Finite Group Databasebeta

← #11900890

Subgroups — #11900890

Order 1152.

2579 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596303C211yesmaximal, characteristic, complemented
2C3×#5828C211yesmaximal, characteristic, complemented
3C3×Dic3×#41C211yesmaximal, characteristic, complemented
4#10595376C212yesmaximal, complemented
5#10595367C212yesmaximal, complemented
6#10595172C212yesmaximal, complemented
7#10595131C212yesmaximal, complemented
8#10595129C214yesmaximal, complemented
9#10595116C214yesmaximal, complemented
10#10595050C211yesmaximal, characteristic, complemented
11#10595023C211yesmaximal, characteristic, complemented
12#10594954C211yesmaximal, characteristic, complemented
13#10594933C214yesmaximal, complemented
14C4×#3804C214yesmaximal, complemented
15C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
16#86018—31nomaximal
17#85836—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3828C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×#3804C2214yes—
22C22×D3×Dic3C2212yes—
23#64156C2211yescharacteristic, complemented
24#64153C2211yescharacteristic, complemented
25#64149C2211yescharacteristic, complemented
26#64148C2214yes—
27#64145C2211yescharacteristic, complemented
28C4×#638C2214yescomplemented
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C3×#946C2212yes—
31C3×Q8×Dic3C2212yescomplemented
32C3×#938C2212yes—
33C3×#937C2212yes—
34C3×#935C2212yes—
35C3×D4×Dic3C2214yes—
36C3×D4×Dic3C2212yescomplemented
37C3×C4×#67C2214yes—
38C3×#926C2211yescharacteristic
39C3×#926C2211yescharacteristic
40C3×#926C2212yescomplemented
41C2×C3×C4×Dic3C2211yescharacteristic
42C2×C3×C4×Dic3C2212yescomplemented
43#63982C2214yes—
44#63977C2212yes—
45Dic3×#67C2214yes—
46#63971C2214yes—
47#63969C2214yes—
48#63966C2212yes—
49#63956C2214yescomplemented
50#63955C2214yescomplemented
51C2×Dic32C2212yes—
52#63953C2214yescomplemented
53#63952C2214yes—
54#63952C2214yescomplemented
55#63919C2212yescomplemented
56C4×#627C2214yescomplemented
57#63909C2212yes—
58C4×#626C2214yes—
59#63899C2214yes—
60#63894C2212yescomplemented
61#63890C2214yes—
62C4×#624C2212yescomplemented
63#63880C2214yes—
64#63877C2214yes—
65C4×D3×Dic3C2212yes—
66C4×D3×Dic3C2212yes—
67C4×D3×Dic3C2212yes—
68C4×D3×Dic3C2212yes—
69#63874C2212yescomplemented
70#63872C2212yescomplemented
71#63857C2212yes—
72#63848C2214yescomplemented
73#63847C2214yescomplemented
74#63844C2212yescomplemented
75#63837C2214yescomplemented
76#63836C2214yescomplemented
77C3×#525—31no—
78C3×C4×#41—31no—
79#5832—31no—
80#5832—31no—
81#5832—61no—
82#5828D311yescharacteristic, complemented
83Dic3×#41D311yescharacteristic, complemented
84#5791—31no—
85C22×C4×Dic3—31no—
86#5649—34no—
87#5624—32no—
88#5622—32no—
89#5600—32no—
90#5596—32no—
