Finite Group Databasebeta

← #11900895

Subgroups — #11900895

Order 1152.

2535 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595988C211yesmaximal, characteristic, complemented
2C3×#5524C211yesmaximal, characteristic, complemented
3C3×#5522C211yesmaximal, characteristic, complemented
4#10595032C211yesmaximal, characteristic, complemented
5#10595022C211yesmaximal, characteristic, complemented
6Dic3×#235C211yesmaximal, characteristic, complemented
7C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
8#10594444C212yesmaximal, complemented
9#10594426C212yesmaximal, complemented
10#10594385C212yesmaximal, complemented
11#10594367C212yesmaximal, complemented
12#10594131C214yesmaximal, complemented
13#10594054C214yesmaximal, complemented
14#10593910C214yesmaximal, complemented
15C4×#3795C214yesmaximal, complemented
16#86018—31nomaximal
17#85836—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2212yes—
22C2×#3795C2214yes—
23C32×#117C2211yescharacteristic
24#64135C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26#64099C2212yescomplemented
27#64097C2212yescomplemented
28#64087C2214yes—
29C4×#634C2214yescomplemented
30C2×C3×C4×Dic3C2211yescharacteristic
31C3×#897C2212yes—
32C3×#895C2212yes—
33C3×#893C2212yescomplemented
34C3×#887C2212yescomplemented
35C3×#886C2212yes—
36C3×#882C2212yes—
37C3×#67⋊C4C2214yes—
38C3×C4×D12C2214yes—
39C3×#872C2212yescomplemented
40C3×C42×D3C2212yescomplemented
41#63980C2214yes—
42#63976C2212yes—
43Dic3×#67C2214yes—
44#63961C2212yes—
45C2×Dic32C2212yes—
46#63914C2211yescharacteristic, complemented
47#63913C2214yescomplemented
48#63908C2212yes—
49C4×#625C2214yes—
50C4×#625C2214yescomplemented
51#63896C2214yes—
52Dic3×D12C2214yes—
53Dic3×D12C2212yescomplemented
54#63891C2214yes—
55#63885C2214yes—
56#63884C2214yes—
57#63879C2214yes—
58#63879C2214yescomplemented
59#63877C2214yes—
60#63877C2214yescomplemented
61C4×D3×Dic3C2212yes—
62C4×D3×Dic3C2212yes—
63C4×D3×Dic3C2212yes—
64C4×D3×Dic3C2212yes—
65C4×D3×Dic3C2212yescomplemented
66#63873C2211yescharacteristic, complemented
67#63863C2211yescharacteristic, complemented
68#63863C2211yescharacteristic, complemented
69#63861C2214yescomplemented
70#63858C2214yescomplemented
71#63856C2212yes—
72#63855C2212yescomplemented
73#63847C2214yescomplemented
74#63844C2214yescomplemented
75Dic3×Dic6C2212yescomplemented
76#63841C2214yescomplemented
77C3×#525—31no—
78C3×C4×#41—31no—
79#5832—31no—
80#5832—31no—
81#5828—31no—
82Dic3×#41—31no—
83#5791—31no—
84C22×C4×Dic3—31no—
85#5649—34no—
86#5624—32no—
87#5622—32no—
88#5600—32no—
89#5596—32no—
90#5586—34no—
91#5580—32no—
92#5578—32no—
93#5557—32no—
94#5548—32no—
