Finite Group Databasebeta

← #11904660

Subgroups — #11904660

Order 1152.

3481 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C2×#64307C211yesmaximal, characteristic, complemented
3#10596262C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5#672C214yesmaximal, complemented
6#10595070C212yesmaximal, complemented
7#10595069C212yesmaximal, complemented
8#10595065C214yesmaximal, complemented
9#10595064C212yesmaximal, complemented
10D3×#930C212yesmaximal, complemented
11#10595043C211yesmaximal, characteristic, complemented
12#10595040C211yesmaximal, characteristic, complemented
13#10595006C212yesmaximal, complemented
14#10595004C212yesmaximal, complemented
15#10594986C211yesmaximal, characteristic, complemented
16#10594900C212yesmaximal, complemented
17#10594892C212yesmaximal, complemented
18#87275—31nomaximal
19#85949—31nomaximal
20C23×C32×C4C2211yescharacteristic, complemented
21C2×#3828C2211yescharacteristic, complemented
22C22×C3×#67C2212yescomplemented
23C22×C3×#67C2212yescomplemented
24C2×C3×#235—28no—
25C2×C3×#235C2211yescharacteristic
26C2×C3×#235C2212yescomplemented
27C2×C3×#235C2211yescharacteristic, complemented
28C2×C3×#235C2211yescharacteristic, complemented
29C2×C3×#235C2212yescomplemented
30C2×C3×#235C2211yescharacteristic, complemented
31C22×C3×D12C2211yescharacteristic, complemented
32C22×C3×D12C2211yescharacteristic, complemented
33C22×C3×C4×D3C2212yescomplemented
34C22×C3×Dic6C2211yescharacteristic, complemented
35C2×D3×#67C2214yescomplemented
36C2×D3×#67C2214yescomplemented
37#64307—28no—
38C2×#3802C2212yescomplemented
39C2×D3×D12C2212yescomplemented
40C2×#3796C2212yescomplemented
41C2×#3795C2212yescomplemented
42#64162C2212yescomplemented
43#64139C2211yescharacteristic, complemented
44#64139C2211yescharacteristic, complemented
45#64138C2212yescomplemented
46C4×#638C2212yescomplemented
47C4×#638C2212yescomplemented
48#64135C2211yescharacteristic, complemented
49#64133C2211yescharacteristic, complemented
50#64133C2211yescharacteristic, complemented
51C3×#930C2212yescomplemented
52C3×#930C2212yescomplemented
53C3×#930C2212yescomplemented
54C3×#930C2212yescomplemented
55C2×C3×(C2×D3)⋊C4C2212yescomplemented
56C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
57#63983C2214yescomplemented
58#63979C2214yescomplemented
59#63978C2214yescomplemented
60#63978C2214yescomplemented
61#63976C2214yescomplemented
62#63976C2214yescomplemented
63Dic3×#67C2214yescomplemented
64Dic3×#67C2214yescomplemented
65#63970C2214yescomplemented
66#63970C2214yescomplemented
67#63922C2214yescomplemented
68D3×(C2×D3)⋊C4C2214yescomplemented
69#63916C2212yescomplemented
70#63914C2212yescomplemented
71#63909C2212yescomplemented
72#63908C2212yescomplemented
73#63908C2212yescomplemented
74#63907C2214yescomplemented
75#63906C2214yescomplemented
76#63905C2214yescomplemented
77#63898C2212yescomplemented
78D3×C4⋊Dic3C2212yescomplemented
79#63887C2214yescomplemented
80#63885C2214yescomplemented
81#63879C2214yescomplemented
82#63871C2212yescomplemented
83#63863C2212yescomplemented
84#63857C2212yescomplemented
85#63843C2212yescomplemented
86#63841C2212yescomplemented
87C22×C3×#41—31no—
88C2×#1009—31no—
89C2×#1004—31no—
90C22×#235D311yescharacteristic, complemented
91C2×C3×#121—31no—
92#5834—32no—
93#5833—32no—
94#5833—31no—
95#5830—31no—
96#5830—32no—
97#5829—32no—
98#5829—34no—
99#5827—31no—
100#5817—32no—
101#5805—31no—
102D4×#67—34no—
103D4×#67—34no—
104D4×#67—32no—
105#5791—31no—
106#5791—31no—
107#5791—32no—
108#5791—61no—
109C2×#930—32no—