91#5586—34no—
92#5580—32no—
93#5578—32no—
94#5557—32no—
95#5548—32no—
96#5547—34no—
97#5538—34no—
98#5538—34no—
99C4×#237—34no—
100#5528—34no—
101#5524—31no—
102#5522—31no—
103#5517—31no—
104#5517—31no—
105C4×#235—34no—
106C4×#235—31no—
107C2×C42×D3—31no—
108C23×C3×D3C2311yescharacteristic
109C32×#41—24no—
110C2×C32×Q8C2311yescharacteristic
111C2×C32×D4C2312yes—
112C2×C32×D4C2311yescharacteristic
113C22×C32×C4C2312yes—
114C22×C32×C4C2311yescharacteristic
115C2×#638C2314yes—
116C2×#638C2312yes—
117C22×C3⋊Dic3C2312yes—
118#3828—24no—
119C2×C4⋊(C3⋊D3)C2311yescharacteristic
120C2×C4×C3⋊D3C2312yes—
121C2×#634C2311yescharacteristic
122C2×C3×#67C2314yes—
123C22×C3×Dic3C2312yes—
124C22×C3×Dic3C2314yes—
125C22×C3×Dic3C2311yescharacteristic
126C2×C3×C4×D3—24no—
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2312yes—
129C2×#627C2314yes—
130C2×#626C2314yes—
131C2×#624C2314yes—
132#3804—216no—
133C2×D3×Dic3—28no—
134C2×D3×Dic3C2312yes—
135C2×D3×Dic3C2312yes—
136C2×D3×Dic3C2312yes—
137C2×D3×Dic3C2312yes—
138#3757C2314yes—
139#3752C2314yes—
140#3750C2314yes—
141C4×C3⋊Dic3C2311yescharacteristic
142C4×C3⋊Dic3C2312yes—
143C4×C3⋊Dic3C2311yescharacteristic
144C3×#217C2312yes—
145C3×#217C2312yes—
146C3×#217C2314yes—
147C3×#217C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×C4⋊Dic3C2312yes—
150C3×C4⋊Dic3C2312yes—
151C3×C4⋊Dic3C2314yes—
152C3×Dic3⋊C4C2314yes—
153C3×C4×Dic3C2311yescharacteristic
154C3×C4×Dic3C2311yescharacteristic
155C3×C4×Dic3C2312yes—
156C3×C4×Dic3C2312yes—
157C3×C4×Dic3C2314yes—
158C3×C4×Dic3C2312yes—
159#3724C2314yes—
160#3724C2314yes—
161Dic3⋊Dic3C2314yes—
162Dic3⋊Dic3C2314yes—
163Dic3⋊Dic3C2314yes—
164#3722C2314yes—
165#3722C2314yes—
166(C2×D3)⋊Dic3C2314yes—
167Dic32C2312yes—
168Dic32C2312yes—
169Dic32C2314yes—
170Dic32C2312yes—
171Dic32C2312yes—
172#3444—91noSylow
173C2×C3×#41—21no—
174C2×C3×#41C2×D311yescharacteristic
175C2×C3×#41C2×D311yescharacteristic
176C23×C3×C4—31no—
177C23×Dic3—32no—
178C2×#237—34no—
179C2×#235—31no—
180C2×#235—31no—
181C2×#235—34no—
182C2×#235—61no—
183C22×C4×D3—32no—
184C22×C4×D3C2×D311yescharacteristic
185C3×#123—32no—
186C3×C22⋊Q8—32no—
187C3×#121—32no—
188C3×#120—32no—
189C3×C4×Q8—32no—
190C3×C4×D4—34no—
191C3×C4×D4—32no—
192C3×C4×D4—34no—
193C3×#117—31no—
194C3×#117—31no—
195C3×#117—32no—
196C2×C3×C42—31no—
197C2×C3×C42—32no—
198#953—32no—
199#947—31no—
200#947—31no—
201#947—61no—
202#946C2×D312yes—
203Q8×Dic3C2×D312yescomplemented
204#944—31no—
205#944—31no—
206#944—61no—
207#940—31no—
208#940—31no—
209#940—61no—
210#939—34no—
211#939—34no—
212#939—34no—
213#939—64no—
214#938C2×D312yes—
215#937C2×D312yes—
216#936—31no—
217#936—31no—
218#936—61no—
219#935—34no—
220#935C2×D312yes—
221D4×Dic3—34no—
222D4×Dic3C2×D314yes—
223D4×Dic3C2×D312yescomplemented
