Finite Group Databasebeta

← #11901802

Subgroups — #11901802

Order 1152.

2235 conjugacy classes of subgroups.

The subgroup lattice has 869 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
3C2×C3×#872C211yesmaximal, characteristic, complemented
4#10595049C211yesmaximal, characteristic, complemented
5#10595036C214yesmaximal, complemented
6#10595029C211yesmaximal, characteristic, complemented
7#10595023C211yesmaximal, characteristic, complemented
8#10595022C211yesmaximal, characteristic, complemented
9#10594842C214yesmaximal, complemented
10#10593986C212yesmaximal, complemented
11#10593983C212yesmaximal, complemented
12#10593980C214yesmaximal, complemented
13#10593973C214yesmaximal, complemented
14#10593880C212yesmaximal, complemented
15#10593878C212yesmaximal, complemented
16#85837—31nomaximal
17#85738—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C4×#638C2214yes—
23#64135C2211yescharacteristic
24C4×C4⋊(C3⋊D3)C2212yescomplemented
25#64081C2212yescomplemented
26C42×C3⋊D3C2212yescomplemented
27C4×#634C2212yescomplemented
28C3×C4×#67C2214yes—
29C2×C3×(C2×D3)⋊C4C2212yes—
30C3×#926C2211yescharacteristic
31C2×C3×Dic3⋊C4C2212yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×C4×D12C2212yescomplemented
34C3×#872C2212yes—
35C3×#872C2212yes—
36C3×#872C2212yes—
37C3×#872C2212yes—
38C3×#872C2212yescomplemented
39C3×C42×D3C2212yescomplemented
40C3×C4×Dic6C2212yescomplemented
41#63978C2214yes—
42#63977C2212yes—
43#63976C2212yes—
44#63966C2212yes—
45#63964C2214yes—
46#63961C2212yes—
47#63918C2212yescomplemented
48C4×#627C2214yescomplemented
49#63915C2214yes—
50#63912C2214yes—
51#63911C2211yescharacteristic, complemented
52#63909C2212yes—
53#63908C2212yes—
54#63906C2214yes—
55#63905C2214yes—
56C4×#626C2214yes—
57C4×#626C2214yescomplemented
58C4×#625C2214yes—
59#63870C2214yescomplemented
60#63869C2212yescomplemented
61#63868C2214yescomplemented
62#63867C2214yescomplemented
63#63866C2211yescharacteristic, complemented
64#63865C2214yescomplemented
65#63864C2211yescharacteristic, complemented
66#63862C2214yes—
67#63862C2214yescomplemented
68#63860C2211yescharacteristic, complemented
69#63859C2214yes—
70#63857C2212yes—
71#63856C2212yes—
72#63853C2214yes—
73#63853C2214yescomplemented
74#63852C2214yes—
75#63851C2214yescomplemented
76#63850C2214yescomplemented
77C3×C4×#41—31no—
78C2×C3×#117—31no—
79#5832—31no—
80#5828—31no—
81#5791—31no—
82#5791—31no—
83#5583—32no—
84#5582—32no—
85#5564—34no—
86#5562—32no—
87#5561—32no—
88#5560—34no—
89#5535—32no—
90#5534—32no—
91#5534—32no—
92#5528—34no—
93#5528—34no—
94#5528—34no—
95#5524—31no—
96#5518—32no—
