6C2211yescharacteristic
48C3×C4×Dic6C2211yescharacteristic
49C3×C4×Dic6C2211yescharacteristic
50#63966C2214yes—
51#63964C2214yes—
52#63955C2214yes—
53#63952C2214yes—
54#63918C2212yes—
55#63895C2214yes—
56#63894C2212yes—
57#63888C2214yes—
58#63873C2212yes—
59#63872C2212yes—
60#63871C2212yes—
61#63871C2212yes—
62#63869C2212yes—
63#63868C2214yes—
64#63868C2214yes—
65#63867C2214yes—
66#63867C2214yes—
67#63866C2212yes—
68#63864C2212yes—
69#63849C2212yes—
70#63848C2214yes—
71#63848C2214yes—
72#63847C2214yes—
73#63846C2214yes—
74#63846C2214yes—
75#63844C2212yes—
76#63843C2212yes—
77#63843C2212yes—
78Dic3×Dic6C2212yes—
79Dic3×Dic6C2212yes—
80#63839C2214yes—
81#63837C2214yes—
82#63837C2214yes—
83#63836C2214yes—
84#63836C2214yes—
85C3×#533—31no—
86C2×C3×C4×Q8—31no—
87Q8×#67—32no—
88#5732—31no—
89#5727—31no—
90#5721—31no—
91#5721—31no—
92#5696—34no—
93#5642—32no—
94#5632—32no—
95#5624—32no—
96#5622—32no—
97#5584—31no—
98#5584—32no—
99#5583—34no—
100#5583—32no—
101#5583—32no—
102Q8×D12—31no—
103#5572—32no—
104#5572—32no—
105#5570—31no—
106#5569—32no—
107#5568—32no—
108#5567—31no—
109#5567—32no—
110#5531—34no—
111#5513—34no—
112#5513—32no—
113#5479—31no—
114#5479—31no—
115#5479—32no—
116#5479—61no—
117#5470—32no—
118#5470D311yescharacteristic, complemented
119C2×C4×Dic6D311yescharacteristic, complemented
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C2×#638C2312yes—
124C2×C4⋊(C3⋊D3)C2311yescharacteristic
125C2×C4×C3⋊D3C2312yes—
126C2×#634C2311yescharacteristic
127C22×C3×Dic3C2312yes—
128C22×C3×Dic3C2312yes—
129C2×C3×Dic6—24no—
130C2×C3×Dic6C2312yes—
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2312yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×C3×Dic6C2311yescharacteristic
135C2×#627C2314yes—
136C2×#624C2314yes—
137#3797—28no—
138C32×C42C2311yescharacteristic
139C32×C42C2311yescharacteristic
140C32×C42C2311yescharacteristic
141C32×C42C2311yescharacteristic
142#3757C2312yes—
143#3752C2312yes—
144#3752C2312yes—
145#3752C2312yes—
146#3752C2312yes—
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2311yescharacteristic
149#3750C2312yes—
150#3750C2312yes—
151#3750C2312yes—
152#3750C2312yes—
153C4×C3⋊Dic3C2312yes—
154C3×#217C2314yes—
155C3×C4⋊Dic3C2312yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2311yescharacteristic
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2312yes—
162C3×Dic3⋊C4C2312yes—
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2312yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2314yes—
167C3×Dic3⋊C4C2314yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2312yes—
172C3×C4×Dic3C2314yes—
173#3724C2314yes—
174#3724C2314yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181#3722C2314yes—
182#3722C2314yes—
