Finite Group Databasebeta

← #11900893

Subgroups — #11900893

Order 1152.

2589 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595995C211yesmaximal, characteristic, complemented
2C3×#5522C211yesmaximal, characteristic, complemented
3C3×#5517C211yesmaximal, characteristic, complemented
4#10595034C211yesmaximal, characteristic, complemented
5#10595029C211yesmaximal, characteristic, complemented
6#10594954C211yesmaximal, characteristic, complemented
7C2×C4×#624C211yesmaximal, characteristic, complemented
8#10594518C212yesmaximal, complemented
9#10594464C212yesmaximal, complemented
10#10594447C212yesmaximal, complemented
11#10594397C212yesmaximal, complemented
12#10594216C214yesmaximal, complemented
13#10594066C214yesmaximal, complemented
14C4×#3799C214yesmaximal, complemented
15#10593934C214yesmaximal, complemented
16#86257—31nomaximal
17#85836—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C22×#624C2212yes—
22C2×#3799C2214yes—
23C32×#117C2211yescharacteristic
24#64106C2212yes—
25#64104C2212yes—
26#64095C2212yes—
27#64091C2212yes—
28C4×C4⋊(C3⋊D3)C2214yes—
29C3×#926C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#893C2212yescomplemented
33C3×#890C2212yescomplemented
34C3×#888C2212yescomplemented
35C3×#887C2212yescomplemented
36C3×#67⋊C4C2214yes—
37C3×#878C2214yes—
38C3×#872C2212yescomplemented
39C3×C42×D3C2212yescomplemented
40C3×C4×Dic6C2214yescomplemented
41#63981C2212yes—
42#63978C2214yes—
43#63962C2212yes—
44C2×Dic32C2212yes—
45#63952C2214yes—
46#63916C2212yes—
47#63911C2211yescharacteristic, complemented
48#63910C2214yes—
49#63907C2214yescomplemented
50#63904C2214yes—
51#63904C2214yescomplemented
52C4×#626C2214yes—
53C4×#626C2214yescomplemented
54#63897C2214yes—
55#63894C2214yes—
56#63894C2212yescomplemented
57#63888C2214yes—
58C4×#624C2212yes—
59C4×#624C2212yes—
60C4×#624C2212yes—
61C4×#624C2212yes—
62C4×#624C2212yescomplemented
63#63874C2212yescomplemented
64#63871C2212yes—
65#63866C2211yescharacteristic, complemented
66#63864C2211yescharacteristic, complemented
67#63861C2214yescomplemented
68#63860C2211yescharacteristic, complemented
69#63854C2214yes—
70#63848C2214yescomplemented
71#63845C2214yescomplemented
72#63844C2212yescomplemented
73Dic3×Dic6C2214yescomplemented
74#63841C2214yescomplemented
75#63836C2214yes—
76#63836C2214yescomplemented
77C3×#533—31no—
78C3×C4×#41—31no—
79#5832—31no—
80#5828—31no—
81#5728—32no—
82#5725—32no—
83#5691—32no—
84#5691—32no—
85#5627—34no—
86#5624—34no—
87#5580—32no—
88#5580—34no—
89#5578—32no—
90C4×#239—34no—
91#5557—32no—
92#5548—32no—
93#5547—34no—
94#5538—34no—
95#5528—34no—
96#5524—31no—
97#5524—31no—
98#5524—31no—
99#5524—61no—
100#5522—31no—