97#5517—31no—
98#5515—34no—
99#5494—34no—
100#5479—34no—
101#5477—31no—
102C4×#235—31no—
103C4×#235—31no—
104C4×#235—61no—
105C4×#235D311yescharacteristic, complemented
106C2×#872D311yescharacteristic, complemented
107#5470—31no—
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2312yes—
110C22×C32×C4C2311yescharacteristic
111C2×#638C2312yes—
112#3828—24no—
113C2×C4⋊(C3⋊D3)C2311yescharacteristic
114C2×C4×C3⋊D3C2312yes—
115C2×C4×C3⋊D3C2314yes—
116C2×#634C2311yescharacteristic
117C2×C3×#67C2312yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2312yes—
120C3×#235—24no—
121C2×C3×D12C2311yescharacteristic
122C2×C3×C4×D3—24no—
123C2×C3×C4×D3C2312yes—
124C2×C3×C4×D3C2312yes—
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2314yes—
127C2×C3×Dic6C2311yescharacteristic
128C2×#627C2314yes—
129C2×#626C2314yes—
130C2×#626C2314yes—
131C2×#625C2314yes—
132C32×C42C2312yes—
133C32×C42C2311yescharacteristic
134C32×C42C2311yescharacteristic
135#3757C2312yes—
136#3752C2314yes—
137C4⋊(C3⋊Dic3)C2312yes—
138#3750C2314yes—
139C4×C3⋊Dic3C2314yes—
140C4×C3⋊Dic3C2312yes—
141C3×#217C2312yes—
142C3×(C2×D3)⋊C4C2312yes—
143C3×(C2×D3)⋊C4C2312yes—
144C3×(C2×D3)⋊C4C2312yes—
145C3×(C2×D3)⋊C4C2312yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×C4⋊Dic3C2312yes—
148C3×Dic3⋊C4C2312yes—
149C3×Dic3⋊C4C2312yes—
150C3×Dic3⋊C4C2312yes—
151C3×Dic3⋊C4C2312yes—
152C3×Dic3⋊C4C2314yes—
153C3×C4×Dic3C2311yescharacteristic
154C3×C4×Dic3C2311yescharacteristic
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2312yes—
157C3×C4×Dic3C2314yes—
158#3724C2314yes—
159#3724C2314yes—
160Dic3⋊Dic3C2314yes—
161Dic3⋊Dic3C2314yes—
162Dic3⋊Dic3C2314yes—
163Dic3⋊Dic3C2314yes—
164#3722C2314yes—
165#3722C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167(C2×D3)⋊Dic3C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yes—
170#3455—91noSylow
171C2×C3×#41—31no—
172C23×C3×C4—31no—
173C2×#235—31no—
174C2×#235—31no—
175C2×#235—61no—
176C2×#235C2×D311yescharacteristic
177C22×C4×D3C2×D311yescharacteristic
178C3×C4×Q8—32no—
179C3×C4×D4—34no—
180C3×C4×D4—32no—
181C3×#117—31no—
182C3×#117—32no—
183C3×#117—32no—
184C3×#117—32no—
185C3×#117—32no—
186C3×#117—32no—
187C2×C3×C4⋊C4—32no—
188C2×C3×C22⋊C4—32no—
189C2×C3×C42—21no—
190C2×C3×C42—31no—
191C2×C3×C42—32no—
192C2×C3×C42C2×D311yescharacteristic
193C2×C3×C42C2×D311yescharacteristic
194#953—32no—
195#953—32no—
196#947—31no—
197#946—32no—
198#944—31no—
199#940—31no—
200#939—34no—
201#938—32no—
202#937—32no—
203#936—31no—
204#935—32no—
205#930—34no—
206#930—32no—
207#930—34no—
208#930—32no—
209#929—32no—
210#929—32no—
211#929—34no—
212#929—34no—
