Finite Group Databasebeta

← #11904774

Subgroups — #11904774

Order 1152.

3179 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3#10595997C211yesmaximal, characteristic, complemented
4C3×#5524C211yesmaximal, characteristic, complemented
5C3×#5523C211yesmaximal, characteristic, complemented
6#10595043C211yesmaximal, characteristic, complemented
7C2×#63857C211yesmaximal, characteristic, complemented
8#10594626C212yesmaximal, complemented
9D3×#897C212yesmaximal, complemented
10#10594522C212yesmaximal, complemented
11#10594380C212yesmaximal, complemented
12#10594292C214yesmaximal, complemented
13#10594077C214yesmaximal, complemented
14#10594003C212yesmaximal, complemented
15#10593899C212yesmaximal, complemented
16Dic6×D12C212yesmaximal, complemented
17#10593895C212yesmaximal, complemented
18#86042—31nomaximal
19#85901—31nomaximal
20C2×#3828C2211yescharacteristic
21C22×#634C2211yescharacteristic, complemented
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2211yescharacteristic, complemented
24C22×C3×C4×D3C2211yescharacteristic
25C2×D3×#67C2212yes—
26C2×#3805C2214yescomplemented
27C2×#3804C2212yes—
28D3×#235—28no—
29C2×D3×D12C2211yescharacteristic
30C2×C4×D32C2212yes—
31C2×#3799C2211yescharacteristic
32C2×#3798C2212yes—
33#64298—28no—
34C2×#3795C2211yescharacteristic
35C2×#3795C2212yescomplemented
36C2×#3795C2212yescomplemented
37C2×D3×Dic6C2211yescharacteristic
38C2×D3×Dic6C2212yescomplemented
39C2×D3×Dic6C2212yescomplemented
40C32×#117C2211yescharacteristic, complemented
41#64106C2212yescomplemented
42#64106C2212yescomplemented
43#64095C2214yescomplemented
44#64084C2212yescomplemented
45#64078C2212yescomplemented
46C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
47C3×#897C2211yescharacteristic
48C3×#897C2211yescharacteristic, complemented
49C3×#895C2211yescharacteristic
50C3×#895C2211yescharacteristic, complemented
51C3×#892C2212yescomplemented
52C3×D3×C4⋊C4C2212yescomplemented
53C3×#886C2212yescomplemented
54C3×#882C2212yes—
55C3×#67⋊C4C2214yescomplemented
56C3×C4×D12C2212yes—
57C3×C4×D12C2212yescomplemented
58C3×C4×D12C2212yescomplemented
59C3×C4×Dic6C2212yescomplemented
60#63978C2214yescomplemented
61C2×Dic3⋊Dic3C2212yescomplemented
62C2×(C2×D3)⋊Dic3C2212yes—
63#63922C2214yes—
64D3×(C2×D3)⋊C4C2214yes—
65#63918C2214yescomplemented
66#63916C2212yescomplemented
67#63909C2212yescomplemented
68#63908C2214yescomplemented
69#63906C2214yescomplemented
70#63895C2214yescomplemented
71#63893C2214yes—
72#63893C2214yescomplemented
73Dic3×D12C2214yes—
74#63891C2214yescomplemented
75#63891C2214yescomplemented
76#63890C2214yescomplemented
