Finite Group Databasebeta

← #11904208

Subgroups — #11904208

Order 1152.

2299 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596199C211yesmaximal, characteristic, complemented
2C3×#5732C211yesmaximal, characteristic, complemented
3C3×#5727C211yesmaximal, characteristic, complemented
4#10595401C212yesmaximal, complemented
5#10595379C212yesmaximal, complemented
6#10595377C212yesmaximal, complemented
7D3×Q8×Dic3C212yesmaximal, complemented
8#10594556C212yesmaximal, complemented
9#10594442C214yesmaximal, complemented
10#10594432C214yesmaximal, complemented
11#10594387C212yesmaximal, complemented
12#10594381C212yesmaximal, complemented
13#10594358C212yesmaximal, complemented
14#10593895C211yesmaximal, characteristic, complemented
15C4×#3796C211yesmaximal, characteristic, complemented
16C4×#3796C211yesmaximal, characteristic, complemented
17#10593860C211yesmaximal, characteristic, complemented
18#86981—31nomaximal
19#86744—31nomaximal
20C2×C3×D3×Q8C2212yes—
21C2×#3796C2211yescharacteristic
22C2×#3796C2211yescharacteristic
23C2×#3795C2212yes—
24C32×C4⋊Q8C2211yescharacteristic
25#64155C2212yes—
26Q8×C3⋊Dic3C2212yes—
27#64106C2212yes—
28#64101C2212yes—
29#64099C2212yes—
30#64096C2212yes—
31C42×C3⋊D3C2211yescharacteristic
32#64078C2211yescharacteristic
33C3×#947C2212yes—
34C3×#946C2212yes—
35C3×Q8×Dic3C2212yes—
36C3×#898C2214yes—
37C3×#897C2212yes—
38C3×#896C2214yes—
39C3×#893C2212yes—
40C3×#892C2212yes—
41C3×#888C2212yes—
42C3×C4×D12C2211yescharacteristic
43C3×C4×D12C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45C3×C4×Dic6C2211yescharacteristic
46#63908C2212yes—
47#63907C2214yes—
48#63906C2214yes—
49C4×#626C2212yes—
50C4×#626C2212yes—
51#63902C2214yes—
52#63898C2211yescharacteristic
53#63898C2211yescharacteristic
54#63891C2214yes—
55#63891C2214yes—
56#63890C2214yes—
57D3×C4⋊Dic3C2212yes—
58D3×C4⋊Dic3C2214yes—
59#63887C2214yes—
60#63881C2212yes—
61#63881C2212yes—
62#63879C2214yes—
63#63878C2214yes—
64#63878C2212yes—
65#63878C2212yes—
66#63877C2214yes—
67C4×D3×Dic3C2212yes—
68C4×D3×Dic3C2214yes—
69C4×D3×Dic3C2212yes—
70#63869C2212yes—
71#63868C2214yes—
72#63866C2212yes—
73#63861C2214yes—
74#63857C2212yes—
75#63849C2211yescharacteristic
76#63849C2211yescharacteristic
77#63846C2214yes—
78#63845C2214yes—
79#63844C2212yes—
80#63843C2211yescharacteristic
81#63843C2214yes—
82#63843C2211yescharacteristic
83Dic3×Dic6C2212yes—
84Dic3×Dic6C2214yes—
85C3×#556—31no—
86C3×D4×Q8—31no—
87#5817—32no—
88C2×Q8×Dic3—32no—
89#5732—32no—
90#5732D311yescharacteristic, complemented
91#5728—31no—
92#5728—31no—
93#5728—32no—
94#5728—61no—
95#5727D311yescharacteristic, complemented
96#5708—34no—
97#5706—34no—
98#5680—32no—
99#5677—32no—
100#5642—32no—
