Finite Group Databasebeta

← #11901221

Subgroups — #11901221

Order 1152.

3277 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic, complemented
2C22×#3796C211yesmaximal, characteristic, complemented
3C3⋊D3×#117C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C3×#5525C211yesmaximal, characteristic, complemented
6#10595040C211yesmaximal, characteristic, complemented
7#10594855C211yesmaximal, characteristic, complemented
8#10594632C214yesmaximal, complemented
9#10594528C214yesmaximal, complemented
10#10594296C214yesmaximal, complemented
11#10594082C214yesmaximal, complemented
12#10594010C212yesmaximal, complemented
13#10593971C212yesmaximal, complemented
14#10593908C212yesmaximal, complemented
15#10593907C212yesmaximal, complemented
16#86338—31nomaximal
17#86313—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic, complemented
22C22×C3×Dic6C2211yescharacteristic, complemented
23C2×#3811C2212yes—
24C22×#626C2212yes—
25C2×#3805C2212yes—
26C22×D3×Dic3C2212yescomplemented
27#64306—28no—
28C2×#3802C2211yescharacteristic, complemented
29C2×C4×D32C2212yescomplemented
30C2×#3798C2212yescomplemented
31C2×#3797C2211yescharacteristic, complemented
32C2×#3796—28no—
33C2×#3796C2212yes—
34C2×#3796C2212yes—
35C2×#3796C2212yescomplemented
36C2×#3796C2212yescomplemented
37C2×#3796C2211yescharacteristic, complemented
38C2×#3796C2211yescharacteristic, complemented
39C32×#117C2211yescharacteristic, complemented
40#64135C2211yescharacteristic, complemented
41#64101C2212yescomplemented
42C4⋊C4×C3⋊D3C2212yescomplemented
43C22⋊C4×C3⋊D3C2212yes—
44#64086C2212yescomplemented
45#64081C2212yescomplemented
46C42×C3⋊D3C2212yescomplemented
47C3×#897C2214yescomplemented
48C3×#895C2214yescomplemented
49C3×#886C2214yescomplemented
50C3×#882C2214yescomplemented
51C3×#875C2212yescomplemented
52C3×#875C2212yescomplemented
53C3×#874C2212yescomplemented
54C3×#869C2212yescomplemented
55#63976C2214yescomplemented
56#63961C2214yescomplemented
57#63922C2218yescomplemented
58#63916C2218yescomplemented
59#63914C2212yescomplemented
60#63912C2218yescomplemented
61#63908C2214yescomplemented
62#63902C2218yescomplemented
63#63899C2218yescomplemented
64#63898C2218yescomplemented
65#63885C2218yescomplemented
66#63873C2212yescomplemented
67#63863C2212yescomplemented
68#63863C2212yescomplemented
69#63856C2214yescomplemented
70#63854C2218yescomplemented
71C2×D3×#41—31no—
72C2×D3×#41—31no—
73C22×#239—31no—
74C22×#237—31no—
75C3×#536—31no—
76C3×#535—31no—
77#5830—31no—
78#5825—31no—
79#5816—31no—
80#5805—31no—
81#5725—32no—
82#5724—32no—
83#5716—32no—
84#5715—32no—