213C4×#67—34no—
214C4×#67—34no—
215C4×#67—34no—
216C4×#67—34no—
217C4×#67—34no—
218C4×#67—34no—
219C4×#67—64no—
220C4×#67C2×D314yes—
221C2×(C2×D3)⋊C4C2×D312yes—
222#926—31no—
223#926—31no—
224#926—61no—
225#926C2×D311yescharacteristic
226#924—32no—
227#924—34no—
228#924—32no—
229#924—34no—
230C2×Dic3⋊C4C2×D312yes—
231C2×C4×Dic3C2×D311yescharacteristic
232#898—34no—
233#898—34no—
234#898—34no—
235#897—32no—
236#896—34no—
237#896—34no—
238#896—34no—
239#895—32no—
240#894—34no—
241#894—34no—
242#894—34no—
243#890—32no—
244#889—34no—
245#889—34no—
246#889—34no—
247#888—32no—
248#886—32no—
249#885—34no—
250#885—34no—
251#885—34no—
252#884—34no—
253#884—34no—
254#884—34no—
255#883—34no—
256#883—34no—
257#883—34no—
258#882—32no—
259#879—34no—
260#879—34no—
261#879—34no—
262#878—34no—
263#876—34no—
264#876—34no—
265#875—31no—
266#875—31no—
267#875—34no—
268#874—31no—
269C4×D12—34no—
270C4×D12—34no—
271C4×D12—32no—
272C4×D12—32no—
273C4×D12—62no—
274C4×D12C2×D312yescomplemented
275#872—32no—
276#872—32no—
277#872—62no—
278#872C2×D312yes—
279#872C2×D312yes—
280#872C2×D312yes—
281#872C2×D312yes—
282#872C2×D312yescomplemented
283C42×D3—32no—
284C42×D3—32no—
285C42×D3—62no—
286C42×D3C2×D312yescomplemented
287#870—32no—
288#870—34no—
289#869—31no—
290#869—32no—
291C4×Dic6—32no—
292C4×Dic6—32no—
293C4×Dic6—34no—
294C4×Dic6—34no—
295C4×Dic6—62no—
296C4×Dic6C2×D312yescomplemented
297C23×C32C2411yescharacteristic
298C22×C3⋊D3C2412yes—
299C22×C3×D3—22no—
300C22×C3×D3—42no—
301C22×C3×D3C2412yes—
302C22×C3×D3C2412yes—
303C2×C32×C4—42no—
304C2×C32×C4#4114yes—
305C2×C32×C4C2412yes—
306C2×C32×C4C2412yes—
307C2×C32×C4C2411yescharacteristic
308C2×C32×C4C2411yescharacteristic
309#638—24no—
310C2×C3⋊Dic3C2412yes—
311C2×C3⋊Dic3C2414yes—
312C4⋊(C3⋊D3)—22no—
313C4×C3⋊D3—24no—
314C4×C3⋊D3—44no—
315#634—22no—
316C3×#67—24no—
317C2×C3×Dic3—22no—
318C2×C3×Dic3—42no—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2414yes—
323C2×C3×Dic3C2412yes—
324C3×D12—22no—
325C3×C4×D3—24no—
326C3×C4×D3—24no—
327C3×C4×D3—24no—
328C3×C4×D3—44no—
329C3×Dic6—22no—
330#627—44no—
331#626—44no—
332#626—44no—
333#625—44no—
334#542—92no—
335#542—92no—
336#541—92no—
337#540—92no—
338#539—94no—
339#538—94no—
340#533—91no—
341#532—91no—
342#529—94no—
343#529—94no—
344#525—91no—
345#525—91no—
346C4×#41—31no—
347C4×#41—91no—
348C2×#117—31no—
349C24×C3—31no—
350C23×D3C22×D311yescharacteristic
351C3×#41—64no—
352C2×C3×Q8—31no—
353C2×C3×D4—32no—
354C2×C3×D4—31no—
355C22×C3×C4—21no—
356C22×C3×C4—22no—
357C22×C3×C4—31no—
358C22×C3×C4—32no—
359C22×C3×C4—32no—
360C22×C3×C4—32no—
361C22×C3×C4—32no—
