Finite Group Databasebeta

← #11900894

Subgroups — #11900894

Order 1152.

2579 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic, complemented
2C3×#5524C211yesmaximal, characteristic, complemented
3C3×#5517C211yesmaximal, characteristic, complemented
4#10595029C211yesmaximal, characteristic, complemented
5#10595023C211yesmaximal, characteristic, complemented
6#10594958C211yesmaximal, characteristic, complemented
7C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
8#10594453C212yesmaximal, complemented
9#10594427C212yesmaximal, complemented
10#10594387C212yesmaximal, complemented
11#10594369C212yesmaximal, complemented
12#10594144C214yesmaximal, complemented
13#10594055C214yesmaximal, complemented
14#10593911C214yesmaximal, complemented
15C4×#3796C214yesmaximal, complemented
16#86257—31nomaximal
17#86018—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2212yes—
22C2×#3796C2214yes—
23C32×#117C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25#64102C2212yescomplemented
26#64096C2212yescomplemented
27#64090C2214yes—
28#64081C2212yescomplemented
29C42×C3⋊D3C2212yescomplemented
30C3×#926C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C3×#897C2212yes—
33C3×#895C2212yes—
34C3×#890C2212yescomplemented
35C3×#888C2212yescomplemented
36C3×#886C2212yes—
37C3×#882C2212yes—
38C3×#878C2214yes—
39C3×C4×D12C2214yes—
40C3×C4×Dic6C2214yescomplemented
41#63978C2214yes—
42#63977C2212yes—
43#67⋊Dic3C2214yes—
44#63966C2212yes—
45C2×Dic32C2212yes—
46#63911C2211yescharacteristic, complemented
47#63909C2212yes—
48#63907C2214yescomplemented
49C4×#626C2214yes—
50C4×#626C2214yescomplemented
51#63898C2214yes—
52#63898C2212yescomplemented
53#63890C2214yes—
54#63887C2214yes—
55#63886C2214yes—
56#63884C2214yes—
57#63881C2214yes—
58#63881C2214yescomplemented
59#63878C2214yes—
60#63878C2214yescomplemented
61C4×D3×Dic3C2212yes—
62C4×D3×Dic3C2212yes—
63C4×D3×Dic3C2212yes—
64C4×D3×Dic3C2212yes—
65C4×D3×Dic3C2212yescomplemented
66#63866C2211yescharacteristic, complemented
67#63864C2211yescharacteristic, complemented
68#63860C2211yescharacteristic, complemented
69#63858C2214yescomplemented
70#63857C2212yes—
71#63855C2212yescomplemented
72#63849C2214yescomplemented
73#63848C2214yescomplemented
74#63846C2214yescomplemented
75#63843C2214yescomplemented
76#63843C2212yescomplemented
77C3×#533—31no—
78C3×#525—31no—
79#5832—31no—
80Dic3×#41—31no—
81#5791—31no—
82C22×C4×Dic3—31no—
83#5728—32no—
84#5725—32no—
85#5691—32no—
86#5691—32no—
87#5649—34no—
88#5627—34no—
89#5624—32no—
90#5624—34no—
91#5622—32no—
92#5600—32no—
93#5596—32no—
94#5586—34no—
95#5580—34no—
96C4×#239—34no—
97#5538—34no—
98C4×#237—34no—
99#5524—31no—