85#5675—32no—
86#5674—32no—
87#5668—32no—
88#5668—32no—
89#5656—34no—
90#5653—34no—
91#5629—34no—
92#5627—34no—
93#5608—34no—
94#5606—34no—
95#5589—34no—
96#5586—34no—
97#5526D311yescharacteristic, complemented
98#5525D311yescharacteristic, complemented
99D3×#117—31no—
100D3×#117—31no—
101D3×#117—61no—
102C23×C3⋊D3C2311yescharacteristic
103C23×C3×D3C2312yes—
104C22×D32C2312yes—
105C22×C32×C4C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C2×C4×C3⋊D3D418yescomplemented
108C2×C4×C3⋊D3C2314yes—
109C2×C4×C3⋊D3C2311yescharacteristic
110C2×C4×C3⋊D3C2311yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C3×#67C2312yes—
114C2×C3×#67C2312yes—
115C22×C3×Dic3C2312yes—
116C3×#235—24no—
117C3×#235—24no—
118C2×C3×D12—24no—
119C2×C3×D12C2312yes—
120C2×C3×D12C2312yes—
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2311yescharacteristic
123C2×C3×D12C2318yes—
124C2×C3×C4×D3C2312yes—
125C2×C3×C4×D3C2312yes—
126C2×C3×Dic6—24no—
127C2×C3×Dic6C2312yes—
128C2×C3×Dic6C2312yes—
129C2×C3×Dic6C2311yescharacteristic
130C2×C3×Dic6C2311yescharacteristic
131#3811—28no—
132C2×#627C2312yes—
133C2×#626—28no—
134C2×#626C2314yes—
135C2×#626C2314yes—
136C2×#626C2312yes—
137C2×#626C2312yes—
138C2×#625C2312yes—
139C2×#625C2318yes—
140C2×#624C2312yes—
141#3805—28no—
142C2×D3×Dic3—28no—
143C2×D3×Dic3C2314yes—
144C2×D3×Dic3C2314yes—
145C2×D3×Dic3C2312yes—
146C2×D3×Dic3C2312yes—
147#3802—24no—
148C4×D32—28no—
149#3798—28no—
150#3797—24no—
151#3796—28no—
152#3796—28no—
153#3796—28no—
154#3796—28no—
155#3796—24no—
156#3796—24no—
157C32×C4⋊C4C2312yes—
158C32×C22⋊C4C2312yes—
159C32×C42C2312yes—
160#3757C2312yes—
161#3752C2314yes—
162C4⋊(C3⋊Dic3)C2312yes—
163#3750C2314yes—
164C4×C3⋊Dic3C2312yes—
165C4×C3⋊Dic3C2314yes—
166C3×(C2×D3)⋊C4C2318yes—
167C3×(C2×D3)⋊C4C2318yes—
168C3×C4⋊Dic3C2318yes—
169#3724C2318yes—
170(C2×D3)⋊Dic3C2318yes—
171(C2×D3)⋊Dic3C2318yes—
172#3449—91noSylow
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C22×C3×Q8—31no—
176C22×C3×D4—31no—
177C22×#67—32no—
178C23×Dic3—32no—
179D3×#41—68no—
180D3×#41—68no—
181C2×#239—31no—
182C2×#239—32no—
183C2×#239—32no—
184C2×#239—32no—
185C2×#239—32no—
186C2×#239—31no—
187C2×#239—68no—
188C2×D3×Q8—31no—
189C2×D3×Q8—31no—
190C2×#237—32no—
191C2×#237—32no—
192C2×#237—31no—
193C2×#237—32no—
194C2×#237—32no—
195C2×#237—32no—
196C2×#237—32no—
197C2×#237—31no—
198C2×#237—68no—
199C2×D3×D4—32no—
200C2×D3×D4—32no—
201C2×D3×D4—31no—
202C2×D3×D4—31no—
203C2×#235—32no—
204C2×#235—32no—
205C2×#235C2×D311yescharacteristic
206C2×#235C2×D311yescharacteristic
207C22×D12—32no—
