Finite Group Databasebeta

← #11900891

Subgroups — #11900891

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#10596262C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic, complemented
3C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
4#10595498C214yesmaximal, complemented
5#10595049C211yesmaximal, characteristic, complemented
6#10595029C211yesmaximal, characteristic, complemented
7#10594955C212yesmaximal, complemented
8#10594954C211yesmaximal, characteristic, complemented
9#10594949C212yesmaximal, complemented
10#10594948C214yesmaximal, complemented
11Dic3×#235C211yesmaximal, characteristic, complemented
12#10594910C212yesmaximal, complemented
13C4×#3804C214yesmaximal, complemented
14#10594839C214yesmaximal, complemented
15#10594808C212yesmaximal, complemented
16#86018—31nomaximal
17#85680—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C23×C3×Dic3C2212yes—
21C2×C3×#235C2211yescharacteristic
22C2×#3804C2214yes—
23#64162C2212yes—
24#64139C2212yes—
25#64138C2212yes—
26C4×#638C2214yes—
27#64135C2211yescharacteristic
28#64133C2212yes—
29C3×#953C2212yes—
30C3×#930C2212yes—
31C3×#929C2212yes—
32C3×C4×#67C2214yes—
33C3×#926C2211yescharacteristic
34C3×#924C2212yes—
35C2×C3×C4×Dic3C2212yes—
36C2×C3×C4×Dic3C2212yes—
37C2×C3×C4×Dic3C2212yes—
38C2×C3×C4×Dic3C2211yescharacteristic
39C2×C3×C4×Dic3C2212yes—
40C2×C3×C4×Dic3C2212yes—
41C2×C3×C4×Dic3C2211yescharacteristic
42#63978C2214yes—
43#63978C2214yes—
44Dic3×#67C2214yes—
45Dic3×#67C2214yes—
46#63966C2214yes—
47#63964C2214yes—
48#63964C2214yes—
49#63961C2214yes—
50#63955C2214yes—
51#63952C2214yes—
52#63952C2214yes—
53#63918C2212yescomplemented
54C4×#627C2214yescomplemented
55#63911C2211yescharacteristic, complemented
56C4×#626C2214yescomplemented
57#63894C2212yescomplemented
58Dic3×D12C2212yescomplemented
59C4×#624C2212yescomplemented
60#63880C2214yescomplemented
61#63877C2214yescomplemented
62C4×D3×Dic3C2212yescomplemented
63#63874C2212yescomplemented
64#63869C2212yescomplemented
65#63868C2214yescomplemented
66#63867C2214yescomplemented
67#63866C2211yescharacteristic, complemented
68#63864C2211yescharacteristic, complemented
69#63860C2211yescharacteristic, complemented
70#63859C2214yescomplemented
71#63855C2212yescomplemented
72#63852C2214yescomplemented
73#63844C2212yescomplemented
74Dic3×Dic6C2212yescomplemented
75#63837C2214yescomplemented
76#63836C2214yescomplemented
77C3×#525—31no—
78C22×C3×C42—31no—
79#5832—31no—
80Dic3×#41—31no—
81#5791—31no—
82#5791—31no—
83#5791—34no—
84#5791—61no—
85#5791D311yescharacteristic, complemented
86C22×C4×Dic3D311yescharacteristic, complemented
87#5649—34no—
88#5624—32no—
89#5622—32no—
90#5600—32no—
91#5596—32no—
92#5586—34no—
