Finite Group Databasebeta

← #11904649

Subgroups — #11904649

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
1C2×#64307C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3#10595995C211yesmaximal, characteristic, complemented
4C3×#5525C211yesmaximal, characteristic, complemented
5C3×#5523C211yesmaximal, characteristic, complemented
6#10595043C211yesmaximal, characteristic, complemented
7C2×#63916C211yesmaximal, characteristic, complemented
8#10594628C212yesmaximal, complemented
9#10594626C212yesmaximal, complemented
10D3×#895C212yesmaximal, complemented
11#10594522C212yesmaximal, complemented
12#10594292C214yesmaximal, complemented
13#10594277C214yesmaximal, complemented
14#10594005C212yesmaximal, complemented
15#10594004C212yesmaximal, complemented
16#10593901C212yesmaximal, complemented
17#10593900C212yesmaximal, complemented
18#86331—31nomaximal
19#85900—31nomaximal
20C2×#3828C2211yescharacteristic, complemented
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2211yescharacteristic, complemented
24C22×C3×D12C2211yescharacteristic, complemented
25C2×#3811C2212yescomplemented
26C2×D3×#67C2214yescomplemented
27C22×#626C2212yescomplemented
28C2×#3805C2212yescomplemented
29#64307—28no—
30#64306—28no—
31C2×#3802C2211yescharacteristic, complemented
32C2×#3802C2212yescomplemented
33C2×D3×D12C2212yescomplemented
34C2×D3×D12C2214yescomplemented
35C2×C4×D32C2212yescomplemented
36C2×#3798C2212yescomplemented
37C2×#3797C2211yescharacteristic, complemented
38C2×#3796C2211yescharacteristic, complemented
39C2×#3796C2211yescharacteristic, complemented
40C2×#3796C2212yescomplemented
41C2×#3795C2212yescomplemented
42C32×#117C2211yescharacteristic, complemented
43#64106C2211yescharacteristic, complemented
44#64106C2211yescharacteristic, complemented
45#64104C2211yescharacteristic, complemented
46#64104C2211yescharacteristic, complemented
47#64095C2212yescomplemented
48#64091C2212yescomplemented
49C4×C4⋊(C3⋊D3)C2212yescomplemented
50C4×C4⋊(C3⋊D3)C2212yescomplemented
51C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
52C3×#895C2212yescomplemented
53C3×#895C2212yescomplemented
54C3×#892C2212yescomplemented
55C3×D3×C4⋊C4C2212yescomplemented
56C3×#882C2214yescomplemented
57C3×#67⋊C4C2214yescomplemented
58C3×#875C2212yescomplemented
59C3×#874C2212yescomplemented
60C3×C4×D12C2212yescomplemented
61C3×C4×Dic6C2212yescomplemented
62#63978C2214yescomplemented
63C2×(C2×D3)⋊Dic3C2212yescomplemented
64#63923C2214yescomplemented
65#63922C2214yescomplemented
66#63922C2214yescomplemented
67D3×(C2×D3)⋊C4C2214yescomplemented
68#63916C2212yescomplemented
69#63916C2212yescomplemented
70#63916C2212yescomplemented
71#63916C2212yescomplemented
72#63916C2212yescomplemented
73#63911C2214yescomplemented
74#63910C2214yescomplemented
75#63909C2212yescomplemented
76#63908C2214yescomplemented
77#63906C2214yescomplemented
78#63893C2214yescomplemented
79Dic3×D12C2214yescomplemented
80#63891C2214yescomplemented
81#63886C2214yescomplemented
82#63886C2214yescomplemented
83#63880C2214yescomplemented
84#63871C2212yescomplemented
85#63857C2212yescomplemented
86#63852C2214yescomplemented
87C2×#1009—31no—
88C2×D3×#41—31no—
89C2×D3×#41—31no—
90C2×#1004—31no—
91C3×#535—31no—
92C3×#520—31no—
93#5833—31no—
94C2×#938—31no—
95#5718—32no—
96#5717—32no—
97#5677—32no—
98#5676—32no—
99#5608—32no—
100#5607—32no—
101#5606—32no—
102D3×#121—32no—
103#5591—34no—