101#5522D311yescharacteristic, complemented
102#5517D311yescharacteristic, complemented
103#5477—31no—
104C4×#235—31no—
105C4×#235—34no—
106C2×C42×D3—31no—
107C2×C42×D3—31no—
108C23×C3⋊D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C2×#638C2312yes—
111C22×C3⋊Dic3C2311yescharacteristic
112#3828—24no—
113C2×C4⋊(C3⋊D3)C2314yes—
114C2×C4⋊(C3⋊D3)C2311yescharacteristic
115C2×C4×C3⋊D3—24no—
116C2×C4×C3⋊D3C2312yes—
117C2×C4×C3⋊D3C2312yes—
118C2×C4×C3⋊D3C2312yes—
119C2×#634C2311yescharacteristic
120C2×C3×#67C2312yes—
121C22×C3×Dic3C2312yes—
122C22×C3×Dic3C2312yes—
123C3×#235—24no—
124C2×C3×D12C2311yescharacteristic
125C2×C3×C4×D3C2314yes—
126C2×C3×C4×D3C2312yes—
127C2×C3×Dic6C2314yes—
128C2×C3×Dic6C2311yescharacteristic
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#624—28no—
132C2×#624C2314yes—
133C2×#624C2312yes—
134C2×#624C2312yes—
135C2×#624C2312yes—
136C2×#624C2312yes—
137#3799—216no—
138C32×C4⋊C4C2312yes—
139C32×C22⋊C4C2312yes—
140C32×C42C2312yes—
141#3752C2314yes—
142#3752C2314yes—
143C4⋊(C3⋊Dic3)C2314yes—
144C3×#217C2312yes—
145C3×(C2×D3)⋊C4C2314yes—
146C3×C4⋊Dic3C2314yes—
147C3×C4⋊Dic3C2312yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2314yes—
150C3×Dic3⋊C4C2314yes—
151C3×C4×Dic3C2314yes—
152C3×C4×Dic3C2312yes—
153C3×C4×Dic3C2311yescharacteristic
154C3×C4×Dic3C2311yescharacteristic
155C3×C4×Dic3C2311yescharacteristic
156C3×C4×Dic3C2311yescharacteristic
157C3×C4×Dic3C2312yes—
158C3×C4×Dic3C2312yes—
159#3724C2314yes—
160Dic3⋊Dic3C2314yes—
161Dic3⋊Dic3C2314yes—
162#3722C2314yes—
163#3722C2314yes—
164#3722C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167Dic32C2314yes—
168Dic32C2312yes—
169Dic32C2312yes—
170Dic32C2312yes—
171Dic32C2312yes—
172#3444—91noSylow
173C2×C3×#41—31no—
174C2×#239—34no—
175C2×#235—31no—
176C2×#235—31no—
177C2×#235—34no—
178C2×#235—61no—
179C2×#235C2×D311yescharacteristic
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—32no—
183C22×C4×D3—32no—
184C22×C4×D3—61no—
185C3×C4⋊Q8—32no—
186C3×#125—32no—
187C3×C22⋊Q8—34no—
188C3×C4×Q8—32no—
189C3×C4×Q8—34no—
190C3×C4×D4—32no—
191C3×C4×D4—34no—
192C3×#117—21no—
193C3×#117—31no—
194C3×#117—32no—
195C3×#117C2×D311yescharacteristic
196C3×#117C2×D311yescharacteristic
197C2×C3×C42—31no—
198C2×C3×C42—31no—
199C2×C3×C42—32no—
200#947—34no—
201#947—31no—
202#946—32no—
203#946—34no—
204Q8×Dic3—34no—
205#944—31no—
206#940—31no—
207#939—34no—
208#938—32no—
209#937—32no—
210#936—31no—
211#935—32no—
212#930—34no—
213C4×#67—34no—
214C4×#67—34no—
215C4×#67—34no—
216C4×#67—34no—
217C4×#67—34no—
218#926—34no—
219#926C2×D311yescharacteristic
220C2×C4×Dic3—32no—
221C2×C4×Dic3—32no—
222C2×C4×Dic3C2×D311yescharacteristic
223C2×C4×Dic3C2×D311yescharacteristic
