Finite Group Databasebeta

← #11904191

Subgroups — #11904191

Order 1152.

2343 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C3×#5470C211yesmaximal, characteristic, complemented
4#10594970C212yesmaximal, complemented
5#10594841C212yesmaximal, complemented
6#10594836C214yesmaximal, complemented
7#10594834C212yesmaximal, complemented
8#10594830C212yesmaximal, complemented
9C4×#3799C212yesmaximal, complemented
10#10593903C211yesmaximal, characteristic, complemented
11C4×#3797C212yesmaximal, complemented
12#10593875C212yesmaximal, complemented
13#10593873C212yesmaximal, complemented
14#10593872C214yesmaximal, complemented
15#10593869C211yesmaximal, characteristic, complemented
16#10593863C211yesmaximal, characteristic, complemented
17#10593861C211yesmaximal, characteristic, complemented
18#86278—31nomaximal
19#85844—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×#3799C2212yes—
23C2×#3797C2212yes—
24C2×C32×C42C2211yescharacteristic
25C4×#638C2212yes—
26C4×#638C2212yes—
27#64135C2211yescharacteristic
28C4×C4⋊(C3⋊D3)C2211yescharacteristic
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30#64081C2212yes—
31C42×C3⋊D3C2212yes—
32C4×#634C2211yescharacteristic
33C4×#634C2211yescharacteristic
34C3×C4×#67C2212yes—
35C3×C4×#67C2212yes—
36C3×#926C2212yes—
37C3×#926C2211yescharacteristic
38C3×#924C2212yes—
39C3×#924C2212yes—
40C3×C4×D12C2211yescharacteristic
41C3×C4×D12C2211yescharacteristic
42C3×#872C2212yes—
43C3×C42×D3C2212yes—
44C3×#870C2212yes—
45C3×#869C2211yescharacteristic
46C3×#869C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48C3×C4×Dic6C2212yes—
49C3×C4×Dic6C2212yes—
50C3×C4×Dic6C2211yescharacteristic
51#63975C2214yes—
52#63959C2214yes—
53#63958C2214yes—
54#63956C2214yes—
55#63918C2212yes—
56C4×#627C2214yes—
57#63916C2212yes—
58#63904C2214yes—
59C4×#626C2214yes—
60#63900C2212yes—
61#63895C2214yes—
62#63894C2212yes—
63#63883C2214yes—
64C4×#624C2214yes—
65#63872C2212yes—
66#63871C2212yes—
67#63867C2214yes—
68#63866C2212yes—
69#63863C2212yes—
70#63862C2214yes—
71#63858C2214yes—
72#63857C2212yes—
73#63856C2212yes—
74#63855C2214yes—
75#63854C2214yes—
76#63853C2214yes—
77#63851C2214yes—
78#63846C2214yes—
79#63843C2212yes—
80#63843C2212yes—
81Dic3×Dic6C2212yes—
82#63841C2212yes—
83#63838C2214yes—
84#63836C2214yes—
85C3×#533—31no—
86C3×C4×#41—31no—
87#5831—32no—
88#5732—31no—
89#5727—31no—
90#5726—31no—
91#5721—31no—
92#5693—34no—
93#5641—32no—
94#5639—32no—
95#5633—32no—
96#5631—32no—
97#5580—32no—
98#5578—32no—
99Q8×D12—31no—
100C4×#239—32no—
101C4×D3×Q8—32no—
102C4×D3×Q8—32no—
103#5570—31no—
104#5557—34no—
105#5557—32no—
106#5551—32no—
107#5551—31no—
108#5542—32no—
109#5542—31no—
110#5529—32no—
111#5529—34no—
112#5528—34no—
113C4×#235—31no—
114C4×#235—31no—