95#5547—34no—
96#5538—34no—
97#5538—34no—
98C4×#237—34no—
99#5528—34no—
100#5524D311yescharacteristic, complemented
101#5522D311yescharacteristic, complemented
102#5517—31no—
103#5517—31no—
104#5517—61no—
105C4×#235—31no—
106C4×#235—34no—
107C2×C42×D3—31no—
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2311yescharacteristic
110C22×C3⋊Dic3C2312yes—
111C2×#634C2314yes—
112C2×C3×#67C2312yes—
113C2×C3×#67C2312yes—
114C22×C3×Dic3C2312yes—
115C22×C3×Dic3C2311yescharacteristic
116C3×#235—24no—
117C3×#235—24no—
118C2×C3×D12C2314yes—
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3—24no—
122C2×C3×C4×D3C2314yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×C4×D3C2312yes—
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2312yes—
127C2×C3×Dic6C2311yescharacteristic
128C2×C3×Dic6C2311yescharacteristic
129C2×#625C2314yes—
130C2×#625C2314yes—
131C2×D3×Dic3—28no—
132C2×D3×Dic3C2314yes—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2312yes—
135C2×D3×Dic3C2312yes—
136C2×D3×Dic3C2312yes—
137#3795—216no—
138C32×C4⋊C4C2312yes—
139C32×C22⋊C4C2312yes—
140C32×C42C2312yes—
141#3757C2312yes—
142C4⋊(C3⋊Dic3)C2314yes—
143C4⋊(C3⋊Dic3)C2312yes—
144#3750C2314yes—
145#3750C2314yes—
146C4×C3⋊Dic3C2312yes—
147C4×C3⋊Dic3C2312yes—
148C4×C3⋊Dic3C2311yescharacteristic
149C4×C3⋊Dic3C2311yescharacteristic
150C3×(C2×D3)⋊C4C2314yes—
151C3×(C2×D3)⋊C4C2314yes—
152C3×(C2×D3)⋊C4C2314yes—
153C3×C4⋊Dic3C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×C4×Dic3C2314yes—
156C3×C4×Dic3C2312yes—
157C3×C4×Dic3C2311yescharacteristic
158C3×C4×Dic3C2311yescharacteristic
159#3724C2314yes—
160#3724C2314yes—
161Dic3⋊Dic3C2314yes—
162(C2×D3)⋊Dic3C2314yes—
163(C2×D3)⋊Dic3C2314yes—
164(C2×D3)⋊Dic3C2314yes—
165(C2×D3)⋊Dic3C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167Dic32C2312yes—
168Dic32C2314yes—
169Dic32C2312yes—
170Dic32C2312yes—
171Dic32C2312yes—
172#3444—91noSylow
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C23×C3×C4—31no—
176C23×Dic3—32no—
177C2×#237—34no—
178C2×#235—34no—
179C2×#235C2×D311yescharacteristic
180C2×#235C2×D311yescharacteristic
181C22×C4×D3—32no—
182C22×C4×D3C2×D311yescharacteristic
183C3×#123—32no—
184C3×C22⋊Q8—32no—
185C3×#121—32no—
186C3×#120—32no—
187C3×C4×Q8—32no—
188C3×C4×D4—32no—
189C3×C4×D4—34no—
190C3×C4×D4—34no—
191C3×#117—21no—
192C3×#117—32no—
193C3×#117C2×D311yescharacteristic
194C3×#117C2×D311yescharacteristic
195C2×C3×C42—31no—
196C2×C3×C42—32no—
197#953—32no—
198#947—31no—
199#947—31no—
200#946—32no—
201Q8×Dic3—32no—
202#944—31no—
203#944—31no—
204#940—31no—
205#940—31no—
206#939—34no—
207#939—34no—
208#939—34no—
209#938—32no—
210#937—32no—
211#936—31no—