100#5524D311yescharacteristic, complemented
101#5522—31no—
102#5522—31no—
103#5522—31no—
104#5522—61no—
105#5517D311yescharacteristic, complemented
106#5477—31no—
107C2×C42×D3—31no—
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C2×#638C2312yes—
111C22×C3⋊Dic3C2312yes—
112#3828—24no—
113C2×C4⋊(C3⋊D3)C2311yescharacteristic
114C2×C4×C3⋊D3C2314yes—
115C2×C4×C3⋊D3C2312yes—
116C2×#634C2311yescharacteristic
117C2×C3×#67C2312yes—
118C22×C3×Dic3C2312yes—
119C22×C3×Dic3C2311yescharacteristic
120C3×#235—24no—
121C2×C3×D12C2314yes—
122C2×C3×D12C2311yescharacteristic
123C2×C3×C4×D3—24no—
124C2×C3×C4×D3C2312yes—
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2312yes—
127C2×C3×Dic6C2314yes—
128C2×C3×Dic6C2311yescharacteristic
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×D3×Dic3—28no—
132C2×D3×Dic3C2314yes—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2312yes—
135C2×D3×Dic3C2312yes—
136C2×D3×Dic3C2312yes—
137#3796—216no—
138C32×C4⋊C4C2312yes—
139C32×C22⋊C4C2312yes—
140C32×C42C2312yes—
141#3752C2314yes—
142#3750C2314yes—
143C4×C3⋊Dic3C2311yescharacteristic
144C4×C3⋊Dic3C2314yes—
145C4×C3⋊Dic3C2311yescharacteristic
146C4×C3⋊Dic3C2312yes—
147C3×#217C2312yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×C4⋊Dic3C2314yes—
151C3×C4⋊Dic3C2314yes—
152C3×C4⋊Dic3C2312yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×C4×Dic3C2311yescharacteristic
156C3×C4×Dic3C2311yescharacteristic
157C3×C4×Dic3C2312yes—
158C3×C4×Dic3C2312yes—
159Dic3⋊Dic3C2314yes—
160Dic3⋊Dic3C2314yes—
161Dic3⋊Dic3C2314yes—
162#3722C2314yes—
163#3722C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167Dic32C2314yes—
168Dic32C2312yes—
169Dic32C2312yes—
170Dic32C2312yes—
171Dic32C2312yes—
172#3444—91noSylow
173C2×C3×#41—31no—
174C23×C3×C4—31no—
175C23×Dic3—32no—
176C2×#239—34no—
177C2×#237—34no—
178C2×#235—31no—
179C2×#235—31no—
180C2×#235—61no—
181C2×#235C2×D311yescharacteristic
182C22×C4×D3—32no—
183C22×C4×D3C2×D311yescharacteristic
184C3×C4⋊Q8—32no—
185C3×#125—32no—
186C3×#123—32no—
187C3×C22⋊Q8—32no—
188C3×C22⋊Q8—34no—
189C3×#121—32no—
190C3×#120—32no—
191C3×C4×Q8—34no—
192C3×C4×D4—34no—
193C3×#117—21no—
194C3×#117—31no—
195C3×#117C2×D311yescharacteristic
196C3×#117C2×D311yescharacteristic
197C2×C3×C42—31no—
198#953—32no—
199#947—34no—
200#947—31no—
201#946—34no—
202Q8×Dic3—34no—
203Q8×Dic3—32no—
204#944—31no—
205#940—31no—
206#939—34no—
207#939—34no—
208#936—31no—
209#935—34no—
210D4×Dic3—34no—
211D4×Dic3—34no—
212D4×Dic3—32no—
213#930—34no—
214#930—32no—
215#929—32no—
216C4×#67—34no—
217C4×#67—34no—
218#926—32no—
219#926C2×D311yescharacteristic
220#924—32no—
221C2×C4×Dic3—31no—
222C2×C4×Dic3—31no—