115C4×#235—32no—
116C4×#235—61no—
117C4×#235D311yescharacteristic, complemented
118#5470—32no—
119#5470D311yescharacteristic, complemented
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2311yescharacteristic
122C22×C32×C4C2311yescharacteristic
123C2×#638C2312yes—
124#3828—24no—
125C2×C4⋊(C3⋊D3)C2311yescharacteristic
126C2×C4×C3⋊D3C2312yes—
127C2×C4×C3⋊D3C2312yes—
128C2×C4×C3⋊D3C2312yes—
129C2×#634C2311yescharacteristic
130C2×C3×#67C2312yes—
131C3×#235—24no—
132C2×C3×D12C2311yescharacteristic
133C2×C3×C4×D3C2312yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×C4×D3C2312yes—
136C2×C3×Dic6C2312yes—
137C2×C3×Dic6C2312yes—
138C2×C3×Dic6C2311yescharacteristic
139C2×#627C2314yes—
140C2×#626C2314yes—
141C2×#624C2314yes—
142C2×#624C2314yes—
143#3799—28no—
144#3797—28no—
145C32×C42C2311yescharacteristic
146C32×C42C2311yescharacteristic
147C32×C42C2311yescharacteristic
148C32×C42C2311yescharacteristic
149#3757C2312yes—
150#3752C2312yes—
151#3752C2312yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154#3750C2312yes—
155#3750C2312yes—
156C4×C3⋊Dic3C2312yes—
157C4×C3⋊Dic3C2312yes—
158C4×C3⋊Dic3C2312yes—
159C3×#217C2314yes—
160C3×#217C2312yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×C4⋊Dic3C2312yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2312yes—
168C3×C4⋊Dic3C2311yescharacteristic
169C3×Dic3⋊C4C2314yes—
170C3×Dic3⋊C4C2314yes—
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2312yes—
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2314yes—
175C3×C4×Dic3C2312yes—
176C3×C4×Dic3C2312yes—
177#3724C2314yes—
178Dic3⋊Dic3C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183#3722C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187Dic32C2314yes—
188Dic32C2314yes—
189#3482—91noSylow
190C2×C3×#41—31no—
191C2×#239—32no—
192C2×D3×Q8—32no—
193C2×D3×Q8—32no—
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—32no—
197C2×#235—61no—
198C2×#235C2×D311yescharacteristic
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8—31no—
201C3×#125—32no—
202C3×C22⋊Q8—32no—
203C3×C22⋊Q8—32no—
204C3×C4×Q8—31no—
205C3×C4×Q8—31no—
206C3×C4×Q8—32no—
207C3×C4×Q8—32no—
208C3×C4×D4—32no—
209C3×C4×D4—32no—
210C3×C4×D4—31no—
211C3×C4×D4—31no—
212C3×#117—32no—
213C3×#117—31no—
214C3×#117—32no—
215C2×C3×C42—21no—
216C2×C3×C42—32no—
217C2×C3×C42C2×D311yescharacteristic
218C2×C3×C42C2×D311yescharacteristic
219#947—32no—
220#946—32no—
221#946—32no—
222Q8×Dic3—32no—
223Q8×Dic3—32no—
224Q8×Dic3—32no—
225#944—32no—
226#938—34no—
227#938—32no—
228#936—32no—
229#936—34no—
230C4×#67—32no—
231C4×#67—32no—
232C4×#67—32no—
233C4×#67—32no—
234C4×#67—34no—
235C4×#67—34no—
236C4×#67—62no—
237C4×#67—62no—
238C4×#67C2×D312yes—
239C4×#67C2×D312yes—
240#926—31no—
241#926—31no—
242#926—32no—
243#926—34no—