224#930—32no—
225#929—32no—
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—34no—
235#926C2×D311yescharacteristic
236#926C2×D311yescharacteristic
237#926C2×D312yescomplemented
238#924—32no—
239C2×C4×Dic3—31no—
240C2×C4×Dic3—31no—
241C2×C4×Dic3—32no—
242C2×C4×Dic3—32no—
243C2×C4×Dic3—32no—
244C2×C4×Dic3—32no—
245C2×C4×Dic3—32no—
246C2×C4×Dic3—32no—
247C2×C4×Dic3—61no—
248C2×C4×Dic3C2×D311yescharacteristic
249C2×C4×Dic3C2×D312yescomplemented
250#898—34no—
251#898—34no—
252#897—32no—
253#896—34no—
254#895—32no—
255#894—34no—
256#893—32no—
257#892—34no—
258#890—32no—
259#890—32no—
260#889—34no—
261#889—34no—
262#888—32no—
263#888—32no—
264#887—34no—
265#887—32no—
266#886—32no—
267#886—34no—
268#885—34no—
269#885—34no—
270#884—34no—
271#883—34no—
272#882—32no—
273#67⋊C4—34no—
274#67⋊C4—34no—
275#67⋊C4—34no—
276#879—34no—
277#879—34no—
278#878—34no—
279#878—34no—
280#878—34no—
281#877—34no—
282#877—34no—
283C4×D12—34no—
284C4×D12—34no—
285C4×D12—32no—
286#872—34no—
287#872—34no—
288#872—32no—
289#872—32no—
290C42×D3—32no—
291C42×D3—32no—
292C42×D3—32no—
293C42×D3—32no—
294C42×D3—32no—
295C42×D3—32no—
296C4×Dic6—32no—
297C4×Dic6—34no—
298C4×Dic6—34no—
299C4×Dic6—34no—
300C23×C32C2412yes—
301C23×C32C2411yescharacteristic
302C22×C3⋊D3C2412yes—
303C22×C3×D3—22no—
304C22×C3×D3—24no—
305C22×C3×D3C2412yes—
306C32×Q8—22no—
307C32×D4—24no—
308C32×D4—22no—
309C2×C32×C4—24no—
310C2×C32×C4#4114yescomplemented
311C2×C32×C4C2412yes—
312C2×C32×C4C2411yescharacteristic
313C2×C32×C4C2411yescharacteristic
314#638—24no—
315#638—28no—
316C2×C3⋊Dic3—24no—
317C2×C3⋊Dic3C2412yes—
318C2×C3⋊Dic3C2412yes—
319C2×C3⋊Dic3C2412yes—
320C4⋊(C3⋊D3)—22no—
321C4×C3⋊D3—24no—
322#634—22no—
323C3×#67—28no—
324C2×C3×Dic3—22no—
325C2×C3×Dic3—24no—
326C2×C3×Dic3—28no—
327C2×C3×Dic3C2412yes—
328C2×C3×Dic3C2412yes—
329C2×C3×Dic3C2414yes—
330C2×C3×Dic3C2414yes—
331C2×C3×Dic3C2412yes—
332C3×C4×D3—24no—
333C3×C4×D3—24no—
334#627—28no—
335#626—28no—
336#624—28no—
337D3×Dic3—24no—
338D3×Dic3—24no—
339D3×Dic3—24no—
340D3×Dic3#4118yescomplemented
341#533—91no—
342#533—92no—
343#532—92no—
344#532—91no—
345#529—94no—
346#529—92no—
347#529—94no—
348#529—92no—
349#525—31no—
350#525—91no—
351#525—94no—
352C4×#41—31no—
353C4×#41—91no—
354C4×#41—94no—
355C22×C42—91no—
356C24×C3—31no—
357C23×D3C22×D311yescharacteristic
358C3×#41—24no—
359C3×#41—24no—
360C3×#41—44no—
361C2×C3×Q8—21no—
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C22×D311yescharacteristic
364C2×C3×D4—21no—
365C2×C3×D4—22no—
366C2×C3×D4—34no—
367C2×C3×D4C22×D312yes—
368C2×C3×D4C22×D311yescharacteristic
369C2×C3×D4C22×D312yes—
370C2×C3×D4C22×D311yescharacteristic
371C22×C3×C4—21no—
372C22×C3×C4—22no—
373C22×C3×C4—31no—
374C22×C3×C4—32no—