77D3×C4⋊Dic3C2214yescomplemented
78#63886C2214yescomplemented
79#63880C2214yescomplemented
80#63871C2212yescomplemented
81#63857C2212yes—
82#63857C2212yes—
83#63857C2212yescomplemented
84#63857C2212yescomplemented
85#63857C2212yescomplemented
86#63852C2214yescomplemented
87C2×#1010—31no—
88C2×#1010—31no—
89C2×D3×#41—31no—
90C22×#235—31no—
91C3×#525—31no—
92C3×#520—31no—
93#5833—31no—
94C2×#924—31no—
95#5655—34no—
96#5628—32no—
97D3×C22⋊Q8—32no—
98#5608—32no—
99#5606—32no—
100#5591—34no—
101#5576—32no—
102Q8×D12—32no—
103#5555—34no—
104#5555—32no—
105#5554—34no—
106#5554—32no—
107#5552—32no—
108#5551—32no—
109#5550—32no—
110D4×Dic6—32no—
111#5526—31no—
112#5526—31no—
113#5526—32no—
114#5526—61no—
115#5524—32no—
116#5524D311yescharacteristic, complemented
117#5523D311yescharacteristic, complemented
118#5510—31no—
119#5510—32no—
120C2×#897—31no—
121C2×#897—32no—
122C23×C3×D3C2311yescharacteristic
123C22×D32C2312yes—
124C22×C32×C4C2311yescharacteristic
125C2×#638C2312yes—
126C22×C3⋊Dic3C2312yes—
127#3828—24no—
128C2×C4⋊(C3⋊D3)C2311yescharacteristic
129C2×C4×C3⋊D3C2312yes—
130C2×#634—24no—
131C2×#634C2311yescharacteristic
132C2×#634C2312yes—
133C2×#634C2312yes—
134C2×C3×#67C2312yes—
135C2×C3×#67C2312yes—
136C22×C3×Dic3C2311yescharacteristic
137C22×C3×Dic3C2312yes—
138C3×#235—24no—
139C3×#235D418yescomplemented
140C2×C3×D12C2312yes—
141C2×C3×D12C2311yescharacteristic
142C2×C3×D12C2312yes—
143C2×C3×D12C2311yescharacteristic
144C2×C3×C4×D3—24no—
145C2×C3×C4×D3C2311yescharacteristic
146C2×C3×C4×D3C2311yescharacteristic
147C2×C3×C4×D3C2311yescharacteristic
148C2×C3×C4×D3C2312yes—
149C2×C3×C4×D3C2311yescharacteristic
150C2×C3×C4×D3C2314yes—
151C2×C3×C4×D3C2312yes—
152C2×C3×Dic6C2311yescharacteristic
153C2×C3×Dic6C2311yescharacteristic
154D3×#67—28no—
155C2×#627C2312yes—
156C2×#627C2314yes—
157C2×#626C2312yes—
158C2×#626C2312yes—
159C2×#626C2314yes—
160C2×#625C2312yes—
161C2×#625C2314yes—
162C2×#624C2312yes—
163#3805—216no—
164#3804—28no—
165C2×D3×Dic3C2312yes—
166C2×D3×Dic3C2314yes—
167C2×D3×Dic3C2314yes—
168C2×D3×Dic3C2312yes—
169D3×D12—24no—
170C4×D32—28no—
171#3799—24no—
172#3798—28no—
173#3795—24no—
174#3795—28no—
175#3795—28no—
176D3×Dic6—28no—
177D3×Dic6—24no—
178D3×Dic6—28no—
179C32×C4⋊C4C2311yescharacteristic
180C32×C4⋊C4C2311yescharacteristic
181C32×C22⋊C4C2312yes—
182C32×C42C2312yes—
183#3752C2314yes—
184#3752C2314yes—
185C4⋊(C3⋊Dic3)C2314yes—
186C4⋊(C3⋊Dic3)C2314yes—
187C3×(C2×D3)⋊C4C2314yes—
188C3×(C2×D3)⋊C4C2312yes—
189C3×(C2×D3)⋊C4C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×C4⋊Dic3C2312yes—
193C3×C4⋊Dic3C2312yes—
194C3×C4⋊Dic3C2312yes—
195C3×C4⋊Dic3C2312yes—