212#936—31no—
213#935—32no—
214#935—34no—
215D4×Dic3—34no—
216D4×Dic3—34no—
217D4×Dic3—32no—
218#930—32no—
219#929—32no—
220C4×#67—34no—
221C4×#67—34no—
222C4×#67—34no—
223C4×#67—34no—
224C4×#67—34no—
225C4×#67—34no—
226C4×#67—34no—
227#926—31no—
228#926—31no—
229#926—34no—
230#926—32no—
231#926—61no—
232#924—32no—
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—32no—
236C2×C4×Dic3—32no—
237C2×C4×Dic3—32no—
238C2×C4×Dic3—32no—
239C2×C4×Dic3—32no—
240C2×C4×Dic3—32no—
241C2×C4×Dic3—32no—
242C2×C4×Dic3—61no—
243C2×C4×Dic3C2×D311yescharacteristic
244#898—34no—
245#898—34no—
246#897C2×D312yes—
247#896—34no—
248#895C2×D312yes—
249#894—34no—
250#893C2×D312yescomplemented
251#892—34no—
252#890—32no—
253#890—32no—
254#890—62no—
255#889—34no—
256#889—34no—
257#888—32no—
258#888—32no—
259#888—62no—
260#887—34no—
261#887C2×D312yescomplemented
262#886—34no—
263#886C2×D312yes—
264#885—34no—
265#885—34no—
266#884—34no—
267#883—34no—
268#882C2×D312yes—
269#67⋊C4—34no—
270#67⋊C4—34no—
271#67⋊C4C2×D314yes—
272#879—34no—
273#879—34no—
274#878—34no—
275#878—34no—
276#878—34no—
277#878—64no—
278#877—34no—
279#877—34no—
280C4×D12—34no—
281C4×D12—32no—
282C4×D12C2×D314yes—
283#872—32no—
284#872—34no—
285#872—34no—
286#872C2×D312yescomplemented
287C42×D3—32no—
288C42×D3—32no—
289C42×D3—32no—
290C42×D3—32no—
291C42×D3—32no—
292C42×D3C2×D312yescomplemented
293C4×Dic6—32no—
294C4×Dic6—34no—
295C4×Dic6—34no—
296C4×Dic6—34no—
297C4×Dic6—64no—
298C23×C32C2411yescharacteristic
299C22×C3×D3—22no—
300C22×C3×D3—24no—
301C22×C3×D3C2412yes—
302C22×C3×D3C2412yes—
303C22×C3×D3C2412yes—
304C2×C32×C4#4114yescomplemented
305C2×C32×C4C2414yes—
306C2×C32×C4C2411yescharacteristic
307C2×C32×C4C2411yescharacteristic
308C2×C3⋊Dic3—24no—
309C2×C3⋊Dic3C2412yes—
310C2×C3⋊Dic3C2414yes—
311C2×C3⋊Dic3C2412yes—
312#634—28no—
313C3×#67—24no—
314C3×#67—24no—
315C2×C3×Dic3—22no—
316C2×C3×Dic3—24no—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C2×C3×Dic3C2412yes—
322C3×D12—28no—
323C3×D12—22no—
324C3×D12—22no—
325C3×C4×D3—24no—
326C3×C4×D3—24no—
327C3×C4×D3—24no—
328C3×C4×D3—24no—
329C3×C4×D3—28no—
330C3×Dic6—22no—
331C3×Dic6—22no—
332#625—28no—
333#625—28no—
334D3×Dic3—24no—
335D3×Dic3—24no—
336D3×Dic3—28no—
337D3×Dic3—24no—
338D3×Dic3#4118yescomplemented
339#533—92no—
340#533—91no—
341#532—92no—
342#532—91no—
343#529—94no—
344#529—92no—
345#529—94no—
346#529—92no—
347#525—31no—
348#525—94no—
349#525—91no—
350C4×#41—31no—
351C4×#41—94no—
352C4×#41—91no—
353C22×C42—91no—
354C24×C3—31no—
355C23×D3C22×D311yescharacteristic
356C3×#41—64no—
357C3×#41—64no—
358C2×C3×Q8—31no—
359C2×C3×Q8—31no—
360C2×C3×D4—32no—
361C2×C3×D4—32no—