101#5642—34no—
102#5631—32no—
103#5624—32no—
104#5624—34no—
105#5622—32no—
106#5581—32no—
107C4×#239—31no—
108C4×#239—31no—
109C4×D3×Q8—32no—
110#5570—31no—
111#5567—31no—
112#5555—32no—
113#5555—31no—
114#5551—31no—
115C4×#237—32no—
116C4×#237—31no—
117C4×#237—31no—
118#5533—32no—
119#5522—32no—
120C2×C32×Q8C2312yes—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×#634C2312yes—
125C3×D3×Q8—28no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×D12C2311yescharacteristic
128C2×C3×C4×D3C2312yes—
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2312yes—
131C2×C3×Dic6C2314yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×C3×Dic6C2311yescharacteristic
134C2×#626C2312yes—
135C2×#626C2312yes—
136C2×#625C2314yes—
137C2×D3×Dic3C2314yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2312yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2312yes—
142#3796—24no—
143#3796—24no—
144#3795—28no—
145C32×C4⋊C4C2312yes—
146C32×C4⋊C4C2312yes—
147C32×C42C2311yescharacteristic
148#3752C2314yes—
149C4⋊(C3⋊Dic3)C2312yes—
150C4⋊(C3⋊Dic3)C2312yes—
151C4⋊(C3⋊Dic3)C2314yes—
152#3750C2314yes—
153C4×C3⋊Dic3C2311yescharacteristic
154C4×C3⋊Dic3C2311yescharacteristic
155C4×C3⋊Dic3C2311yescharacteristic
156C4×C3⋊Dic3C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2314yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×(C2×D3)⋊C4C2314yes—
161C3×(C2×D3)⋊C4C2312yes—
162C3×C4⋊Dic3C2311yescharacteristic
163C3×C4⋊Dic3C2311yescharacteristic
164C3×C4⋊Dic3C2314yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2311yescharacteristic
167C3×Dic3⋊C4C2314yes—
168C3×Dic3⋊C4C2312yes—
169C3×Dic3⋊C4C2312yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2314yes—
172C3×C4×Dic3C2312yes—
173#3724C2314yes—
174Dic3⋊Dic3C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2314yes—
179#3722C2312yes—
180#3722C2312yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2312yes—
184Dic32C2314yes—
185Dic32C2312yes—
186Dic32C2312yes—
187Dic32C2312yes—
188Dic32C2312yes—
189#3482—91noSylow
190C22×C3×Q8—32no—
191C2×#239—31no—
192C2×#239—31no—
193C2×D3×Q8C2×D312yes—
194C2×#237—32no—
195C2×#237—31no—
196C2×#237—31no—
197C2×#235—32no—
198C3×C4⋊Q8—21no—
199C3×C4⋊Q8—32no—
200C3×C4⋊Q8C2×D311yescharacteristic
201C3×C4⋊Q8C2×D311yescharacteristic
202C3×#126—34no—
203C3×#124—32no—
204C3×C22⋊Q8—32no—
205C3×C22⋊Q8—34no—
206C3×C22⋊Q8—32no—
207C3×C4×Q8—32no—
208C3×C4×Q8—31no—
209C3×C4×Q8—31no—
210C3×C4×D4—32no—
211C3×C4×D4—31no—
212C3×C4×D4—31no—
213C3×#117—32no—
214#947—34no—
215#947C2×D312yes—
216#946—32no—
217#946—32no—
218#946—34no—
219#946—62no—
220#946C2×D312yes—
221Q8×Dic3—32no—
222Q8×Dic3—32no—
223Q8×Dic3—34no—
224Q8×Dic3—31no—
225Q8×Dic3—31no—
226Q8×Dic3—34no—
227Q8×Dic3—32no—