223C2×C4×Dic3—32no—
224C2×C4×Dic3—32no—
225C2×C4×Dic3—32no—
226C2×C4×Dic3—32no—
227C2×C4×Dic3—32no—
228C2×C4×Dic3—32no—
229C2×C4×Dic3—32no—
230C2×C4×Dic3—61no—
231C2×C4×Dic3C2×D311yescharacteristic
232#898—34no—
233#898—34no—
234#898—34no—
235#897—32no—
236#897C2×D312yes—
237#895—34no—
238#895—32no—
239#895C2×D312yes—
240#894—34no—
241#894—34no—
242#893—32no—
243#893—34no—
244#893—32no—
245#893—32no—
246#893—34no—
247#893—34no—
248#893—62no—
249#892—34no—
250#892—34no—
251#892—34no—
252#892—34no—
253#890—34no—
254#890C2×D312yescomplemented
255#889—34no—
256#888C2×D312yescomplemented
257#887—34no—
258#887—32no—
259#887—32no—
260#887—32no—
261#887—62no—
262#886—32no—
263#886—34no—
264#886C2×D312yes—
265#885—34no—
266#882—32no—
267#882C2×D312yes—
268#67⋊C4—34no—
269#67⋊C4—34no—
270#67⋊C4—34no—
271#67⋊C4—34no—
272#67⋊C4—34no—
273#67⋊C4—64no—
274#879—34no—
275#878—34no—
276#878C2×D314yes—
277#877—34no—
278#877—34no—
279#875—31no—
280#875—31no—
281#874—31no—
282C4×D12—34no—
283C4×D12—34no—
284C4×D12C2×D314yes—
285#872—32no—
286#872—32no—
287#872—32no—
288#872—62no—
289C42×D3—32no—
290C42×D3—32no—
291C42×D3—32no—
292C42×D3—32no—
293C42×D3—32no—
294C42×D3—32no—
295C42×D3—32no—
296C42×D3—62no—
297#869—31no—
298C4×Dic6C2×D314yescomplemented
299C23×C32C2411yescharacteristic
300C22×C3⋊D3C2412yes—
301C22×C3×D3—22no—
302C22×C3×D3—24no—
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—24no—
311C2×C3⋊Dic3C2412yes—
312C2×C3⋊Dic3C2412yes—
313C2×C3⋊Dic3C2412yes—
314C4⋊(C3⋊D3)—22no—
315C4×C3⋊D3—24no—
316C4×C3⋊D3—28no—
317#634—22no—
318C3×#67—24no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—24no—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2414yes—
325C2×C3×Dic3C2412yes—
326C3×D12—28no—
327C3×D12—22no—
328C3×C4×D3—24no—
329C3×C4×D3—24no—
330C3×C4×D3—24no—
331C3×Dic6—22no—
332C3×Dic6—28no—
333#626—28no—
334#626—28no—
335D3×Dic3—24no—
336D3×Dic3—28no—
337D3×Dic3—24no—
338D3×Dic3—24no—
339D3×Dic3#4118yescomplemented
340#533—31no—
341#533—92no—
342#532—91no—
343#532—92no—
344#529—94no—
345#529—92no—
346#529—94no—
347#529—92no—
348#525—31no—
349#525—91no—
350#525—94no—
351C4×#41—91no—
352C4×#41—94no—
353C4×#41—91no—
354C22×C42—91no—
355C24×C3—31no—
356C23×D3C22×D311yescharacteristic
357C3×#41—64no—
358C2×C3×Q8—31no—
359C2×C3×Q8—34no—
360C2×C3×D4—32no—
361C2×C3×D4—31no—
362C2×C3×D4—34no—
363C22×C3×C4—21no—
364C22×C3×C4—31no—
365C22×C3×C4—32no—
366C22×C3×C4—32no—
367C22×C3×C4—32no—
368C22×C3×C4—32no—
369C22×C3×C4—64no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C2×#67—32no—
373C2×#67—32no—
374C2×#67—34no—
375C2×#67—34no—
376C2×#67—62no—
377C2×#67C22×D312yes—
378C22×Dic3—32no—
379C22×Dic3—32no—