93#5538—34no—
94C4×#237—34no—
95#5522—31no—
96#5517—31no—
97#5479—32no—
98#5479—34no—
99#5479—34no—
100#5479—32no—
101#5477—31no—
102#5477—32no—
103C4×#235—31no—
104C4×#235—34no—
105C4×#235—31no—
106#5470—31no—
107#5470—32no—
108C24×C32C2311yescharacteristic
109C22×C32×C4—24no—
110C22×C32×C4C2312yes—
111C22×C32×C4C2312yes—
112C22×C32×C4C2311yescharacteristic
113C22×C32×C4C2311yescharacteristic
114C2×#638C2314yes—
115C2×#638C2312yes—
116#3828—24no—
117C2×C4⋊(C3⋊D3)C2311yescharacteristic
118C2×C4×C3⋊D3C2312yes—
119C2×#634C2311yescharacteristic
120C2×C3×#67C2314yes—
121C2×C3×#67C2312yes—
122C22×C3×Dic3—28no—
123C22×C3×Dic3C2312yes—
124C22×C3×Dic3C2312yes—
125C22×C3×Dic3C2312yes—
126C22×C3×Dic3C2312yes—
127C22×C3×Dic3C2312yes—
128C22×C3×Dic3C2312yes—
129C3×#235—24no—
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2314yes—
134C2×#626C2314yes—
135C2×#624C2314yes—
136#3804—216no—
137C2×D3×Dic3C2314yes—
138#3757C2314yes—
139#3757C2312yes—
140#3752C2314yes—
141C4⋊(C3⋊Dic3)C2312yes—
142#3750C2314yes—
143C4×C3⋊Dic3C2312yes—
144C3×#217C2314yes—
145C3×#217C2312yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×C4⋊Dic3C2312yes—
148C3×Dic3⋊C4C2314yes—
149C3×C4×Dic3C2312yes—
150C3×C4×Dic3C2312yes—
151C3×C4×Dic3C2312yes—
152C3×C4×Dic3C2312yes—
153C3×C4×Dic3C2311yescharacteristic
154C3×C4×Dic3C2312yes—
155C3×C4×Dic3C2311yescharacteristic
156C3×C4×Dic3C2311yescharacteristic
157C3×C4×Dic3C2311yescharacteristic
158C3×C4×Dic3C2312yes—
159C3×C4×Dic3C2312yes—
160#3724C2314yes—
161#3724C2314yes—
162Dic3⋊Dic3C2314yes—
163Dic3⋊Dic3C2314yes—
164Dic3⋊Dic3C2314yes—
165Dic3⋊Dic3C2314yes—
166#3722C2314yes—
167#3722C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yes—
170Dic32C2314yes—
171Dic32C2314yes—
172#3444—91noSylow
173C2×C3×#41—31no—
174C23×C3×C4—21no—
175C23×C3×C4—32no—
176C23×C3×C4C2×D311yescharacteristic
177C23×C3×C4C2×D311yescharacteristic
178C23×Dic3C2×D312yes—
179C2×#237—34no—
180C2×#235—31no—
181C2×#235—31no—
182C2×#235—34no—
183C2×#235—61no—
184C2×#235C2×D311yescharacteristic
185C3×#123—32no—
186C3×C22⋊Q8—32no—
187C3×#121—32no—
188C3×#120—32no—
189C3×C4×D4—34no—
190C3×#117—31no—
191C2×C3×C42—32no—
192C2×C3×C42—31no—
193C2×C3×C42—32no—
194C2×C3×C42—31no—
195C2×C3×C42—32no—
196C2×C3×C42—32no—
197C2×C3×C42—32no—
198#953—32no—
199#953—32no—
200#953—62no—
201#953C2×D312yes—
202#947—31no—
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—32no—
214#930—32no—
215#930—34no—
216#930—34no—
217#930—62no—
218#930C2×D312yes—
219#929—32no—
220#929—32no—
221#929—34no—
222#929—34no—
223#929—62no—
224#929C2×D312yes—
225C4×#67—34no—
226C4×#67—34no—
227C4×#67—34no—
228C4×#67—34no—
229C4×#67—34no—
230C4×#67—34no—
231C4×#67—34no—