244#926—61no—
245#926C2×D311yescharacteristic
246#926C2×D312yes—
247#924—32no—
248#924—32no—
249#924—34no—
250#924C2×D312yes—
251#924C2×D312yes—
252#898—34no—
253#898—34no—
254#897—32no—
255#897—32no—
256#897—34no—
257#896—34no—
258#896—34no—
259#895—32no—
260#894—34no—
261#894—34no—
262#893—34no—
263#893—32no—
264#892—32no—
265#892—34no—
266D3×C4⋊C4—32no—
267D3×C4⋊C4—32no—
268D3×C4⋊C4—34no—
269D3×C4⋊C4—34no—
270#890—32no—
271#890—34no—
272#890—32no—
273#889—34no—
274#889—34no—
275#888—32no—
276#887—32no—
277#887—32no—
278#887—34no—
279#887—34no—
280#885—34no—
281#884—34no—
282#883—34no—
283#883—34no—
284#883—34no—
285#883—34no—
286#879—34no—
287#879—34no—
288#879—34no—
289#879—34no—
290C4×D12—34no—
291C4×D12—31no—
292C4×D12—31no—
293C4×D12—31no—
294C4×D12—31no—
295C4×D12—32no—
296C4×D12—61no—
297C4×D12—61no—
298C4×D12C2×D311yescharacteristic
299C4×D12C2×D311yescharacteristic
300#872—34no—
301#872—32no—
302#872—32no—
303#872—34no—
304#872—62no—
305#872C2×D312yes—
306C42×D3—32no—
307C42×D3—32no—
308C42×D3—34no—
309C42×D3—34no—
310C42×D3—62no—
311C42×D3C2×D312yes—
312#870—34no—
313#870C2×D312yes—
314#869—32no—
315#869—32no—
316#869C2×D311yescharacteristic
317#869C2×D311yescharacteristic
318C4×Dic6—32no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—31no—
322C4×Dic6—31no—
323C4×Dic6—34no—
324C4×Dic6—34no—
325C4×Dic6—61no—
326C4×Dic6—61no—
327C4×Dic6C2×D311yescharacteristic
328C4×Dic6C2×D312yes—
329C4×Dic6C2×D312yes—
330C4×Dic6C2×D311yescharacteristic
331C23×C32C2411yescharacteristic
332C22×C3⋊D3C2412yes—
333C22×C3×D3C2412yes—
334C2×C32×C4—22no—
335C2×C32×C4—22no—
336C2×C32×C4—22no—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340C2×C32×C4C2411yescharacteristic
341C2×C32×C4C2411yescharacteristic
342C2×C32×C4C2411yescharacteristic
343#638—24no—
344C2×C3⋊Dic3C2412yes—
345C2×C3⋊Dic3C2412yes—
346C2×C3⋊Dic3C2412yes—
347C4⋊(C3⋊D3)#4114yescomplemented
348C4×C3⋊D3—24no—
349C4×C3⋊D3—24no—
350C4×C3⋊D3—24no—
351#634—22no—
352C3×#67—24no—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2414yes—
355C2×C3×Dic3C2414yes—
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2412yes—
358C3×D12—22no—
359C3×C4×D3—24no—
360C3×C4×D3—24no—
361C3×C4×D3—24no—
362C3×Dic6—24no—
363C3×Dic6—24no—
364C3×Dic6#4114yescomplemented
365#627—28no—
366#626—28no—
367#624—28no—
368#624—28no—
369#557—91no—
370#556—92no—
371#556—91no—
372#552—92no—
373#552—94no—
374D4×Q8—91no—
375#548—92no—
376#547—92no—
377#547—91no—
378#533—31no—
379#533—92no—
380#529—94no—
381#529—92no—
382C4×#41—31no—
383C4×#41—92no—
384C4×#41—91no—
385C2×C4×Q8—92no—
386C3×#41—64no—
387C2×C3×Q8—31no—
388C2×C3×Q8—32no—
389C2×C3×Q8—32no—
390C2×C3×D4—32no—
391C2×C3×D4—31no—
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—32no—