228Q8×Dic3—62no—
229Q8×Dic3C2×D312yes—
230#944—32no—
231#938—32no—
232D4×Dic3—31no—
233D4×Dic3—31no—
234#930—32no—
235#930—34no—
236C4×#67—34no—
237C4×#67—32no—
238C4×#67—32no—
239C2×C4⋊Dic3—32no—
240C2×C4⋊Dic3—34no—
241#924—32no—
242C2×C4×Dic3—32no—
243C2×C4×Dic3—32no—
244C2×C4×Dic3—34no—
245#898—34no—
246#898—34no—
247#898C2×D314yes—
248#897—32no—
249#897—32no—
250#897—32no—
251#897—62no—
252#897C2×D312yes—
253#896C2×D314yes—
254#894—34no—
255#893—31no—
256#893—31no—
257#893—32no—
258#893—32no—
259#893C2×D312yes—
260#892—32no—
261#892—32no—
262#892—32no—
263#892—32no—
264#892—34no—
265#892—31no—
266#892—31no—
267#892—31no—
268#892—31no—
269#892—62no—
270#892C2×D312yes—
271D3×C4⋊C4—34no—
272D3×C4⋊C4—32no—
273#890—32no—
274#890—32no—
275#890—34no—
276#890—34no—
277#890—32no—
278#890—62no—
279#889—34no—
280#889—34no—
281#888C2×D312yes—
282#887—34no—
283#887—31no—
284#887—31no—
285#887—32no—
286#887—32no—
287#887—32no—
288#887—62no—
289#886—34no—
290#886—34no—
291#886—34no—
292#885—34no—
293#884—34no—
294#883—34no—
295#883—34no—
296#67⋊C4—34no—
297#67⋊C4—34no—
298#67⋊C4—34no—
299#67⋊C4—32no—
300#67⋊C4—32no—
301#879—34no—
302#878—34no—
303#877—32no—
304#877—34no—
305#877—32no—
306#877—34no—
307#876—34no—
308C4×D12—32no—
309C4×D12—32no—
310C4×D12C2×D311yescharacteristic
311C4×D12C2×D311yescharacteristic
312#872—34no—
313C42×D3—32no—
314C42×D3—34no—
315C42×D3—32no—
316C42×D3—31no—
317C42×D3—31no—
318C42×D3—61no—
319#870—32no—
320#869—32no—
321#869—31no—
322#869—31no—
323#869—61no—
324C4×Dic6—32no—
325C4×Dic6—34no—
326C4×Dic6—32no—
327C4×Dic6C2×D311yescharacteristic
328C4×Dic6C2×D311yescharacteristic
329C22×C3⋊D3C2411yescharacteristic
330C22×C3×D3C2412yes—
331C22×C3×D3C2412yes—
332C32×Q8—24no—
333C2×C32×C4C2414yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3C2411yescharacteristic
338C2×C3⋊Dic3C2411yescharacteristic
339C2×C3⋊Dic3C2414yes—
340C2×C3⋊Dic3C2411yescharacteristic
341C4×C3⋊D3—22no—
342C4×C3⋊D3—22no—
343C4×C3⋊D3—22no—
344#634—24no—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C2×C3×Dic3C2412yes—
351C3×D12—22no—
352C3×D12#4114yescomplemented
353C3×C4×D3—24no—
354C3×C4×D3—24no—
355C3×C4×D3—28no—
356C3×Dic6—22no—
357C3×Dic6—28no—
358C3×Dic6#4114yescomplemented
359#626—24no—
360#626—24no—
361#625—28no—
362D3×Dic3—28no—
363D3×Dic3—24no—
364D3×Dic3—24no—
365D3×Dic3—24no—
366D3×Dic3—24no—
367#557—91no—
368#556—31no—
369#556—92no—
370#552—92no—
371#552—94no—
372D4×Q8—31no—
373#548—92no—
374#547—91no—
375#547—92no—
376#533—92no—
377#533—91no—
378#529—92no—
379#529—94no—
380C4×#41—92no—
381C4×#41—91no—
382C4×#41—91no—
383C2×C4×Q8—92no—
384C2×C3×Q8—22no—
385C2×C3×Q8—31no—
386C2×C3×Q8—31no—
387C2×C3×Q8—34no—
388C2×C3×Q8—68no—