362C22×C3×C4—34no—
363C22×C3×C4—64no—
364C22×C3×C4C22×D312yes—
365C22×C3×C4C22×D312yes—
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C2×#67—32no—
369C2×#67—32no—
370C2×#67—34no—
371C2×#67—34no—
372C2×#67—34no—
373C2×#67—34no—
374C2×#67—62no—
375C2×#67C22×D312yes—
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D312yes—
378#235—24no—
379#235—68no—
380#235—64no—
381#235—64no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—34no—
385C2×D12—34no—
386C2×D12—61no—
387C2×D12C22×D311yescharacteristic
388C2×C4×D3—24no—
389C2×C4×D3—32no—
390C2×C4×D3—32no—
391C2×C4×D3—34no—
392C2×C4×D3—34no—
393C2×C4×D3—62no—
394C2×C4×D3—64no—
395C2×C4×D3C22×D312yes—
396C2×C4×D3C22×D312yes—
397C2×C4×D3C22×D312yes—
398C2×C4×D3C22×D314yes—
399C2×Dic6—31no—
400C2×Dic6—31no—
401C2×Dic6—34no—
402C2×Dic6—34no—
403C2×Dic6—61no—
404C2×Dic6C22×D311yescharacteristic
405C3×C4⋊C4—32no—
406C3×C4⋊C4—32no—
407C3×C4⋊C4—32no—
408C3×C4⋊C4—34no—
409C3×C4⋊C4—32no—
410C3×C4⋊C4—32no—
411C3×C22⋊C4—32no—
412C3×C22⋊C4—32no—
413C3×C22⋊C4—32no—
414C3×C22⋊C4—34no—
415C3×C22⋊C4—32no—
416C3×C22⋊C4—32no—
417C3×C42—22no—
418C3×C42—21no—
419C3×C42—21no—
420C3×C42—32no—
421C3×C42—32no—
422C3×C42—31no—
423C3×C42—31no—
424C3×C42—34no—
425C3×C42C22×D312yes—
426C3×C42C22×D312yes—
427C3×C42C22×D311yescharacteristic
428C3×C42C22×D311yescharacteristic
429C3×C42C22×D311yescharacteristic
430C3×C42C22×D311yescharacteristic
431#217—32no—
432#217—32no—
433#217—34no—
434#217—34no—
435#217—34no—
436#217—34no—
437#217—62no—
438#217C22×D312yes—
439(C2×D3)⋊C4—34no—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—34no—
442(C2×D3)⋊C4—34no—
443(C2×D3)⋊C4—34no—
444(C2×D3)⋊C4—34no—
445(C2×D3)⋊C4—34no—
446(C2×D3)⋊C4—34no—
447(C2×D3)⋊C4—34no—
448(C2×D3)⋊C4—34no—
449(C2×D3)⋊C4—64no—
450(C2×D3)⋊C4C22×D312yes—
451(C2×D3)⋊C4C22×D312yes—
452(C2×D3)⋊C4C22×D312yes—
453(C2×D3)⋊C4C22×D312yes—
454(C2×D3)⋊C4C22×D314yes—
455C4⋊Dic3—32no—
456C4⋊Dic3—32no—
457C4⋊Dic3—34no—
458C4⋊Dic3—34no—
459C4⋊Dic3—34no—
460C4⋊Dic3—34no—
461C4⋊Dic3—62no—
462C4⋊Dic3C22×D312yes—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—64no—
474Dic3⋊C4C22×D314yes—
475Dic3⋊C4C22×D312yes—
476Dic3⋊C4C22×D312yes—
477Dic3⋊C4C22×D312yes—
478Dic3⋊C4C22×D312yes—
479C4×Dic3—32no—
480C4×Dic3—32no—
481C4×Dic3—34no—
482C4×Dic3—34no—
483C4×Dic3—64no—
484C4×Dic3—62no—
485C4×Dic3C22×D312yes—
486C4×Dic3C22×D312yes—
487C4×Dic3C22×D314yes—
488C4×Dic3C22×D311yescharacteristic
489C4×Dic3C22×D311yescharacteristic
490C22×C32—22no—
491C22×C32C2×#4112yes—
492C22×C32C2511yescharacteristic
493C2×C3⋊D3—22no—
494C2×C3⋊D3—24no—
495C2×C3×D3—22no—
496C2×C3×D3—22no—