396C22×C3×C4—32no—
397C22×C3×C4—32no—
398C22×C3×C4C22×D311yescharacteristic
399C22×C3×C4C22×D311yescharacteristic
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D311yescharacteristic
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C2×#67—32no—
405C2×#67—32no—
406C2×#67—34no—
407C2×#67—62no—
408C2×#67C22×D312yes—
409#239—68no—
410D3×Q8—68no—
411D3×Q8—68no—
412#235—24no—
413#235—68no—
414#235—64no—
415#235—64no—
416#235—68no—
417C2×D12—31no—
418C2×D12—31no—
419C2×D12—34no—
420C2×D12—61no—
421C2×D12C22×D311yescharacteristic
422C2×C4×D3—32no—
423C2×C4×D3—32no—
424C2×C4×D3—32no—
425C2×C4×D3—32no—
426C2×C4×D3—32no—
427C2×C4×D3—32no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—34no—
432C2×C4×D3—62no—
433C2×C4×D3—62no—
434C2×C4×D3—62no—
435C2×C4×D3C22×D312yes—
436C2×C4×D3C22×D312yes—
437C2×C4×D3C22×D312yes—
438C2×Dic6—31no—
439C2×Dic6—31no—
440C2×Dic6—34no—
441C2×Dic6—34no—
442C2×Dic6—61no—
443C2×Dic6C22×D312yes—
444C2×Dic6C22×D312yes—
445C2×Dic6C22×D311yescharacteristic
446C3×C4⋊C4—32no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—32no—
449C3×C4⋊C4—34no—
450C3×C4⋊C4—32no—
451C3×C4⋊C4—32no—
452C3×C4⋊C4—34no—
453C3×C4⋊C4—32no—
454C3×C4⋊C4—31no—
455C3×C4⋊C4—32no—
456C3×C22⋊C4—32no—
457C3×C22⋊C4—34no—
458C3×C22⋊C4—32no—
459C3×C22⋊C4—32no—
460C3×C42—21no—
461C3×C42—21no—
462C3×C42—21no—
463C3×C42—21no—
464C3×C42—32no—
465C3×C42—32no—
466C3×C42—34no—
467C3×C42—32no—
468C3×C42C22×D311yescharacteristic
469C3×C42C22×D311yescharacteristic
470C3×C42C22×D311yescharacteristic
471C3×C42C22×D311yescharacteristic
472C3×C42C22×D311yescharacteristic
473C3×C42C22×D311yescharacteristic
474C3×C42C22×D311yescharacteristic
475C3×C42C22×D311yescharacteristic
476#217—32no—
477#217—32no—
478#217—34no—
479#217—34no—
480#217—34no—
481#217—62no—
482#217C22×D312yes—
483#217C22×D314yes—
484(C2×D3)⋊C4—34no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—32no—
488(C2×D3)⋊C4—32no—
489(C2×D3)⋊C4—32no—
490(C2×D3)⋊C4—32no—
491(C2×D3)⋊C4—34no—
492(C2×D3)⋊C4—34no—
493(C2×D3)⋊C4—62no—
494(C2×D3)⋊C4—62no—
495(C2×D3)⋊C4C22×D312yes—
496(C2×D3)⋊C4C22×D312yes—
497C4⋊Dic3—31no—
498C4⋊Dic3—31no—
499C4⋊Dic3—31no—
500C4⋊Dic3—31no—
501C4⋊Dic3—34no—
502C4⋊Dic3—34no—
503C4⋊Dic3—34no—
504C4⋊Dic3—34no—
505C4⋊Dic3—34no—
506C4⋊Dic3—61no—
507C4⋊Dic3—61no—
508C4⋊Dic3C22×D312yes—
509C4⋊Dic3C22×D312yes—
510C4⋊Dic3C22×D311yescharacteristic
511C4⋊Dic3C22×D311yescharacteristic
512C4⋊Dic3C22×D312yes—
513C4⋊Dic3C22×D312yes—
514Dic3⋊C4—32no—
515Dic3⋊C4—32no—
516Dic3⋊C4—32no—
517Dic3⋊C4—32no—
518Dic3⋊C4—34no—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—62no—
526Dic3⋊C4—62no—
527Dic3⋊C4C22×D314yes—
528Dic3⋊C4C22×D314yes—
529Dic3⋊C4C22×D312yes—
530Dic3⋊C4C22×D312yes—
531C4×Dic3—32no—
532C4×Dic3—32no—
533C4×Dic3—32no—