208C22×D12C2×D311yescharacteristic, complemented
209C22×C4×D3—31no—
210C22×C4×D3—31no—
211C22×C4×D3—32no—
212C22×C4×D3—32no—
213C22×C4×D3—32no—
214C22×C4×D3—61no—
215C22×Dic6C2×D311yescharacteristic, complemented
216C3×C4⋊Q8—32no—
217C3×#127—32no—
218C3×#124—32no—
219C3×#124—32no—
220C3×#123—34no—
221C3×C22⋊Q8—34no—
222C3×#121—34no—
223C3×#120—34no—
224C3×#117—21no—
225C3×#117C2×D311yescharacteristic, complemented
226C3×#117C2×D311yescharacteristic, complemented
227#953—34no—
228#947—32no—
229#947—32no—
230#946—34no—
231#944—32no—
232#944—32no—
233#940—32no—
234#940—32no—
235#939—38no—
236#938—34no—
237#938—38no—
238#937—34no—
239#937—38no—
240#936—32no—
241#936—32no—
242#935—34no—
243D4×Dic3—38no—
244#930—34no—
245#929—34no—
246#926—31no—
247#926—31no—
248#926—61no—
249#924—34no—
250#897C2×D314yescomplemented
251#896—38no—
252#895—38no—
253#895C2×D314yescomplemented
254#894—38no—
255#893—38no—
256#892—32no—
257#892—32no—
258#892—62no—
259D3×C4⋊C4—32no—
260D3×C4⋊C4—32no—
261D3×C4⋊C4—62no—
262#886C2×D314yescomplemented
263#884—38no—
264#884—38no—
265#884—38no—
266#883—38no—
267#882—38no—
268#882C2×D314yescomplemented
269#67⋊C4—38no—
270#67⋊C4—38no—
271D3×C22⋊C4—32no—
272D3×C22⋊C4—32no—
273D3×C22⋊C4—62no—
274#878—38no—
275#877—32no—
276#877—32no—
277#877—62no—
278#875C2×D312yescomplemented
279#875C2×D312yescomplemented
280#874C2×D312yescomplemented
281#872—32no—
282#872—32no—
283#872—62no—
284C42×D3—32no—
285C42×D3—32no—
286C42×D3—62no—
287#869C2×D312yescomplemented
288C23×C32C2411yescharacteristic
289C22×C3⋊D3—42no—
290C22×C3⋊D3C2×D414yes—
291C22×C3⋊D3C2411yescharacteristic
292C22×C3⋊D3C2411yescharacteristic
293C22×C3×D3—24no—
294C22×C3×D3—44no—
295C22×C3×D3C2412yes—
296C22×C3×D3C2412yes—
297C22×C3×D3C2414yes—
298C2×D32—24no—
299C2×D32—44no—
300C2×C32×C4C2×D414yes—
301C2×C32×C4C2414yes—
302C2×C32×C4C2411yescharacteristic
303C2×C32×C4C2411yescharacteristic
304C2×C3⋊Dic3C2×D414yes—
305C2×C3⋊Dic3C2414yes—
306C2×C3⋊Dic3C2411yescharacteristic
307C2×C3⋊Dic3C2411yescharacteristic
308C4×C3⋊D3—44no—
309C4×C3⋊D3C2×D414yes—
310C4×C3⋊D3C2×D414yes—
311C4×C3⋊D3C2×D414yes—
312C4×C3⋊D3C2×D414yes—
313C3×#67—24no—
314C3×#67—24no—
315C2×C3×Dic3—24no—
316C2×C3×Dic3C2412yes—
317C2×C3×Dic3C2414yes—
318C2×C3×Dic3C2412yes—
319C3×D12—24no—
320C3×D12—24no—
321C3×D12—22no—
322C3×D12—22no—
323C3×D12—48no—
324C3×C4×D3—24no—
325C3×C4×D3—24no—
326C3×Dic6—24no—
327C3×Dic6—24no—
328C3×Dic6—22no—
329C3×Dic6—22no—
330#627—24no—
331#626—28no—
332#626—28no—
333#626—24no—
334#626—24no—
335#625—24no—
336#625—48no—
337#624—24no—
338D3×Dic3—28no—
339D3×Dic3—28no—
340D3×Dic3—24no—