110C2×#930D311yescharacteristic, complemented
111#5612—32no—
112#5609—32no—
113#5608—32no—
114#5607—32no—
115#5606—32no—
116D3×#121—32no—
117#5599—32no—
118#5598—32no—
119#5510—31no—
120#5504—31no—
121#5490—34no—
122C24×C32C2311yescharacteristic
123C23×C3×D3C2312yes—
124C23×C3×D3C2312yes—
125C22×D32C2314yes—
126C22×C32×C4—24no—
127C22×C32×C4C2311yescharacteristic
128C22×C32×C4C2311yescharacteristic
129C22×C32×C4C2311yescharacteristic
130C22×C32×C4C2311yescharacteristic
131C22×C32×C4C2311yescharacteristic
132C22×C32×C4C2311yescharacteristic
133C2×#638C2312yes—
134C2×#638C2312yes—
135C2×#638C2312yes—
136#3828—24no—
137C2×C4⋊(C3⋊D3)C2311yescharacteristic
138C2×C4×C3⋊D3C2312yes—
139C2×#634C2311yescharacteristic
140C2×C3×#67—28no—
141C2×C3×#67—44no—
142C2×C3×#67C2314yes—
143C2×C3×#67C2312yes—
144C2×C3×#67C2312yes—
145C2×C3×#67C2312yes—
146C2×C3×#67C2314yes—
147C2×C3×#67C2312yes—
148C22×C3×Dic3C2312yes—
149C22×C3×Dic3C2312yes—
150C3×#235—24no—
151C3×#235—28no—
152C3×#235—24no—
153C3×#235—28no—
154C3×#235—24no—
155C3×#235D418yescomplemented
156C2×C3×D12—24no—
157C2×C3×D12—24no—
158C2×C3×D12C2312yes—
159C2×C3×D12C2312yes—
160C2×C3×D12C2312yes—
161C2×C3×D12C2311yescharacteristic
162C2×C3×D12C2311yescharacteristic
163C2×C3×C4×D3—28no—
164C2×C3×C4×D3C2312yes—
165C2×C3×C4×D3C2312yes—
166C2×C3×C4×D3C2312yes—
167C2×C3×C4×D3C2312yes—
168C2×C3×Dic6—24no—
169C2×C3×Dic6C2311yescharacteristic
170C2×C3×Dic6C2312yes—
171C2×C3×Dic6C2311yescharacteristic
172D3×#67—216no—
173D3×#67—48no—
174C2×#626C2314yes—
175C2×#626C2314yes—
176C2×#625C2314yes—
177C2×#625C2314yes—
178C2×#625C2314yes—
179C2×D3×Dic3C2314yes—
180C2×D3×Dic3C2314yes—
181#3802—28no—
182D3×D12—28no—
183#3796—28no—
184#3795—28no—
185#3757C2312yes—
186#3757C2312yes—
187#3757C2312yes—
188#3752C2312yes—
189#3752C2312yes—
190C4⋊(C3⋊Dic3)C2311yescharacteristic
191C4⋊(C3⋊Dic3)C2311yescharacteristic
192#3750C2312yes—
193#3750C2312yes—
194C4×C3⋊Dic3C2312yes—
195C3×(C2×D3)⋊C4C2314yes—
196C3×(C2×D3)⋊C4C2314yes—
197C3×C4⋊Dic3C2312yes—
198C3×C4⋊Dic3C2312yes—
199Dic3⋊Dic3C2314yes—
200Dic3⋊Dic3C2314yes—
201#3722C2314yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204(C2×D3)⋊Dic3C2314yes—
205(C2×D3)⋊Dic3C2314yes—
206Dic32C2314yes—
207#3488—91noSylow
208C2×C3×#41—31no—
209C2×C3×#41—31no—
210C2×C3×#41—32no—
211C2×C3×#41—32no—
212C2×C3×#41—31no—
213C2×C3×#41—31no—
214C2×C3×#41—68no—
215C22×C3×Q8—31no—
216C22×C3×D4—32no—
217C22×C3×D4—32no—
218C22×C3×D4—31no—
219C22×C3×D4—31no—
220C23×C3×C4—21no—
221C23×C3×C4—32no—
222C23×C3×C4C2×D311yescharacteristic, complemented
223C23×C3×C4C2×D311yescharacteristic, complemented
224C22×#67—34no—
225C22×#67—34no—
226C22×#67C2×D312yescomplemented
227C22×#67C2×D312yescomplemented
228#1009—68no—
229C2×#239—32no—
230#1004—68no—
231C2×#237—32no—
232C2×#237—32no—
233C2×D3×D4—34no—
234C2×D3×D4—34no—
235C2×D3×D4—32no—
236C2×D3×D4—32no—
237C2×D3×D4—32no—
238C2×#235—28no—
239C2×#235—31no—
240C2×#235—31no—
241C2×#235—32no—
242C2×#235—61no—
243C2×#235C2×D311yescharacteristic
244C2×#235C2×D312yescomplemented
245C2×#235C2×D311yescharacteristic, complemented
246C2×#235C2×D311yescharacteristic, complemented
247C2×#235C2×D312yescomplemented
248C2×#235C2×D311yescharacteristic, complemented
249C22×D12—32no—
250C22×D12C2×D311yescharacteristic, complemented
251C22×D12C2×D311yescharacteristic, complemented
252C22×C4×D3C2×D312yescomplemented
253C22×Dic6C2×D311yescharacteristic, complemented
254C3×#121—32no—
255C3×#121—32no—
256C3×#121—32no—
257C3×#121—32no—
258C2×C3×C4⋊C4—31no—
259C2×C3×C22⋊C4—32no—