375C22×C3×C4—34no—
376C22×C3×C4—32no—
377C22×C3×C4—32no—
378C22×C3×C4—64no—
379C22×C3×C4C22×D312yes—
380C22×C3×C4C22×D312yes—
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C2×#67—32no—
384C2×#67—34no—
385C2×#67—32no—
386C2×#67—34no—
387C2×#67—34no—
388C2×#67—64no—
389C2×#67—62no—
390C2×#67C22×D314yes—
391C22×Dic3—32no—
392C22×Dic3—32no—
393C22×Dic3—32no—
394C22×Dic3—32no—
395C22×Dic3—32no—
396C22×Dic3—32no—
397C22×Dic3—62no—
398C22×Dic3—68no—
399C22×Dic3C22×D314yes—
400C22×Dic3C22×D312yes—
401C22×Dic3C22×D311yescharacteristic
402#237—616no—
403#235—616no—
404#235—64no—
405#235—64no—
406#235—124no—
407C2×D12—34no—
408C2×D12—31no—
409C2×D12—31no—
410C2×D12—61no—
411C2×C4×D3—24no—
412C2×C4×D3—32no—
413C2×C4×D3—32no—
414C2×C4×D3—32no—
415C2×C4×D3—32no—
416C2×C4×D3—32no—
417C2×C4×D3—32no—
418C2×C4×D3—34no—
419C2×C4×D3—34no—
420C2×C4×D3—62no—
421C2×C4×D3—68no—
422C2×C4×D3C22×D312yes—
423C2×C4×D3C22×D312yes—
424C2×Dic6—31no—
425C2×Dic6—31no—
426C2×Dic6—34no—
427C2×Dic6—34no—
428C2×Dic6—61no—
429C3×C4⋊C4—32no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—32no—
432C3×C4⋊C4—34no—
433C3×C22⋊C4—34no—
434C3×C22⋊C4—32no—
435C3×C22⋊C4—32no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C42—32no—
439C3×C42—32no—
440C3×C42—32no—
441C3×C42—34no—
442C3×C42—31no—
443C3×C42—31no—
444#217—34no—
445#217—34no—
446#217—34no—
447#217—64no—
448#217C22×D312yes—
449#217C22×D312yes—
450#217C22×D314yes—
451#217C22×D314yes—
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—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—64no—
460(C2×D3)⋊C4C22×D314yes—
461C4⋊Dic3—34no—
462C4⋊Dic3—34no—
463C4⋊Dic3—34no—
464C4⋊Dic3C22×D312yes—
465C4⋊Dic3C22×D314yes—
466C4⋊Dic3C22×D312yes—
467Dic3⋊C4—34no—
468Dic3⋊C4—34no—
469Dic3⋊C4—34no—
470Dic3⋊C4—34no—
471Dic3⋊C4—34no—
472Dic3⋊C4—34no—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—34no—
476Dic3⋊C4—64no—
477Dic3⋊C4C22×D314yes—
478C4×Dic3—32no—
479C4×Dic3—32no—
480C4×Dic3—31no—
481C4×Dic3—31no—
482C4×Dic3—31no—
483C4×Dic3—31no—
484C4×Dic3—32no—
485C4×Dic3—34no—
486C4×Dic3—32no—
487C4×Dic3—32no—
488C4×Dic3—32no—
489C4×Dic3—34no—
490C4×Dic3—32no—
491C4×Dic3—32no—
492C4×Dic3—32no—
493C4×Dic3—32no—
494C4×Dic3—62no—
495C4×Dic3—61no—
496C4×Dic3—61no—
497C4×Dic3C22×D312yes—
498C4×Dic3C22×D312yes—
499C4×Dic3C22×D311yescharacteristic
500C4×Dic3C22×D311yescharacteristic
501C4×Dic3C22×D314yes—
502C4×Dic3C22×D312yes—
503C22×C32—22no—
504C22×C32—24no—
505C22×C32—22no—
506C22×C32C2×#4112yes—
507C22×C32C2511yescharacteristic
508C2×C3⋊D3—24no—
509C2×C3⋊D3—22no—
510C2×C3×D3—28no—
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3C2×#4114yes—
514C32×C4—22no—
515C32×C4C2×#4112yes—
516C32×C4C2×#4112yes—
517C3⋊Dic3—22no—
518C3⋊Dic3—22no—
519C3⋊Dic3C2×#4114yes—