380C22×Dic3—32no—
381C22×Dic3—34no—
382C22×Dic3—32no—
383C22×Dic3—32no—
384C22×Dic3—32no—
385C22×Dic3—62no—
386C22×Dic3—68no—
387C22×Dic3C22×D312yes—
388C22×Dic3C22×D311yescharacteristic
389#239—616no—
390#237—616no—
391#235—24no—
392#235—68no—
393#235—64no—
394#235—64no—
395C2×D12—34no—
396C2×D12—34no—
397C2×D12—31no—
398C2×D12—31no—
399C2×D12—61no—
400C2×D12C22×D314yes—
401C2×D12C22×D311yescharacteristic
402C2×C4×D3—24no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—34no—
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—34no—
411C2×C4×D3—34no—
412C2×C4×D3—62no—
413C2×C4×D3—64no—
414C2×C4×D3—68no—
415C2×C4×D3C22×D312yes—
416C2×C4×D3C22×D312yes—
417C2×C4×D3C22×D312yes—
418C2×Dic6—31no—
419C2×Dic6—31no—
420C2×Dic6—61no—
421C2×Dic6C22×D314yes—
422C2×Dic6C22×D311yescharacteristic
423C3×C4⋊C4—22no—
424C3×C4⋊C4—34no—
425C3×C4⋊C4—32no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—34no—
428C3×C4⋊C4—34no—
429C3×C4⋊C4C22×D312yes—
430C3×C4⋊C4C22×D312yes—
431C3×C22⋊C4—22no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—34no—
435C3×C22⋊C4C22×D312yes—
436C3×C22⋊C4C22×D312yes—
437C3×C42—22no—
438C3×C42—31no—
439C3×C42—32no—
440C3×C42—31no—
441C3×C42—32no—
442C3×C42C22×D312yes—
443C3×C42C22×D312yes—
444#217—34no—
445#217—34no—
446#217—34no—
447#217C22×D312yes—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—34no—
450(C2×D3)⋊C4—34no—
451(C2×D3)⋊C4—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—64no—
458(C2×D3)⋊C4C22×D314yes—
459(C2×D3)⋊C4C22×D314yes—
460C4⋊Dic3—34no—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3C22×D314yes—
464C4⋊Dic3C22×D314yes—
465C4⋊Dic3C22×D312yes—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—64no—
472Dic3⋊C4C22×D314yes—
473Dic3⋊C4C22×D314yes—
474C4×Dic3—31no—
475C4×Dic3—31no—
476C4×Dic3—32no—
477C4×Dic3—31no—
478C4×Dic3—34no—
479C4×Dic3—34no—
480C4×Dic3—31no—
481C4×Dic3—32no—
482C4×Dic3—32no—
483C4×Dic3—32no—
484C4×Dic3—32no—
485C4×Dic3—32no—
486C4×Dic3—34no—
487C4×Dic3—32no—
488C4×Dic3—34no—
489C4×Dic3—32no—
490C4×Dic3—32no—
491C4×Dic3—32no—
492C4×Dic3—61no—
493C4×Dic3—64no—
494C4×Dic3—61no—
495C4×Dic3—62no—
496C4×Dic3C22×D312yes—
497C4×Dic3C22×D312yes—
498C4×Dic3C22×D311yescharacteristic
499C4×Dic3C22×D311yescharacteristic
500C22×C32—22no—
501C22×C32C2×#4112yes—
502C22×C32C2511yescharacteristic
503C2×C3⋊D3—22no—
504C2×C3⋊D3—24no—
505C2×C3×D3—28no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—24no—
509C2×C3×D3—22no—
510C2×C3×D3C2×#4114yes—
511C32×C4—24no—
512C32×C4C2×#4112yes—
513C32×C4C2×#4112yes—
514C3⋊Dic3—22no—
515C3⋊Dic3—22no—
516C3⋊Dic3C2×#4114yes—
517C3×Dic3—22no—
518C3×Dic3—24no—
519C3×Dic3—22no—
520C3×Dic3—22no—