389C2×C3×Q8C22×D312yes—
390C2×C3×Q8C22×D312yes—
391C2×C3×D4—31no—
392C2×C3×D4—31no—
393C22×C3×C4—32no—
394C22×C3×C4—34no—
395C22×C3×C4—32no—
396C2×#67—34no—
397C2×#67—34no—
398C2×#67—32no—
399C2×#67—32no—
400C22×Dic3—32no—
401C22×Dic3—32no—
402C22×Dic3—32no—
403C22×Dic3—34no—
404C22×Dic3—32no—
405#239—64no—
406#239—64no—
407D3×Q8—28no—
408#237—64no—
409#237—68no—
410#237—64no—
411#235—68no—
412C2×D12—32no—
413C2×D12—32no—
414C2×D12C22×D311yescharacteristic
415C2×D12C22×D311yescharacteristic
416C2×C4×D3—32no—
417C2×C4×D3—34no—
418C2×C4×D3—32no—
419C2×C4×D3—32no—
420C2×C4×D3—32no—
421C2×C4×D3—31no—
422C2×C4×D3—31no—
423C2×C4×D3—31no—
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—31no—
427C2×C4×D3—61no—
428C2×C4×D3—61no—
429C2×C4×D3—61no—
430C2×C4×D3C22×D312yes—
431C2×C4×D3C22×D312yes—
432C2×C4×D3C22×D314yes—
433C2×Dic6—32no—
434C2×Dic6—32no—
435C2×Dic6—62no—
436C2×Dic6C22×D314yes—
437C2×Dic6C22×D311yescharacteristic
438C2×Dic6C22×D311yescharacteristic
439C3×C4⋊C4—22no—
440C3×C4⋊C4—22no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—34no—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—31no—
445C3×C4⋊C4—32no—
446C3×C4⋊C4—32no—
447C3×C4⋊C4—31no—
448C3×C4⋊C4—34no—
449C3×C4⋊C4C22×D312yes—
450C3×C4⋊C4C22×D312yes—
451C3×C4⋊C4C22×D312yes—
452C3×C4⋊C4C22×D312yes—
453C3×C22⋊C4—34no—
454C3×C22⋊C4—32no—
455C3×C22⋊C4—32no—
456C3×C22⋊C4—34no—
457C3×C22⋊C4—34no—
458C3×C42—21no—
459C3×C42—32no—
460C3×C42—32no—
461C3×C42—34no—
462C3×C42C22×D311yescharacteristic
463C3×C42C22×D311yescharacteristic
464#217—32no—
465#217—34no—
466#217—32no—
467(C2×D3)⋊C4—32no—
468(C2×D3)⋊C4—32no—
469(C2×D3)⋊C4—34no—
470(C2×D3)⋊C4—34no—
471(C2×D3)⋊C4—34no—
472(C2×D3)⋊C4—32no—
473(C2×D3)⋊C4—32no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4—32no—
476(C2×D3)⋊C4—64no—
477(C2×D3)⋊C4C22×D314yes—
478(C2×D3)⋊C4C22×D312yes—
479(C2×D3)⋊C4C22×D312yes—
480(C2×D3)⋊C4C22×D314yes—
481(C2×D3)⋊C4C22×D314yes—
482C4⋊Dic3—32no—
483C4⋊Dic3—34no—
484C4⋊Dic3—32no—
485C4⋊Dic3—32no—
486C4⋊Dic3—32no—
487C4⋊Dic3—34no—
488C4⋊Dic3—34no—
489C4⋊Dic3—34no—
490C4⋊Dic3—32no—
491C4⋊Dic3—32no—
492C4⋊Dic3—34no—
493C4⋊Dic3—62no—
494C4⋊Dic3—62no—
495C4⋊Dic3—64no—
496C4⋊Dic3C22×D311yescharacteristic
497C4⋊Dic3C22×D311yescharacteristic
498C4⋊Dic3C22×D311yescharacteristic
499C4⋊Dic3C22×D311yescharacteristic
500C4⋊Dic3C22×D314yes—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—32no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—34no—
507Dic3⋊C4—34no—
508Dic3⋊C4—34no—
509Dic3⋊C4—32no—
510Dic3⋊C4—64no—
511Dic3⋊C4C22×D312yes—
512Dic3⋊C4C22×D312yes—
513Dic3⋊C4C22×D314yes—
514C4×Dic3—31no—
515C4×Dic3—31no—
516C4×Dic3—31no—
517C4×Dic3—31no—
518C4×Dic3—34no—
519C4×Dic3—31no—
520C4×Dic3—31no—