520C3×Dic3—22no—
521C3×Dic3—24no—
522C3×Dic3—24no—
523C3×Dic3—22no—
524C3×Dic3C2×#4114yes—
525C2×#41—94no—
526C2×#41—91no—
527C2×#41D3211yescharacteristic
528C23×C4—31no—
529C23×C4—92no—
530C4⋊Q8—92no—
531C4⋊Q8—91no—
532#127—91no—
533#126—94no—
534#126—94no—
535#125—94no—
536#125—92no—
537#124—94no—
538#124—91no—
539#124—91no—
540#123—32no—
541#123—94no—
542#123—92no—
543#123—94no—
544C22⋊Q8—32no—
545C22⋊Q8—94no—
546C22⋊Q8—94no—
547C22⋊Q8—92no—
548#121—32no—
549#121—94no—
550#121—92no—
551#121—94no—
552#120—32no—
553#120—92no—
554C4×Q8—32no—
555C4×Q8—94no—
556C4×Q8—92no—
557C4×Q8—94no—
558C4×D4—34no—
559C4×D4—32no—
560C4×D4—34no—
561C4×D4—94no—
562C4×D4—92no—
563C4×D4—94no—
564C4×D4—94no—
565C4×D4—94no—
566C4×D4—94no—
567C4×D4—94no—
568#117—31no—
569#117—32no—
570#117—31no—
571#117—92no—
572#117—94no—
573#117—94no—
574#117—94no—
575C2×C42—32no—
576C2×C42—31no—
577C2×C42—92no—
578C2×C42—92no—
579C2×C42—92no—
580C2×C42—92no—
581C2×C42—92no—
582C2×C42—92no—
583C2×C42—91no—
584C23×C3—21no—
585C23×C3—22no—
586C23×C3—32no—
587C23×C3—64no—
588C23×C3—62no—
589C23×C3C23×D312yes—
590C23×C3C23×D312yes—
591C23×C3C23×D311yescharacteristic
592C23×C3C23×D311yescharacteristic
593C22×D3—22no—
594C22×D3—24no—
595C22×D3—32no—
596C22×D3—32no—
597C22×D3—62no—
598C22×D3C23×D312yes—
599C3×Q8—22no—
600C3×Q8—22no—
601C3×Q8—42no—
602C3×D4—24no—
603C3×D4—24no—
604C3×D4—22no—
605C3×D4—22no—
606C3×D4—42no—
607C3×D4—44no—
608C3×D4—68no—
609C2×C3×C4—24no—
610C2×C3×C4—24no—
611C2×C3×C4—21no—
612C2×C3×C4—22no—
613C2×C3×C4—21no—
614C2×C3×C4—24no—
615C2×C3×C4—32no—
616C2×C3×C4—32no—
617C2×C3×C4—32no—
618C2×C3×C4—34no—
619C2×C3×C4—34no—
620C2×C3×C4—44no—
621C2×C3×C4—64no—
622C2×C3×C4—68no—
623C2×C3×C4—62no—
624C2×C3×C4—64no—
625C2×C3×C4—64no—
626C2×C3×C4#23514yescomplemented
627C2×C3×C4#23714yescomplemented
628C2×C3×C4C23×D312yes—
629C2×C3×C4C23×D312yes—
630C2×C3×C4C23×D311yescharacteristic
631C2×C3×C4C23×D311yescharacteristic
632C2×C3×C4C23×D311yescharacteristic
633C2×C3×C4C23×D311yescharacteristic
634#67—28no—
635#67—68no—
636#67—68no—
637#67—68no—
638#67—64no—
639#67—64no—
640#67—128no—
641#67—124no—
642C2×Dic3—22no—
643C2×Dic3—28no—
644C2×Dic3—24no—
645C2×Dic3—32no—
646C2×Dic3—32no—
647C2×Dic3—38no—
648C2×Dic3—32no—
649C2×Dic3—32no—
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—62no—
653C2×Dic3—62no—
654C2×Dic3—62no—
655C2×Dic3—64no—
656C2×Dic3—64no—
657C2×Dic3—64no—
658C2×Dic3—64no—
659C2×Dic3—64no—
660C2×Dic3—124no—
661C2×Dic3C23×D312yes—
662C2×Dic3C23×D312yes—
663C2×Dic3C23×D314yes—
664C2×Dic3C23×D314yes—
665C2×Dic3C23×D312yes—
666D12—68no—
667D12—62no—
668D12—62no—
669D12—122no—
670C4×D3—24no—
671C4×D3—24no—
672C4×D3—38no—
673C4×D3—68no—
674C4×D3—64no—
675C4×D3—64no—
676C4×D3—64no—
677C4×D3—64no—