341D3×Dic3—24no—
342C22×#41—91no—
343C22×#41—91no—
344#537—94no—
345#536—31no—
346#536—92no—
347#536—91no—
348#535—31no—
349#535—92no—
350#535—91no—
351#534—94no—
352#532—92no—
353#532—92no—
354#525—94no—
355#525—94no—
356C2×#117—91no—
357C24×C3—32no—
358C23×D3—31no—
359C23×D3—31no—
360C23×D3—32no—
361C23×D3—32no—
362C23×D3—61no—
363C23×D3C22×D312yes—
364C3×#41—64no—
365C3×#41—64no—
366C2×C3×Q8—31no—
367C2×C3×Q8—32no—
368C2×C3×Q8—32no—
369C2×C3×Q8—31no—
370C2×C3×Q8—64no—
371C2×C3×D4—32no—
372C2×C3×D4—32no—
373C2×C3×D4—31no—
374C2×C3×D4—32no—
375C2×C3×D4—32no—
376C2×C3×D4—31no—
377C2×C3×D4—38no—
378C2×C3×D4—64no—
379C22×C3×C4—21no—
380C22×C3×C4—32no—
381C22×C3×C4—32no—
382C22×C3×C4—32no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C2×#67—32no—
386C2×#67—32no—
387C2×#67—38no—
388C2×#67—38no—
389C2×#67—34no—
390C2×#67—32no—
391C2×#67—34no—
392C2×#67—32no—
393C2×#67—68no—
394C2×#67C22×D312yes—
395C2×#67C22×D312yes—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—34no—
399C22×Dic3—32no—
400C22×Dic3—34no—
401C22×Dic3—32no—
402C22×Dic3—61no—
403C22×Dic3—68no—
404C22×Dic3C22×D312yes—
405#239—68no—
406#239—68no—
407#239—68no—
408#239—68no—
409#239—64no—
410#239—64no—
411D3×Q8—64no—
412D3×Q8—64no—
413#237—68no—
414#237—68no—
415#237—68no—
416#237—68no—
417#237—64no—
418#237—64no—
419#237—68no—
420#237—68no—
421D3×D4—64no—
422D3×D4—64no—
423D3×D4—68no—
424D3×D4—68no—
425#235—24no—
426#235—24no—
427#235—68no—
428#235—68no—
429C2×D12—24no—
430C2×D12—34no—
431C2×D12—32no—
432C2×D12—34no—
433C2×D12—32no—
434C2×D12—68no—
435C2×D12C22×D311yescharacteristic
436C2×D12C22×D312yes—
437C2×D12C22×D311yescharacteristic
438C2×D12C22×D312yes—
439C2×D12C22×D318yes—
440C2×C4×D3—38no—
441C2×C4×D3—38no—
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—31no—
449C2×C4×D3—31no—
450C2×C4×D3—32no—
451C2×C4×D3—34no—
452C2×C4×D3—34no—
453C2×C4×D3—32no—
454C2×C4×D3—32no—
455C2×C4×D3—32no—
456C2×C4×D3—34no—
457C2×C4×D3—34no—
458C2×C4×D3—61no—
459C2×C4×D3—61no—
460C2×C4×D3—61no—
461C2×C4×D3—61no—
462C2×C4×D3—68no—
463C2×C4×D3—64no—
464C2×C4×D3—68no—
465C2×C4×D3—68no—
466C2×C4×D3—68no—
467C2×C4×D3C22×D312yes—
468C2×C4×D3C22×D312yes—
469C2×Dic6—24no—
470C2×Dic6—32no—
471C2×Dic6—32no—
472C2×Dic6C22×D311yescharacteristic
473C2×Dic6C22×D312yes—
474C2×Dic6C22×D311yescharacteristic
475C2×Dic6C22×D312yes—
476C3×C4⋊C4—22no—
477C3×C4⋊C4—38no—
478C3×C4⋊C4C22×D312yes—
479C3×C4⋊C4C22×D312yes—
480C3×C22⋊C4—22no—
481C3×C22⋊C4—38no—
482C3×C22⋊C4—38no—
483C3×C22⋊C4C22×D312yes—
484C3×C22⋊C4C22×D312yes—
485C3×C42—22no—
486C3×C42C22×D312yes—
487C3×C42C22×D312yes—