521C3×Dic3C2×#4114yes—
522C2×#41—31no—
523C2×#41—94no—
524C2×#41—91no—
525C23×C4—31no—
526C23×C4—92no—
527C4⋊Q8—32no—
528C4⋊Q8—91no—
529#127—91no—
530#126—94no—
531#126—94no—
532#125—32no—
533#125—94no—
534#124—91no—
535#124—91no—
536#124—94no—
537#123—32no—
538#123—94no—
539#123—92no—
540#123—94no—
541C22⋊Q8—32no—
542C22⋊Q8—34no—
543C22⋊Q8—94no—
544C22⋊Q8—92no—
545#121—32no—
546#121—92no—
547#121—94no—
548#121—94no—
549#120—32no—
550#120—92no—
551C4×Q8—34no—
552C4×Q8—94no—
553C4×Q8—92no—
554C4×Q8—92no—
555C4×D4—34no—
556C4×D4—94no—
557C4×D4—94no—
558C4×D4—94no—
559C4×D4—94no—
560C4×D4—94no—
561C4×D4—94no—
562C4×D4—92no—
563C4×D4—92no—
564C4×D4—94no—
565#117—31no—
566#117—92no—
567#117—94no—
568#117—94no—
569#117—94no—
570#117—92no—
571#117D3211yescharacteristic
572C2×C42—31no—
573C2×C42—92no—
574C2×C42—92no—
575C2×C42—92no—
576C2×C42—92no—
577C2×C42—92no—
578C2×C42—92no—
579C2×C42—91no—
580C2×C42—92no—
581C23×C3—21no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—64no—
585C23×C3—62no—
586C23×C3C23×D311yescharacteristic
587C23×C3C23×D311yescharacteristic
588C22×D3—22no—
589C22×D3—24no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—62no—
593C22×D3C23×D312yes—
594C22×D3C23×D312yes—
595C3×Q8—68no—
596C3×Q8—62no—
597C3×D4—68no—
598C3×D4—64no—
599C3×D4—62no—
600C2×C3×C4—21no—
601C2×C3×C4—24no—
602C2×C3×C4—21no—
603C2×C3×C4—24no—
604C2×C3×C4—32no—
605C2×C3×C4—32no—
606C2×C3×C4—32no—
607C2×C3×C4—32no—
608C2×C3×C4—34no—
609C2×C3×C4—64no—
610C2×C3×C4—62no—
611C2×C3×C4—64no—
612C2×C3×C4—64no—
613C2×C3×C4—64no—
614C2×C3×C4#23714yescomplemented
615C2×C3×C4#23914yescomplemented
616C2×C3×C4C23×D314yes—
617C2×C3×C4C23×D314yes—
618C2×C3×C4C23×D311yescharacteristic
619C2×C3×C4C23×D311yescharacteristic
620C2×C3×C4C23×D311yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622#67—24no—
623#67—68no—
624#67—68no—
625#67—64no—
626#67—64no—
627#67—68no—
628C2×Dic3—22no—
629C2×Dic3—24no—
630C2×Dic3—32no—
631C2×Dic3—32no—
632C2×Dic3—38no—
633C2×Dic3—32no—
634C2×Dic3—32no—
635C2×Dic3—32no—
636C2×Dic3—32no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—62no—
640C2×Dic3—68no—
641C2×Dic3—64no—
642C2×Dic3—64no—
643C2×Dic3—64no—
644C2×Dic3—64no—
645C2×Dic3—64no—
646C2×Dic3—124no—
647C2×Dic3C23×D312yes—
648C2×Dic3C23×D312yes—
649C2×Dic3C23×D312yes—
650C2×Dic3C23×D314yes—
651C2×Dic3C23×D312yes—
652D12—28no—
653D12—22no—
654D12—64no—
655D12—68no—
656D12—68no—
657D12—62no—
658D12—62no—
659C4×D3—24no—
660C4×D3—24no—
661C4×D3—24no—
662C4×D3—38no—
663C4×D3—68no—
664C4×D3—68no—
665C4×D3—64no—
666C4×D3—68no—
667C4×D3—68no—
668C4×D3—64no—
669C4×D3—64no—
670C4×D3—64no—
671C4×D3—64no—
672C4×D3—128no—
673Dic6—22no—