232C4×#67—64no—
233C4×#67C2×D314yes—
234#926—31no—
235#926—31no—
236#926—34no—
237#926—32no—
238#926—61no—
239#926C2×D311yescharacteristic
240#924—32no—
241#924—32no—
242#924—34no—
243#924—34no—
244#924—62no—
245#924C2×D312yes—
246C2×C4×Dic3—32no—
247C2×C4×Dic3C2×D312yes—
248C2×C4×Dic3C2×D311yescharacteristic
249C2×C4×Dic3C2×D311yescharacteristic
250C2×C4×Dic3C2×D312yes—
251C2×C4×Dic3C2×D312yes—
252C2×C4×Dic3C2×D312yes—
253C2×C4×Dic3C2×D312yes—
254#898—34no—
255#893—32no—
256#892—34no—
257#890—32no—
258#889—34no—
259#888—32no—
260#887—34no—
261#887—32no—
262#886—34no—
263#885—34no—
264#67⋊C4—34no—
265#67⋊C4—34no—
266#67⋊C4—34no—
267#879—34no—
268#878—34no—
269#878—34no—
270#877—34no—
271#877—34no—
272#876—34no—
273#876—34no—
274#875—31no—
275#875—31no—
276#875—34no—
277#874—31no—
278C4×D12—32no—
279C4×D12—34no—
280C4×D12—34no—
281C4×D12—32no—
282#872—32no—
283#872—34no—
284#872—34no—
285#872—32no—
286#872—32no—
287C42×D3—32no—
288C42×D3—32no—
289C42×D3—32no—
290#870—32no—
291#870—34no—
292#869—31no—
293#869—32no—
294C4×Dic6—32no—
295C4×Dic6—32no—
296C4×Dic6—34no—
297C4×Dic6—34no—
298C4×Dic6—34no—
299C23×C32—24no—
300C23×C32—22no—
301C23×C32C2411yescharacteristic
302C23×C32C2412yes—
303C22×C3⋊D3C2412yes—
304C22×C3×D3C2412yes—
305C2×C32×C4—22no—
306C2×C32×C4—24no—
307C2×C32×C4—24no—
308C2×C32×C4#4114yescomplemented
309C2×C32×C4C2412yes—
310C2×C32×C4C2411yescharacteristic
311C2×C32×C4C2411yescharacteristic
312#638—28no—
313#638—24no—
314C2×C3⋊Dic3C2412yes—
315C2×C3⋊Dic3C2414yes—
316C4⋊(C3⋊D3)—22no—
317C4×C3⋊D3—24no—
318#634—22no—
319C3×#67—28no—
320C3×#67—24no—
321C2×C3×Dic3—24no—
322C2×C3×Dic3—24no—
323C2×C3×Dic3—24no—
324C2×C3×Dic3—24no—
325C2×C3×Dic3—24no—
326C2×C3×Dic3#4118yescomplemented
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2414yes—
329C2×C3×Dic3C2412yes—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C3×D12—22no—
334C3×C4×D3—24no—
335C3×Dic6—22no—
336#627—28no—
337#626—28no—
338#624—28no—
339D3×Dic3—28no—
340#533—91no—
341#533—92no—
342#532—92no—
343#532—91no—
344#529—94no—
345#529—92no—
346#529—92no—
347#529—94no—
348#525—31no—
349#525—94no—
350#525—91no—
351C4×#41—91no—
352C4×#41—94no—
353C4×#41—91no—
354C22×C42—31no—
355C24×C3—21no—
356C24×C3C22×D311yescharacteristic
357C24×C3C22×D311yescharacteristic
358C3×#41—64no—
359C2×C3×Q8—31no—
360C2×C3×D4—32no—
361C2×C3×D4—34no—
362C2×C3×D4—31no—
363C22×C3×C4—24no—
364C22×C3×C4—24no—
365C22×C3×C4—21no—
366C22×C3×C4—22no—
367C22×C3×C4—22no—
368C22×C3×C4—21no—
369C22×C3×C4—32no—
370C22×C3×C4—32no—
371C22×C3×C4—32no—
372C22×C3×C4—32no—
373C22×C3×C4—32no—
374C22×C3×C4—32no—
375C22×C3×C4—32no—
376C22×C3×C4—44no—
377C22×C3×C4—68no—
378C22×C3×C4C22×D312yes—