104#5590—34no—
105#5577—32no—
106#5576—32no—
107#5554—34no—
108#5554—32no—
109D4×D12—34no—
110D4×D12—32no—
111#5525—32no—
112#5525D311yescharacteristic, complemented
113#5524—31no—
114#5524—31no—
115#5524—32no—
116#5524—61no—
117#5523D311yescharacteristic, complemented
118#5510—31no—
119#5510—32no—
120C2×#895—31no—
121C2×#895—32no—
122C23×C3⋊D3C2311yescharacteristic
123C23×C3×D3C2312yes—
124C22×D32C2312yes—
125C22×D32C2314yes—
126C22×C32×C4C2311yescharacteristic
127C2×#638C2312yes—
128C22×C3⋊Dic3C2311yescharacteristic
129#3828—24no—
130C2×C4⋊(C3⋊D3)C2312yes—
131C2×C4⋊(C3⋊D3)C2311yescharacteristic
132C2×C4⋊(C3⋊D3)C2312yes—
133C2×C4×C3⋊D3—24no—
134C2×C4×C3⋊D3C2311yescharacteristic
135C2×C4×C3⋊D3C2312yes—
136C2×C4×C3⋊D3C2311yescharacteristic
137C2×C4×C3⋊D3C2311yescharacteristic
138C2×C4×C3⋊D3C2311yescharacteristic
139C2×#634C2311yescharacteristic
140C2×C3×#67C2312yes—
141C2×C3×#67C2312yes—
142C22×C3×Dic3C2312yes—
143C3×#235—24no—
144C3×#235D418yescomplemented
145C2×C3×D12—24no—
146C2×C3×D12C2312yes—
147C2×C3×D12C2312yes—
148C2×C3×D12C2311yescharacteristic
149C2×C3×D12C2314yes—
150C2×C3×D12C2314yes—
151C2×C3×D12C2311yescharacteristic
152C2×C3×C4×D3C2312yes—
153C2×C3×C4×D3C2314yes—
154C2×C3×C4×D3C2312yes—
155C2×C3×Dic6C2311yescharacteristic
156C2×C3×Dic6C2311yescharacteristic
157#3811—28no—
158D3×#67—216no—
159C2×#627C2312yes—
160C2×#626—44no—
161C2×#626C2312yes—
162C2×#626C2312yes—
163C2×#626C2314yes—
164C2×#626C2314yes—
165C2×#626C2314yes—
166C2×#626C2314yes—
167C2×#625C2314yes—
168C2×#625C2312yes—
169C2×#624C2312yes—
170#3805—28no—
171C2×D3×Dic3C2314yes—
172C2×D3×Dic3C2312yes—
173C2×D3×Dic3C2312yes—
174#3802—24no—
175#3802—28no—
176D3×D12—28no—
177D3×D12—48no—
178C4×D32—28no—
179#3798—28no—
180#3797—24no—
181#3796—24no—
182#3796—24no—
183#3796—28no—
184#3795—28no—
185C32×C4⋊C4C2311yescharacteristic
186C32×C4⋊C4C2311yescharacteristic
187C32×C22⋊C4C2312yes—
188C32×C42C2312yes—
189#3752C2312yes—
190#3752C2312yes—
191#3752C2312yes—
192#3752C2312yes—
193C4⋊(C3⋊Dic3)C2312yes—
194C4⋊(C3⋊Dic3)C2312yes—
195C3×(C2×D3)⋊C4C2314yes—
196C3×(C2×D3)⋊C4C2314yes—
197C3×(C2×D3)⋊C4C2314yes—
198C3×C4⋊Dic3C2312yes—
199C3×C4⋊Dic3C2312yes—
200C3×Dic3⋊C4C2314yes—
201C3×C4×Dic3C2314yes—
202Dic3⋊Dic3C2314yes—
203#3722C2314yes—
204(C2×D3)⋊Dic3C2314yes—
205(C2×D3)⋊Dic3C2314yes—
206(C2×D3)⋊Dic3C2314yes—
207#3488—91noSylow
208C2×C3×#41—31no—
209C2×C3×#41—31no—
210C22×C3×D4—31no—
211C22×#67—34no—
212C22×#67—32no—
213#1009—68no—
214D3×#41—68no—
215D3×#41—68no—
216C2×#239—31no—
217C2×#239—31no—
218C2×#239—32no—
219C2×D3×Q8—31no—
220C2×D3×Q8—31no—
221#1004—68no—
222C2×#237—32no—
223C2×#237—32no—
224C2×#237—32no—
225C2×#237—32no—
226C2×#237—31no—
227C2×#237—31no—
228C2×D3×D4—34no—
229C2×D3×D4—32no—
230C2×D3×D4—32no—
231C2×D3×D4—32no—
232C2×D3×D4—31no—
233C2×D3×D4—31no—
234C2×D3×D4—32no—
235C2×D3×D4—32no—
236C2×D3×D4—34no—
237C2×#235—31no—
238C2×#235—31no—
239C2×#235—32no—
240C2×#235—32no—
241C2×#235—32no—
242C2×#235—61no—
243C2×#235C2×D311yescharacteristic
244C2×#235C2×D311yescharacteristic, complemented
245C22×D12—32no—
246C22×D12—32no—
247C22×D12—34no—
248C22×D12C2×D311yescharacteristic, complemented
249C22×C4×D3—31no—
250C22×C4×D3—31no—
251C22×C4×D3—32no—
252C22×C4×D3—32no—
253C22×C4×D3—61no—
254C3×#127—32no—
255C3×#124—32no—
256C3×#121—32no—
257C3×#121—32no—
258C3×#120—34no—
259C3×C4×Q8—32no—
260C3×C4×D4—34no—
261C3×C4×D4—32no—
262C3×#117—21no—