521C4×Dic3—34no—
522C4×Dic3—32no—
523C4×Dic3—34no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—32no—
528C4×Dic3—32no—
529C4×Dic3—32no—
530C4×Dic3—32no—
531C4×Dic3—32no—
532C4×Dic3—61no—
533C4×Dic3—61no—
534C4×Dic3—61no—
535C4×Dic3—64no—
536C4×Dic3C22×D312yes—
537C4×Dic3C22×D312yes—
538C4×Dic3C22×D314yes—
539C22×C32C2511yescharacteristic
540C2×C3⋊D3—21no—
541C2×C3⋊D3—21no—
542C2×C3⋊D3—21no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—22no—
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3C2×#4114yes—
549C32×C4—21no—
550C32×C4—24no—
551C32×C4C2×#4112yes—
552C32×C4C2×#4112yes—
553C3⋊Dic3—21no—
554C3⋊Dic3—21no—
555C3⋊Dic3—24no—
556C3⋊Dic32−1+412yes—
557C3×Dic3—22no—
558C3×Dic3—22no—
559C3×Dic3—22no—
560C3×Dic3—22no—
561C3×Dic3—22no—
562C3×Dic3C2×#4114yes—
563C2×#41—92no—
564C2×#41—91no—
565C2×#41—91no—
566C22×Q8—32no—
567C4⋊Q8—32no—
568C4⋊Q8—92no—
569C4⋊Q8—91no—
570C4⋊Q8D3211yescharacteristic
571#126—34no—
572#126—94no—
573#126—94no—
574#125—92no—
575#125—94no—
576#125—94no—
577#125—92no—
578#124—32no—
579#124—94no—
580#123—94no—
581#123—94no—
582#123—94no—
583C22⋊Q8—32no—
584C22⋊Q8—34no—
585C22⋊Q8—32no—
586C22⋊Q8—94no—
587C22⋊Q8—92no—
588C22⋊Q8—92no—
589C22⋊Q8—92no—
590#121—94no—
591#121—92no—
592C4×Q8—32no—
593C4×Q8—31no—
594C4×Q8—31no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×Q8—94no—
598C4×Q8—91no—
599C4×Q8—94no—
600C4×Q8—91no—
601C4×Q8—92no—
602C4×Q8—92no—
603C4×D4—32no—
604C4×D4—31no—
605C4×D4—31no—
606C4×D4—92no—
607C4×D4—92no—
608C4×D4—94no—
609C4×D4—92no—
610C4×D4—92no—
611C4×D4—94no—
612C4×D4—91no—
613C4×D4—91no—
614#117—32no—
615#117—94no—
616#117—92no—
617#117—92no—
618#117—94no—
619#117—91no—
620#117—91no—
621#117—92no—
622C2×C4⋊C4—92no—
623C2×C4⋊C4—94no—
624C2×C42—94no—
625C2×C42—92no—
626C2×C42—92no—
627C2×C42—91no—
628C23×C3—32no—
629C23×C3—32no—
630C22×D3—31no—
631C22×D3—31no—
632C22×D3—61no—
633C22×D3C23×D312yes—
634C22×D3C23×D312yes—
635C3×Q8—24no—
636C3×Q8—24no—
637C3×Q8—34no—
638C3×Q8—44no—
639C3×Q8—68no—
640C3×Q8—62no—
641C3×D4—34no—
642C3×D4—62no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—24no—
647C2×C3×C4—32no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—32no—
652C2×C3×C4—32no—
653C2×C3×C4—68no—
654C2×C3×C4—64no—
655C2×C3×C4—64no—
656C2×C3×C4C23×D314yes—
657C2×C3×C4C23×D314yes—
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664#67—64no—
665#67—68no—
666#67—68no—
667#67—64no—
668C2×Dic3—31no—
669C2×Dic3—31no—
670C2×Dic3—31no—
671C2×Dic3—31no—
672C2×Dic3—31no—
673C2×Dic3—31no—
674C2×Dic3—34no—
675C2×Dic3—34no—
676C2×Dic3—61no—
677C2×Dic3—61no—
678C2×Dic3—61no—
679C2×Dic3—64no—
680C2×Dic3—64no—
681C2×Dic3—64no—
682C2×Dic3—64no—
683C2×Dic3—68no—
684C2×Dic3—64no—