183#3722C2314yes—
184Dic32C2314yes—
185Dic32C2314yes—
186Dic32C2314yes—
187#3523—91noSylow
188C22×C3×Q8—31no—
189C2×D3×Q8—32no—
190C2×D3×Q8—32no—
191C22×Dic6C2×D311yescharacteristic
192C3×C4⋊Q8—31no—
193C3×C4⋊Q8—31no—
194C3×#125—32no—
195C3×C22⋊Q8—32no—
196C3×C22⋊Q8—32no—
197C3×C4×Q8—31no—
198C3×C4×Q8—32no—
199C3×C4×Q8—32no—
200C3×C4×Q8—31no—
201C3×C4×Q8—31no—
202C3×C4×Q8—32no—
203C3×C4×Q8—32no—
204C3×C4×Q8—31no—
205C3×#117—32no—
206C2×C3×C4⋊C4—32no—
207C2×C3×C4⋊C4—31no—
208C2×C3×C42—21no—
209C2×C3×C42—32no—
210C2×C3×C42C2×D311yescharacteristic
211C2×C3×C42C2×D311yescharacteristic
212#947—32no—
213#946—32no—
214#946—32no—
215#946—34no—
216Q8×Dic3—32no—
217Q8×Dic3—32no—
218Q8×Dic3—32no—
219Q8×Dic3—32no—
220#944—32no—
221#944—32no—
222#944—34no—
223#944—32no—
224#930—31no—
225#930—31no—
226#930—61no—
227#929—32no—
228#929—32no—
229#929—34no—
230#929—62no—
231C4×#67—32no—
232C4×#67—32no—
233C4×#67—34no—
234C4×#67—62no—
235#926—34no—
236#926C2×D312yes—
237C2×C4⋊Dic3C2×D311yescharacteristic
238#924—31no—
239#924—31no—
240#924—34no—
241#924—61no—
242#924C2×D312yes—
243#924C2×D312yes—
244C2×Dic3⋊C4C2×D312yes—
245C2×C4×Dic3C2×D312yes—
246#898—34no—
247#898—34no—
248#898—34no—
249#898—34no—
250#898—34no—
251#898—34no—
252#897—32no—
253#897—32no—
254#897—34no—
255#896—34no—
256#896—34no—
257#893—32no—
258#892—32no—
259#892—32no—
260#892—34no—
261#892—34no—
262#890—34no—
263#890—32no—
264#890—34no—
265#890—32no—
266#890—32no—
267#889—34no—
268#889—34no—
269#889—34no—
270#889—34no—
271#889—34no—
272#889—34no—
273#888—34no—
274#888—32no—
275#887—32no—
276#887—32no—
277#887—34no—
278#887—32no—
279#887—34no—
280#886—34no—
281#67⋊C4—34no—
282#878—34no—
283#877—34no—
284#876—32no—
285#876—32no—
286#876—34no—
287#876—34no—
288#876—62no—
289#875—32no—
290#875—31no—
291#875—31no—
292#875—61no—
293C4×D12—31no—
294C4×D12—31no—
295C4×D12—32no—
296C4×D12—61no—
297#872—32no—
298#872—32no—
299#872—34no—
300#872—34no—
301#872—62no—
302#870—31no—
303#870—31no—
304#870—32no—
305#870—34no—
306#870—34no—
307#870—61no—
308#870C2×D312yes—
309#869—32no—
310#869—32no—
311#869C2×D311yescharacteristic
312#869C2×D311yescharacteristic
313C4×Dic6—32no—
314C4×Dic6—32no—
315C4×Dic6—31no—
316C4×Dic6—31no—
317C4×Dic6—32no—
318C4×Dic6—34no—
319C4×Dic6—34no—
320C4×Dic6—61no—
321C4×Dic6C2×D312yes—
322C4×Dic6C2×D311yescharacteristic
323C4×Dic6C2×D311yescharacteristic
324C4×Dic6C2×D312yes—
325C4×Dic6C2×D311yescharacteristic
326C4×Dic6C2×D311yescharacteristic
327C4×Dic6C2×D312yes—
328C4×Dic6C2×D312yes—
329C23×C32C2411yescharacteristic
330C22×C3⋊D3C2412yes—
331C2×C32×C4—22no—
332C2×C32×C4—22no—
333C2×C32×C4—22no—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340#638—24no—
341C2×C3⋊Dic3C2412yes—