678C4×D3—64no—
679C4×D3—68no—
680C4×D3—124no—
681Dic6—68no—
682Dic6—68no—
683Dic6—62no—
684Dic6—62no—
685Dic6—122no—
686C2×C32—22no—
687C2×C32—42no—
688C2×C32C22×#4111yescharacteristic
689C2×C32C22×#4112yes—
690C3⋊D3—42no—
691C3×D3—24no—
692C24—31no—
693#41—24no—
694#41—1816no—
695#41—184no—
696C2×Q8—94no—
697C2×Q8—91no—
698C2×Q8C2×D3211yescharacteristic
699C2×D4—34no—
700C2×D4—94no—
701C2×D4—92no—
702C2×D4—94no—
703C2×D4—91no—
704C2×D4C2×D3212yes—
705C2×D4C2×D3211yescharacteristic
706C22×C4—32no—
707C22×C4—34no—
708C22×C4—31no—
709C22×C4—32no—
710C22×C4—32no—
711C22×C4—64no—
712C22×C4—94no—
713C22×C4—92no—
714C22×C4—92no—
715C22×C4—92no—
716C22×C4—92no—
717C22×C4—92no—
718C22×C4—92no—
719C22×C4—188no—
720C22×C4C2×D3212yes—
721C22×C4C2×D3211yescharacteristic
722C4⋊C4—32no—
723C4⋊C4—34no—
724C4⋊C4—32no—
725C4⋊C4—34no—
726C4⋊C4—94no—
727C4⋊C4—94no—
728C4⋊C4—94no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—94no—
732C22⋊C4—32no—
733C22⋊C4—34no—
734C22⋊C4—32no—
735C22⋊C4—34no—
736C22⋊C4—34no—
737C22⋊C4—94no—
738C22⋊C4—94no—
739C22⋊C4—94no—
740C22⋊C4—94no—
741C22⋊C4—94no—
742C42—32no—
743C42—34no—
744C42—31no—
745C42—31no—
746C42—32no—
747C42—32no—
748C42—92no—
749C42—92no—
750C42—92no—
751C42—92no—
752C42—94no—
753C42—91no—
754C42—91no—
755C42—92no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—24no—
761C22×C3—24no—
762C22×C3—22no—
763C22×C3—21no—
764C22×C3—34no—
765C22×C3—42no—
766C22×C3—44no—
767C22×C3—42no—
768C22×C3—68no—
769C22×C3—62no—
770C22×C3—62no—
771C22×C3C2×#23512yes—
772C22×C3C2×#23712yes—
773C22×C3C24×D311yescharacteristic
774C22×C3C24×D311yescharacteristic
775C2×D3—28no—
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—62no—
779C2×D3—62no—
780C2×D3—64no—
781C2×D3—64no—
782C2×D3—122no—
783C2×D3—124no—
784C2×D3D3×#4114yes—
785C3×C4—22no—
786C3×C4—22no—
787C3×C4—22no—
788C3×C4—22no—
789C3×C4—34no—
790C3×C4—42no—
791C3×C4—62no—
792C3×C4—64no—
793C3×C4—64no—
794C3×C4—62no—
795C3×C4C2×#23512yes—
796C3×C4C2×#23512yes—
797C3×C4C2×#23712yes—
798C3×C4C2×#23712yes—
799Dic3—22no—
800Dic3—24no—
801Dic3—24no—
802Dic3—22no—
803Dic3—34no—
804Dic3—34no—
805Dic3—64no—
806Dic3—62no—
807Dic3—62no—
808Dic3—62no—
809Dic3—62no—
810Dic3—122no—
811Dic3—122no—
812Dic3D3×#4114yes—
813C32#344411yescharacteristic, complemented, Sylow
814C23—32no—
815C23—64no—
816C23—62no—
817C23—92no—
818C23C22×D3212yes—
819C23C22×D3211yescharacteristic
820Q8—22no—
821Q8—188no—
822Q8—182no—
823D4—24no—
824D4—22no—
825D4—68no—
826D4—188no—
827D4—188no—
828D4—184no—
829D4—182no—
830C2×C4—24no—
831C2×C4—32no—
832C2×C4—32no—
833C2×C4—34no—
834C2×C4—34no—
835C2×C4—32no—
836C2×C4—64no—
837C2×C4—68no—
838C2×C4—62no—
839C2×C4—64no—
840C2×C4—64no—
841C2×C4—98no—
842C2×C4—92no—
843C2×C4—92no—