497C2×C3×D3—22no—
498C2×C3×D3—24no—
499C2×C3×D3—22no—
500C2×C3×D3—44no—
501C32×C4—22no—
502C32×C4—22no—
503C32×C4C2×#4112yes—
504C32×C4C2×#4112yes—
505C3⋊Dic3—22no—
506C3⋊Dic3—24no—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—22no—
510C3×Dic3—24no—
511C3×Dic3—22no—
512C2×#41—31no—
513C2×#41—91no—
514C23×C4—31no—
515C4⋊Q8—92no—
516C4⋊Q8—91no—
517#127—91no—
518#126—94no—
519#126—94no—
520#126—94no—
521#126—94no—
522#125—94no—
523#125—92no—
524#125—94no—
525#124—94no—
526#124—91no—
527#124—91no—
528#124—94no—
529#123—94no—
530#123—94no—
531#123—92no—
532#123—94no—
533#123—94no—
534#123—92no—
535C22⋊Q8—94no—
536C22⋊Q8—94no—
537C22⋊Q8—92no—
538C22⋊Q8—94no—
539C22⋊Q8—92no—
540#121—94no—
541#121—94no—
542#121—92no—
543#121—92no—
544#121—94no—
545#120—92no—
546#120—92no—
547C4×Q8—32no—
548C4×Q8—94no—
549C4×Q8—92no—
550C4×D4—34no—
551C4×D4—32no—
552C4×D4—94no—
553C4×D4—94no—
554C4×D4—94no—
555C4×D4—94no—
556C4×D4—92no—
557#117—31no—
558#117—32no—
559#117—32no—
560#117—32no—
561#117—32no—
562#117—32no—
563#117—91no—
564#117—92no—
565C2×C4⋊C4—32no—
566C2×C22⋊C4—32no—
567C2×C42—31no—
568C2×C42—32no—
569C2×C42—92no—
570C2×C42D3211yescharacteristic
571C23×C3—21no—
572C23×C3—32no—
573C23×C3—32no—
574C23×C3—62no—
575C23×C3—122no—
576C23×C3C23×D311yescharacteristic
577C23×C3C23×D311yescharacteristic
578C22×D3—22no—
579C22×D3—32no—
580C22×D3—32no—
581C22×D3—42no—
582C22×D3—62no—
583C22×D3C23×D312yes—
584C22×D3C23×D312yes—
585C3×Q8—62no—
586C3×D4—64no—
587C3×D4—62no—
588C2×C3×C4—22no—
589C2×C3×C4—21no—
590C2×C3×C4—22no—
591C2×C3×C4—21no—
592C2×C3×C4—24no—
593C2×C3×C4—32no—
594C2×C3×C4—32no—
595C2×C3×C4—32no—
596C2×C3×C4—34no—
597C2×C3×C4—32no—
598C2×C3×C4—42no—
599C2×C3×C4—42no—
600C2×C3×C4—44no—
601C2×C3×C4—62no—
602C2×C3×C4—64no—
603C2×C3×C4—64no—
604C2×C3×C4—64no—
605C2×C3×C4—124no—
606C2×C3×C4—122no—
607C2×C3×C4#23514yes—
608C2×C3×C4#23514yes—
609C2×C3×C4C23×D312yes—
610C2×C3×C4C23×D312yes—
611C2×C3×C4C23×D312yes—
612C2×C3×C4C23×D312yes—
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C23×D311yescharacteristic
616C2×C3×C4C23×D311yescharacteristic
617#67—24no—
618#67—68no—
619#67—64no—
620#67—64no—
621#67—124no—
622#67—124no—
623#67—124no—
624#67—124no—
625C2×Dic3—22no—
626C2×Dic3—32no—
627C2×Dic3—32no—
628C2×Dic3—34no—
629C2×Dic3—34no—
630C2×Dic3—42no—
631C2×Dic3—62no—
632C2×Dic3—64no—
633C2×Dic3C23×D312yes—
634C2×Dic3C23×D314yes—
635C2×Dic3C23×D312yes—
636C2×Dic3C23×D312yes—
637C2×Dic3C23×D312yes—
638D12—22no—
639D12—64no—
640D12—62no—
641D12—62no—
642D12—124no—
643D12—124no—
644C4×D3—24no—
645C4×D3—24no—
646C4×D3—24no—
647C4×D3—44no—