488#217—32no—
489#217—32no—
490#217—38no—
491#217—38no—
492#217—62no—
493(C2×D3)⋊C4—38no—
494(C2×D3)⋊C4—38no—
495(C2×D3)⋊C4—34no—
496(C2×D3)⋊C4—34no—
497(C2×D3)⋊C4—64no—
498(C2×D3)⋊C4C22×D318yes—
499(C2×D3)⋊C4C22×D318yes—
500C4⋊Dic3—32no—
501C4⋊Dic3—32no—
502C4⋊Dic3—62no—
503C4⋊Dic3C22×D318yes—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—38no—
507Dic3⋊C4—38no—
508Dic3⋊C4—64no—
509C4×Dic3—32no—
510C4×Dic3—32no—
511C4×Dic3—34no—
512C4×Dic3—34no—
513C4×Dic3—62no—
514C4×Dic3—64no—
515C22×C32—22no—
516C22×C32C22×D412yes—
517C22×C32C2511yescharacteristic
518C2×C3⋊D3—22no—
519C2×C3⋊D3—22no—
520C2×C3⋊D3—44no—
521C2×C3⋊D3C22×D412yes—
522C2×C3⋊D3C22×D412yes—
523C2×C3×D3—24no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—24no—
527C2×C3×D3—28no—
528C2×C3×D3—24no—
529C2×C3×D3—48no—
530D32—48no—
531C32×C4—24no—
532C32×C4C22×D412yes—
533C32×C4C22×D412yes—
534C3⋊Dic3—24no—
535C3⋊Dic3C22×D412yes—
536C3⋊Dic3C22×D412yes—
537C3×Dic3—24no—
538C3×Dic3—22no—
539C3×Dic3—22no—
540C2×#41—31no—
541C2×#41—31no—
542C2×#41—92no—
543C2×#41—92no—
544C2×#41—92no—
545C2×#41—91no—
546C2×#41—92no—
547C2×#41—91no—
548C2×#41—92no—
549C2×#41—92no—
550C2×#41—188no—
551C2×#41—188no—
552C22×Q8—31no—
553C22×Q8—91no—
554C22×D4—31no—
555C22×D4—92no—
556C22×D4—92no—
557C22×D4—91no—
558C23×C4—92no—
559C23×C4—92no—
560C23×C4—91no—
561C4⋊Q8—32no—
562C4⋊Q8—92no—
563#127—32no—
564#127—92no—
565#124—32no—
566#124—32no—
567#124—92no—
568#124—92no—
569#123—34no—
570#123—98no—
571#123—94no—
572C22⋊Q8—34no—
573C22⋊Q8—98no—
574C22⋊Q8—94no—
575#121—34no—
576#121—98no—
577#121—98no—
578#121—98no—
579#121—94no—
580#120—34no—
581#120—98no—
582#120—94no—
583C4×D4—98no—
584C4×D4—98no—
585#117—91no—
586#117—92no—
587#117—92no—
588#117—92no—
589#117D3211yescharacteristic, complemented
590C2×C4⋊C4—92no—
591C2×C22⋊C4—92no—
592C2×C42—92no—
593C23×C3—21no—
594C23×C3—32no—
595C23×C3—34no—
596C23×C3—32no—
597C23×C3—64no—
598C23×C3—124no—
599C23×C3C23×D311yescharacteristic
600C23×C3C23×D311yescharacteristic
601C22×D3—24no—
602C22×D3—31no—
603C22×D3—31no—
604C22×D3—31no—
605C22×D3—31no—
606C22×D3—34no—
607C22×D3—34no—
608C22×D3—44no—
609C22×D3—61no—
610C22×D3—64no—
611C22×D3—61no—
612C22×D3—64no—
613C22×D3—64no—
614C22×D3—124no—
615C22×D3—124no—
616C22×D3—122no—
617C22×D3—122no—
618C22×D3—124no—
619C22×D3C23×D312yes—
620C22×D3C23×D314yes—
621C22×D3C23×D312yes—
622C3×Q8—62no—
623C3×Q8—62no—
624C3×Q8—64no—
625C3×Q8—64no—
626C3×D4—64no—
627C3×D4—64no—
628C3×D4—62no—
629C3×D4—62no—
630C3×D4—64no—
631C3×D4—64no—
632C3×D4—128no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—24no—