224#898—34no—
225#898—34no—
226#898—34no—
227#897—32no—
228#897—32no—
229#897—32no—
230#897—62no—
231#896—34no—
232#895—32no—
233#895—32no—
234#895—32no—
235#895—34no—
236#895—62no—
237#894—34no—
238#894—34no—
239#894—34no—
240#893—34no—
241#893—34no—
242#893—32no—
243#893—34no—
244#893C2×D312yescomplemented
245#892—34no—
246#892—34no—
247#892—34no—
248#890—34no—
249#890C2×D312yescomplemented
250#889—34no—
251#888C2×D312yescomplemented
252#887—32no—
253#887C2×D312yescomplemented
254#886—32no—
255#886—32no—
256#886—32no—
257#886—62no—
258#885—34no—
259#884—34no—
260#883—34no—
261#882—32no—
262#882—32no—
263#882—32no—
264#882—62no—
265#67⋊C4—34no—
266#67⋊C4C2×D314yes—
267#879—34no—
268#878C2×D314yes—
269#875—31no—
270#875—31no—
271#874—31no—
272C4×D12—34no—
273C4×D12—34no—
274C4×D12—34no—
275C4×D12—34no—
276C4×D12—34no—
277C4×D12—32no—
278C4×D12—64no—
279#872—34no—
280#872—34no—
281#872—32no—
282#872—32no—
283#872C2×D312yescomplemented
284C42×D3—32no—
285C42×D3—32no—
286C42×D3—32no—
287C42×D3—32no—
288C42×D3—32no—
289C42×D3—32no—
290C42×D3—32no—
291C42×D3—32no—
292C42×D3—32no—
293C42×D3—32no—
294C42×D3C2×D312yescomplemented
295#869—31no—
296C4×Dic6—34no—
297C4×Dic6—32no—
298C4×Dic6C2×D314yescomplemented
299C23×C32C2411yescharacteristic
300C22×C3⋊D3—22no—
301C22×C3⋊D3—24no—
302C22×C3⋊D3C2412yes—
303C22×C3⋊D3C2412yes—
304C22×C3×D3C2412yes—
305C2×C32×C4#4114yescomplemented
306C2×C32×C4C2414yes—
307C2×C32×C4C2411yescharacteristic
308C2×C32×C4C2411yescharacteristic
309#638—24no—
310C2×C3⋊Dic3—22no—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C4⋊(C3⋊D3)—28no—
314C4⋊(C3⋊D3)—22no—
315C4×C3⋊D3—24no—
316C4×C3⋊D3—24no—
317C4×C3⋊D3—24no—
318#634—22no—
319C3×#67—24no—
320C2×C3×Dic3—24no—
321C2×C3×Dic3—24no—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2414yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2412yes—
328C3×D12—22no—
329C3×C4×D3—24no—
330C3×C4×D3—28no—
331C3×Dic6—22no—
332C3×Dic6—28no—
333#626—28no—
334#626—28no—
335#624—24no—
336#624—28no—
337#624—24no—
338#624—24no—
339#624#4118yescomplemented
340#533—31no—
341#533—92no—
342#532—91no—
343#532—92no—
344#529—94no—
345#529—94no—
346#529—92no—
347#529—92no—
348#525—91no—
349#525—94no—
350#525—91no—
351C4×#41—31no—
352C4×#41—91no—
353C4×#41—94no—
354C22×C42—91no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—61no—
358C3×#41—64no—
359C2×C3×Q8—31no—
360C2×C3×Q8—34no—
361C2×C3×D4—32no—
362C2×C3×D4—31no—
363C22×C3×C4—21no—
364C22×C3×C4—32no—
365C22×C3×C4—32no—
366C22×C3×C4—34no—
367C22×C3×C4—32no—
368C22×C3×C4C22×D311yescharacteristic
369C22×C3×C4C22×D311yescharacteristic
370C2×#67—32no—
371C2×#67—32no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—62no—