260#953—32no—
261#953—32no—
262#953—34no—
263#953—34no—
264#953—62no—
265#947—32no—
266#947—34no—
267#946—34no—
268#946—32no—
269Q8×Dic3—32no—
270#940—34no—
271#940—34no—
272#940—32no—
273#940—32no—
274#939—34no—
275#939—34no—
276#939—34no—
277#939—34no—
278#939—34no—
279#938—34no—
280#938—34no—
281#938—32no—
282#938—32no—
283#938—32no—
284#937—34no—
285#937—34no—
286#937—34no—
287#937—34no—
288#937—34no—
289#936—32no—
290D4×Dic3—34no—
291D4×Dic3—34no—
292D4×Dic3—32no—
293#930—31no—
294#930—31no—
295#930—31no—
296#930—31no—
297#930—34no—
298#930—34no—
299#930—32no—
300#930—32no—
301#930—34no—
302#930—32no—
303#930—61no—
304#930—61no—
305#930C2×D312yescomplemented
306#930C2×D312yescomplemented
307#930C2×D312yescomplemented
308#930C2×D312yescomplemented
309#929—32no—
310#929—32no—
311#929—34no—
312#929—62no—
313C4×#67—32no—
314C4×#67—32no—
315C4×#67—32no—
316C4×#67—32no—
317C4×#67—34no—
318C4×#67—34no—
319C4×#67—34no—
320C4×#67—62no—
321C4×#67—62no—
322C2×(C2×D3)⋊C4—34no—
323C2×(C2×D3)⋊C4C2×D312yescomplemented
324#926—31no—
325#926—31no—
326#926—32no—
327#926—61no—
328C2×C4⋊Dic3—32no—
329C2×C4⋊Dic3C2×D311yescharacteristic, complemented
330#924—31no—
331#924—31no—
332#924—31no—
333#924—31no—
334#924—32no—
335#924—61no—
336#924—61no—
337#897—32no—
338#897—32no—
339#895—32no—
340#895—32no—
341#893—32no—
342#892—32no—
343D3×C4⋊C4—32no—
344#887—32no—
345#885—34no—
346#884—34no—
347#884—34no—
348#883—34no—
349#882—34no—
350#67⋊C4—34no—
351D3×C22⋊C4—34no—
352#878—34no—
353C23×C32—22no—
354C23×C32—22no—
355C23×C32—41no—
356C23×C32C2411yescharacteristic
357C23×C32C2411yescharacteristic
358C23×C32C2411yescharacteristic
359C22×C3⋊D3C2412yes—
360C22×C3×D3—24no—
361C22×C3×D3—24no—
362C22×C3×D3—24no—
363C22×C3×D3—42no—
364C22×C3×D3—42no—
365C22×C3×D3—42no—
366C22×C3×D3C2414yes—
367C22×C3×D3C2412yes—
368C22×C3×D3C2412yes—
369C2×D32—28no—
370C2×D32—44no—
371C2×D32—44no—
372C2×C32×C4—22no—
373C2×C32×C4—22no—
374C2×C32×C4—22no—
375C2×C32×C4—22no—
376C2×C32×C4—22no—
377C2×C32×C4C2×D414yescomplemented
378C2×C32×C4C2411yescharacteristic
379C2×C32×C4C2411yescharacteristic
380C2×C32×C4C2411yescharacteristic
381C2×C32×C4C2411yescharacteristic
382#638—24no—
383#638—24no—
384#638—42no—
385C2×C3⋊Dic3C2412yes—
386C2×C3⋊Dic3C2412yes—
387C2×C3⋊Dic3C2412yes—
388C4⋊(C3⋊D3)—22no—
389C4×C3⋊D3—24no—
390#634—22no—
391C3×#67—24no—
392C3×#67—28no—
393C3×#67—24no—
394C3×#67—24no—
395C3×#67—44no—
396C3×#67C2×D418yescomplemented
397C2×C3×Dic3—24no—
398C2×C3×Dic3—42no—
399C2×C3×Dic3C2414yes—
400C2×C3×Dic3C2412yes—
401C2×C3×Dic3C2412yes—
402C3×D12—24no—
403C3×D12—24no—
404C3×D12—24no—
405C3×D12—22no—
406C3×D12C2×D414yescomplemented
407C3×C4×D3—24no—
408C3×C4×D3—24no—
409C3×C4×D3—24no—
410C3×C4×D3C2×D418yescomplemented
411C3×Dic6—22no—
412C3×Dic6—24no—
413C3×Dic6C2×D414yescomplemented
414#626—28no—
415#626—44no—
416#625—28no—
417#625—44no—
418#625—44no—
419D3×Dic3—28no—
420D3×Dic3—44no—
421C2×H(5,𝔽2)—91no—
422C22×#41—31no—
423#550—92no—
424#548—92no—
425#546—94no—
426#546—92no—
427D42—92no—
428D42—94no—
429#537—91no—
430#537—92no—
431#535—92no—
432#535—91no—
433#525—92no—
434#525—91no—
435C2×#121—31no—
436C2×#121—92no—
437#520—91no—
438C24×C3—21no—
439C24×C3—32no—
440C24×C3—32no—
441C24×C3C22×D311yescharacteristic
442C24×C3C22×D311yescharacteristic
443C23×D3—34no—
444C23×D3—34no—
445C23×D3C22×D312yes—
446C23×D3C22×D312yes—
447C3×#41—38no—
448C3×#41—68no—
449C3×#41—68no—
450C3×#41—64no—
451C3×#41—64no—
452C3×#41—64no—
453C2×C3×Q8—31no—
454C2×C3×Q8—32no—
455C2×C3×Q8—31no—
456C2×C3×Q8—64no—