636C2×C3×C4—24no—
637C2×C3×C4—32no—
638C2×C3×C4—34no—
639C2×C3×C4—32no—
640C2×C3×C4—64no—
641C2×C3×C4—64no—
642C2×C3×C4—64no—
643C2×C3×C4D3×D414yes—
644C2×C3×C4D3×D414yes—
645C2×C3×C4C23×D314yes—
646C2×C3×C4C23×D314yes—
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651#67—24no—
652#67—24no—
653#67—64no—
654#67—64no—
655#67—68no—
656#67—68no—
657#67—64no—
658#67—64no—
659#67—128no—
660#67—128no—
661C2×Dic3—24no—
662C2×Dic3—34no—
663C2×Dic3—34no—
664C2×Dic3—31no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—31no—
668C2×Dic3—34no—
669C2×Dic3—34no—
670C2×Dic3—64no—
671C2×Dic3—61no—
672C2×Dic3—61no—
673C2×Dic3—64no—
674C2×Dic3—64no—
675C2×Dic3—64no—
676C2×Dic3—68no—
677C2×Dic3—68no—
678C2×Dic3C23×D312yes—
679C2×Dic3C23×D314yes—
680C2×Dic3C23×D312yes—
681D12—24no—
682D12—24no—
683D12—22no—
684D12—22no—
685D12—48no—
686D12—68no—
687D12—68no—
688D12—64no—
689D12—64no—
690C4×D3—24no—
691C4×D3—24no—
692C4×D3—34no—
693C4×D3—34no—
694C4×D3—34no—
695C4×D3—34no—
696C4×D3—34no—
697C4×D3—34no—
698C4×D3—34no—
699C4×D3—34no—
700C4×D3—64no—
701C4×D3—64no—
702C4×D3—64no—
703C4×D3—64no—
704C4×D3—64no—
705C4×D3—64no—
706C4×D3—64no—
707C4×D3—64no—
708C4×D3—68no—
709C4×D3—68no—
710C4×D3—124no—
711C4×D3—124no—
712C4×D3—128no—
713Dic6—24no—
714Dic6—24no—
715Dic6—22no—
716Dic6—22no—
717Dic6—64no—
718Dic6—64no—
719C2×C32—22no—
720C2×C32C23×D411yescharacteristic
721C2×C32#58512yes—
722C3⋊D3—22no—
723C3⋊D3—22no—
724C3×D3—42no—
725C3×D3—42no—
726C3×D3—44no—
727C24—32no—
728C24—92no—
729C24—91no—
730#41—64no—
731#41—64no—
732#41—188no—
733#41—188no—
734#41—188no—
735#41—188no—
736#41—188no—
737#41—188no—
738#41—184no—
739#41—184no—
740C2×Q8—32no—
741C2×Q8—31no—
742C2×Q8—32no—
743C2×Q8—31no—
744C2×Q8—64no—
745C2×Q8—92no—
746C2×Q8—184no—
747C2×D4—32no—
748C2×D4—32no—
749C2×D4—32no—
750C2×D4—31no—
751C2×D4—32no—
752C2×D4—31no—
753C2×D4—38no—
754C2×D4—64no—
755C2×D4—94no—
756C2×D4—92no—
757C2×D4—94no—
758C2×D4—92no—
759C2×D4—92no—
760C2×D4—98no—
761C2×D4—188no—
762C2×D4—184no—
763C2×D4—188no—
764C22×C4—32no—
765C22×C4—32no—
766C22×C4—32no—
767C22×C4—92no—
768C22×C4—92no—
769C22×C4—94no—
770C22×C4—92no—
771C22×C4—94no—
772C22×C4—91no—
773C22×C4—91no—
774C22×C4—91no—
775C22×C4—91no—
776C22×C4—91no—
777C22×C4—98no—
778C22×C4—94no—
779C22×C4—188no—
780C22×C4—188no—
781C22×C4C2×D3211yescharacteristic
782C4⋊C4—38no—
783C4⋊C4—98no—
784C4⋊C4—94no—
785C4⋊C4—92no—
786C4⋊C4C2×D3212yes—
787C22⋊C4—38no—
788C22⋊C4—38no—
789C22⋊C4—98no—
790C22⋊C4—98no—
791C22⋊C4—92no—
792C22⋊C4—94no—
793C22⋊C4C2×D3212yes—
794C42—94no—
795C42—92no—