263C3×#117—32no—
264C3×#117C2×D311yescharacteristic, complemented
265C3×#117C2×D311yescharacteristic, complemented
266C2×C3×C4⋊C4—31no—
267C2×C3×C4⋊C4—32no—
268C2×#217—32no—
269#946—32no—
270#940—34no—
271#939—34no—
272#939—34no—
273#939—34no—
274#938—34no—
275#938—32no—
276#938—32no—
277#938—32no—
278#938—32no—
279#938—32no—
280#937—34no—
281#937—34no—
282D4×Dic3—34no—
283#930—34no—
284#930—34no—
285#930—34no—
286#930—32no—
287C2×(C2×D3)⋊C4—32no—
288C2×(C2×D3)⋊C4—34no—
289C2×C4⋊Dic3C2×D311yescharacteristic, complemented
290#924—32no—
291#897—32no—
292#897—32no—
293#897—31no—
294#897—31no—
295#897—31no—
296#897—31no—
297#897—34no—
298#897—61no—
299#897—61no—
300#895—32no—
301#895—32no—
302#895—34no—
303#895—32no—
304#895—32no—
305#895—34no—
306#895—32no—
307#895—32no—
308#895—31no—
309#895—31no—
310#895—31no—
311#895—31no—
312#895—34no—
313#895—61no—
314#895—61no—
315#895C2×D312yescomplemented
316#895C2×D312yescomplemented
317#892C2×D312yescomplemented
318D3×C4⋊C4C2×D312yescomplemented
319#886—32no—
320#886—32no—
321#886—34no—
322#886—62no—
323#885—34no—
324#884—34no—
325#884—34no—
326#883—34no—
327#882—34no—
328#882—34no—
329#882—32no—
330#882—32no—
331#882—34no—
332#882—34no—
333#882—62no—
334#882C2×D314yescomplemented
335#67⋊C4—34no—
336#67⋊C4C2×D314yescomplemented
337D3×C22⋊C4—34no—
338#878—34no—
339#875—34no—
340#875C2×D312yescomplemented
341#874—34no—
342#874C2×D312yescomplemented
343C4×D12—34no—
344C4×D12—32no—
345C4×D12—32no—
346C4×D12—32no—
347C4×D12—32no—
348C4×D12—34no—
349C4×D12—62no—
350C4×D12—62no—
351C4×D12C2×D312yescomplemented
352C4×Dic6C2×D312yescomplemented
353C23×C32C2411yescharacteristic
354C22×C3⋊D3—22no—
355C22×C3⋊D3—22no—
356C22×C3⋊D3—41no—
357C22×C3⋊D3C2412yes—
358C22×C3⋊D3C2411yescharacteristic
359C22×C3⋊D3C2411yescharacteristic
360C22×C3×D3—24no—
361C22×C3×D3—42no—
362C22×C3×D3—42no—
363C22×C3×D3C2414yes—
364C22×C3×D3C2412yes—
365C22×C3×D3C2412yes—
366C2×D32—24no—
367C2×D32—24no—
368C2×D32—28no—
369C2×D32—42no—
370C2×D32—44no—
371C2×D32—44no—
372C2×C32×C4C2×D414yescomplemented
373C2×C32×C4C2412yes—
374C2×C32×C4C2412yes—
375C2×C32×C4C2411yescharacteristic
376C2×C32×C4C2411yescharacteristic
377#638—24no—
378C2×C3⋊Dic3—22no—
379C2×C3⋊Dic3C2411yescharacteristic
380C2×C3⋊Dic3C2411yescharacteristic
381C2×C3⋊Dic3C2412yes—
382C4⋊(C3⋊D3)—24no—
383C4⋊(C3⋊D3)—22no—
384C4⋊(C3⋊D3)—42no—
385C4×C3⋊D3—22no—
386C4×C3⋊D3—24no—
387C4×C3⋊D3—22no—
388C4×C3⋊D3—22no—
389C4×C3⋊D3—22no—
390#634—22no—
391C3×#67—24no—
392C3×#67C2×D418yescomplemented
393C2×C3×Dic3—42no—
394C2×C3×Dic3C2414yes—
395C2×C3×Dic3C2412yes—
396C2×C3×Dic3C2412yes—
397C3×D12—24no—
398C3×D12—24no—
399C3×D12—22no—
400C3×D12—44no—
401C3×D12—44no—
402C3×D12C2×D414yescomplemented
403C3×C4×D3—24no—
404C3×C4×D3—44no—
405C3×C4×D3C2×D418yescomplemented
406C3×Dic6—22no—
407C3×Dic6C2×D414yescomplemented
408#627—24no—
409#626—28no—
410#626—24no—
411#626—24no—
412#626—28no—
413#626—44no—
414#626—44no—
415#625—28no—
416#625—24no—
417#624—24no—
418D3×Dic3—24no—
419D3×Dic3—28no—
420D3×Dic3—24no—
421C2×H(5,𝔽2)—91no—
422C22×#41—91no—
423#550—92no—
424#548—92no—
425#546—94no—
426#546—92no—
427D42—94no—
428D42—92no—
429#537—92no—
430#537—91no—
431#535—31no—
432#535—92no—
433#525—92no—
434#525—91no—
435C2×#121—92no—
436C2×#121—91no—
437#520—31no—
438C24×C3—32no—
439C23×D3—31no—
440C23×D3—31no—
441C23×D3—32no—
442C23×D3—32no—
443C23×D3—34no—
444C23×D3—34no—