685C2×Dic3C23×D312yes—
686C2×Dic3C23×D312yes—
687C2×Dic3C23×D312yes—
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D312yes—
690C2×Dic3C23×D312yes—
691D12—22no—
692D12—64no—
693D12—64no—
694D12#23914yescomplemented
695C4×D3—24no—
696C4×D3—24no—
697C4×D3—28no—
698C4×D3—62no—
699C4×D3—62no—
700C4×D3—64no—
701C4×D3—64no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—68no—
705C4×D3—64no—
706C4×D3—62no—
707C4×D3—62no—
708C4×D3—62no—
709C4×D3—62no—
710C4×D3—122no—
711C4×D3—122no—
712Dic6—22no—
713Dic6—28no—
714Dic6—64no—
715Dic6—64no—
716Dic6—124no—
717Dic6#23714yescomplemented
718C2×C32C22×#4111yescharacteristic
719C2×C32C22×#4111yescharacteristic
720C2×C32C2×2−1+411yescharacteristic
721C3⋊D3—41no—
722C3×D3—24no—
723C3×D3—42no—
724#41—188no—
725#41—184no—
726#41—184no—
727C2×Q8—31no—
728C2×Q8—31no—
729C2×Q8—34no—
730C2×Q8—68no—
731C2×Q8—92no—
732C2×Q8C2×D3212yes—
733C2×D4—31no—
734C2×D4—31no—
735C2×D4—92no—
736C2×D4—92no—
737C2×D4—94no—
738C22×C4—34no—
739C22×C4—32no—
740C22×C4—32no—
741C22×C4—92no—
742C22×C4—94no—
743C22×C4—92no—
744C22×C4—92no—
745C22×C4—92no—
746C22×C4—91no—
747C22×C4—91no—
748C22×C4—91no—
749C4⋊C4—31no—
750C4⋊C4—34no—
751C4⋊C4—31no—
752C4⋊C4—31no—
753C4⋊C4—32no—
754C4⋊C4—31no—
755C4⋊C4—32no—
756C4⋊C4—34no—
757C4⋊C4—92no—
758C4⋊C4—94no—
759C4⋊C4—94no—
760C4⋊C4—92no—
761C4⋊C4—94no—
762C4⋊C4—94no—
763C4⋊C4—92no—
764C4⋊C4—94no—
765C4⋊C4—94no—
766C4⋊C4—92no—
767C4⋊C4C2×D3212yes—
768C4⋊C4C2×D3212yes—
769C22⋊C4—34no—
770C22⋊C4—34no—
771C22⋊C4—32no—
772C22⋊C4—32no—
773C22⋊C4—34no—
774C22⋊C4—92no—
775C22⋊C4—92no—
776C22⋊C4—92no—
777C22⋊C4—92no—
778C22⋊C4—94no—
779C22⋊C4—94no—
780C42—34no—
781C42—32no—
782C42—32no—
783C42—92no—
784C42—92no—
785C42—92no—
786C42—92no—
787C42—94no—
788C42—91no—
789C42—91no—
790C42—91no—
791C42—94no—
792C42C2×D3211yescharacteristic
793C22×C3—21no—
794C22×C3—34no—
795C22×C3—62no—
796C22×C3—62no—
797C22×C3—62no—
798C22×C3—62no—
799C22×C3—62no—
800C22×C3C24×D311yescharacteristic
801C22×C3C24×D311yescharacteristic
802C2×D3—22no—
803C2×D3—22no—
804C2×D3—22no—
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—62no—
808C2×D3—61no—
809C2×D3—61no—
810C2×D3—61no—
811C2×D3—61no—
812C2×D3—61no—
813C2×D3—61no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3C2×#23914yes—
817C3×C4—22no—
818C3×C4—24no—
819C3×C4—24no—
820C3×C4—21no—
821C3×C4—21no—
822C3×C4—22no—
823C3×C4—22no—
824C3×C4—34no—
825C3×C4—44no—
826C3×C4—62no—
827C3×C4—62no—
828C3×C4—62no—
829C3×C4—62no—
830C3×C4—62no—
831C3×C4C2×#23712yes—
832C3×C4C2×#23912yes—
833C3×C4D3×#4112yes—
834C3×C4D3×#4112yes—
835Dic3—22no—
836Dic3—22no—
837Dic3—22no—
838Dic3—22no—
839Dic3—22no—
840Dic3—32no—
841Dic3—32no—
842Dic3—62no—
843Dic3—61no—
844Dic3—64no—