457C2×C3×D4—32no—
458C2×C3×D4—34no—
459C2×C3×D4—32no—
460C2×C3×D4—32no—
461C2×C3×D4—32no—
462C2×C3×D4—34no—
463C2×C3×D4—31no—
464C2×C3×D4—32no—
465C2×C3×D4—32no—
466C2×C3×D4—31no—
467C2×C3×D4—32no—
468C2×C3×D4—64no—
469C2×C3×D4—68no—
470C2×C3×D4—64no—
471C2×C3×D4—124no—
472C22×C3×C4—24no—
473C22×C3×C4—24no—
474C22×C3×C4—21no—
475C22×C3×C4—21no—
476C22×C3×C4—21no—
477C22×C3×C4—21no—
478C22×C3×C4—21no—
479C22×C3×C4—21no—
480C22×C3×C4—32no—
481C22×C3×C4—32no—
482C22×C3×C4—32no—
483C22×C3×C4—32no—
484C22×C3×C4—32no—
485C22×C3×C4—32no—
486C22×C3×C4—44no—
487C22×C3×C4—68no—
488C22×C3×C4C22×D311yescharacteristic
489C22×C3×C4C22×D311yescharacteristic
490C22×C3×C4C22×D311yescharacteristic
491C22×C3×C4C22×D311yescharacteristic
492C22×C3×C4C22×D311yescharacteristic
493C22×C3×C4C22×D311yescharacteristic
494C22×C3×C4C22×D311yescharacteristic
495C22×C3×C4C22×D311yescharacteristic
496C22×C3×C4C22×D311yescharacteristic
497C22×C3×C4C22×D311yescharacteristic
498C22×C3×C4C22×D311yescharacteristic
499C22×C3×C4C22×D311yescharacteristic
500C2×#67—28no—
501C2×#67—32no—
502C2×#67—32no—
503C2×#67—32no—
504C2×#67—32no—
505C2×#67—34no—
506C2×#67—34no—
507C2×#67—32no—
508C2×#67—32no—
509C2×#67—34no—
510C2×#67—34no—
511C2×#67—34no—
512C2×#67—34no—
513C2×#67—34no—
514C2×#67—34no—
515C2×#67—44no—
516C2×#67—62no—
517C2×#67—62no—
518C2×#67—62no—
519C2×#67—616no—
520C2×#67—128no—
521C2×#67C22×D314yes—
522C2×#67C22×D312yes—
523C2×#67C22×D312yes—
524C2×#67C22×D312yes—
525C2×#67C22×D314yes—
526C2×#67C22×D312yes—
527C22×Dic3—34no—
528C22×Dic3—34no—
529C22×Dic3C22×D312yes—
530C22×Dic3C22×D312yes—
531#239—68no—
532#237—68no—
533#237—68no—
534D3×D4—68no—
535D3×D4—616no—
536D3×D4—68no—
537D3×D4—68no—
538D3×D4—128no—
539#235—24no—
540#235—28no—
541#235—24no—
542#235—28no—
543#235—24no—
544#235—68no—
545#235—64no—
546#235—64no—
547#235—124no—
548#235#6718yescomplemented
549C2×D12—24no—
550C2×D12—24no—
551C2×D12—34no—
552C2×D12—31no—
553C2×D12—31no—
554C2×D12—34no—
555C2×D12—61no—
556C2×D12—68no—
557C2×D12C22×D312yes—
558C2×D12C22×D311yescharacteristic
559C2×D12C22×D312yes—
560C2×D12C22×D312yes—
561C2×D12C22×D311yescharacteristic
562C2×C4×D3—28no—
563C2×C4×D3—34no—
564C2×C4×D3—32no—
565C2×C4×D3—32no—
566C2×C4×D3—34no—
567C2×C4×D3—62no—
568C2×C4×D3C22×D312yes—
569C2×C4×D3C22×D312yes—
570C2×C4×D3C22×D312yes—
571C2×C4×D3C22×D312yes—
572C2×Dic6—24no—
573C2×Dic6—31no—
574C2×Dic6—31no—
575C2×Dic6—61no—
576C2×Dic6C22×D312yes—
577C2×Dic6C22×D311yescharacteristic
578C2×Dic6C22×D311yescharacteristic
579C3×C4⋊C4—32no—
580C3×C4⋊C4—32no—
581C3×C22⋊C4—34no—
582C3×C22⋊C4—34no—
583#217—32no—
584#217—32no—
585#217—32no—
586#217—32no—
587#217—32no—
588#217—32no—
589#217—34no—
590#217—34no—
591#217—34no—
592#217—34no—
593#217—62no—
594#217—62no—
595#217—62no—
596(C2×D3)⋊C4—34no—
597(C2×D3)⋊C4—34no—
598(C2×D3)⋊C4—34no—
599(C2×D3)⋊C4—34no—
600(C2×D3)⋊C4—32no—
601(C2×D3)⋊C4—32no—
602(C2×D3)⋊C4—32no—
603(C2×D3)⋊C4—32no—
604(C2×D3)⋊C4—34no—
605(C2×D3)⋊C4—34no—
606(C2×D3)⋊C4—62no—
607(C2×D3)⋊C4—62no—
608(C2×D3)⋊C4C22×D314yes—
609(C2×D3)⋊C4C22×D314yes—
610C4⋊Dic3—31no—
611C4⋊Dic3—31no—
612C4⋊Dic3—31no—
613C4⋊Dic3—31no—
614C4⋊Dic3—34no—
615C4⋊Dic3—34no—
616C4⋊Dic3—61no—
617C4⋊Dic3—61no—
618C4⋊Dic3C22×D312yes—
619C4⋊Dic3C22×D312yes—
620Dic3⋊C4—32no—
621Dic3⋊C4—32no—
622Dic3⋊C4—32no—
623Dic3⋊C4—32no—
624Dic3⋊C4—34no—
625Dic3⋊C4—34no—
626Dic3⋊C4—62no—
627Dic3⋊C4—62no—
628C4×Dic3—32no—
629C4×Dic3—32no—
630C4×Dic3—34no—
631C4×Dic3—34no—
632C4×Dic3—62no—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32—21no—