375C2×#67C22×D312yes—
376C22×Dic3—31no—
377C22×Dic3—31no—
378C22×Dic3—61no—
379C22×Dic3C22×D312yes—
380C22×Dic3C22×D312yes—
381#239—616no—
382#235—24no—
383#235—616no—
384#235—64no—
385#235—64no—
386#235—124no—
387C2×D12—34no—
388C2×D12—34no—
389C2×D12—34no—
390C2×D12—31no—
391C2×D12—34no—
392C2×D12—31no—
393C2×D12—64no—
394C2×D12—61no—
395C2×D12C22×D311yescharacteristic
396C2×C4×D3—32no—
397C2×C4×D3—32no—
398C2×C4×D3—32no—
399C2×C4×D3—32no—
400C2×C4×D3—32no—
401C2×C4×D3—32no—
402C2×C4×D3—32no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—62no—
413C2×C4×D3—62no—
414C2×C4×D3—62no—
415C2×C4×D3—68no—
416C2×C4×D3—68no—
417C2×C4×D3—64no—
418C2×C4×D3—64no—
419C2×C4×D3—124no—
420C2×C4×D3C22×D312yes—
421C2×C4×D3C22×D314yes—
422C2×Dic6—31no—
423C2×Dic6—31no—
424C2×Dic6—61no—
425C2×Dic6C22×D314yes—
426C2×Dic6C22×D311yescharacteristic
427C3×C4⋊C4—22no—
428C3×C4⋊C4—32no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4C22×D312yes—
434C3×C4⋊C4C22×D312yes—
435C3×C22⋊C4—22no—
436C3×C22⋊C4—32no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4C22×D312yes—
439C3×C22⋊C4C22×D312yes—
440C3×C42—22no—
441C3×C42—32no—
442C3×C42—34no—
443C3×C42—31no—
444C3×C42—31no—
445C3×C42—31no—
446C3×C42—32no—
447C3×C42—31no—
448C3×C42—32no—
449C3×C42C22×D312yes—
450C3×C42C22×D312yes—
451#217—34no—
452#217—34no—
453#217C22×D312yes—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—34no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4—34no—
466(C2×D3)⋊C4—64no—
467(C2×D3)⋊C4—64no—
468(C2×D3)⋊C4C22×D314yes—
469C4⋊Dic3—34no—
470C4⋊Dic3—34no—
471C4⋊Dic3—34no—
472C4⋊Dic3—34no—
473C4⋊Dic3—64no—
474C4⋊Dic3C22×D312yes—
475C4⋊Dic3C22×D314yes—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4—34no—
479Dic3⋊C4—34no—
480Dic3⋊C4C22×D314yes—
481Dic3⋊C4C22×D314yes—
482Dic3⋊C4C22×D314yes—
483C4×Dic3—32no—
484C4×Dic3—34no—
485C4×Dic3—32no—
486C4×Dic3—32no—
487C4×Dic3—32no—
488C4×Dic3—32no—
489C4×Dic3—32no—
490C4×Dic3—32no—
491C4×Dic3—32no—
492C4×Dic3—34no—
493C4×Dic3C22×D312yes—
494C4×Dic3C22×D312yes—
495C4×Dic3C22×D311yescharacteristic
496C4×Dic3C22×D311yescharacteristic
497C4×Dic3C22×D312yes—
498C4×Dic3C22×D311yescharacteristic
499C4×Dic3C22×D311yescharacteristic
500C4×Dic3C22×D314yes—
501C22×C32—22no—
502C22×C32C2×#4112yes—
503C22×C32C2511yescharacteristic
504C2×C3⋊D3—28no—
505C2×C3⋊D3—22no—
506C2×C3⋊D3—22no—
507C2×C3⋊D3—24no—
508C2×C3⋊D3—22no—
509C2×C3⋊D3C2×#4114yes—
510C2×C3×D3—24no—
511C2×C3×D3—22no—
512C32×C4—24no—
513C32×C4C2×#4112yes—
514C32×C4C2×#4112yes—
515C3⋊Dic3—22no—
516C3⋊Dic3—22no—
517C3×Dic3—22no—
518C3×Dic3—22no—
519C3×Dic3—24no—
520C3×Dic3—22no—
521C3×Dic3C2×#4114yes—
522C3×Dic3C2×#4114yes—
523C2×#41—31no—