445C23×D3—61no—
446C23×D3C22×D312yes—
447C3×#41—38no—
448C3×#41—64no—
449C2×C3×Q8—31no—
450C2×C3×Q8—31no—
451C2×C3×D4—32no—
452C2×C3×D4—32no—
453C2×C3×D4—31no—
454C2×C3×D4—32no—
455C2×C3×D4—32no—
456C2×C3×D4—31no—
457C2×C3×D4—34no—
458C2×C3×D4—34no—
459C2×C3×D4—64no—
460C22×C3×C4—21no—
461C22×C3×C4—32no—
462C22×C3×C4—32no—
463C22×C3×C4—32no—
464C22×C3×C4—34no—
465C22×C3×C4C22×D311yescharacteristic
466C22×C3×C4C22×D311yescharacteristic
467C2×#67—32no—
468C2×#67—32no—
469C2×#67—32no—
470C2×#67—34no—
471C2×#67—34no—
472C2×#67—32no—
473C2×#67—34no—
474C2×#67—32no—
475C2×#67—34no—
476C2×#67—32no—
477C2×#67—34no—
478C2×#67—34no—
479C2×#67—62no—
480C2×#67—616no—
481C2×#67—124no—
482C2×#67C22×D312yes—
483C2×#67C22×D312yes—
484C22×Dic3—31no—
485C22×Dic3—31no—
486C22×Dic3—34no—
487C22×Dic3—32no—
488C22×Dic3—32no—
489C22×Dic3—61no—
490C22×Dic3C22×D312yes—
491#239—64no—
492#239—68no—
493#239—64no—
494D3×Q8—64no—
495D3×Q8—64no—
496#237—64no—
497#237—68no—
498#237—68no—
499#237—68no—
500#237—68no—
501#237—64no—
502D3×D4—64no—
503D3×D4—68no—
504D3×D4—68no—
505D3×D4—616no—
506D3×D4—68no—
507D3×D4—68no—
508D3×D4—64no—
509D3×D4—68no—
510D3×D4—128no—
511#235—24no—
512#235—68no—
513#235—68no—
514#235—64no—
515#235—64no—
516#235—68no—
517#235—124no—
518#235D1218yescomplemented
519C2×D12—24no—
520C2×D12—34no—
521C2×D12—32no—
522C2×D12—34no—
523C2×D12—32no—
524C2×D12—32no—
525C2×D12—32no—
526C2×D12—31no—
527C2×D12—31no—
528C2×D12—34no—
529C2×D12—34no—
530C2×D12—32no—
531C2×D12—32no—
532C2×D12—62no—
533C2×D12—62no—
534C2×D12—61no—
535C2×D12—68no—
536C2×D12—128no—
537C2×D12—124no—
538C2×D12C22×D311yescharacteristic
539C2×D12C22×D312yes—
540C2×D12C22×D312yes—
541C2×D12C22×D314yes—
542C2×D12C22×D314yes—
543C2×D12C22×D311yescharacteristic
544C2×C4×D3—32no—
545C2×C4×D3—34no—
546C2×C4×D3—32no—
547C2×C4×D3—31no—
548C2×C4×D3—31no—
549C2×C4×D3—32no—
550C2×C4×D3—31no—
551C2×C4×D3—31no—
552C2×C4×D3—32no—
553C2×C4×D3—31no—
554C2×C4×D3—31no—
555C2×C4×D3—31no—
556C2×C4×D3—31no—
557C2×C4×D3—32no—
558C2×C4×D3—32no—
559C2×C4×D3—61no—
560C2×C4×D3—61no—
561C2×C4×D3—62no—
562C2×C4×D3—61no—
563C2×C4×D3—61no—
564C2×C4×D3—68no—
565C2×C4×D3—64no—
566C2×C4×D3—64no—
567C2×C4×D3—68no—
568C2×C4×D3—124no—
569C2×C4×D3C22×D312yes—
570C2×C4×D3C22×D314yes—
571C2×C4×D3C22×D312yes—
572C2×Dic6—31no—
573C2×Dic6—31no—
574C2×Dic6—32no—
575C2×Dic6—32no—
576C2×Dic6—61no—
577C2×Dic6C22×D311yescharacteristic
578C2×Dic6C22×D311yescharacteristic
579C3×C4⋊C4—21no—
580C3×C4⋊C4—21no—
581C3×C4⋊C4—34no—
582C3×C4⋊C4—32no—
583C3×C4⋊C4—32no—
584C3×C4⋊C4C22×D311yescharacteristic
585C3×C4⋊C4C22×D311yescharacteristic
586C3×C4⋊C4C22×D311yescharacteristic
587C3×C4⋊C4C22×D311yescharacteristic
588C3×C22⋊C4—22no—
589C3×C22⋊C4—34no—
590C3×C22⋊C4—34no—
591C3×C22⋊C4—34no—
592C3×C22⋊C4C22×D312yes—
593C3×C22⋊C4C22×D312yes—
594C3×C42—22no—
595C3×C42—34no—
596C3×C42C22×D312yes—
597C3×C42C22×D312yes—
598#217—34no—
599#217—34no—
600#217—34no—
601(C2×D3)⋊C4—34no—
602(C2×D3)⋊C4—34no—
603(C2×D3)⋊C4—34no—
604(C2×D3)⋊C4—32no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—32no—
607(C2×D3)⋊C4—32no—
608(C2×D3)⋊C4—32no—
609(C2×D3)⋊C4—32no—
610(C2×D3)⋊C4—32no—
611(C2×D3)⋊C4—32no—
612(C2×D3)⋊C4—34no—
613(C2×D3)⋊C4—34no—
614(C2×D3)⋊C4—62no—
615(C2×D3)⋊C4—62no—
616(C2×D3)⋊C4—62no—
617(C2×D3)⋊C4—62no—
618(C2×D3)⋊C4C22×D314yes—
619(C2×D3)⋊C4C22×D314yes—
620(C2×D3)⋊C4C22×D314yes—
621C4⋊Dic3—32no—
622C4⋊Dic3—32no—