362C2×C3×D4—31no—
363C2×C3×D4—34no—
364C2×C3×D4—31no—
365C22×C3×C4—21no—
366C22×C3×C4—31no—
367C22×C3×C4—32no—
368C22×C3×C4—32no—
369C22×C3×C4—32no—
370C22×C3×C4—32no—
371C22×C3×C4—34no—
372C22×C3×C4—32no—
373C22×C3×C4—64no—
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C2×#67—34no—
377C2×#67—34no—
378C2×#67—34no—
379C2×#67—34no—
380C2×#67C22×D312yes—
381C2×#67C22×D312yes—
382C22×Dic3—32no—
383C22×Dic3—32no—
384C22×Dic3—32no—
385C22×Dic3—34no—
386C22×Dic3—32no—
387C22×Dic3—32no—
388C22×Dic3—32no—
389C22×Dic3—62no—
390C22×Dic3—68no—
391C22×Dic3C22×D312yes—
392C22×Dic3C22×D311yescharacteristic
393#237—616no—
394#235—24no—
395#235—24no—
396#235—616no—
397C2×D12C22×D311yescharacteristic
398C2×D12C22×D314yes—
399C2×D12C22×D311yescharacteristic
400C2×C4×D3—24no—
401C2×C4×D3—32no—
402C2×C4×D3—32no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—34no—
406C2×C4×D3—68no—
407C2×C4×D3C22×D312yes—
408C2×C4×D3C22×D312yes—
409C2×C4×D3C22×D312yes—
410C2×C4×D3C22×D312yes—
411C2×C4×D3C22×D314yes—
412C2×Dic6—34no—
413C2×Dic6—34no—
414C2×Dic6—64no—
415C2×Dic6C22×D311yescharacteristic
416C2×Dic6C22×D311yescharacteristic
417C3×C4⋊C4—22no—
418C3×C4⋊C4—34no—
419C3×C4⋊C4—34no—
420C3×C4⋊C4C22×D312yes—
421C3×C4⋊C4C22×D312yes—
422C3×C22⋊C4—22no—
423C3×C22⋊C4—34no—
424C3×C22⋊C4—34no—
425C3×C22⋊C4—34no—
426C3×C22⋊C4C22×D312yes—
427C3×C22⋊C4C22×D312yes—
428C3×C42—22no—
429C3×C42—32no—
430C3×C42—34no—
431C3×C42—31no—
432C3×C42—31no—
433C3×C42C22×D312yes—
434C3×C42C22×D312yes—
435#217—32no—
436#217—32no—
437#217—34no—
438#217—34no—
439#217—34no—
440#217—34no—
441#217—34no—
442#217—62no—
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)⋊C4C22×D314yes—
449(C2×D3)⋊C4C22×D314yes—
450(C2×D3)⋊C4C22×D314yes—
451C4⋊Dic3—34no—
452C4⋊Dic3—32no—
453C4⋊Dic3—34no—
454C4⋊Dic3—32no—
455C4⋊Dic3—34no—
456C4⋊Dic3—64no—
457C4⋊Dic3—62no—
458C4⋊Dic3C22×D314yes—
459Dic3⋊C4—34no—
460Dic3⋊C4—34no—
461Dic3⋊C4—34no—
462Dic3⋊C4—34no—
463Dic3⋊C4—34no—
464Dic3⋊C4—34no—
465Dic3⋊C4—34no—
466Dic3⋊C4—34no—
467Dic3⋊C4—34no—
468Dic3⋊C4—64no—
469Dic3⋊C4—64no—
470Dic3⋊C4C22×D314yes—
471C4×Dic3—32no—
472C4×Dic3—32no—
473C4×Dic3—32no—
474C4×Dic3—32no—
475C4×Dic3—31no—
476C4×Dic3—31no—
477C4×Dic3—31no—
478C4×Dic3—31no—
479C4×Dic3—32no—
480C4×Dic3—34no—
481C4×Dic3—32no—
482C4×Dic3—32no—
483C4×Dic3—32no—
484C4×Dic3—32no—
485C4×Dic3—34no—
486C4×Dic3—32no—
487C4×Dic3—32no—
488C4×Dic3—32no—
489C4×Dic3—62no—
490C4×Dic3—62no—
491C4×Dic3—61no—
492C4×Dic3—61no—
493C4×Dic3C22×D311yescharacteristic
494C4×Dic3C22×D314yes—
495C4×Dic3C22×D311yescharacteristic
496C4×Dic3C22×D312yes—
497C22×C32—22no—
498C22×C32C2×#4112yes—
499C22×C32C2511yescharacteristic