636C22×C32—21no—
637C22×C32—21no—
638C22×C32—21no—
639C22×C32—21no—
640C22×C32—44no—
641C22×C32C22×D412yes—
642C22×C32H(5,𝔽2)12yescomplemented
643C22×C32C2511yescharacteristic
644C2×C3⋊D3—22no—
645C2×C3⋊D3—22no—
646C2×C3⋊D3—22no—
647C2×C3×D3—22no—
648C2×C3×D3—22no—
649C2×C3×D3—24no—
650C2×C3×D3—22no—
651C2×C3×D3—22no—
652C2×C3×D3—24no—
653C2×C3×D3—22no—
654C2×C3×D3—24no—
655C2×C3×D3—48no—
656C2×C3×D3—84no—
657C2×C3×D3C22×D414yes—
658D32—88no—
659C32×C4—21no—
660C32×C4—21no—
661C32×C4C22×D412yes—
662C32×C4C22×D412yes—
663C3⋊Dic3—22no—
664C3⋊Dic3—22no—
665C3⋊Dic3—22no—
666C3×Dic3—22no—
667C3×Dic3—24no—
668C3×Dic3C22×D414yes—
669H(5,𝔽2)—188no—
670C2×#41—31no—
671C2×#41—32no—
672C2×#41—31no—
673C2×#41—31no—
674C2×#41—32no—
675C2×#41—31no—
676C2×#41—68no—
677C2×#41—92no—
678C2×#41—92no—
679C2×#41—91no—
680C22×Q8—31no—
681C22×D4—32no—
682C22×D4—32no—
683C22×D4—31no—
684C22×D4—31no—
685C22×D4—92no—
686C22×D4—92no—
687C22×D4—94no—
688C22×D4—94no—
689C23×C4—32no—
690C23×C4D3211yescharacteristic, complemented
691#127—94no—
692#127—92no—
693#124—94no—
694#124—92no—
695#123—94no—
696#123—92no—
697C22⋊Q8—94no—
698C22⋊Q8—92no—
699C22⋊Q8—92no—
700C22⋊Q8—91no—
701C22⋊Q8—91no—
702#121—32no—
703#121—32no—
704#121—32no—
705#121—32no—
706#121—94no—
707#121—94no—
708#121—92no—
709#121—92no—
710#121—92no—
711#121—94no—
712#121—92no—
713#121—94no—
714#121—94no—
715#121—94no—
716#121—91no—
717#121—91no—
718#120—94no—
719#120—94no—
720#120—94no—
721#120—94no—
722#120—92no—
723C4×Q8—92no—
724C4×D4—94no—
725C4×D4—92no—
726C4×D4—94no—
727C4×D4—94no—
728C4×D4—92no—
729C4×D4—92no—
730#117—92no—
731#117—91no—
732C2×C4⋊C4—31no—
733C2×C4⋊C4—92no—
734C2×C22⋊C4—32no—
735C2×C22⋊C4—94no—
736C23×C3—22no—
737C23×C3—22no—
738C23×C3—22no—
739C23×C3—22no—
740C23×C3—21no—
741C23×C3—21no—
742C23×C3—21no—
743C23×C3—32no—
744C23×C3—34no—
745C23×C3—32no—
746C23×C3—42no—
747C23×C3—42no—
748C23×C3—41no—
749C23×C3—41no—
750C23×C3—42no—
751C23×C3—64no—
752C23×C3—64no—
753C23×C3—64no—
754C23×C3—122no—
755C23×C3—122no—
756C23×C3—122no—
757C23×C3C23×D311yescharacteristic
758C23×C3C23×D311yescharacteristic
759C23×C3C23×D311yescharacteristic
760C23×C3C23×D311yescharacteristic
761C23×C3C23×D311yescharacteristic
762C23×C3C23×D311yescharacteristic
763C22×D3—24no—
764C22×D3—24no—
765C22×D3—24no—
766C22×D3—32no—
767C22×D3—32no—
768C22×D3—42no—
769C22×D3—42no—
770C22×D3—42no—
771C22×D3—62no—
772C22×D3—68no—
773C22×D3—68no—
774C22×D3—124no—
775C22×D3—124no—
776C22×D3—124no—
777C22×D3—124no—
778C22×D3C23×D314yes—
779C22×D3C23×D312yes—
780C22×D3C23×D312yes—
781C3×Q8—34no—
782C3×Q8—64no—
783C3×Q8—62no—
784C3×D4—38no—
785C3×D4—34no—
786C3×D4—64no—
787C3×D4—64no—
788C3×D4—64no—
789C3×D4—64no—
790C3×D4—68no—
791C3×D4—62no—
792C3×D4—64no—
793C3×D4—64no—
794C3×D4—124no—
795C2×C3×C4—22no—
796C2×C3×C4—22no—
797C2×C3×C4—22no—
798C2×C3×C4—22no—
799C2×C3×C4—22no—
800C2×C3×C4—22no—
801C2×C3×C4—22no—
802C2×C3×C4—22no—
803C2×C3×C4—22no—
804C2×C3×C4—22no—
805C2×C3×C4—21no—
806C2×C3×C4—21no—
807C2×C3×C4—21no—
808C2×C3×C4—21no—
809C2×C3×C4—24no—
810C2×C3×C4—32no—
811C2×C3×C4—38no—
812C2×C3×C4—34no—
813C2×C3×C4—32no—
814C2×C3×C4—42no—
815C2×C3×C4—42no—
816C2×C3×C4—42no—
817C2×C3×C4—42no—
818C2×C3×C4—42no—
819C2×C3×C4—64no—
820C2×C3×C4—64no—
821C2×C3×C4—64no—
822C2×C3×C4—64no—
823C2×C3×C4—122no—
824C2×C3×C4D3×D414yescomplemented
825C2×C3×C4C2×#6714yescomplemented
826C2×C3×C4C23×D311yescharacteristic
827C2×C3×C4C23×D311yescharacteristic
828C2×C3×C4C23×D311yescharacteristic
829C2×C3×C4C23×D311yescharacteristic