623C4⋊Dic3—32no—
624C4⋊Dic3—32no—
625C4⋊Dic3—34no—
626C4⋊Dic3—62no—
627C4⋊Dic3—62no—
628C4⋊Dic3C22×D312yes—
629C4⋊Dic3C22×D312yes—
630Dic3⋊C4—34no—
631Dic3⋊C4C22×D314yes—
632C4×Dic3C22×D314yes—
633C22×C32—21no—
634C22×C32—21no—
635C22×C32C22×D412yes—
636C22×C32C2511yescharacteristic
637C2×C3⋊D3—21no—
638C2×C3⋊D3—21no—
639C2×C3⋊D3—21no—
640C2×C3⋊D3—21no—
641C2×C3⋊D3—22no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—22no—
644C2×C3⋊D3—22no—
645C2×C3⋊D3—44no—
646C2×C3⋊D3H(5,𝔽2)12yescomplemented
647C2×C3×D3—22no—
648C2×C3×D3—22no—
649C2×C3×D3—22no—
650C2×C3×D3—24no—
651C2×C3×D3—24no—
652C2×C3×D3—22no—
653C2×C3×D3—22no—
654C2×C3×D3—24no—
655C2×C3×D3—84no—
656C2×C3×D3C22×D414yes—
657D32—48no—
658D32—88no—
659C32×C4—22no—
660C32×C4—22no—
661C32×C4C22×D412yes—
662C32×C4C22×D412yes—
663C3⋊Dic3—21no—
664C3⋊Dic3—22no—
665C3⋊Dic3—21no—
666C3×Dic3—22no—
667C3×Dic3—24no—
668C3×Dic3C22×D414yes—
669H(5,𝔽2)—188no—
670C2×#41—31no—
671C2×#41—31no—
672C2×#41—92no—
673C2×#41—92no—
674C2×#41—92no—
675C2×#41—91no—
676C2×#41—92no—
677C2×#41—91no—
678C2×#41—91no—
679C2×#41—188no—
680C22×Q8—91no—
681C22×D4—31no—
682C22×D4—92no—
683C22×D4—94no—
684C22×D4—92no—
685C22×D4—92no—
686C22×D4—91no—
687C22×D4—92no—
688C22×D4—94no—
689C23×C4—92no—
690C23×C4—91no—
691#127—32no—
692#127—94no—
693#124—32no—
694#124—94no—
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—94no—
705#121—94no—
706#121—92no—
707#121—92no—
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—34no—
719#120—94no—
720#120—94no—
721#120—94no—
722#120—92no—
723C4×Q8—32no—
724C4×D4—34no—
725C4×D4—32no—
726C4×D4—94no—
727C4×D4—94no—
728C4×D4—92no—
729C4×D4—92no—
730#117—32no—
731#117D3211yescharacteristic, complemented
732C2×C4⋊C4—31no—
733C2×C4⋊C4—32no—
734C2×C22⋊C4—94no—
735C2×C22⋊C4—92no—
736C23×C3—21no—
737C23×C3—32no—
738C23×C3—34no—
739C23×C3—32no—
740C23×C3—64no—
741C23×C3—122no—
742C23×C3—122no—
743C23×C3C23×D311yescharacteristic
744C23×C3C23×D311yescharacteristic
745C22×D3—24no—
746C22×D3—31no—
747C22×D3—31no—
748C22×D3—32no—
749C22×D3—32no—
750C22×D3—31no—
751C22×D3—31no—
752C22×D3—42no—
753C22×D3—42no—
754C22×D3—61no—
755C22×D3—61no—
756C22×D3—62no—
757C22×D3—64no—
758C22×D3—64no—
759C22×D3—64no—
760C22×D3—68no—
761C22×D3—62no—
762C22×D3—62no—
763C22×D3—62no—
764C22×D3—62no—
765C22×D3—64no—
766C22×D3—68no—
767C22×D3—122no—
768C22×D3—122no—
769C22×D3—122no—
770C22×D3—122no—
771C22×D3—124no—
772C22×D3—124no—
773C22×D3—124no—
774C22×D3—124no—
775C22×D3—121no—
776C22×D3—121no—
777C22×D3—122no—
778C22×D3C23×D314yes—
779C22×D3C23×D312yes—
780C22×D3C23×D312yes—
781C3×Q8—34no—
782C3×Q8—62no—
783C3×D4—38no—
784C3×D4—34no—
785C3×D4—64no—
786C3×D4—64no—
787C3×D4—64no—
788C3×D4—62no—
789C3×D4—124no—
790C3×D4—124no—
791C2×C3×C4—21no—
792C2×C3×C4—21no—
793C2×C3×C4—22no—
794C2×C3×C4—22no—
795C2×C3×C4—24no—
796C2×C3×C4—32no—
797C2×C3×C4—38no—
798C2×C3×C4—32no—
799C2×C3×C4—34no—
800C2×C3×C4—64no—
801C2×C3×C4—124no—
802C2×C3×C4—122no—
803C2×C3×C4C2×D1214yescomplemented
804C2×C3×C4D3×D414yescomplemented
805C2×C3×C4C23×D312yes—
806C2×C3×C4C23×D312yes—
807C2×C3×C4C23×D312yes—
808C2×C3×C4C23×D312yes—
809C2×C3×C4C23×D311yescharacteristic
810C2×C3×C4C23×D311yescharacteristic
811C2×C3×C4C23×D311yescharacteristic
812C2×C3×C4C23×D311yescharacteristic
813#67—24no—
814#67—68no—
815#67—64no—
816#67—68no—
817#67—64no—
818#67—64no—
819#67—64no—
820#67—64no—
821#67—68no—
822#67—64no—