796C42C2×D3212yes—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—21no—
801C22×C3—42no—
802C22×C3—64no—
803C22×C3—62no—
804C22×C3—62no—
805C22×C3—64no—
806C22×C3—68no—
807C22×C3—64no—
808C22×C3—128no—
809C22×C3C2×D3×D412yes—
810C22×C3C2×D3×D412yes—
811C22×C3C24×D311yescharacteristic
812C22×C3C24×D311yescharacteristic
813C2×D3—22no—
814C2×D3—22no—
815C2×D3—24no—
816C2×D3—24no—
817C2×D3—28no—
818C2×D3—24no—
819C2×D3—32no—
820C2×D3—32no—
821C2×D3—32no—
822C2×D3—32no—
823C2×D3—48no—
824C2×D3—62no—
825C2×D3—62no—
826C2×D3—64no—
827C2×D3—62no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—62no—
831C2×D3—122no—
832C2×D3—128no—
833C2×D3—128no—
834C2×D3—124no—
835C2×D3—124no—
836C2×D3—128no—
837C3×C4—24no—
838C3×C4—24no—
839C3×C4—22no—
840C3×C4—22no—
841C3×C4—44no—
842C3×C4—62no—
843C3×C4—62no—
844C3×C4—64no—
845C3×C4C2×D3×D412yes—
846C3×C4C2×D3×D412yes—
847C3×C4C2×D3×D412yes—
848C3×C4C2×D3×D412yes—
849Dic3—24no—
850Dic3—22no—
851Dic3—22no—
852Dic3—32no—
853Dic3—32no—
854Dic3—32no—
855Dic3—32no—
856Dic3—62no—
857Dic3—62no—
858Dic3—64no—
859Dic3—64no—
860Dic3—124no—
861C32#344911yescharacteristic, complemented, Sylow
862C23—32no—
863C23—34no—
864C23—32no—
865C23—64no—
866C23—91no—
867C23—91no—
868C23—94no—
869C23—124no—
870C23—184no—
871C23—362no—
872C23—364no—
873C23C22×D3211yescharacteristic
874Q8—64no—
875Q8—64no—
876Q8—62no—
877Q8—62no—
878Q8—184no—
879D4—64no—
880D4—64no—
881D4—64no—
882D4—64no—
883D4—62no—
884D4—62no—
885D4—128no—
886D4—184no—
887D4—184no—
888D4—188no—
889D4—188no—
890D4—184no—
891D4—368no—
892C2×C4—32no—
893C2×C4—34no—
894C2×C4—32no—
895C2×C4—64no—
896C2×C4—64no—
897C2×C4—64no—
898C2×C4—94no—
899C2×C4—91no—
900C2×C4—91no—
901C2×C4—94no—
902C2×C4—94no—
903C2×C4—94no—
904C2×C4—94no—
905C2×C4—94no—
906C2×C4—184no—
907C2×C4—184no—
908C2×C4—184no—
909C2×C4—188no—
910C2×C4—188no—
911C2×C4—364no—
912C2×C4#380214yes—
913C2×C4C22×D3214yes—
914C2×C4C22×D3211yescharacteristic
915C2×C4C22×D3211yescharacteristic
916C2×C3—22no—
917C2×C3—22no—
918C2×C3—21no—
919C2×C3—22no—
920C2×C3—42no—
921C2×C3—122no—
922C2×C3—122no—
923C2×C3—124no—
924C2×C3C22×D3×D411yescharacteristic
925C2×C3C22×D3×D411yescharacteristic
926C2×C3#596612yes—
927C2×C3#596812yes—
928D3—44no—
929D3—42no—
930D3—42no—
931D3—64no—
932D3—62no—
933D3—62no—
934D3—62no—
935D3—62no—
936D3—122no—
937C22—22no—
938C22—62no—
939C22—62no—
940C22—64no—
941C22—64no—
942C22—68no—
943C22—64no—
944C22—92no—
945C22—92no—
946C22—128no—
947C22—182no—
948C22—182no—
949C22—364no—
950C22—368no—
951C22C2×#380212yes—
952C22C23×D3211yescharacteristic
953C4—24no—
954C4—62no—