379C22×C3×C4C22×D312yes—
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D312yes—
382C22×C3×C4C22×D312yes—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C2×#67—32no—
387C2×#67—34no—
388C2×#67—32no—
389C2×#67—34no—
390C2×#67—34no—
391C2×#67—64no—
392C2×#67—62no—
393C2×#67C22×D312yes—
394C2×#67C22×D314yes—
395C22×Dic3—28no—
396C22×Dic3—34no—
397C22×Dic3C22×D312yes—
398C22×Dic3C22×D312yes—
399C22×Dic3C22×D312yes—
400C22×Dic3C22×D312yes—
401C22×Dic3C22×D312yes—
402C22×Dic3C22×D312yes—
403#237—616no—
404#235—24no—
405#235—616no—
406#235—64no—
407#235—64no—
408#235—124no—
409C2×D12—34no—
410C2×D12—31no—
411C2×D12—31no—
412C2×D12—61no—
413C2×D12C22×D311yescharacteristic
414C2×C4×D3—34no—
415C2×C4×D3—32no—
416C2×C4×D3—32no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3—62no—
420C2×C4×D3C22×D312yes—
421C2×Dic6—31no—
422C2×Dic6—31no—
423C2×Dic6—34no—
424C2×Dic6—34no—
425C2×Dic6—61no—
426C2×Dic6C22×D311yescharacteristic
427C3×C4⋊C4—32no—
428C3×C4⋊C4—34no—
429C3×C22⋊C4—34no—
430C3×C22⋊C4—32no—
431C3×C22⋊C4—34no—
432C3×C42—32no—
433C3×C42—32no—
434C3×C42—32no—
435C3×C42—32no—
436C3×C42—31no—
437C3×C42—32no—
438C3×C42—31no—
439C3×C42—31no—
440C3×C42—32no—
441C3×C42—31no—
442C3×C42—32no—
443#217—34no—
444#217—32no—
445#217—32no—
446#217—34no—
447#217—34no—
448#217—34no—
449#217—64no—
450#217—62no—
451#217C22×D312yes—
452#217C22×D314yes—
453(C2×D3)⋊C4—34no—
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—64no—
462(C2×D3)⋊C4C22×D314yes—
463C4⋊Dic3—32no—
464C4⋊Dic3—32no—
465C4⋊Dic3—34no—
466C4⋊Dic3—34no—
467C4⋊Dic3—34no—
468C4⋊Dic3—34no—
469C4⋊Dic3—62no—
470C4⋊Dic3C22×D312yes—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—34no—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4—34no—
479Dic3⋊C4—34no—
480Dic3⋊C4—34no—
481Dic3⋊C4—64no—
482Dic3⋊C4C22×D314yes—
483C4×Dic3—32no—
484C4×Dic3—32no—
485C4×Dic3—34no—
486C4×Dic3—34no—
487C4×Dic3—34no—
488C4×Dic3—34no—
489C4×Dic3—62no—
490C4×Dic3C22×D312yes—
491C4×Dic3C22×D312yes—
492C4×Dic3C22×D311yescharacteristic
493C4×Dic3C22×D311yescharacteristic
494C4×Dic3C22×D312yes—
495C4×Dic3C22×D312yes—
496C4×Dic3C22×D312yes—
497C4×Dic3C22×D312yes—
498C4×Dic3C22×D312yes—
499C4×Dic3C22×D311yescharacteristic
500C4×Dic3C22×D311yescharacteristic
501C22×C32—28no—
502C22×C32—22no—
503C22×C32—22no—
504C22×C32—22no—
505C22×C32C2×#4112yes—
506C22×C32C2×#4114yes—
507C22×C32C2511yescharacteristic
508C2×C3⋊D3—24no—
509C2×C3⋊D3—22no—
510C2×C3×D3—24no—
511C2×C3×D3—22no—
512C32×C4—22no—
513C32×C4C2×#4112yes—
514C32×C4C2×#4112yes—
515C3⋊Dic3—24no—
516C3⋊Dic3—22no—
517C3×Dic3—24no—
518C3×Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3—22no—
521C3×Dic3C2×#4114yes—
522C3×Dic3C2×#4114yes—