196C3×Dic3⋊C4C2314yes—
197C3×C4×Dic3C2314yes—
198Dic3⋊Dic3C2314yes—
199Dic3⋊Dic3C2314yes—
200Dic3⋊Dic3C2314yes—
201#3722C2314yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204(C2×D3)⋊Dic3C2314yes—
205#3489—91noSylow
206C2×C3×#41—31no—
207C2×C3×#41—31no—
208C23×C3×C4—31no—
209C22×#67—32no—
210#1010—68no—
211#1010—68no—
212D3×#41—68no—
213C2×#239—31no—
214C2×D3×Q8—31no—
215C2×D3×Q8—32no—
216C2×D3×Q8—32no—
217C2×#237—34no—
218C2×#237—34no—
219C2×#237—32no—
220C2×#237—31no—
221C2×#237—32no—
222C2×#237—32no—
223C2×D3×D4—32no—
224C2×D3×D4—31no—
225C2×#235—31no—
226C2×#235—31no—
227C2×#235—32no—
228C2×#235—31no—
229C2×#235—32no—
230C2×#235—32no—
231C2×#235—32no—
232C2×#235—32no—
233C2×#235—31no—
234C2×#235—61no—
235C2×#235—68no—
236C2×#235C2×D311yescharacteristic
237C2×#235C2×D311yescharacteristic, complemented
238C22×D12—31no—
239C22×C4×D3—32no—
240C22×C4×D3—32no—
241C22×C4×D3C2×D311yescharacteristic
242C22×Dic6—31no—
243C22×Dic6—31no—
244C22×Dic6—31no—
245C22×Dic6—32no—
246C22×Dic6—32no—
247C22×Dic6—61no—
248C3×#123—32no—
249C3×C22⋊Q8—31no—
250C3×C22⋊Q8—31no—
251C3×#121—31no—
252C3×#121—31no—
253C3×#120—32no—
254C3×C4×Q8—32no—
255C3×C4×D4—34no—
256C3×C4×D4—32no—
257C3×C4×D4—32no—
258C3×C4×D4—32no—
259C3×#117—21no—
260C3×#117—32no—
261C3×#117C2×D311yescharacteristic, complemented
262C3×#117C2×D311yescharacteristic, complemented
263C2×C3×C4⋊C4—31no—
264C2×C3×C4⋊C4—32no—
265C2×#217—32no—
266#946—32no—
267#939—34no—
268#939—34no—
269#938—34no—
270#938—32no—
271#937—34no—
272D4×Dic3—34no—
273#930—34no—
274#930—34no—
275#930—34no—
276#930—32no—
277C2×(C2×D3)⋊C4—32no—
278C2×(C2×D3)⋊C4—34no—
279C2×C4⋊Dic3—32no—
280C2×C4⋊Dic3—34no—
281C2×C4⋊Dic3C2×D311yescharacteristic, complemented
282#924—32no—
283#924—32no—
284#924—32no—
285#924—32no—
286#924—32no—
287C2×Dic3⋊C4—32no—
288#897—32no—
289#897—32no—
290#897—32no—
291#897—32no—
292#897—32no—
293#897—32no—
294#897—32no—
295#897—32no—
296#897—32no—
297#897—32no—
298#897—34no—
299#897—34no—
300#897—34no—
301#897—62no—
302#897—62no—
303#897C2×D311yescharacteristic
304#897C2×D311yescharacteristic, complemented
305#896—34no—
306#895—32no—
307#895—34no—
308#895—32no—
309#895C2×D311yescharacteristic
310#895C2×D311yescharacteristic, complemented
311#894—34no—
312#892C2×D312yescomplemented
313D3×C4⋊C4—34no—
314D3×C4⋊C4C2×D312yescomplemented
315#888—34no—
316#886—34no—
317#886—34no—
318#886—34no—
319#886—34no—
320#886—34no—
321#886—64no—
322#886C2×D312yescomplemented
323#885—34no—
324#884—34no—
325#883—34no—
326#883—34no—
327#882—34no—
328#882C2×D312yes—
329#67⋊C4—34no—
330#67⋊C4C2×D314yescomplemented
331D3×C22⋊C4—34no—
332#878—34no—