955C4—62no—
956C4—64no—
957C4—92no—
958C4—92no—
959C4—184no—
960C4C2×#380212yes—
961C4C2×#380212yes—
962C3—21no—
963C3#8631311yescharacteristic, complemented
964C3#8633811yescharacteristic, complemented
965C2—22no—
966C2—124no—
967C2—122no—
968C2—122no—
969C2—182no—
970C2—182no—
971C2C22×#380211yescharacteristic
972C2#1059669812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3449
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64306C2semidirect
2. C22×#3796C2semidirect
3. C3⋊D3×#117C2semidirect
4. C3×#5526C2semidirect
5. C3×#5525C2semidirect
6. #10595040C2semidirect
7. #10594855C2semidirect
8. #10594632C2semidirect
9. #10594528C2semidirect
10. #10594296C2semidirect
11. #10594082C2semidirect
12. #10594010C2semidirect
13. #10593971C2semidirect
14. #10593908C2semidirect
15. #10593907C2semidirect
21. C22×C3×D12C22semidirect
22. C22×C3×Dic6C22semidirect
26. C22×D3×Dic3C22semidirect
28. C2×#3802C22semidirect
29. C2×C4×D32C22semidirect
30. C2×#3798C22semidirect
31. C2×#3797C22semidirect
35. C2×#3796C22semidirect
36. C2×#3796C22semidirect
37. C2×#3796C22semidirect
38. C2×#3796C22semidirect
39. C32×#117C22semidirect
40. #64135C22semidirect
41. #64101C22semidirect
42. C4⋊C4×C3⋊D3C22semidirect
44. #64086C22semidirect
45. #64081C22semidirect
46. C42×C3⋊D3C22semidirect
47. C3×#897C22semidirect
48. C3×#895C22semidirect
49. C3×#886C22semidirect
50. C3×#882C22semidirect
51. C3×#875C22semidirect
52. C3×#875C22semidirect
53. C3×#874C22semidirect
54. C3×#869C22semidirect
55. #63976C22semidirect
56. #63961C22semidirect
57. #63922C22semidirect
58. #63916C22semidirect
59. #63914C22semidirect
60. #63912C22semidirect
61. #63908C22semidirect
62. #63902C22semidirect
63. #63899C22semidirect
64. #63898C22semidirect
65. #63885C22semidirect
66. #63873C22semidirect
67. #63863C22semidirect
68. #63863C22semidirect
69. #63856C22semidirect
70. #63854C22semidirect
97. #5526D3semidirect
98. #5525D3semidirect
107. C2×C4×C3⋊D3D4semidirect
208. C22×D12C2×D3semidirect
215. C22×Dic6C2×D3semidirect
225. C3×#117C2×D3semidirect
226. C3×#117C2×D3semidirect
250. #897C2×D3semidirect
253. #895C2×D3semidirect
262. #886C2×D3semidirect
268. #882C2×D3semidirect
278. #875C2×D3semidirect
279. #875C2×D3semidirect
280. #874C2×D3semidirect
287. #869C2×D3semidirect
589. #117D32semidirect
861. C32#3449semidirect
963. C3#86313semidirect
964. C3#86338semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C22×#37962
C3⋊D3×#1172
C3×#55262
C3×#55252
#105950402
#105948552
#105946322
#105945282
#105942962
#105940822
#105940102
#105939712
#105939082
#105939072
#863383
#863133