830C2×C3×C4C23×D311yescharacteristic
831C2×C3×C4C23×D311yescharacteristic
832C2×C3×C4C23×D311yescharacteristic
833C2×C3×C4C23×D311yescharacteristic
834#67—28no—
835#67—24no—
836#67—24no—
837#67—24no—
838#67—44no—
839#67—68no—
840#67—64no—
841#67—64no—
842#67—64no—
843#67—64no—
844#67—68no—
845#67—68no—
846#67—124no—
847#67—124no—
848#67—124no—
849#67—124no—
850#67—124no—
851#67—124no—
852#67—124no—
853#67—122no—
854#67—122no—
855#67—124no—
856#67C2×#6718yescomplemented
857C2×Dic3—24no—
858C2×Dic3—32no—
859C2×Dic3—32no—
860C2×Dic3—32no—
861C2×Dic3—32no—
862C2×Dic3—32no—
863C2×Dic3—32no—
864C2×Dic3—42no—
865C2×Dic3—62no—
866C2×Dic3—62no—
867C2×Dic3—62no—
868C2×Dic3—68no—
869C2×Dic3—124no—
870C2×Dic3C23×D314yes—
871C2×Dic3C23×D312yes—
872C2×Dic3C23×D312yes—
873D12—24no—
874D12—24no—
875D12—24no—
876D12—22no—
877D12—68no—
878D12—62no—
879D12—62no—
880D12—122no—
881D12—124no—
882D12C2×#6714yescomplemented
883C4×D3—24no—
884C4×D3—24no—
885C4×D3—24no—
886C4×D3—68no—
887C4×D3—64no—
888C4×D3—64no—
889C4×D3—124no—
890C4×D3—124no—
891C4×D3C2×#6718yescomplemented
892Dic6—22no—
893Dic6—24no—
894Dic6—62no—
895Dic6—62no—
896Dic6—122no—
897Dic6C2×#6714yescomplemented
898C2×C32—22no—
899C2×C32—22no—
900C2×C32—41no—
901C2×C32C23×D411yescharacteristic
902C2×C32C2×H(5,𝔽2)11yescharacteristic
903C2×C32#58511yescharacteristic
904C3⋊D3—42no—
905C3×D3—24no—
906C3×D3—44no—
907C3×D3—42no—
908C24—32no—
909C24—32no—
910C24—94no—
911C24C2×D3211yescharacteristic
912#41—38no—
913#41—68no—
914#41—68no—
915#41—64no—
916#41—64no—
917#41—64no—
918#41—188no—
919#41—188no—
920#41—184no—
921C2×Q8—31no—
922C2×Q8—32no—
923C2×Q8—31no—
924C2×Q8—64no—
925C2×Q8—91no—
926C2×D4—32no—
927C2×D4—34no—
928C2×D4—32no—
929C2×D4—32no—
930C2×D4—32no—
931C2×D4—34no—
932C2×D4—31no—
933C2×D4—32no—
934C2×D4—32no—
935C2×D4—32no—
936C2×D4—31no—
937C2×D4—64no—
938C2×D4—68no—
939C2×D4—64no—
940C2×D4—94no—
941C2×D4—94no—
942C2×D4—94no—
943C2×D4—92no—
944C2×D4—92no—
945C2×D4—94no—
946C2×D4—94no—
947C2×D4—92no—
948C2×D4—91no—
949C2×D4—124no—
950C2×D4—188no—
951C2×D4—188no—
952C2×D4—1816no—
953C2×D4—368no—
954C22×C4—24no—
955C22×C4—32no—
956C22×C4—32no—
957C22×C4—32no—
958C22×C4—32no—
959C22×C4—32no—
960C22×C4—32no—
961C22×C4—68no—
962C22×C4—94no—
963C22×C4—94no—
964C22×C4—92no—
965C22×C4C2×D3211yescharacteristic
966C22×C4C2×D3211yescharacteristic
967C22×C4C2×D3211yescharacteristic
968C22×C4C2×D3211yescharacteristic
969C22×C4C2×D3211yescharacteristic
970C22×C4C2×D3211yescharacteristic
971C4⋊C4—32no—
972C4⋊C4—32no—
973C4⋊C4—94no—
974C4⋊C4—94no—
975C4⋊C4—91no—
976C4⋊C4—91no—
977C4⋊C4—92no—
978C4⋊C4—92no—
979C22⋊C4—34no—
980C22⋊C4—34no—
981C22⋊C4—94no—
982C22⋊C4—94no—
983C22⋊C4—94no—
984C22⋊C4—94no—
985C22⋊C4—94no—
986C22⋊C4—92no—
987C22⋊C4—92no—
988C22⋊C4—92no—
989C22⋊C4—92no—
990C22⋊C4—92no—
991C42—94no—
992C42—92no—
993C22×C3—21no—
994C22×C3—21no—
995C22×C3—21no—
996C22×C3—21no—
997C22×C3—21no—
998C22×C3—21no—
999C22×C3—21no—
1000C22×C3—21no—
1001C22×C3—22no—
1002C22×C3—21no—
1003C22×C3—21no—
1004C22×C3—21no—
1005C22×C3—21no—
1006C22×C3—21no—
1007C22×C3—21no—
1008C22×C3—22no—
1009C22×C3—22no—
1010C22×C3—21no—
1011C22×C3—34no—
1012C22×C3—41no—
1013C22×C3—41no—
1014C22×C3—41no—
1015C22×C3—41no—
1016C22×C3—41no—
1017C22×C3—41no—
1018C22×C3—44no—
1019C22×C3—44no—
1020C22×C3—48no—
1021C22×C3—62no—
1022C22×C3—62no—
1023C22×C3—62no—
1024C22×C3—62no—
1025C22×C3—64no—
1026C22×C3—62no—
1027C22×C3—64no—
1028C22×C3—64no—
1029C22×C3—128no—
1030C22×C3—244no—
1031C22×C3C2×D3×D412yes—
1032C22×C3#100412yescomplemented