500C2×C3×D3—28no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—24no—
504C2×C3×D3—24no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3C2×#4114yes—
508C32×C4—24no—
509C32×C4C2×#4112yes—
510C32×C4C2×#4112yes—
511C3⋊Dic3—22no—
512C3⋊Dic3—24no—
513C3⋊Dic3C2×#4114yes—
514C3×Dic3—22no—
515C3×Dic3—22no—
516C3×Dic3—22no—
517C3×Dic3—22no—
518C3×Dic3C2×#4114yes—
519C2×#41—31no—
520C2×#41—31no—
521C2×#41—94no—
522C23×C4—31no—
523C23×C4—92no—
524C4⋊Q8—91no—
525C4⋊Q8—92no—
526#127—91no—
527#126—94no—
528#126—94no—
529#125—94no—
530#125—92no—
531#124—94no—
532#124—91no—
533#124—91no—
534#123—32no—
535#123—94no—
536#123—94no—
537#123—92no—
538C22⋊Q8—32no—
539C22⋊Q8—94no—
540C22⋊Q8—92no—
541C22⋊Q8—94no—
542#121—32no—
543#121—94no—
544#121—92no—
545#121—94no—
546#120—32no—
547#120—92no—
548C4×Q8—32no—
549C4×Q8—94no—
550C4×Q8—92no—
551C4×Q8—94no—
552C4×D4—32no—
553C4×D4—34no—
554C4×D4—34no—
555C4×D4—94no—
556C4×D4—92no—
557C4×D4—94no—
558C4×D4—94no—
559C4×D4—94no—
560C4×D4—94no—
561C4×D4—94no—
562#117—32no—
563#117—94no—
564#117—94no—
565#117—92no—
566#117—94no—
567#117—91no—
568#117D3211yescharacteristic
569C2×C42—31no—
570C2×C42—32no—
571C2×C42—92no—
572C2×C42—92no—
573C2×C42—92no—
574C2×C42—92no—
575C2×C42—92no—
576C2×C42—92no—
577C2×C42—91no—
578C23×C3—21no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—64no—
583C23×C3—62no—
584C23×C3C23×D311yescharacteristic
585C23×C3C23×D311yescharacteristic
586C22×D3—22no—
587C22×D3—24no—
588C22×D3C23×D312yes—
589C22×D3C23×D312yes—
590C22×D3C23×D312yes—
591C3×Q8—62no—
592C3×Q8—62no—
593C3×D4—68no—
594C3×D4—64no—
595C3×D4—64no—
596C3×D4—62no—
597C3×D4—62no—
598C2×C3×C4—21no—
599C2×C3×C4—24no—
600C2×C3×C4—21no—
601C2×C3×C4—24no—
602C2×C3×C4—32no—
603C2×C3×C4—32no—
604C2×C3×C4—32no—
605C2×C3×C4—32no—
606C2×C3×C4—32no—
607C2×C3×C4—68no—
608C2×C3×C4—64no—
609C2×C3×C4—62no—
610C2×C3×C4—64no—
611C2×C3×C4—64no—
612C2×C3×C4—64no—
613C2×C3×C4—64no—
614C2×C3×C4#23514yescomplemented
615C2×C3×C4#23714yescomplemented
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—24no—
624#67—68no—
625#67—68no—
626#67—68no—
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—34no—
636C2×Dic3—34no—
637C2×Dic3—62no—
638C2×Dic3—62no—
639C2×Dic3—64no—
640C2×Dic3—64no—
641C2×Dic3—64no—
642C2×Dic3—64no—
643C2×Dic3—64no—
644C2×Dic3—68no—
645C2×Dic3—64no—
646C2×Dic3—124no—
647C2×Dic3C23×D312yes—
648C2×Dic3C23×D312yes—
649C2×Dic3C23×D312yes—
650C2×Dic3C23×D312yes—
651C2×Dic3C23×D312yes—
652D12—28no—
653D12—22no—
654D12—22no—
655C4×D3—24no—
656C4×D3—24no—
657C4×D3—24no—
658C4×D3—24no—
659C4×D3—28no—
660C4×D3—38no—
661C4×D3—64no—
662C4×D3—64no—
663C4×D3—68no—
664C4×D3—64no—