648C4×D3—68no—
649C4×D3—64no—
650C4×D3—64no—
651C4×D3—124no—
652C4×D3—124no—
653C4×D3—128no—
654Dic6—22no—
655Dic6—64no—
656Dic6—62no—
657Dic6—62no—
658Dic6—124no—
659Dic6—124no—
660C2×C32—22no—
661C2×C32C22×#4111yescharacteristic
662C2×C32#58512yes—
663C3⋊D3—42no—
664C3×D3—42no—
665C3×D3—42no—
666C24—31no—
667#41—64no—
668#41—184no—
669C2×Q8—31no—
670C2×Q8—94no—
671C2×Q8—91no—
672C2×D4—32no—
673C2×D4—31no—
674C2×D4—94no—
675C2×D4—94no—
676C2×D4—92no—
677C2×D4—94no—
678C2×D4—91no—
679C22×C4—31no—
680C22×C4—32no—
681C22×C4—32no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—34no—
685C22×C4—64no—
686C22×C4—92no—
687C22×C4—94no—
688C22×C4C2×D3212yes—
689C22×C4C2×D3211yescharacteristic
690C4⋊C4—32no—
691C4⋊C4—32no—
692C4⋊C4—32no—
693C4⋊C4—32no—
694C4⋊C4—32no—
695C4⋊C4—34no—
696C4⋊C4—94no—
697C4⋊C4—94no—
698C4⋊C4—94no—
699C4⋊C4—94no—
700C4⋊C4—94no—
701C4⋊C4—94no—
702C4⋊C4—92no—
703C4⋊C4—94no—
704C22⋊C4—32no—
705C22⋊C4—32no—
706C22⋊C4—32no—
707C22⋊C4—32no—
708C22⋊C4—32no—
709C22⋊C4—34no—
710C22⋊C4—94no—
711C22⋊C4—94no—
712C22⋊C4—94no—
713C22⋊C4—94no—
714C22⋊C4—94no—
715C22⋊C4—94no—
716C22⋊C4—92no—
717C22⋊C4—94no—
718C42—31no—
719C42—31no—
720C42—34no—
721C42—32no—
722C42—32no—
723C42—94no—
724C42—92no—
725C42C2×D3212yes—
726C42C2×D3211yescharacteristic
727C42C2×D3211yescharacteristic
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—42no—
733C22×C3—62no—
734C22×C3—62no—
735C22×C3—64no—
736C22×C3—62no—
737C22×C3—62no—
738C22×C3—124no—
739C22×C3C2×#23512yes—
740C22×C3C2×#23512yes—
741C22×C3C24×D311yescharacteristic
742C22×C3C24×D311yescharacteristic
743C2×D3—22no—
744C2×D3—22no—
745C2×D3—24no—
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—44no—
749C2×D3—64no—
750C2×D3—62no—
751C2×D3—62no—
752C2×D3—64no—
753C2×D3—64no—
754C2×D3—124no—
755C3×C4—24no—
756C3×C4—22no—
757C3×C4—22no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—22no—
761C3×C4—22no—
762C3×C4—42no—
763C3×C4—62no—
764C3×C4—62no—
765C3×C4—62no—
766C3×C4—64no—
767C3×C4—62no—
768C3×C4C2×#23512yes—
769C3×C4C2×#23512yes—
770C3×C4C2×#23512yes—
771C3×C4C2×#23512yes—
772Dic3—22no—
773Dic3—22no—
774Dic3—22no—
775Dic3—24no—
776Dic3—22no—
777Dic3—64no—
778Dic3—62no—
779Dic3—62no—
780Dic3—64no—
781Dic3—64no—
782Dic3—124no—
783C32#345511yescharacteristic, complemented, Sylow
784C23—32no—
785C23—32no—
786C23—62no—
787C23—92no—
788C23—122no—
789C23C22×D3211yescharacteristic
790Q8—62no—
791Q8—182no—
792Q8—364no—
793D4—64no—
794D4—62no—
795D4—184no—
796D4—182no—
797D4—364no—
798D4—364no—
799D4—364no—
800C2×C4—32no—
801C2×C4—34no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—42no—