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2412yes—
344C4⋊(C3⋊D3)—22no—
345C4×C3⋊D3—24no—
346#634—22no—
347C2×C3×Dic3—24no—
348C2×C3×Dic3—24no—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2414yes—
351C2×C3×Dic3C2414yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355C3×Dic6—24no—
356C3×Dic6—22no—
357C3×Dic6—24no—
358C3×Dic6—24no—
359C3×Dic6#4114yes—
360#627—28no—
361#624—28no—
362#557—92no—
363#557—91no—
364#557—91no—
365#556—92no—
366#556—91no—
367#552—94no—
368#552—92no—
369D4×Q8—91no—
370D4×Q8—92no—
371#541—92no—
372#541—94no—
373#533—31no—
374#533—92no—
375#529—92no—
376#529—91no—
377#519—92no—
378C2×C4×Q8—31no—
379C2×C3×Q8—31no—
380C2×C3×Q8—32no—
381C2×C3×Q8—31no—
382C2×C3×Q8—32no—
383C2×C3×Q8—32no—
384C2×C3×Q8—64no—
385C22×C3×C4—21no—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—32no—
389C22×C3×C4—32no—
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C2×#67—32no—
397C2×#67—32no—
398C2×#67—62no—
399C22×Dic3C22×D312yes—
400C22×Dic3C22×D312yes—
401D3×Q8—68no—
402D3×Q8—68no—
403C2×D12—31no—
404C2×D12—31no—
405C2×D12—61no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—34no—
409C2×C4×D3—34no—
410C2×C4×D3—62no—
411C2×Dic6—24no—
412C2×Dic6—31no—
413C2×Dic6—31no—
414C2×Dic6—34no—
415C2×Dic6—34no—
416C2×Dic6—61no—
417C2×Dic6C22×D312yes—
418C2×Dic6C22×D312yes—
419C2×Dic6C22×D311yescharacteristic
420C2×Dic6C22×D312yes—
421C2×Dic6C22×D311yescharacteristic
422C3×C4⋊C4—32no—
423C3×C4⋊C4—31no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—32no—
427C3×C4⋊C4—34no—
428C3×C4⋊C4—32no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4—32no—
431C3×C4⋊C4—32no—
432C3×C4⋊C4—32no—
433C3×C4⋊C4—32no—
434C3×C4⋊C4—31no—
435C3×C22⋊C4—34no—
436C3×C42—21no—
437C3×C42—21no—
438C3×C42—21no—
439C3×C42—21no—
440C3×C42—32no—
441C3×C42—32no—
442C3×C42—32no—
443C3×C42—34no—
444C3×C42—32no—
445C3×C42C22×D311yescharacteristic
446C3×C42C22×D311yescharacteristic
447C3×C42C22×D311yescharacteristic
448C3×C42C22×D311yescharacteristic
449C3×C42C22×D311yescharacteristic
450C3×C42C22×D311yescharacteristic
451C3×C42C22×D311yescharacteristic
452C3×C42C22×D311yescharacteristic
453#217—32no—
454#217—32no—
455#217—62no—
456#217C22×D314yes—
457(C2×D3)⋊C4—32no—
458(C2×D3)⋊C4—32no—
459(C2×D3)⋊C4—32no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—32no—
462(C2×D3)⋊C4—32no—
463(C2×D3)⋊C4—32no—
464(C2×D3)⋊C4—32no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—34no—
467(C2×D3)⋊C4—34no—
468(C2×D3)⋊C4—34no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—62no—
473(C2×D3)⋊C4—62no—
474(C2×D3)⋊C4—62no—
475C4⋊Dic3—31no—
476C4⋊Dic3—31no—
477C4⋊Dic3—31no—
478C4⋊Dic3—31no—
479C4⋊Dic3—34no—
480C4⋊Dic3—34no—
481C4⋊Dic3—34no—
482C4⋊Dic3—34no—
483C4⋊Dic3—34no—
484C4⋊Dic3—34no—
485C4⋊Dic3—61no—