524C2×#41—94no—
525C2×#41—91no—
526C23×C4—92no—
527C23×C4—91no—
528C4⋊Q8—32no—
529C4⋊Q8—91no—
530#127—91no—
531#126—94no—
532#126—94no—
533#125—32no—
534#125—94no—
535#124—91no—
536#124—91no—
537#124—94no—
538#123—94no—
539#123—92no—
540#123—94no—
541#123—92no—
542C22⋊Q8—34no—
543C22⋊Q8—94no—
544C22⋊Q8—92no—
545C22⋊Q8—92no—
546#121—94no—
547#121—92no—
548#121—94no—
549#121—92no—
550#120—92no—
551#120—92no—
552C4×Q8—32no—
553C4×Q8—34no—
554C4×Q8—92no—
555C4×Q8—94no—
556C4×D4—32no—
557C4×D4—34no—
558C4×D4—94no—
559C4×D4—92no—
560C4×D4—94no—
561C4×D4—94no—
562C4×D4—94no—
563C4×D4—94no—
564C4×D4—94no—
565C4×D4—94no—
566#117—31no—
567#117—32no—
568#117—92no—
569#117—94no—
570#117—94no—
571#117—94no—
572#117D3211yescharacteristic
573C2×C42—31no—
574C2×C42—31no—
575C2×C42—32no—
576C2×C42—92no—
577C2×C42—92no—
578C2×C42—92no—
579C2×C42—92no—
580C2×C42—92no—
581C2×C42—92no—
582C23×C3—21no—
583C23×C3—32no—
584C23×C3C23×D311yescharacteristic
585C23×C3C23×D311yescharacteristic
586C22×D3—32no—
587C22×D3—32no—
588C22×D3—32no—
589C22×D3—32no—
590C22×D3—62no—
591C22×D3—62no—
592C22×D3—64no—
593C22×D3—64no—
594C22×D3—62no—
595C22×D3—62no—
596C22×D3—124no—
597C22×D3—122no—
598C22×D3C23×D312yes—
599C3×Q8—68no—
600C3×Q8—62no—
601C3×D4—64no—
602C3×D4—62no—
603C2×C3×C4—21no—
604C2×C3×C4—24no—
605C2×C3×C4—21no—
606C2×C3×C4—24no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—32no—
611C2×C3×C4—34no—
612C2×C3×C4—32no—
613C2×C3×C4—68no—
614C2×C3×C4—64no—
615C2×C3×C4—64no—
616C2×C3×C4—64no—
617C2×C3×C4#23514yescomplemented
618C2×C3×C4#23914yescomplemented
619C2×C3×C4C23×D314yes—
620C2×C3×C4C23×D314yes—
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D311yescharacteristic
623C2×C3×C4C23×D311yescharacteristic
624C2×C3×C4C23×D311yescharacteristic
625#67—24no—
626#67—68no—
627#67—64no—
628#67—64no—
629#67—68no—
630#67—124no—
631C2×Dic3—24no—
632C2×Dic3—24no—
633C2×Dic3—32no—
634C2×Dic3—32no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—62no—
640C2×Dic3—62no—
641C2×Dic3—122no—
642C2×Dic3C23×D312yes—
643C2×Dic3C23×D312yes—
644C2×Dic3C23×D314yes—
645C2×Dic3C23×D312yes—
646C2×Dic3C23×D312yes—
647C2×Dic3C23×D312yes—
648D12—22no—
649D12—68no—
650D12—68no—
651D12—68no—
652D12—68no—
653D12—62no—
654D12—62no—
655D12—122no—
656D12—128no—
657C4×D3—24no—
658C4×D3—28no—
659C4×D3—38no—
660C4×D3—38no—
661C4×D3—64no—
662C4×D3—64no—
663C4×D3—68no—
664C4×D3—64no—
665C4×D3—64no—
666C4×D3—64no—
667C4×D3—64no—
668C4×D3—64no—
669C4×D3—64no—
670C4×D3—64no—
671C4×D3—64no—
672C4×D3—64no—
673C4×D3—64no—
674C4×D3—68no—
675C4×D3—124no—
676C4×D3—124no—
677C4×D3—124no—
678Dic6—22no—
679Dic6—28no—
680Dic6—62no—
681Dic6—62no—
682Dic6—122no—
683C2×C32—22no—