333#878—34no—
334#875—32no—
335#875—32no—
336#875—34no—
337#875—62no—
338C4×D12—34no—
339C4×D12—34no—
340C4×D12C2×D312yes—
341C4×D12C2×D312yescomplemented
342C4×D12C2×D312yescomplemented
343#869—32no—
344#869—32no—
345#869—34no—
346#869—62no—
347C4×Dic6C2×D312yescomplemented
348C23×C32C2411yescharacteristic
349C22×C3⋊D3C2412yes—
350C22×C3×D3—22no—
351C22×C3×D3—22no—
352C22×C3×D3—41no—
353C22×C3×D3C2411yescharacteristic
354C22×C3×D3C2412yes—
355C22×C3×D3C2412yes—
356C22×C3×D3C2411yescharacteristic
357C2×D32—24no—
358C2×D32—24no—
359C2×D32—42no—
360C2×C32×C4C2×D414yes—
361C2×C32×C4C2412yes—
362C2×C32×C4C2412yes—
363C2×C32×C4C2411yescharacteristic
364C2×C32×C4C2411yescharacteristic
365#638—24no—
366C2×C3⋊Dic3—24no—
367C2×C3⋊Dic3C2412yes—
368C2×C3⋊Dic3C2414yes—
369C4⋊(C3⋊D3)—22no—
370C4×C3⋊D3—24no—
371#634—24no—
372#634—24no—
373#634—22no—
374C3×#67—24no—
375C3×#67C2×D418yes—
376C2×C3×Dic3—22no—
377C2×C3×Dic3—42no—
378C2×C3×Dic3C2414yes—
379C2×C3×Dic3C2412yes—
380C2×C3×Dic3C2411yescharacteristic
381C2×C3×Dic3C2411yescharacteristic
382C2×C3×Dic3C2412yes—
383C3×D12—24no—
384C3×D12—22no—
385C3×D12—42no—
386C3×D12C2×D414yes—
387C3×C4×D3—24no—
388C3×C4×D3—22no—
389C3×C4×D3—22no—
390C3×C4×D3—22no—
391C3×C4×D3—22no—
392C3×C4×D3—44no—
393C3×C4×D3C2×D418yes—
394C3×Dic6—22no—
395C3×Dic6C2×D414yes—
396#627—28no—
397#627—24no—
398#626—24no—
399#626—24no—
400#626—44no—
401#625—28no—
402#625—24no—
403#624—24no—
404D3×Dic3—28no—
405D3×Dic3—24no—
406D3×Dic3—28no—
407D3×Dic3—24no—
408C2×2−1+4—91no—
409C22×#41—91no—
410D4×Q8—92no—
411#548—92no—
412#547—92no—
413#547—94no—
414#546—92no—
415#546—94no—
416#537—92no—
417#537—91no—
418#536—92no—
419#536—91no—
420#525—31no—
421#525—92no—
422C2×C22⋊Q8—92no—
423C2×C22⋊Q8—91no—
424#520—31no—
425C24×C3—31no—
426C23×D3—32no—
427C23×D3—32no—
428C23×D3C22×D311yescharacteristic
429C3×#41—38no—
430C3×#41—64no—
431C2×C3×Q8—31no—
432C2×C3×Q8—31no—
433C2×C3×D4—32no—
434C2×C3×D4—32no—
435C2×C3×D4—31no—
436C2×C3×D4—32no—
437C2×C3×D4—31no—
438C2×C3×D4—32no—
439C22×C3×C4—21no—
440C22×C3×C4—32no—
441C22×C3×C4—31no—
442C22×C3×C4—32no—
443C22×C3×C4—31no—
444C22×C3×C4—31no—
445C22×C3×C4—31no—
446C22×C3×C4—31no—
447C22×C3×C4—32no—
448C22×C3×C4—34no—
449C22×C3×C4—64no—
450C22×C3×C4C22×D311yescharacteristic
451C22×C3×C4C22×D311yescharacteristic
452C2×#67—32no—
453C2×#67—32no—
454C2×#67—34no—
455C2×#67—32no—
456C2×#67—34no—
457C2×#67—32no—
458C2×#67—32no—
459C2×#67—32no—
460C2×#67—34no—
461C2×#67—62no—
462C2×#67—68no—
463C2×#67C22×D312yes—
464C2×#67C22×D312yes—
465C22×Dic3—32no—
466C22×Dic3—32no—
467C22×Dic3—32no—
468C22×Dic3—34no—
469C22×Dic3—32no—