486C4⋊Dic3—61no—
487C4⋊Dic3C22×D312yes—
488C4⋊Dic3C22×D312yes—
489C4⋊Dic3C22×D311yescharacteristic
490C4⋊Dic3C22×D311yescharacteristic
491C4⋊Dic3C22×D312yes—
492C4⋊Dic3C22×D312yes—
493C4⋊Dic3C22×D312yes—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—32no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—32no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—62no—
513Dic3⋊C4—62no—
514Dic3⋊C4—62no—
515Dic3⋊C4—62no—
516Dic3⋊C4C22×D312yes—
517Dic3⋊C4C22×D314yes—
518Dic3⋊C4C22×D312yes—
519Dic3⋊C4C22×D312yes—
520Dic3⋊C4C22×D312yes—
521Dic3⋊C4C22×D314yes—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—34no—
525C4×Dic3—34no—
526C4×Dic3—34no—
527C4×Dic3—34no—
528C4×Dic3—34no—
529C4×Dic3—34no—
530C4×Dic3—62no—
531C4×Dic3C22×D312yes—
532C4×Dic3C22×D314yes—
533C4×Dic3C22×D312yes—
534C4×Dic3C22×D312yes—
535C4×Dic3C22×D312yes—
536C22×C32—21no—
537C22×C32—21no—
538C22×C322−1+412yes—
539C22×C32C2511yescharacteristic
540C2×C3⋊D3—22no—
541C2×C3⋊D3—22no—
542C2×C3⋊D3—22no—
543C32×C4—21no—
544C32×C4—21no—
545C32×C4—21no—
546C32×C4—21no—
547C32×C4C2×#4112yes—
548C32×C42−1+412yes—
549C3⋊Dic3—22no—
550C3⋊Dic3—22no—
551C3⋊Dic3—22no—
552C3×Dic3—24no—
553C3×Dic3—22no—
554C3×Dic3—24no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3C2×#4114yes—
558C22×Q8—31no—
559C22×Q8—92no—
560C4⋊Q8—31no—
561C4⋊Q8—31no—
562C4⋊Q8—92no—
563C4⋊Q8—92no—
564C4⋊Q8—94no—
565C4⋊Q8—92no—
566#126—94no—
567#126—94no—
568#126—94no—
569#126—94no—
570#126—92no—
571#125—32no—
572#125—92no—
573#125—94no—
574#125—94no—
575#125—94no—
576#125—94no—
577#125—94no—
578#125—92no—
579#125—91no—
580#124—92no—
581#124—91no—
582#123—94no—
583#123—92no—
584C22⋊Q8—32no—
585C22⋊Q8—32no—
586C22⋊Q8—94no—
587C22⋊Q8—94no—
588C22⋊Q8—92no—
589C22⋊Q8—94no—
590C22⋊Q8—92no—
591C22⋊Q8—91no—
592#121—91no—
593C4×Q8—31no—
594C4×Q8—32no—
595C4×Q8—31no—
596C4×Q8—31no—
597C4×Q8—32no—
598C4×Q8—31no—
599C4×Q8—32no—
600C4×Q8—32no—
601C4×Q8—94no—
602C4×Q8—94no—
603C4×Q8—92no—
604C4×Q8—92no—
605C4×Q8—92no—
606C4×Q8—92no—
607C4×Q8—92no—
608C4×Q8—91no—
609C4×D4—92no—
610C4×D4—94no—
611C4×D4—92no—
612C4×D4—91no—
613#117—32no—
614#117—94no—
615#117—94no—
616#117—94no—
617#117—92no—
618#117—92no—
619C2×C4⋊C4—32no—
620C2×C4⋊C4—31no—
621C2×C42—32no—
622C2×C42D3211yescharacteristic
623C23×C3—21no—
624C23×C3C23×D311yescharacteristic
625C23×C3C23×D311yescharacteristic
626C22×D3—32no—
627C22×D3—32no—
628C22×D3—62no—
629C3×Q8—34no—
630C3×Q8—64no—
631C3×Q8—64no—
632C3×Q8—64no—
633C3×Q8—62no—
634C2×C3×C4—22no—
635C2×C3×C4—22no—
636C2×C3×C4—22no—
637C2×C3×C4—22no—
638C2×C3×C4—22no—
639C2×C3×C4—22no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—32no—
647C2×C3×C4—32no—
648C2×C3×C4—34no—
649C2×C3×C4—34no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—42no—