844C2×C4—92no—
845C2×C4—188no—
846C2×C4—184no—
847C2×C4—184no—
848C2×C4—184no—
849C2×C4—184no—
850C2×C4—184no—
851C2×C4#380414yescomplemented
852C2×C4C22×D3212yes—
853C2×C4C22×D3211yescharacteristic
854C2×C4C22×D3211yescharacteristic
855C2×C3—22no—
856C2×C3—22no—
857C2×C3—22no—
858C2×C3—21no—
859C2×C3—42no—
860C2×C3—42no—
861C2×C3—42no—
862C2×C3—64no—
863C2×C3—82no—
864C2×C3C22×#23511yescharacteristic
865C2×C3C22×#23711yescharacteristic
866C2×C3C2×D3×#4112yes—
867C2×C3C2×D3×#4112yes—
868D3—24no—
869D3—122no—
870D3—122no—
871D3—242no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—34no—
876C22—68no—
877C22—62no—
878C22—62no—
879C22—184no—
880C22—182no—
881C22C2×#380412yes—
882C22C23×D3211yescharacteristic
883C4—22no—
884C4—34no—
885C4—62no—
886C4—64no—
887C4—64no—
888C4—62no—
889C4—94no—
890C4—182no—
891C4—182no—
892C4C2×#380412yes—
893C4C2×#380412yes—
894C3—21no—
895C3#8583611yescharacteristic, complemented
896C3#8601811yescharacteristic, complemented
897C2—22no—
898C2—42no—
899C2—64no—
900C2—362no—
901C2D32×#4112yes—
902C2C22×#380411yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596303C2semidirect
2. C3×#5828C2semidirect
3. C3×Dic3×#41C2semidirect
4. #10595376C2semidirect
5. #10595367C2semidirect
6. #10595172C2semidirect
7. #10595131C2semidirect
8. #10595129C2semidirect
9. #10595116C2semidirect
10. #10595050C2semidirect
11. #10595023C2semidirect
12. #10594954C2semidirect
13. #10594933C2semidirect
14. C4×#3804C2semidirect
15. C2×C4×D3×Dic3C2semidirect
23. #64156C22semidirect
24. #64153C22semidirect
25. #64149C22semidirect
27. #64145C22semidirect
28. C4×#638C22semidirect
31. C3×Q8×Dic3C22semidirect
36. C3×D4×Dic3C22semidirect
40. C3×#926C22semidirect
42. C2×C3×C4×Dic3C22semidirect
49. #63956C22semidirect
50. #63955C22semidirect
52. #63953C22semidirect
54. #63952C22semidirect
55. #63919C22semidirect
56. C4×#627C22semidirect
60. #63894C22semidirect
62. C4×#624C22semidirect
69. #63874C22semidirect
70. #63872C22semidirect
72. #63848C22semidirect
73. #63847C22semidirect
74. #63844C22semidirect
75. #63837C22semidirect
76. #63836C22semidirect
82. #5828D3semidirect
83. Dic3×#41D3semidirect
203. Q8×Dic3C2×D3semidirect
223. D4×Dic3C2×D3semidirect
237. #926C2×D3semidirect
249. C2×C4×Dic3C2×D3semidirect
310. C2×C32×C4#41semidirect
340. D3×Dic3#41semidirect
626. C2×C3×C4#235semidirect
627. C2×C3×C4#237semidirect
813. C32#3444semidirect
851. C2×C4#3804semidirect
895. C3#85836semidirect
896. C3#86018semidirect

Maximal subgroups

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

subgroupindex
#105963032
C3×#58282
C3×Dic3×#412
#105953762
#105953672
#105951722
#105951312
#105951292
#105951162
#105950502
#105950232
#105949542
#105949332
C4×#38042
C2×C4×D3×Dic32
#860183
#858363