523C2×#41—31no—
524C2×#41—94no—
525C2×#41—91no—
526C23×C4—32no—
527C23×C4D3211yescharacteristic
528C4⋊Q8—92no—
529C4⋊Q8—91no—
530#127—91no—
531#126—94no—
532#126—94no—
533#125—94no—
534#125—92no—
535#124—94no—
536#124—91no—
537#124—91no—
538#123—32no—
539#123—94no—
540#123—94no—
541#123—92no—
542C22⋊Q8—32no—
543C22⋊Q8—94no—
544C22⋊Q8—94no—
545C22⋊Q8—92no—
546#121—32no—
547#121—94no—
548#121—94no—
549#121—92no—
550#120—32no—
551#120—92no—
552C4×Q8—94no—
553C4×Q8—92no—
554C4×Q8—94no—
555C4×Q8—92no—
556C4×D4—34no—
557C4×D4—94no—
558C4×D4—92no—
559C4×D4—94no—
560C4×D4—92no—
561C4×D4—94no—
562C4×D4—94no—
563C4×D4—94no—
564C4×D4—94no—
565C4×D4—94no—
566#117—31no—
567#117—92no—
568#117—94no—
569#117—94no—
570#117—92no—
571#117—94no—
572#117—91no—
573C2×C42—32no—
574C2×C42—31no—
575C2×C42—32no—
576C2×C42—32no—
577C2×C42—32no—
578C2×C42—32no—
579C2×C42—31no—
580C2×C42—92no—
581C2×C42—92no—
582C23×C3—24no—
583C23×C3—22no—
584C23×C3—22no—
585C23×C3—24no—
586C23×C3—22no—
587C23×C3—21no—
588C23×C3—32no—
589C23×C3—42no—
590C23×C3—44no—
591C23×C3C23×D312yes—
592C23×C3C23×D311yescharacteristic
593C23×C3C23×D311yescharacteristic
594C23×C3C23×D312yes—
595C22×D3—32no—
596C22×D3—32no—
597C22×D3—62no—
598C22×D3C23×D312yes—
599C3×Q8—62no—
600C3×D4—68no—
601C3×D4—64no—
602C3×D4—62no—
603C2×C3×C4—22no—
604C2×C3×C4—22no—
605C2×C3×C4—24no—
606C2×C3×C4—24no—
607C2×C3×C4—24no—
608C2×C3×C4—24no—
609C2×C3×C4—21no—
610C2×C3×C4—22no—
611C2×C3×C4—21no—
612C2×C3×C4—24no—
613C2×C3×C4—38no—
614C2×C3×C4—32no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—34no—
618C2×C3×C4—32no—
619C2×C3×C4—32no—
620C2×C3×C4—44no—
621C2×C3×C4—44no—
622C2×C3×C4—42no—
623C2×C3×C4—64no—
624C2×C3×C4—64no—
625C2×C3×C4—64no—
626C2×C3×C4—64no—
627C2×C3×C4—64no—
628C2×C3×C4—64no—
629C2×C3×C4#23514yescomplemented
630C2×C3×C4#23714yescomplemented
631C2×C3×C4C23×D312yes—
632C2×C3×C4C23×D312yes—
633C2×C3×C4C23×D311yescharacteristic
634C2×C3×C4C23×D311yescharacteristic
635C2×C3×C4C23×D311yescharacteristic
636C2×C3×C4C23×D311yescharacteristic
637#67—24no—
638#67—28no—
639#67—64no—
640#67—68no—
641#67—64no—
642#67—68no—
643#67—68no—
644#67—124no—
645#67—128no—
646C2×Dic3—24no—
647C2×Dic3—24no—
648C2×Dic3—24no—
649C2×Dic3—24no—
650C2×Dic3—24no—
651C2×Dic3—32no—
652C2×Dic3—32no—
653C2×Dic3—34no—
654C2×Dic3—34no—
655C2×Dic3—64no—
656C2×Dic3—62no—
657C2×Dic3—68no—
658C2×Dic3#23518yescomplemented
659C2×Dic3C23×D312yes—
660C2×Dic3C23×D314yes—
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D312yes—
663C2×Dic3C23×D312yes—
664C2×Dic3C23×D312yes—
665D12—22no—
666D12—68no—
667D12—62no—
668D12—62no—
669D12—122no—
670C4×D3—24no—
671C4×D3—68no—
672C4×D3—68no—
673C4×D3—64no—
674C4×D3—64no—