653C2×C3×C4—42no—
654C2×C3×C4—42no—
655C2×C3×C4—64no—
656C2×C3×C4—64no—
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669#67—64no—
670#67—64no—
671#67—124no—
672C2×Dic3—24no—
673C2×Dic3—24no—
674C2×Dic3—32no—
675C2×Dic3—32no—
676C2×Dic3—32no—
677C2×Dic3—32no—
678C2×Dic3—32no—
679C2×Dic3—32no—
680C2×Dic3—62no—
681C2×Dic3—62no—
682C2×Dic3—62no—
683C2×Dic3C23×D312yes—
684C2×Dic3C23×D314yes—
685C2×Dic3C23×D314yes—
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689D12—62no—
690D12—62no—
691D12—122no—
692C4×D3—68no—
693C4×D3—64no—
694C4×D3—64no—
695C4×D3—68no—
696C4×D3—124no—
697Dic6—22no—
698Dic6—24no—
699Dic6—24no—
700Dic6—24no—
701Dic6—68no—
702Dic6—62no—
703Dic6—62no—
704Dic6—68no—
705Dic6—122no—
706Dic6#23514yes—
707C2×C32—22no—
708C2×C32C22×#4111yescharacteristic
709C2×C32C2×2−1+411yescharacteristic
710C2×C32C2×2−1+411yescharacteristic
711C3⋊D3—42no—
712C2×Q8—31no—
713C2×Q8—32no—
714C2×Q8—31no—
715C2×Q8—32no—
716C2×Q8—32no—
717C2×Q8—64no—
718C2×Q8—94no—
719C2×Q8—91no—
720C2×Q8—188no—
721C2×D4—92no—
722C2×D4—91no—
723C22×C4—32no—
724C22×C4—32no—
725C22×C4—94no—
726C22×C4—92no—
727C22×C4C2×D3211yescharacteristic
728C22×C4C2×D3211yescharacteristic
729C22×C4C2×D3211yescharacteristic
730C4⋊C4—32no—
731C4⋊C4—31no—
732C4⋊C4—32no—
733C4⋊C4—31no—
734C4⋊C4—32no—
735C4⋊C4—32no—
736C4⋊C4—32no—
737C4⋊C4—32no—
738C4⋊C4—32no—
739C4⋊C4—32no—
740C4⋊C4—34no—
741C4⋊C4—32no—
742C4⋊C4—34no—
743C4⋊C4—94no—
744C4⋊C4—94no—
745C4⋊C4—94no—
746C4⋊C4—94no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—94no—
750C4⋊C4—94no—
751C4⋊C4—92no—
752C4⋊C4—92no—
753C4⋊C4—91no—
754C4⋊C4—92no—
755C4⋊C4—91no—
756C4⋊C4—92no—
757C22⋊C4—34no—
758C22⋊C4—94no—
759C22⋊C4—94no—
760C22⋊C4—94no—
761C22⋊C4—92no—
762C22⋊C4—92no—
763C22⋊C4—92no—
764C22⋊C4—92no—
765C22⋊C4—92no—
766C42—32no—
767C42—32no—
768C42—32no—
769C42—32no—
770C42—34no—
771C42—94no—
772C42—94no—
773C42—94no—
774C42—92no—
775C42C2×D3211yescharacteristic
776C42C2×D3211yescharacteristic
777C42C2×D3211yescharacteristic
778C42C2×D3211yescharacteristic
779C22×C3—21no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—22no—
784C22×C3—21no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3#100712yes—
788C22×C3#101012yes—
789C22×C3C24×D311yescharacteristic
790C22×C3C24×D311yescharacteristic
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—122no—
798C2×D3—122no—
799C2×D3—122no—
800C3×C4—21no—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—21no—
805C3×C4—21no—
806C3×C4—21no—
807C3×C4—21no—
808C3×C4—22no—
809C3×C4—22no—
810C3×C4—34no—
811C3×C4—41no—
812C3×C4—41no—
813C3×C4—41no—
814C3×C4—41no—
815C3×C4—64no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—64no—
819C3×C4—62no—
820C3×C4C2×#23512yes—