534C4×Dic3—32no—
535C4×Dic3—32no—
536C4×Dic3—32no—
537C4×Dic3—34no—
538C4×Dic3—34no—
539C4×Dic3—34no—
540C4×Dic3—34no—
541C4×Dic3—62no—
542C4×Dic3—62no—
543C4×Dic3—62no—
544C4×Dic3C22×D312yes—
545C4×Dic3C22×D314yes—
546C4×Dic3C22×D312yes—
547C4×Dic3C22×D312yes—
548C22×C32—21no—
549C22×C32—21no—
550C22×C32—21no—
551C22×C32C2511yescharacteristic
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3C2×#4114yes—
555C2×C3×D3—22no—
556C2×C3×D3—22no—
557C2×C3×D3—22no—
558C32×C4—21no—
559C32×C4—21no—
560C32×C4—21no—
561C32×C4C2×#4112yes—
562C32×C4C2×#4112yes—
563C32×C42−1+412yes—
564C3⋊Dic3—22no—
565C3⋊Dic3—22no—
566C3⋊Dic3—22no—
567C3×Dic3—22no—
568C3×Dic3—24no—
569C3×Dic3—24no—
570C3×Dic3—22no—
571C3×Dic3C2×#4114yes—
572C2×#41—31no—
573C2×#41—92no—
574C2×#41—91no—
575C22×Q8—92no—
576C4⋊Q8—31no—
577C4⋊Q8—31no—
578C4⋊Q8—92no—
579C4⋊Q8—92no—
580#126—94no—
581#126—94no—
582#126—94no—
583#125—32no—
584#125—94no—
585#125—94no—
586#125—92no—
587#124—94no—
588#124—92no—
589#123—94no—
590#123—94no—
591#123—94no—
592C22⋊Q8—32no—
593C22⋊Q8—32no—
594C22⋊Q8—94no—
595C22⋊Q8—92no—
596C22⋊Q8—94no—
597C22⋊Q8—92no—
598C22⋊Q8—92no—
599#121—94no—
600#121—92no—
601C4×Q8—31no—
602C4×Q8—32no—
603C4×Q8—31no—
604C4×Q8—32no—
605C4×Q8—94no—
606C4×Q8—92no—
607C4×Q8—94no—
608C4×Q8—92no—
609C4×Q8—92no—
610C4×Q8—91no—
611C4×Q8—91no—
612C4×D4—32no—
613C4×D4—32no—
614C4×D4—31no—
615C4×D4—31no—
616C4×D4—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—92no—
620C4×D4—92no—
621C4×D4—91no—
622C4×D4—91no—
623#117—31no—
624#117—32no—
625#117—32no—
626#117—94no—
627#117—94no—
628#117—92no—
629#117—91no—
630#117—92no—
631C2×C4⋊C4—94no—
632C2×C4⋊C4—92no—
633C2×C42—32no—
634C2×C42—94no—
635C2×C42—92no—
636C2×C42D3211yescharacteristic
637C23×C3—21no—
638C23×C3—32no—
639C23×C3C23×D311yescharacteristic
640C23×C3C23×D311yescharacteristic
641C22×D3—32no—
642C22×D3—32no—
643C22×D3—62no—
644C22×D3C23×D312yes—
645C3×Q8—34no—
646C3×Q8—64no—
647C3×Q8—64no—
648C3×D4—64no—
649C3×D4—62no—
650C2×C3×C4—24no—
651C2×C3×C4—22no—
652C2×C3×C4—22no—
653C2×C3×C4—22no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—32no—
664C2×C3×C4—32no—
665C2×C3×C4—34no—
666C2×C3×C4—34no—
667C2×C3×C4—32no—
668C2×C3×C4—42no—
669C2×C3×C4—42no—
670C2×C3×C4—64no—
671C2×C3×C4—64no—
672C2×C3×C4—64no—
673C2×C3×C4C23×D311yescharacteristic
674C2×C3×C4C23×D311yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677C2×C3×C4C23×D311yescharacteristic
678C2×C3×C4C23×D311yescharacteristic
679C2×C3×C4C23×D311yescharacteristic
680C2×C3×C4C23×D311yescharacteristic
681C2×C3×C4C23×D311yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685#67—24no—
686#67—68no—
687#67—64no—
688#67—64no—
689#67—68no—
690C2×Dic3—32no—
691C2×Dic3—32no—
692C2×Dic3—32no—
693C2×Dic3—32no—