1033C22×C3#100912yescomplemented
1034C22×C3C22×#6712yes—
1035C22×C3C24×D311yescharacteristic
1036C22×C3C24×D311yescharacteristic
1037C2×D3—22no—
1038C2×D3—22no—
1039C2×D3—24no—
1040C2×D3—24no—
1041C2×D3—22no—
1042C2×D3—22no—
1043C2×D3—24no—
1044C2×D3—22no—
1045C2×D3—48no—
1046C2×D3—62no—
1047C2×D3—62no—
1048C2×D3—62no—
1049C2×D3—62no—
1050C2×D3—62no—
1051C2×D3—62no—
1052C2×D3—84no—
1053C2×D3—122no—
1054C2×D3—122no—
1055C2×D3—122no—
1056C2×D3—248no—
1057C2×D3—248no—
1058C2×D3C22×#6714yes—
1059C3×C4—21no—
1060C3×C4—21no—
1061C3×C4—21no—
1062C3×C4—21no—
1063C3×C4—22no—
1064C3×C4—22no—
1065C3×C4—34no—
1066C3×C4—41no—
1067C3×C4—41no—
1068C3×C4—62no—
1069C3×C4—64no—
1070C3×C4C2×D3×D412yes—
1071C3×C4C2×D3×D412yes—
1072C3×C4C22×#6712yes—
1073C3×C4C22×#6712yes—
1074Dic3—24no—
1075Dic3—22no—
1076Dic3—62no—
1077Dic3—62no—
1078Dic3—62no—
1079Dic3—62no—
1080Dic3—62no—
1081Dic3—62no—
1082Dic3—122no—
1083Dic3—122no—
1084Dic3—122no—
1085Dic3C22×#6714yes—
1086C32#348811yescharacteristic, complemented, Sylow
1087C23—22no—
1088C23—22no—
1089C23—32no—
1090C23—34no—
1091C23—32no—
1092C23—41no—
1093C23—64no—
1094C23—64no—
1095C23—64no—
1096C23—92no—
1097C23—122no—
1098C23—122no—
1099C23—122no—
1100C23—188no—
1101C23—364no—
1102C23—364no—
1103C23C22×D3211yescharacteristic
1104C23C22×D3211yescharacteristic
1105C23C22×D3211yescharacteristic
1106Q8—34no—
1107Q8—64no—
1108Q8—62no—
1109Q8—182no—
1110D4—38no—
1111D4—34no—
1112D4—64no—
1113D4—64no—
1114D4—64no—
1115D4—68no—
1116D4—64no—
1117D4—64no—
1118D4—64no—
1119D4—62no—
1120D4—124no—
1121D4—188no—
1122D4—188no—
1123D4—184no—
1124D4—184no—
1125D4—182no—
1126D4—364no—
1127D4—362no—
1128D4—364no—
1129D4—364no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—32no—
1136C2×C4—38no—
1137C2×C4—34no—
1138C2×C4—32no—
1139C2×C4—64no—
1140C2×C4—64no—
1141C2×C4—64no—
1142C2×C4—64no—
1143C2×C4—92no—
1144C2×C4—92no—
1145C2×C4—92no—
1146C2×C4—122no—
1147C2×C4—188no—
1148C2×C4—184no—
1149C2×C4—364no—
1150C2×C4D3×#6714yescomplemented
1151C2×C4C22×D3211yescharacteristic
1152C2×C4C22×D3211yescharacteristic
1153C2×C4C22×D3211yescharacteristic
1154C2×C4C22×D3211yescharacteristic
1155C2×C3—22no—
1156C2×C3—22no—
1157C2×C3—22no—
1158C2×C3—22no—
1159C2×C3—21no—
1160C2×C3—21no—
1161C2×C3—21no—
1162C2×C3—42no—
1163C2×C3—42no—
1164C2×C3—42no—
1165C2×C3—41no—
1166C2×C3—41no—
1167C2×C3—64no—
1168C2×C3—122no—
1169C2×C3—124no—
1170C2×C3C22×D3×D411yescharacteristic
1171C2×C3C2×#100411yescharacteristic
1172C2×C3C2×#100911yescharacteristic
1173C2×C3#596411yescharacteristic
1174C2×C3#596411yescharacteristic
1175C2×C3C23×#6711yescharacteristic
1176D3—24no—
1177D3—44no—
1178D3—42no—
1179D3—122no—
1180D3—122no—
1181D3—242no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—21no—
1186C22—21no—
1187C22—21no—
1188C22—21no—
1189C22—34no—
1190C22—44no—
1191C22—62no—
1192C22—62no—
1193C22—64no—
1194C22—62no—
1195C22—62no—
1196C22—64no—
1197C22—62no—
1198C22—64no—
1199C22—128no—
1200C22—182no—
1201C22—182no—
1202C22—182no—
1203C22—244no—
1204C22—728no—
1205C22#6430712yescomplemented
1206C22C2×D3×#6712yes—
1207C22C23×D3211yescharacteristic
1208C4—21no—
1209C4—21no—
1210C4—34no—
1211C4—64no—
1212C4—62no—
1213C4—182no—
1214C4—182no—
1215C4—182no—
1216C4C2×D3×#6712yes—
1217C4C2×D3×#6712yes—
1218C3—21no—
1219C3#8594911yescharacteristic, complemented
1220C3#8727511yescharacteristic, complemented
1221C2—22no—
1222C2—22no—
1223C2—41no—
1224C2—64no—
1225C2—122no—
1226C2—124no—
1227C2—362no—
1228C2C2×#6430711yescharacteristic
1229C2#1059666911yescharacteristic