806C2×C4—62no—
807C2×C4—64no—
808C2×C4—64no—
809C2×C4—64no—
810C2×C4—92no—
811C2×C4—94no—
812C2×C4—124no—
813C2×C4—122no—
814C2×C4—184no—
815C2×C4—364no—
816C2×C4#379814yes—
817C2×C4C22×D3212yes—
818C2×C4C22×D3212yes—
819C2×C4C22×D3211yescharacteristic
820C2×C4C22×D3211yescharacteristic
821C2×C3—22no—
822C2×C3—22no—
823C2×C3—21no—
824C2×C3—22no—
825C2×C3—42no—
826C2×C3—122no—
827C2×C3—122no—
828C2×C3C22×#23511yescharacteristic
829C2×C3C22×#23511yescharacteristic
830C2×C3#596412yes—
831C2×C3#596412yes—
832D3—42no—
833D3—42no—
834D3—124no—
835D3—122no—
836D3—122no—
837C22—22no—
838C22—62no—
839C22—62no—
840C22—64no—
841C22—62no—
842C22—62no—
843C22—124no—
844C22—182no—
845C22—184no—
846C22C2×#379812yes—
847C22C23×D3211yescharacteristic
848C4—22no—
849C4—22no—
850C4—62no—
851C4—62no—
852C4—62no—
853C4—64no—
854C4—62no—
855C4—182no—
856C4—184no—
857C4C2×#379812yes—
858C4C2×#379812yes—
859C3—21no—
860C3#8573811yescharacteristic, complemented
861C3#8583711yescharacteristic, complemented
862C2—22no—
863C2—122no—
864C2—122no—
865C2—362no—
866C2C22×#379811yescharacteristic
867C2#1059666912yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3455
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. C2×C3×#872C2semidirect
4. #10595049C2semidirect
5. #10595036C2semidirect
6. #10595029C2semidirect
7. #10595023C2semidirect
8. #10595022C2semidirect
9. #10594842C2semidirect
10. #10593986C2semidirect
11. #10593983C2semidirect
12. #10593980C2semidirect
13. #10593973C2semidirect
14. #10593880C2semidirect
15. #10593878C2semidirect
24. C4×C4⋊(C3⋊D3)C22semidirect
25. #64081C22semidirect
26. C42×C3⋊D3C22semidirect
27. C4×#634C22semidirect
33. C3×C4×D12C22semidirect
38. C3×#872C22semidirect
39. C3×C42×D3C22semidirect
40. C3×C4×Dic6C22semidirect
47. #63918C22semidirect
48. C4×#627C22semidirect
51. #63911C22semidirect
57. C4×#626C22semidirect
59. #63870C22semidirect
60. #63869C22semidirect
61. #63868C22semidirect
62. #63867C22semidirect
63. #63866C22semidirect
64. #63865C22semidirect
65. #63864C22semidirect
67. #63862C22semidirect
68. #63860C22semidirect
73. #63853C22semidirect
75. #63851C22semidirect
76. #63850C22semidirect
105. C4×#235D3semidirect
106. C2×#872D3semidirect
274. C4×D12C2×D3semidirect
282. #872C2×D3semidirect
286. C42×D3C2×D3semidirect
296. C4×Dic6C2×D3semidirect
783. C32#3455semidirect
860. C3#85738semidirect
861. C3#85837semidirect

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
C2×C3×#8722
#105950492
#105950362
#105950292
#105950232
#105950222
#105948422
#105939862
#105939832
#105939802
#105939732
#105938802
#105938782
#858373
#857383