684C2×C32C22×#4111yescharacteristic
685C2×C32C22×#4112yes—
686C3⋊D3—24no—
687C3⋊D3—42no—
688C3×D3—42no—
689C24—91no—
690#41—64no—
691#41—1816no—
692#41—184no—
693C2×Q8—31no—
694C2×Q8—34no—
695C2×Q8—91no—
696C2×D4—32no—
697C2×D4—31no—
698C2×D4—94no—
699C2×D4—94no—
700C2×D4—92no—
701C2×D4—94no—
702C2×D4—91no—
703C22×C4—32no—
704C22×C4—32no—
705C22×C4—34no—
706C22×C4—32no—
707C22×C4—92no—
708C22×C4—92no—
709C22×C4—92no—
710C22×C4—92no—
711C22×C4—94no—
712C22×C4—91no—
713C22×C4—92no—
714C22×C4—92no—
715C22×C4—92no—
716C22×C4—188no—
717C22×C4—184no—
718C22×C4C2×D3211yescharacteristic
719C4⋊C4—34no—
720C4⋊C4—32no—
721C4⋊C4—34no—
722C4⋊C4—34no—
723C4⋊C4—34no—
724C4⋊C4—94no—
725C4⋊C4—94no—
726C4⋊C4—94no—
727C4⋊C4—94no—
728C4⋊C4C2×D3212yes—
729C22⋊C4—32no—
730C22⋊C4—34no—
731C22⋊C4—94no—
732C22⋊C4—94no—
733C22⋊C4—94no—
734C22⋊C4—94no—
735C22⋊C4—94no—
736C22⋊C4—94no—
737C22⋊C4—94no—
738C22⋊C4C2×D3212yes—
739C42—32no—
740C42—31no—
741C42—31no—
742C42—34no—
743C42—31no—
744C42—31no—
745C42—32no—
746C42—32no—
747C42—92no—
748C42—92no—
749C42—92no—
750C42—92no—
751C42—94no—
752C42C2×D3212yes—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—21no—
757C22×C3—42no—
758C22×C3—62no—
759C22×C3—64no—
760C22×C3C2×#23512yes—
761C22×C3C2×#23912yes—
762C22×C3C24×D311yescharacteristic
763C22×C3C24×D311yescharacteristic
764C2×D3—22no—
765C2×D3—24no—
766C2×D3—34no—
767C2×D3—34no—
768C2×D3—64no—
769C2×D3—68no—
770C2×D3—68no—
771C2×D3—62no—
772C2×D3—62no—
773C2×D3—62no—
774C2×D3—62no—
775C2×D3—62no—
776C2×D3—62no—
777C2×D3—64no—
778C2×D3—64no—
779C2×D3—122no—
780C2×D3—122no—
781C2×D3—128no—
782C2×D3—122no—
783C2×D3—124no—
784C3×C4—24no—
785C3×C4—24no—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—34no—
789C3×C4—34no—
790C3×C4—44no—
791C3×C4—62no—
792C3×C4—62no—
793C3×C4—62no—
794C3×C4—64no—
795C3×C4C2×#23512yes—
796C3×C4C2×#23512yes—
797C3×C4C2×#23912yes—
798C3×C4C2×#23912yes—
799Dic3—22no—
800Dic3—24no—
801Dic3—22no—
802Dic3—22no—
803Dic3—62no—
804Dic3—62no—
805Dic3—62no—
806Dic3—62no—
807Dic3—122no—
808Dic3—122no—
809Dic3D3×#4114yes—
810Dic3D3×#4114yes—
811C32#344411yescharacteristic, complemented, Sylow
812C23—32no—
813C23—92no—
814C23—92no—
815C23—184no—
816C23—182no—
817C23C22×D3211yescharacteristic
818Q8—68no—
819Q8—62no—
820Q8—182no—
821D4—64no—
822D4—62no—
823D4—188no—
824D4—188no—
825D4—188no—
826D4—184no—
827D4—182no—
828C2×C4—32no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—34no—
834C2×C4—68no—
835C2×C4—64no—
836C2×C4—64no—
837C2×C4—64no—
838C2×C4—98no—
839C2×C4—92no—
840C2×C4—92no—
841C2×C4—184no—
842C2×C4—184no—
843C2×C4—188no—
844C2×C4—184no—
845C2×C4—182no—
846C2×C4—184no—
847C2×C4—184no—
848C2×C4—184no—