665Dic6—22no—
666Dic6—22no—
667Dic6—68no—
668Dic6—68no—
669Dic6—128no—
670C2×C32—22no—
671C2×C32C22×#4111yescharacteristic
672C2×C32C22×#4112yes—
673C3×D3—24no—
674C3×D3—42no—
675C3×D3—42no—
676C24—31no—
677#41—64no—
678#41—64no—
679#41—1816no—
680C2×Q8—31no—
681C2×Q8—31no—
682C2×Q8—94no—
683C2×D4—32no—
684C2×D4—32no—
685C2×D4—31no—
686C2×D4—34no—
687C2×D4—31no—
688C2×D4—94no—
689C2×D4—94no—
690C22×C4—32no—
691C22×C4—31no—
692C22×C4—34no—
693C22×C4—32no—
694C22×C4—32no—
695C22×C4—32no—
696C22×C4—32no—
697C22×C4—64no—
698C22×C4—92no—
699C22×C4—92no—
700C22×C4—92no—
701C22×C4—92no—
702C22×C4—94no—
703C22×C4—92no—
704C22×C4—188no—
705C22×C4C2×D3211yescharacteristic
706C4⋊C4—34no—
707C4⋊C4—34no—
708C4⋊C4—94no—
709C4⋊C4—94no—
710C4⋊C4—94no—
711C4⋊C4—94no—
712C4⋊C4—92no—
713C4⋊C4—94no—
714C4⋊C4—94no—
715C4⋊C4C2×D3212yes—
716C22⋊C4—34no—
717C22⋊C4—34no—
718C22⋊C4—34no—
719C22⋊C4—94no—
720C22⋊C4—94no—
721C22⋊C4—94no—
722C22⋊C4—94no—
723C22⋊C4—94no—
724C22⋊C4—92no—
725C22⋊C4C2×D3212yes—
726C42—32no—
727C42—34no—
728C42—31no—
729C42—31no—
730C42—92no—
731C42—92no—
732C42—92no—
733C42—92no—
734C42—94no—
735C42—91no—
736C42—91no—
737C42—92no—
738C42—92no—
739C42C2×D3212yes—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—21no—
744C22×C3—34no—
745C22×C3—42no—
746C22×C3—68no—
747C22×C3—62no—
748C22×C3—62no—
749C22×C3—62no—
750C22×C3—62no—
751C22×C3—64no—
752C22×C3—64no—
753C22×C3C2×#23512yes—
754C22×C3C2×#23712yes—
755C22×C3C24×D311yescharacteristic
756C22×C3C24×D311yescharacteristic
757C2×D3—28no—
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—22no—
761C2×D3—22no—
762C2×D3—24no—
763C2×D3—24no—
764C2×D3D3×#4114yes—
765C3×C4—24no—
766C3×C4—24no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—34no—
770C3×C4—44no—
771C3×C4—62no—
772C3×C4—62no—
773C3×C4—62no—
774C3×C4—62no—
775C3×C4C2×#23512yes—
776C3×C4C2×#23512yes—
777C3×C4C2×#23712yes—
778C3×C4C2×#23712yes—
779Dic3—22no—
780Dic3—22no—
781Dic3—22no—
782Dic3—22no—
783Dic3—34no—
784Dic3—34no—
785Dic3—64no—
786Dic3—64no—
787Dic3—64no—
788Dic3—62no—
789Dic3—62no—
790Dic3—124no—
791Dic3—122no—
792Dic3D3×#4114yes—
793C32#344411yescharacteristic, complemented, Sylow
794C23—32no—
795C23—32no—
796C23—32no—
797C23—64no—
798C23—62no—
799C23C22×D3211yescharacteristic
800Q8—62no—
801Q8—62no—
802Q8—188no—
803D4—68no—
804D4—64no—
805D4—64no—
806D4—62no—
807D4—62no—
808D4—188no—
809D4—188no—
810C2×C4—32no—
811C2×C4—32no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—68no—
816C2×C4—64no—
817C2×C4—62no—
818C2×C4—64no—
819C2×C4—64no—
820C2×C4—64no—
821C2×C4—64no—
822C2×C4—98no—
823C2×C4—92no—
824C2×C4—92no—
825C2×C4—94no—
826C2×C4—184no—