674Dic6—28no—
675Dic6—64no—
676Dic6—62no—
677Dic6—62no—
678C2×C32—22no—
679C2×C32C22×#4111yescharacteristic
680C2×C32C22×#4112yes—
681C3⋊D3—42no—
682C3×D3—24no—
683C3×D3—42no—
684C24—31no—
685#41—64no—
686#41—1816no—
687#41—184no—
688C2×Q8—34no—
689C2×Q8—31no—
690C2×Q8—91no—
691C2×D4—32no—
692C2×D4—34no—
693C2×D4—31no—
694C2×D4—94no—
695C2×D4—94no—
696C2×D4—92no—
697C2×D4—91no—
698C22×C4—32no—
699C22×C4—31no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—64no—
704C22×C4—92no—
705C22×C4—92no—
706C22×C4—92no—
707C22×C4—92no—
708C22×C4—94no—
709C22×C4—92no—
710C22×C4—94no—
711C22×C4—92no—
712C22×C4—188no—
713C22×C4C2×D3211yescharacteristic
714C4⋊C4—32no—
715C4⋊C4—34no—
716C4⋊C4—34no—
717C4⋊C4—34no—
718C4⋊C4—34no—
719C4⋊C4—94no—
720C4⋊C4—94no—
721C4⋊C4—94no—
722C4⋊C4—94no—
723C4⋊C4C2×D3212yes—
724C22⋊C4—32no—
725C22⋊C4—34no—
726C22⋊C4—34no—
727C22⋊C4—94no—
728C22⋊C4—94no—
729C22⋊C4—94no—
730C22⋊C4—94no—
731C22⋊C4—94no—
732C22⋊C4—94no—
733C22⋊C4C2×D3212yes—
734C42—31no—
735C42—31no—
736C42—32no—
737C42—32no—
738C42—92no—
739C42—92no—
740C42—92no—
741C42—92no—
742C42—94no—
743C42—92no—
744C42—94no—
745C42—91no—
746C42—91no—
747C42C2×D3212yes—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—34no—
753C22×C3—42no—
754C22×C3—68no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3—62no—
758C22×C3—64no—
759C22×C3C2×#23712yes—
760C22×C3C2×#23912yes—
761C22×C3C24×D311yescharacteristic
762C22×C3C24×D311yescharacteristic
763C2×D3—28no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—22no—
767C2×D3—24no—
768C2×D3—64no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—64no—
772C2×D3—64no—
773C2×D3—124no—
774C2×D3D3×#4114yes—
775C3×C4—24no—
776C3×C4—24no—
777C3×C4—22no—
778C3×C4—22no—
779C3×C4—34no—
780C3×C4—44no—
781C3×C4—62no—
782C3×C4—62no—
783C3×C4—62no—
784C3×C4—64no—
785C3×C4C2×#23712yes—
786C3×C4C2×#23712yes—
787C3×C4C2×#23912yes—
788C3×C4C2×#23912yes—
789Dic3—22no—
790Dic3—22no—
791Dic3—24no—
792Dic3—22no—
793Dic3—34no—
794Dic3—34no—
795Dic3—64no—
796Dic3—64no—
797Dic3—62no—
798Dic3—62no—
799Dic3—62no—
800Dic3—62no—
801Dic3—122no—
802Dic3D3×#4114yes—
803C32#344411yescharacteristic, complemented, Sylow
804C23—32no—
805C23—32no—
806C23—64no—
807C23—62no—
808C23—92no—
809C23C22×D3211yescharacteristic
810Q8—68no—
811Q8—62no—
812Q8—182no—
813D4—68no—
814D4—64no—
815D4—62no—
816D4—188no—
817D4—188no—
818D4—184no—
819D4—182no—
820C2×C4—32no—
821C2×C4—32no—
822C2×C4—34no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—64no—
826C2×C4—62no—
827C2×C4—64no—
828C2×C4—64no—
829C2×C4—64no—
830C2×C4—98no—
831C2×C4—92no—
832C2×C4—92no—
833C2×C4—92no—
834C2×C4—188no—
835C2×C4—184no—