849C2×C4#379914yescomplemented
850C2×C4C22×D3214yes—
851C2×C4C22×D3211yescharacteristic
852C2×C4C22×D3211yescharacteristic
853C2×C3—22no—
854C2×C3—22no—
855C2×C3—21no—
856C2×C3—22no—
857C2×C3—42no—
858C2×C3—122no—
859C2×C3C22×#23511yescharacteristic
860C2×C3C22×#23911yescharacteristic
861C2×C3C2×D3×#4112yes—
862C2×C3C2×D3×#4112yes—
863D3—42no—
864D3—64no—
865D3—64no—
866D3—124no—
867D3—122no—
868D3—122no—
869D3—242no—
870C22—22no—
871C22—62no—
872C22—64no—
873C22—94no—
874C22—188no—
875C22—182no—
876C22—182no—
877C22—182no—
878C22—184no—
879C22C2×#379912yes—
880C22C23×D3211yescharacteristic
881C4—24no—
882C4—34no—
883C4—34no—
884C4—62no—
885C4—62no—
886C4—62no—
887C4—64no—
888C4—182no—
889C4—182no—
890C4C2×#379912yes—
891C4C2×#379912yes—
892C3—21no—
893C3#8583611yescharacteristic, complemented
894C3#8625711yescharacteristic, complemented
895C2—22no—
896C2—122no—
897C2—184no—
898C2—362no—
899C2C22×#379911yescharacteristic
900C2D32×#4112yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595995C2semidirect
2. C3×#5522C2semidirect
3. C3×#5517C2semidirect
4. #10595034C2semidirect
5. #10595029C2semidirect
6. #10594954C2semidirect
7. C2×C4×#624C2semidirect
8. #10594518C2semidirect
9. #10594464C2semidirect
10. #10594447C2semidirect
11. #10594397C2semidirect
12. #10594216C2semidirect
13. #10594066C2semidirect
14. C4×#3799C2semidirect
15. #10593934C2semidirect
32. C3×#893C22semidirect
33. C3×#890C22semidirect
34. C3×#888C22semidirect
35. C3×#887C22semidirect
38. C3×#872C22semidirect
39. C3×C42×D3C22semidirect
40. C3×C4×Dic6C22semidirect
47. #63911C22semidirect
49. #63907C22semidirect
51. #63904C22semidirect
53. C4×#626C22semidirect
56. #63894C22semidirect
62. C4×#624C22semidirect
63. #63874C22semidirect
65. #63866C22semidirect
66. #63864C22semidirect
67. #63861C22semidirect
68. #63860C22semidirect
70. #63848C22semidirect
71. #63845C22semidirect
72. #63844C22semidirect
73. Dic3×Dic6C22semidirect
74. #63841C22semidirect
76. #63836C22semidirect
101. #5522D3semidirect
102. #5517D3semidirect
244. #893C2×D3semidirect
249. #890C2×D3semidirect
251. #888C2×D3semidirect
253. #887C2×D3semidirect
283. #872C2×D3semidirect
294. C42×D3C2×D3semidirect
298. C4×Dic6C2×D3semidirect
305. C2×C32×C4#41semidirect
339. #624#41semidirect
617. C2×C3×C4#235semidirect
618. C2×C3×C4#239semidirect
811. C32#3444semidirect
849. C2×C4#3799semidirect
893. C3#85836semidirect
894. C3#86257semidirect

Maximal subgroups

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

subgroupindex
#105959952
C3×#55222
C3×#55172
#105950342
#105950292
#105949542
C2×C4×#6242
#105945182
#105944642
#105944472
#105943972
#105942162
#105940662
C4×#37992
#105939342
#862573
#858363