675C4×D3—68no—
676C4×D3—124no—
677Dic6—22no—
678Dic6—68no—
679Dic6—62no—
680Dic6—62no—
681Dic6—68no—
682Dic6—122no—
683C2×C32—22no—
684C2×C32—24no—
685C2×C32C22×#4111yescharacteristic
686C2×C32C22×#4112yes—
687C3⋊D3—42no—
688C3×D3—42no—
689C24C2×D3211yescharacteristic
690#41—64no—
691#41—1816no—
692#41—184no—
693C2×Q8—31no—
694C2×Q8—94no—
695C2×Q8—91no—
696C2×D4—34no—
697C2×D4—32no—
698C2×D4—31no—
699C2×D4—94no—
700C2×D4—94no—
701C2×D4—92no—
702C2×D4—91no—
703C22×C4—24no—
704C22×C4—32no—
705C22×C4—32no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—68no—
712C22×C4—94no—
713C22×C4—94no—
714C22×C4—92no—
715C22×C4C2×D3212yes—
716C22×C4C2×D3211yescharacteristic
717C22×C4C2×D3212yes—
718C22×C4C2×D3211yescharacteristic
719C4⋊C4—32no—
720C4⋊C4—34no—
721C4⋊C4—94no—
722C4⋊C4—94no—
723C4⋊C4—94no—
724C4⋊C4—94no—
725C4⋊C4—94no—
726C4⋊C4—94no—
727C4⋊C4—92no—
728C4⋊C4—94no—
729C22⋊C4—32no—
730C22⋊C4—34no—
731C22⋊C4—34no—
732C22⋊C4—94no—
733C22⋊C4—94no—
734C22⋊C4—94no—
735C22⋊C4—94no—
736C22⋊C4—94no—
737C22⋊C4—92no—
738C22⋊C4—94no—
739C42—32no—
740C42—32no—
741C42—32no—
742C42—32no—
743C42—31no—
744C42—32no—
745C42—31no—
746C42—31no—
747C42—31no—
748C42—32no—
749C42—32no—
750C42—94no—
751C42—94no—
752C42—92no—
753C22×C3—28no—
754C22×C3—28no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—24no—
762C22×C3—22no—
763C22×C3—21no—
764C22×C3—42no—
765C22×C3—42no—
766C22×C3—42no—
767C22×C3—48no—
768C22×C3—64no—
769C22×C3—62no—
770C22×C3C2×#23514yes—
771C22×C3C2×#23512yes—
772C22×C3C2×#23712yes—
773C22×C3D3×#4114yes—
774C22×C3C24×D311yescharacteristic
775C22×C3C24×D311yescharacteristic
776C2×D3—22no—
777C2×D3—24no—
778C2×D3—62no—
779C2×D3—64no—
780C2×D3—62no—
781C2×D3—64no—
782C2×D3—122no—
783C2×D3—124no—
784C3×C4—22no—
785C3×C4—22no—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—34no—
789C3×C4—34no—
790C3×C4—42no—
791C3×C4—64no—
792C3×C4—62no—
793C3×C4—62no—
794C3×C4—62no—
795C3×C4C2×#23512yes—
796C3×C4C2×#23512yes—
797C3×C4C2×#23712yes—
798C3×C4C2×#23712yes—
799Dic3—22no—
800Dic3—22no—
801Dic3—22no—
802Dic3—24no—
803Dic3—62no—
804Dic3—64no—
805Dic3—62no—
806Dic3—64no—
807Dic3—122no—
808Dic3—124no—
809Dic3C2×#23514yes—
810Dic3C2×#23514yes—
811C32#344411yescharacteristic, complemented, Sylow
812C23—24no—
813C23—22no—
814C23—32no—
815C23—92no—
816C23C22×D3212yes—
817C23C22×D3211yescharacteristic
818Q8—62no—
819Q8—188no—
820Q8—182no—
821D4—68no—
822D4—64no—
823D4—62no—
824D4—188no—
825D4—188no—
826D4—184no—
827D4—182no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—38no—
832C2×C4—32no—
833C2×C4—32no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—34no—
837C2×C4—32no—
838C2×C4—64no—
839C2×C4—64no—
840C2×C4—64no—