823#67—68no—
824#67—124no—
825#67—124no—
826#67—124no—
827#67C2×D1218yescomplemented
828C2×Dic3—32no—
829C2×Dic3—32no—
830C2×Dic3—31no—
831C2×Dic3—31no—
832C2×Dic3—31no—
833C2×Dic3—31no—
834C2×Dic3—42no—
835C2×Dic3—62no—
836C2×Dic3—61no—
837C2×Dic3—61no—
838C2×Dic3—64no—
839C2×Dic3—62no—
840C2×Dic3—62no—
841C2×Dic3—64no—
842C2×Dic3—68no—
843C2×Dic3—122no—
844C2×Dic3C23×D314yes—
845C2×Dic3C23×D312yes—
846C2×Dic3C23×D312yes—
847D12—24no—
848D12—24no—
849D12—22no—
850D12—44no—
851D12—44no—
852D12—64no—
853D12—64no—
854D12—68no—
855D12—64no—
856D12—68no—
857D12—64no—
858D12—62no—
859D12—62no—
860D12—122no—
861D12—124no—
862D12—122no—
863D12—122no—
864D12—124no—
865D12—124no—
866D12—124no—
867D12C2×D1214yescomplemented
868C4×D3—24no—
869C4×D3—44no—
870C4×D3—64no—
871C4×D3—64no—
872C4×D3—68no—
873C4×D3—64no—
874C4×D3—62no—
875C4×D3—62no—
876C4×D3—62no—
877C4×D3—62no—
878C4×D3—64no—
879C4×D3—62no—
880C4×D3—62no—
881C4×D3—62no—
882C4×D3—62no—
883C4×D3—64no—
884C4×D3—64no—
885C4×D3—122no—
886C4×D3—122no—
887C4×D3—122no—
888C4×D3—122no—
889C4×D3—124no—
890C4×D3C2×D1218yescomplemented
891Dic6—22no—
892Dic6—64no—
893Dic6—62no—
894Dic6—62no—
895Dic6—64no—
896Dic6—122no—
897Dic6C2×D1214yescomplemented
898C2×C32—22no—
899C2×C32C23×D411yescharacteristic
900C2×C32C2×H(5,𝔽2)11yescharacteristic
901C2×C32#58511yescharacteristic
902C3⋊D3—22no—
903C3⋊D3—41no—
904C3⋊D3—42no—
905C3×D3—24no—
906C3×D3—42no—
907C3×D3—44no—
908C24—32no—
909C24—92no—
910C24—94no—
911C24—91no—
912#41—38no—
913#41—64no—
914#41—188no—
915#41—188no—
916#41—188no—
917#41—184no—
918#41—184no—
919#41—188no—
920#41—184no—
921C2×Q8—31no—
922C2×Q8—31no—
923C2×Q8—92no—
924C2×Q8—91no—
925C2×Q8—184no—
926C2×D4—32no—
927C2×D4—32no—
928C2×D4—31no—
929C2×D4—32no—
930C2×D4—32no—
931C2×D4—31no—
932C2×D4—34no—
933C2×D4—34no—
934C2×D4—64no—
935C2×D4—94no—
936C2×D4—92no—
937C2×D4—94no—
938C2×D4—92no—
939C2×D4—94no—
940C2×D4—94no—
941C2×D4—92no—
942C2×D4—94no—
943C2×D4—92no—
944C2×D4—92no—
945C2×D4—91no—
946C2×D4—92no—
947C2×D4—188no—
948C2×D4—188no—
949C2×D4—184no—
950C2×D4—188no—
951C2×D4—1816no—
952C2×D4—368no—
953C2×D4—364no—
954C22×C4—32no—
955C22×C4—32no—
956C22×C4—32no—
957C22×C4—34no—
958C22×C4—92no—
959C22×C4—92no—
960C22×C4—92no—
961C22×C4—94no—
962C22×C4—91no—
963C22×C4—91no—
964C22×C4—91no—
965C22×C4—92no—
966C22×C4—91no—
967C22×C4—91no—
968C22×C4—188no—
969C22×C4—184no—
970C22×C4C2×D3211yescharacteristic
971C4⋊C4—32no—
972C4⋊C4—34no—
973C4⋊C4—32no—
974C4⋊C4—94no—
975C4⋊C4—92no—
976C4⋊C4—92no—
977C4⋊C4C2×D3211yescharacteristic
978C4⋊C4C2×D3211yescharacteristic
979C22⋊C4—34no—
980C22⋊C4—34no—
981C22⋊C4—34no—
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⋊C4C2×D3212yes—
991C42—34no—
992C42C2×D3212yes—
993C22×C3—21no—
994C22×C3—21no—
995C22×C3—21no—
996C22×C3—21no—
997C22×C3—22no—
998C22×C3—21no—
999C22×C3—34no—
1000C22×C3—41no—
1001C22×C3—41no—
1002C22×C3—62no—
1003C22×C3—62no—
1004C22×C3—62no—
1005C22×C3—64no—
1006C22×C3—64no—
1007C22×C3—62no—
1008C22×C3—62no—
1009C22×C3—64no—
1010C22×C3—244no—
1011C22×C3C22×D1212yes—
1012C22×C3C2×D3×D412yes—
1013C22×C3C24×D311yescharacteristic
1014C22×C3C24×D311yescharacteristic
1015C2×D3—22no—
1016C2×D3—22no—
1017C2×D3—22no—
1018C2×D3—24no—
1019C2×D3—22no—
1020C2×D3—24no—
1021C2×D3—22no—
1022C2×D3—24no—
1023C2×D3—32no—
1024C2×D3—32no—
1025C2×D3—62no—
1026C2×D3—61no—
1027C2×D3—61no—
1028C2×D3—61no—
1029C2×D3—61no—
1030C2×D3—62no—