821C3×C4#100712yes—
822C3×C4D3×#4112yes—
823C3×C4#101012yes—
824Dic3—22no—
825Dic3—24no—
826Dic3—24no—
827Dic3—22no—
828Dic3—22no—
829Dic3—62no—
830Dic3—62no—
831Dic3—62no—
832Dic3—62no—
833Dic3—62no—
834Dic3—62no—
835Dic3—122no—
836Dic3—122no—
837Dic3—122no—
838Dic3C2×#23514yes—
839C32#352311yescharacteristic, complemented, Sylow
840C23—92no—
841C23C22×D3211yescharacteristic
842Q8—34no—
843Q8—64no—
844Q8—64no—
845Q8—62no—
846Q8—64no—
847Q8—188no—
848Q8—182no—
849D4—184no—
850D4—182no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—32no—
855C2×C4—32no—
856C2×C4—32no—
857C2×C4—32no—
858C2×C4—34no—
859C2×C4—34no—
860C2×C4—64no—
861C2×C4—64no—
862C2×C4—92no—
863C2×C4—92no—
864C2×C4—92no—
865C2×C4—188no—
866C2×C4—184no—
867C2×C4C22×D3211yescharacteristic
868C2×C4C22×D3211yescharacteristic
869C2×C4C22×D3211yescharacteristic
870C2×C4C22×D3211yescharacteristic
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3211yescharacteristic
873C2×C3—22no—
874C2×C3—22no—
875C2×C3—21no—
876C2×C3—21no—
877C2×C3—21no—
878C2×C3—42no—
879C2×C3C22×#23511yescharacteristic
880C2×C3C2×#100711yescharacteristic
881C2×C3C2×#100711yescharacteristic
882C2×C3C2×D3×#4111yescharacteristic
883C2×C3C2×#101011yescharacteristic
884C2×C3C2×#101011yescharacteristic
885D3—122no—
886D3—122no—
887D3—242no—
888C22—21no—
889C22—21no—
890C22—182no—
891C22—182no—
892C22—182no—
893C22#6429712yes—
894C22C23×D3211yescharacteristic
895C4—21no—
896C4—21no—
897C4—21no—
898C4—21no—
899C4—34no—
900C4—62no—
901C4—62no—
902C4—64no—
903C4—62no—
904C4—64no—
905C4—182no—
906C4—182no—
907C4—182no—
908C4#6429712yes—
909C4D3×#23512yes—
910C3—21no—
911C3#8580411yescharacteristic, complemented
912C3#8626611yescharacteristic, complemented
913C2—22no—
914C2—362no—
915C2C2×#6429711yescharacteristic
916C2C2×#6429711yescharacteristic
917C2C2×D3×#23511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
prime radical#64139C22
hypercenterC2×C42D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#5470C2semidirect
3. C2×C3×C4×Dic6C2semidirect
5. #10594825C2semidirect
6. #10594808C2semidirect
7. #10594807C2semidirect
8. #10594803C2semidirect
9. #10593903C2semidirect
10. #10593883C2semidirect
11. #10593865C2semidirect
12. #10593864C2semidirect
13. #10593861C2semidirect
14. #10593851C2semidirect
15. #10593850C2semidirect
16. #10593849C2semidirect
17. #10593848C2semidirect
118. #5470D3semidirect
119. C2×C4×Dic6D3semidirect
839. C32#3523semidirect
911. C3#85804semidirect
912. C3#86266semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×#54702
C2×C3×C4×Dic62
#105949552
#105948252
#105948082
#105948072
#105948032
#105939032
#105938832
#105938652
#105938642
#105938612
#105938512
#105938502
#105938492
#105938482
#862663
#858043