694C2×Dic3—32no—
695C2×Dic3—32no—
696C2×Dic3—62no—
697C2×Dic3—62no—
698C2×Dic3—62no—
699C2×Dic3C23×D312yes—
700C2×Dic3C23×D314yes—
701C2×Dic3C23×D314yes—
702C2×Dic3C23×D312yes—
703C2×Dic3C23×D312yes—
704D12—22no—
705D12—34no—
706D12—34no—
707D12—64no—
708D12—68no—
709C4×D3—24no—
710C4×D3—24no—
711C4×D3—24no—
712C4×D3—68no—
713C4×D3—68no—
714C4×D3—68no—
715C4×D3—64no—
716C4×D3—64no—
717C4×D3—68no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—68no—
723C4×D3—124no—
724C4×D3—124no—
725Dic6—24no—
726Dic6—24no—
727Dic6—68no—
728Dic6—64no—
729Dic6—62no—
730Dic6—62no—
731Dic6—68no—
732Dic6#23514yescomplemented
733C2×C32—41no—
734C2×C32C22×#4111yescharacteristic
735C2×C32C22×#4111yescharacteristic
736C2×C32C2×2−1+411yescharacteristic
737C3⋊D3—24no—
738C3×D3—42no—
739#41—64no—
740#41—184no—
741#41—188no—
742C2×Q8—31no—
743C2×Q8—32no—
744C2×Q8—32no—
745C2×Q8—94no—
746C2×Q8—91no—
747C2×Q8—188no—
748C2×D4—32no—
749C2×D4—31no—
750C2×D4—94no—
751C2×D4—92no—
752C2×D4—91no—
753C22×C4—32no—
754C22×C4—32no—
755C22×C4—32no—
756C22×C4—94no—
757C22×C4—94no—
758C22×C4—92no—
759C22×C4—92no—
760C22×C4—92no—
761C22×C4C2×D3211yescharacteristic
762C22×C4C2×D3211yescharacteristic
763C22×C4C2×D3211yescharacteristic
764C4⋊C4—32no—
765C4⋊C4—31no—
766C4⋊C4—32no—
767C4⋊C4—34no—
768C4⋊C4—32no—
769C4⋊C4—31no—
770C4⋊C4—32no—
771C4⋊C4—32no—
772C4⋊C4—34no—
773C4⋊C4—32no—
774C4⋊C4—94no—
775C4⋊C4—94no—
776C4⋊C4—94no—
777C4⋊C4—94no—
778C4⋊C4—94no—
779C4⋊C4—94no—
780C4⋊C4—91no—
781C4⋊C4—92no—
782C4⋊C4—91no—
783C4⋊C4—92no—
784C22⋊C4—32no—
785C22⋊C4—34no—
786C22⋊C4—32no—
787C22⋊C4—32no—
788C22⋊C4—94no—
789C22⋊C4—94no—
790C22⋊C4—94no—
791C22⋊C4—94no—
792C22⋊C4—92no—
793C22⋊C4—92no—
794C22⋊C4—92no—
795C42—32no—
796C42—32no—
797C42—32no—
798C42—34no—
799C42—94no—
800C42—94no—
801C42—92no—
802C42—92no—
803C42—92no—
804C42C2×D3211yescharacteristic
805C42C2×D3211yescharacteristic
806C42C2×D3211yescharacteristic
807C42C2×D3211yescharacteristic
808C22×C3—22no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—62no—
819C22×C3—62no—
820C22×C3—62no—
821C22×C3C24×D311yescharacteristic
822C22×C3C24×D311yescharacteristic
823C2×D3—22no—
824C2×D3—22no—
825C2×D3—22no—
826C2×D3—34no—
827C2×D3—34no—
828C2×D3—64no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—122no—
834C2×D3—122no—
835C3×C4—22no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—21no—
841C3×C4—21no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—22no—
845C3×C4—34no—
846C3×C4—41no—
847C3×C4—41no—
848C3×C4—64no—
849C3×C4—62no—
850C3×C4—62no—
851C3×C4—64no—
852C3×C4C2×#23512yes—
853C3×C4#100712yes—
854C3×C4D3×#4112yes—
855C3×C4D3×#4112yes—
856C3×C4D3×#4112yes—
857C3×C4#101012yes—
858Dic3—24no—
859Dic3—24no—
860Dic3—22no—
861Dic3—22no—
862Dic3—64no—
863Dic3—62no—