1031C2×D3—61no—
1032C2×D3—62no—
1033C2×D3—61no—
1034C2×D3—62no—
1035C2×D3—62no—
1036C2×D3—62no—
1037C2×D3—61no—
1038C2×D3—61no—
1039C2×D3—61no—
1040C2×D3—62no—
1041C2×D3—61no—
1042C2×D3—62no—
1043C2×D3—84no—
1044C2×D3—121no—
1045C2×D3—121no—
1046C2×D3—121no—
1047C2×D3—121no—
1048C2×D3—122no—
1049C2×D3—122no—
1050C2×D3—122no—
1051C2×D3—128no—
1052C2×D3—128no—
1053C2×D3—124no—
1054C2×D3—124no—
1055C2×D3—128no—
1056C2×D3—248no—
1057C2×D3—248no—
1058C2×D3C22×D1214yes—
1059C3×C4—22no—
1060C3×C4—22no—
1061C3×C4—22no—
1062C3×C4—22no—
1063C3×C4—22no—
1064C3×C4—22no—
1065C3×C4—34no—
1066C3×C4—42no—
1067C3×C4—42no—
1068C3×C4—62no—
1069C3×C4—64no—
1070C3×C4C22×D1212yes—
1071C3×C4C22×D1212yes—
1072C3×C4C2×D3×D412yes—
1073C3×C4C2×D3×D412yes—
1074Dic3—22no—
1075Dic3—24no—
1076Dic3—61no—
1077Dic3—62no—
1078Dic3—61no—
1079Dic3—61no—
1080Dic3—62no—
1081Dic3—61no—
1082Dic3—122no—
1083Dic3—121no—
1084Dic3—121no—
1085Dic3C22×D1214yes—
1086C32#348811yescharacteristic, complemented, Sylow
1087C23—32no—
1088C23—34no—
1089C23—32no—
1090C23—64no—
1091C23—91no—
1092C23—92no—
1093C23—91no—
1094C23—122no—
1095C23—122no—
1096C23—182no—
1097C23—184no—
1098C23—188no—
1099C23—184no—
1100C23—182no—
1101C23—361no—
1102C23—362no—
1103C23—364no—
1104C23—364no—
1105C23C22×D3211yescharacteristic
1106Q8—34no—
1107Q8—62no—
1108Q8—184no—
1109Q8—182no—
1110D4—38no—
1111D4—34no—
1112D4—64no—
1113D4—64no—
1114D4—64no—
1115D4—62no—
1116D4—124no—
1117D4—124no—
1118D4—184no—
1119D4—188no—
1120D4—184no—
1121D4—184no—
1122D4—188no—
1123D4—188no—
1124D4—184no—
1125D4—184no—
1126D4—182no—
1127D4—362no—
1128D4—364no—
1129D4—364no—
1130C2×C4—32no—
1131C2×C4—38no—
1132C2×C4—34no—
1133C2×C4—32no—
1134C2×C4—64no—
1135C2×C4—91no—
1136C2×C4—91no—
1137C2×C4—92no—
1138C2×C4—124no—
1139C2×C4—122no—
1140C2×C4—184no—
1141C2×C4—184no—
1142C2×C4—188no—
1143C2×C4—184no—
1144C2×C4—182no—
1145C2×C4—182no—
1146C2×C4—182no—
1147C2×C4—182no—
1148C2×C4—182no—
1149C2×C4—184no—
1150C2×C4D3×D1214yescomplemented
1151C2×C4C22×D3212yes—
1152C2×C4C22×D3212yes—
1153C2×C4C22×D3211yescharacteristic
1154C2×C4C22×D3211yescharacteristic
1155C2×C3—22no—
1156C2×C3—22no—
1157C2×C3—21no—
1158C2×C3—21no—
1159C2×C3—21no—
1160C2×C3—42no—
1161C2×C3—64no—
1162C2×C3—122no—
1163C2×C3—124no—
1164C2×C3C23×D1211yescharacteristic
1165C2×C3C22×D3×D411yescharacteristic
1166C2×C3D3×H(5,𝔽2)11yescharacteristic
1167C2×C3D3×H(5,𝔽2)11yescharacteristic
1168C2×C3#596611yescharacteristic
1169C2×C3#596811yescharacteristic
1170D3—24no—
1171D3—44no—
1172D3—42no—
1173D3—62no—
1174D3—62no—
1175D3—122no—
1176D3—122no—
1177D3—121no—
1178D3—122no—
1179D3—121no—
1180D3—122no—
1181D3—242no—
1182C22—21no—
1183C22—21no—
1184C22—34no—
1185C22—62no—
1186C22—62no—
1187C22—62no—
1188C22—64no—
1189C22—62no—
1190C22—64no—
1191C22—62no—
1192C22—64no—
1193C22—92no—
1194C22—181no—
1195C22—181no—
1196C22—181no—
1197C22—182no—
1198C22—182no—
1199C22—181no—
1200C22—181no—
1201C22—182no—
1202C22—244no—
1203C22—364no—
1204C22—368no—
1205C22—728no—
1206C22C2×D3×D1212yes—
1207C22C23×D3211yescharacteristic
1208C4—22no—
1209C4—22no—
1210C4—34no—
1211C4—62no—
1212C4—64no—
1213C4—181no—
1214C4—182no—
1215C4—181no—
1216C4C2×D3×D1212yes—
1217C4C2×D3×D1212yes—
1218C3—21no—
1219C3#8590011yescharacteristic, complemented
1220C3#8633111yescharacteristic, complemented
1221C2—22no—
1222C2—64no—
1223C2—124no—
1224C2—122no—
1225C2—182no—
1226C2—361no—
1227C2—362no—