1230C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C2×#64307C2semidirect
3. #10596262C2semidirect
4. C2×C3×#930C2semidirect
5. #672C2semidirect
6. #10595070C2semidirect
7. #10595069C2semidirect
8. #10595065C2semidirect
9. #10595064C2semidirect
10. D3×#930C2semidirect
11. #10595043C2semidirect
12. #10595040C2semidirect
13. #10595006C2semidirect
14. #10595004C2semidirect
15. #10594986C2semidirect
16. #10594900C2semidirect
17. #10594892C2semidirect
20. C23×C32×C4C22semidirect
21. C2×#3828C22semidirect
22. C22×C3×#67C22semidirect
23. C22×C3×#67C22semidirect
26. C2×C3×#235C22semidirect
27. C2×C3×#235C22semidirect
28. C2×C3×#235C22semidirect
29. C2×C3×#235C22semidirect
30. C2×C3×#235C22semidirect
31. C22×C3×D12C22semidirect
32. C22×C3×D12C22semidirect
33. C22×C3×C4×D3C22semidirect
34. C22×C3×Dic6C22semidirect
35. C2×D3×#67C22semidirect
36. C2×D3×#67C22semidirect
38. C2×#3802C22semidirect
39. C2×D3×D12C22semidirect
40. C2×#3796C22semidirect
41. C2×#3795C22semidirect
42. #64162C22semidirect
43. #64139C22semidirect
44. #64139C22semidirect
45. #64138C22semidirect
46. C4×#638C22semidirect
47. C4×#638C22semidirect
48. #64135C22semidirect
49. #64133C22semidirect
50. #64133C22semidirect
51. C3×#930C22semidirect
52. C3×#930C22semidirect
53. C3×#930C22semidirect
54. C3×#930C22semidirect
55. C2×C3×(C2×D3)⋊C4C22semidirect
56. C2×C3×C4⋊Dic3C22semidirect
57. #63983C22semidirect
58. #63979C22semidirect
59. #63978C22semidirect
60. #63978C22semidirect
61. #63976C22semidirect
62. #63976C22semidirect
63. Dic3×#67C22semidirect
64. Dic3×#67C22semidirect
65. #63970C22semidirect
66. #63970C22semidirect
67. #63922C22semidirect
68. D3×(C2×D3)⋊C4C22semidirect
69. #63916C22semidirect
70. #63914C22semidirect
71. #63909C22semidirect
72. #63908C22semidirect
73. #63908C22semidirect
74. #63907C22semidirect
75. #63906C22semidirect
76. #63905C22semidirect
77. #63898C22semidirect
78. D3×C4⋊Dic3C22semidirect
79. #63887C22semidirect
80. #63885C22semidirect
81. #63879C22semidirect
82. #63871C22semidirect
83. #63863C22semidirect
84. #63857C22semidirect
85. #63843C22semidirect
86. #63841C22semidirect
90. C22×#235D3semidirect
110. C2×#930D3semidirect
155. C3×#235D4semidirect
222. C23×C3×C4C2×D3semidirect
223. C23×C3×C4C2×D3semidirect
226. C22×#67C2×D3semidirect
227. C22×#67C2×D3semidirect
244. C2×#235C2×D3semidirect
245. C2×#235C2×D3semidirect
246. C2×#235C2×D3semidirect
247. C2×#235C2×D3semidirect
248. C2×#235C2×D3semidirect
250. C22×D12C2×D3semidirect
251. C22×D12C2×D3semidirect
252. C22×C4×D3C2×D3semidirect
253. C22×Dic6C2×D3semidirect
305. #930C2×D3semidirect
306. #930C2×D3semidirect
307. #930C2×D3semidirect
308. #930C2×D3semidirect
323. C2×(C2×D3)⋊C4C2×D3semidirect
329. C2×C4⋊Dic3C2×D3semidirect
377. C2×C32×C4C2×D4semidirect
396. C3×#67C2×D4semidirect
406. C3×D12C2×D4semidirect
410. C3×C4×D3C2×D4semidirect
413. C3×Dic6C2×D4semidirect
548. #235#67semidirect
642. C22×C32H(5,𝔽2)semidirect
690. C23×C4D32semidirect
824. C2×C3×C4D3×D4semidirect
825. C2×C3×C4C2×#67semidirect
856. #67C2×#67semidirect
882. D12C2×#67semidirect
891. C4×D3C2×#67semidirect
897. Dic6C2×#67semidirect
1032. C22×C3#1004semidirect
1033. C22×C3#1009semidirect
1086. C32#3488semidirect
1150. C2×C4D3×#67semidirect
1205. C22#64307semidirect
1219. C3#85949semidirect
1220. C3#87275semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#643072
#105962622
C2×C3×#9302
#6722
#105950702
#105950692
#105950652
#105950642
D3×#9302
#105950432
#105950402
#105950062
#105950042
#105949862
#105949002
#105948922
#872753
#859493