827C2×C4—188no—
828C2×C4—184no—
829C2×C4—184no—
830C2×C4—184no—
831C2×C4#379514yescomplemented
832C2×C4C22×D3214yes—
833C2×C4C22×D3211yescharacteristic
834C2×C4C22×D3211yescharacteristic
835C2×C3—22no—
836C2×C3—22no—
837C2×C3—21no—
838C2×C3—22no—
839C2×C3—42no—
840C2×C3—64no—
841C2×C3—122no—
842C2×C3—122no—
843C2×C3C22×#23511yescharacteristic
844C2×C3C22×#23711yescharacteristic
845C2×C3C2×D3×#4112yes—
846C2×C3C2×D3×#4112yes—
847D3—24no—
848D3—42no—
849D3—42no—
850C22—22no—
851C22—34no—
852C22—68no—
853C22—62no—
854C22—62no—
855C22—62no—
856C22—62no—
857C22—64no—
858C22—64no—
859C22C2×#379512yes—
860C22C23×D3211yescharacteristic
861C4—24no—
862C4—34no—
863C4—62no—
864C4—62no—
865C4—62no—
866C4—62no—
867C4—94no—
868C4—182no—
869C4—184no—
870C4C2×#379512yes—
871C4C2×#379512yes—
872C3—21no—
873C3#8583611yescharacteristic, complemented
874C3#8601811yescharacteristic, complemented
875C2—22no—
876C2—64no—
877C2—122no—
878C2—122no—
879C2C22×#379511yescharacteristic
880C2D32×#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. #10595988C2semidirect
2. C3×#5524C2semidirect
3. C3×#5522C2semidirect
4. #10595032C2semidirect
5. #10595022C2semidirect
6. Dic3×#235C2semidirect
7. C2×C4×D3×Dic3C2semidirect
8. #10594444C2semidirect
9. #10594426C2semidirect
10. #10594385C2semidirect
11. #10594367C2semidirect
12. #10594131C2semidirect
13. #10594054C2semidirect
14. #10593910C2semidirect
15. C4×#3795C2semidirect
26. #64099C22semidirect
27. #64097C22semidirect
29. C4×#634C22semidirect
33. C3×#893C22semidirect
34. C3×#887C22semidirect
39. C3×#872C22semidirect
40. C3×C42×D3C22semidirect
46. #63914C22semidirect
47. #63913C22semidirect
50. C4×#625C22semidirect
53. Dic3×D12C22semidirect
58. #63879C22semidirect
60. #63877C22semidirect
65. C4×D3×Dic3C22semidirect
66. #63873C22semidirect
67. #63863C22semidirect
68. #63863C22semidirect
69. #63861C22semidirect
70. #63858C22semidirect
72. #63855C22semidirect
73. #63847C22semidirect
74. #63844C22semidirect
75. Dic3×Dic6C22semidirect
76. #63841C22semidirect
100. #5524D3semidirect
101. #5522D3semidirect
250. #893C2×D3semidirect
261. #887C2×D3semidirect
286. #872C2×D3semidirect
292. C42×D3C2×D3semidirect
304. C2×C32×C4#41semidirect
338. D3×Dic3#41semidirect
614. C2×C3×C4#235semidirect
615. C2×C3×C4#237semidirect
793. C32#3444semidirect
831. C2×C4#3795semidirect
873. C3#85836semidirect
874. C3#86018semidirect

Maximal subgroups

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

subgroupindex
#105959882
C3×#55242
C3×#55222
#105950322
#105950222
Dic3×#2352
C2×C4×D3×Dic32
#105944442
#105944262
#105943852
#105943672
#105941312
#105940542
#105939102
C4×#37952
#860183
#858363