1228C2C22×D3×D1211yescharacteristic
1229C2#1059669211yescharacteristic
1230C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C2×#64306C2semidirect
3. #10595995C2semidirect
4. C3×#5525C2semidirect
5. C3×#5523C2semidirect
6. #10595043C2semidirect
7. C2×#63916C2semidirect
8. #10594628C2semidirect
9. #10594626C2semidirect
10. D3×#895C2semidirect
11. #10594522C2semidirect
12. #10594292C2semidirect
13. #10594277C2semidirect
14. #10594005C2semidirect
15. #10594004C2semidirect
16. #10593901C2semidirect
17. #10593900C2semidirect
20. C2×#3828C22semidirect
21. C22×C4×C3⋊D3C22semidirect
23. C2×C3×#235C22semidirect
24. C22×C3×D12C22semidirect
25. C2×#3811C22semidirect
26. C2×D3×#67C22semidirect
27. C22×#626C22semidirect
28. C2×#3805C22semidirect
31. C2×#3802C22semidirect
32. C2×#3802C22semidirect
33. C2×D3×D12C22semidirect
34. C2×D3×D12C22semidirect
35. C2×C4×D32C22semidirect
36. C2×#3798C22semidirect
37. C2×#3797C22semidirect
38. C2×#3796C22semidirect
39. C2×#3796C22semidirect
40. C2×#3796C22semidirect
41. C2×#3795C22semidirect
42. C32×#117C22semidirect
43. #64106C22semidirect
44. #64106C22semidirect
45. #64104C22semidirect
46. #64104C22semidirect
47. #64095C22semidirect
48. #64091C22semidirect
49. C4×C4⋊(C3⋊D3)C22semidirect
50. C4×C4⋊(C3⋊D3)C22semidirect
51. C2×C3×C4⋊Dic3C22semidirect
52. C3×#895C22semidirect
53. C3×#895C22semidirect
54. C3×#892C22semidirect
55. C3×D3×C4⋊C4C22semidirect
56. C3×#882C22semidirect
57. C3×#67⋊C4C22semidirect
58. C3×#875C22semidirect
59. C3×#874C22semidirect
60. C3×C4×D12C22semidirect
61. C3×C4×Dic6C22semidirect
62. #63978C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63923C22semidirect
65. #63922C22semidirect
66. #63922C22semidirect
67. D3×(C2×D3)⋊C4C22semidirect
68. #63916C22semidirect
69. #63916C22semidirect
70. #63916C22semidirect
71. #63916C22semidirect
72. #63916C22semidirect
73. #63911C22semidirect
74. #63910C22semidirect
75. #63909C22semidirect
76. #63908C22semidirect
77. #63906C22semidirect
78. #63893C22semidirect
79. Dic3×D12C22semidirect
80. #63891C22semidirect
81. #63886C22semidirect
82. #63886C22semidirect
83. #63880C22semidirect
84. #63871C22semidirect
85. #63857C22semidirect
86. #63852C22semidirect
112. #5525D3semidirect
117. #5523D3semidirect
144. C3×#235D4semidirect
244. C2×#235C2×D3semidirect
248. C22×D12C2×D3semidirect
264. C3×#117C2×D3semidirect
265. C3×#117C2×D3semidirect
289. C2×C4⋊Dic3C2×D3semidirect
315. #895C2×D3semidirect
316. #895C2×D3semidirect
317. #892C2×D3semidirect
318. D3×C4⋊C4C2×D3semidirect
334. #882C2×D3semidirect
336. #67⋊C4C2×D3semidirect
340. #875C2×D3semidirect
342. #874C2×D3semidirect
351. C4×D12C2×D3semidirect
352. C4×Dic6C2×D3semidirect
372. C2×C32×C4C2×D4semidirect
392. C3×#67C2×D4semidirect
402. C3×D12C2×D4semidirect
405. C3×C4×D3C2×D4semidirect
407. C3×Dic6C2×D4semidirect
518. #235D12semidirect
646. C2×C3⋊D3H(5,𝔽2)semidirect
731. #117D32semidirect
803. C2×C3×C4C2×D12semidirect
804. C2×C3×C4D3×D4semidirect
827. #67C2×D12semidirect
867. D12C2×D12semidirect
890. C4×D3C2×D12semidirect
897. Dic6C2×D12semidirect
1086. C32#3488semidirect
1150. C2×C4D3×D12semidirect
1219. C3#85900semidirect
1220. C3#86331semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C2×#643062
#105959952
C3×#55252
C3×#55232
#105950432
C2×#639162
#105946282
#105946262
D3×#8952
#105945222
#105942922
#105942772
#105940052
#105940042
#105939012
#105939002
#863313
#859003