836C2×C4—184no—
837C2×C4—188no—
838C2×C4—184no—
839C2×C4—184no—
840C2×C4—184no—
841C2×C4#379614yescomplemented
842C2×C4C22×D3214yes—
843C2×C4C22×D3211yescharacteristic
844C2×C4C22×D3211yescharacteristic
845C2×C3—22no—
846C2×C3—22no—
847C2×C3—21no—
848C2×C3—22no—
849C2×C3—42no—
850C2×C3—64no—
851C2×C3—122no—
852C2×C3C22×#23711yescharacteristic
853C2×C3C22×#23911yescharacteristic
854C2×C3C2×D3×#4112yes—
855C2×C3C2×D3×#4112yes—
856D3—24no—
857D3—42no—
858D3—124no—
859D3—122no—
860D3—122no—
861C22—22no—
862C22—34no—
863C22—68no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—64no—
868C22—182no—
869C22—184no—
870C22C2×#379612yes—
871C22C23×D3211yescharacteristic
872C4—24no—
873C4—34no—
874C4—62no—
875C4—62no—
876C4—62no—
877C4—64no—
878C4—94no—
879C4—182no—
880C4—182no—
881C4C2×#379612yes—
882C4C2×#379612yes—
883C3—21no—
884C3#8601811yescharacteristic, complemented
885C3#8625711yescharacteristic, complemented
886C2—22no—
887C2—64no—
888C2—122no—
889C2—362no—
890C2C22×#379611yescharacteristic
891C2D32×#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. #10595993C2semidirect
2. C3×#5524C2semidirect
3. C3×#5517C2semidirect
4. #10595029C2semidirect
5. #10595023C2semidirect
6. #10594958C2semidirect
7. C2×C4×D3×Dic3C2semidirect
8. #10594453C2semidirect
9. #10594427C2semidirect
10. #10594387C2semidirect
11. #10594369C2semidirect
12. #10594144C2semidirect
13. #10594055C2semidirect
14. #10593911C2semidirect
15. C4×#3796C2semidirect
25. #64102C22semidirect
26. #64096C22semidirect
28. #64081C22semidirect
29. C42×C3⋊D3C22semidirect
34. C3×#890C22semidirect
35. C3×#888C22semidirect
40. C3×C4×Dic6C22semidirect
46. #63911C22semidirect
48. #63907C22semidirect
50. C4×#626C22semidirect
52. #63898C22semidirect
58. #63881C22semidirect
60. #63878C22semidirect
65. C4×D3×Dic3C22semidirect
66. #63866C22semidirect
67. #63864C22semidirect
68. #63860C22semidirect
69. #63858C22semidirect
71. #63855C22semidirect
72. #63849C22semidirect
73. #63848C22semidirect
74. #63846C22semidirect
75. #63843C22semidirect
76. #63843C22semidirect
100. #5524D3semidirect
105. #5517D3semidirect
254. #890C2×D3semidirect
256. #888C2×D3semidirect
298. C4×Dic6C2×D3semidirect
305. C2×C32×C4#41semidirect
339. D3×Dic3#41semidirect
614. C2×C3×C4#237semidirect
615. C2×C3×C4#239semidirect
803. C32#3444semidirect
841. C2×C4#3796semidirect
884. C3#86018semidirect
885. C3#86257semidirect

Maximal subgroups

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

subgroupindex
#105959932
C3×#55242
C3×#55172
#105950292
#105950232
#105949582
C2×C4×D3×Dic32
#105944532
#105944272
#105943872
#105943692
#105941442
#105940552
#105939112
C4×#37962
#862573
#860183