845Dic3—61no—
846Dic3—64no—
847Dic3—61no—
848Dic3—61no—
849Dic3—124no—
850Dic3—121no—
851Dic3—121no—
852Dic3C2×#23714yes—
853C32#348211yescharacteristic, complemented, Sylow
854C23—32no—
855C23—32no—
856C23—91no—
857Q8—24no—
858Q8—34no—
859Q8—68no—
860Q8—62no—
861Q8—184no—
862D4—34no—
863D4—62no—
864D4—184no—
865D4—184no—
866D4—188no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—32no—
870C2×C4—32no—
871C2×C4—32no—
872C2×C4—32no—
873C2×C4—68no—
874C2×C4—64no—
875C2×C4—64no—
876C2×C4—91no—
877C2×C4—91no—
878C2×C4—91no—
879C2×C4—94no—
880C2×C4—182no—
881C2×C4—184no—
882C2×C4—184no—
883C2×C4—184no—
884C2×C4—188no—
885C2×C4—184no—
886C2×C4—182no—
887C2×C4—182no—
888C2×C4C22×D3214yes—
889C2×C4C22×D3211yescharacteristic
890C2×C4C22×D3211yescharacteristic
891C2×C4C22×D3211yescharacteristic
892C2×C3—21no—
893C2×C3—21no—
894C2×C3—21no—
895C2×C3—64no—
896C2×C3—122no—
897C2×C3C22×#23711yescharacteristic
898C2×C3C22×#23911yescharacteristic
899C2×C3C2×D3×#4111yescharacteristic
900C2×C3C2×D3×#4111yescharacteristic
901C2×C3D3×2−1+411yescharacteristic
902C2×C3D3×2−1+411yescharacteristic
903D3—24no—
904D3—42no—
905D3—122no—
906D3—121no—
907D3—121no—
908C22—34no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—181no—
915C22—181no—
916C22—181no—
917C22C23×D3211yescharacteristic
918C4—24no—
919C4—21no—
920C4—34no—
921C4—62no—
922C4—62no—
923C4—62no—
924C4—62no—
925C4—62no—
926C4—92no—
927C4—181no—
928C4—181no—
929C4—184no—
930C4D3×#23712yes—
931C4D3×#23912yes—
932C3—21no—
933C3#8674411yescharacteristic, complemented
934C3#8698111yescharacteristic, complemented
935C2—64no—
936C2—122no—
937C2—361no—
938C2C2×D3×#23711yescharacteristic
939C2C2×D3×#23911yescharacteristic
940C2#1059668711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596199C2semidirect
2. C3×#5732C2semidirect
3. C3×#5727C2semidirect
4. #10595401C2semidirect
5. #10595379C2semidirect
6. #10595377C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10594556C2semidirect
9. #10594442C2semidirect
10. #10594432C2semidirect
11. #10594387C2semidirect
12. #10594381C2semidirect
13. #10594358C2semidirect
14. #10593895C2semidirect
15. C4×#3796C2semidirect
16. C4×#3796C2semidirect
17. #10593860C2semidirect
90. #5732D3semidirect
95. #5727D3semidirect
352. C3×D12#41semidirect
358. C3×Dic6#41semidirect
694. D12#239semidirect
717. Dic6#237semidirect
853. C32#3482semidirect
933. C3#86744semidirect
934. C3#86981semidirect

Maximal subgroups

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

subgroupindex
#105961992
C3×#57322
C3×#57272
#105954012
#105953792
#105953772
D3×Q8×Dic32
#105945562
#105944422
#105944322
#105943872
#105943812
#105943582
#105938952
C4×#37962
#105938602
#869813
#867443