841C2×C4—64no—
842C2×C4—64no—
843C2×C4—64no—
844C2×C4—94no—
845C2×C4—92no—
846C2×C4—188no—
847C2×C4—188no—
848C2×C4—184no—
849C2×C4#380414yescomplemented
850C2×C4C22×D3212yes—
851C2×C4C22×D3211yescharacteristic
852C2×C4C22×D3211yescharacteristic
853C2×C3—22no—
854C2×C3—24no—
855C2×C3—24no—
856C2×C3—22no—
857C2×C3—22no—
858C2×C3—21no—
859C2×C3—44no—
860C2×C3—42no—
861C2×C3—122no—
862C2×C3C22×#23512yes—
863C2×C3C22×#23511yescharacteristic
864C2×C3C22×#23711yescharacteristic
865C2×C3C2×D3×#4112yes—
866D3—42no—
867D3—122no—
868D3—122no—
869D3—242no—
870C22—28no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—64no—
875C22—62no—
876C22—184no—
877C22—182no—
878C22D3×#23514yes—
879C22C2×#380412yes—
880C22C23×D3211yescharacteristic
881C4—22no—
882C4—34no—
883C4—34no—
884C4—62no—
885C4—62no—
886C4—64no—
887C4—62no—
888C4—184no—
889C4—182no—
890C4C2×#380412yes—
891C4C2×#380412yes—
892C3—21no—
893C3#8568011yescharacteristic, complemented
894C3#8601811yescharacteristic, complemented
895C2—24no—
896C2—22no—
897C2—122no—
898C2—362no—
899C2C2×D3×#23512yes—
900C2C22×#380411yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. #10596262C2semidirect
2. C3×#5791C2semidirect
3. C22×C3×C4×Dic3C2semidirect
4. #10595498C2semidirect
5. #10595049C2semidirect
6. #10595029C2semidirect
7. #10594955C2semidirect
8. #10594954C2semidirect
9. #10594949C2semidirect
10. #10594948C2semidirect
11. Dic3×#235C2semidirect
12. #10594910C2semidirect
13. C4×#3804C2semidirect
14. #10594839C2semidirect
15. #10594808C2semidirect
53. #63918C22semidirect
54. C4×#627C22semidirect
55. #63911C22semidirect
56. C4×#626C22semidirect
57. #63894C22semidirect
58. Dic3×D12C22semidirect
59. C4×#624C22semidirect
60. #63880C22semidirect
61. #63877C22semidirect
62. C4×D3×Dic3C22semidirect
63. #63874C22semidirect
64. #63869C22semidirect
65. #63868C22semidirect
66. #63867C22semidirect
67. #63866C22semidirect
68. #63864C22semidirect
69. #63860C22semidirect
70. #63859C22semidirect
71. #63855C22semidirect
72. #63852C22semidirect
73. #63844C22semidirect
74. Dic3×Dic6C22semidirect
75. #63837C22semidirect
76. #63836C22semidirect
85. #5791D3semidirect
86. C22×C4×Dic3D3semidirect
308. C2×C32×C4#41semidirect
326. C2×C3×Dic3#41semidirect
629. C2×C3×C4#235semidirect
630. C2×C3×C4#237semidirect
658. C2×Dic3#235semidirect
811. C32#3444semidirect
849. C2×C4#3804semidirect
893. C3#85680semidirect
894. C3#86018semidirect

Maximal subgroups

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

subgroupindex
#105962622
C3×#57912
C22×C3×C4×Dic32
#105954982
#105950492
#105950292
#105949552
#105949542
#105949492
#105949482
Dic3×#2352
#105949102
C4×#38042
#105948392
#105948082
#860183
#856803