864Dic3—62no—
865Dic3—62no—
866Dic3—62no—
867Dic3—62no—
868Dic3—62no—
869Dic3—122no—
870Dic3—122no—
871Dic3C2×#23514yes—
872C32#348211yescharacteristic, complemented, Sylow
873C23—32no—
874C23—92no—
875C23C22×D3211yescharacteristic
876Q8—34no—
877Q8—64no—
878Q8—64no—
879Q8—188no—
880Q8—182no—
881D4—64no—
882D4—62no—
883D4—94no—
884D4—188no—
885D4—184no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—32no—
890C2×C4—32no—
891C2×C4—32no—
892C2×C4—34no—
893C2×C4—34no—
894C2×C4—64no—
895C2×C4—64no—
896C2×C4—64no—
897C2×C4—92no—
898C2×C4—92no—
899C2×C4—92no—
900C2×C4—184no—
901C2×C4—188no—
902C2×C4—188no—
903C2×C4—184no—
904C2×C4—184no—
905C2×C4C22×D3211yescharacteristic
906C2×C4C22×D3211yescharacteristic
907C2×C4C22×D3211yescharacteristic
908C2×C4C22×D3211yescharacteristic
909C2×C4C22×D3211yescharacteristic
910C2×C4C22×D3211yescharacteristic
911C2×C3—21no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—42no—
915C2×C3—41no—
916C2×C3—41no—
917C2×C3—122no—
918C2×C3C22×#23511yescharacteristic
919C2×C3C2×#100711yescharacteristic
920C2×C3C2×D3×#4111yescharacteristic
921C2×C3C2×D3×#4111yescharacteristic
922C2×C3C2×D3×#4111yescharacteristic
923C2×C3C2×#101011yescharacteristic
924D3—42no—
925D3—64no—
926D3—64no—
927D3—124no—
928C22—21no—
929C22—21no—
930C22—21no—
931C22—62no—
932C22—62no—
933C22—62no—
934C22—94no—
935C22—182no—
936C22—182no—
937C22C23×D3211yescharacteristic
938C4—21no—
939C4—21no—
940C4—21no—
941C4—34no—
942C4—62no—
943C4—64no—
944C4—62no—
945C4—64no—
946C4—182no—
947C4—182no—
948C4—182no—
949C4#6429712yes—
950C4D3×#23512yes—
951C4#6430612yes—
952C3—21no—
953C3#8584411yescharacteristic, complemented
954C3#8627811yescharacteristic, complemented
955C2—41no—
956C2—122no—
957C2—184no—
958C2C2×#6429711yescharacteristic
959C2C2×D3×#23511yescharacteristic
960C2C2×#6430611yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C4×#3828C2semidirect
2. C3×C4×#235C2semidirect
3. C3×#5470C2semidirect
4. #10594970C2semidirect
5. #10594841C2semidirect
6. #10594836C2semidirect
7. #10594834C2semidirect
8. #10594830C2semidirect
9. C4×#3799C2semidirect
10. #10593903C2semidirect
11. C4×#3797C2semidirect
12. #10593875C2semidirect
13. #10593873C2semidirect
14. #10593872C2semidirect
15. #10593869C2semidirect
16. #10593863C2semidirect
17. #10593861C2semidirect
117. C4×#235D3semidirect
119. #5470D3semidirect
347. C4⋊(C3⋊D3)#41semidirect
364. C3×Dic6#41semidirect
732. Dic6#235semidirect
872. C32#3482semidirect
953. C3#85844semidirect
954. C3#86278semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C3×C4×#2352
C3×#54702
#105949702
#105948412
#105948362
#105948342
#105948302
C4×#37992
#105939032
C4×#37972
#105938752
#105938732
#105938722
#105938692
#105938632
#105938612
#862783
#858443