470C22×Dic3—34no—
471C22×Dic3—62no—
472C22×Dic3C22×D311yescharacteristic
473C22×Dic3C22×D312yes—
474#239—64no—
475D3×Q8—64no—
476D3×Q8—68no—
477D3×Q8—68no—
478#237—64no—
479#237—68no—
480#237—68no—
481#237—616no—
482#237—616no—
483#237—68no—
484D3×D4—64no—
485D3×D4—68no—
486#235—24no—
487#235—68no—
488#235—68no—
489#235—64no—
490#235—64no—
491#235—68no—
492#235—64no—
493#235—68no—
494#235—68no—
495#235—64no—
496#235—124no—
497#235D1218yescomplemented
498C2×D12—32no—
499C2×D12—32no—
500C2×D12—31no—
501C2×D12—31no—
502C2×D12—34no—
503C2×D12—61no—
504C2×D12—64no—
505C2×D12C22×D312yes—
506C2×D12C22×D311yescharacteristic
507C2×D12C22×D312yes—
508C2×D12C22×D311yescharacteristic
509C2×C4×D3—24no—
510C2×C4×D3—34no—
511C2×C4×D3—32no—
512C2×C4×D3—34no—
513C2×C4×D3—32no—
514C2×C4×D3—32no—
515C2×C4×D3—32no—
516C2×C4×D3—32no—
517C2×C4×D3—32no—
518C2×C4×D3—62no—
519C2×C4×D3—68no—
520C2×C4×D3—68no—
521C2×C4×D3C22×D311yescharacteristic
522C2×C4×D3C22×D312yes—
523C2×C4×D3C22×D311yescharacteristic
524C2×C4×D3C22×D311yescharacteristic
525C2×C4×D3C22×D311yescharacteristic
526C2×C4×D3C22×D314yes—
527C2×C4×D3C22×D312yes—
528C2×Dic6—31no—
529C2×Dic6—31no—
530C2×Dic6—32no—
531C2×Dic6—32no—
532C2×Dic6—32no—
533C2×Dic6—32no—
534C2×Dic6—32no—
535C2×Dic6—34no—
536C2×Dic6—32no—
537C2×Dic6—34no—
538C2×Dic6—61no—
539C2×Dic6—62no—
540C2×Dic6—62no—
541C2×Dic6—68no—
542C2×Dic6—64no—
543C2×Dic6—64no—
544C2×Dic6—64no—
545C2×Dic6—68no—
546C2×Dic6—124no—
547C2×Dic6C22×D311yescharacteristic
548C2×Dic6C22×D311yescharacteristic
549C3×C4⋊C4—21no—
550C3×C4⋊C4—21no—
551C3×C4⋊C4—32no—
552C3×C4⋊C4—32no—
553C3×C4⋊C4—34no—
554C3×C4⋊C4—32no—
555C3×C4⋊C4—32no—
556C3×C4⋊C4C22×D311yescharacteristic
557C3×C4⋊C4C22×D311yescharacteristic
558C3×C4⋊C4C22×D311yescharacteristic
559C3×C4⋊C4C22×D311yescharacteristic
560C3×C22⋊C4—22no—
561C3×C22⋊C4—32no—
562C3×C22⋊C4—32no—
563C3×C22⋊C4—32no—
564C3×C22⋊C4—34no—
565C3×C22⋊C4—32no—
566C3×C22⋊C4C22×D312yes—
567C3×C22⋊C4C22×D312yes—
568C3×C42—22no—
569C3×C42—34no—
570C3×C42C22×D312yes—
571C3×C42C22×D312yes—
572#217—34no—
573#217—34no—
574#217—34no—
575(C2×D3)⋊C4—34no—
576(C2×D3)⋊C4—34no—
577(C2×D3)⋊C4—34no—
578(C2×D3)⋊C4—34no—
579(C2×D3)⋊C4—34no—
580(C2×D3)⋊C4—34no—
581(C2×D3)⋊C4—34no—
582(C2×D3)⋊C4—34no—
583(C2×D3)⋊C4—34no—
584(C2×D3)⋊C4—64no—
585(C2×D3)⋊C4—64no—
586(C2×D3)⋊C4C22×D312yes—
587(C2×D3)⋊C4C22×D312yes—
588(C2×D3)⋊C4C22×D312yes—
589(C2×D3)⋊C4C22×D312yes—
590(C2×D3)⋊C4C22×D314yes—
591C4⋊Dic3—34no—
592C4⋊Dic3—34no—
593C4⋊Dic3—34no—
594C4⋊Dic3—34no—
595C4⋊Dic3—34no—
596C4⋊Dic3—34no—
597C4⋊Dic3—34no—
598C4⋊Dic3—64no—
599C4⋊Dic3—64no—
600C4⋊Dic3C22×D312yes—
601C4⋊Dic3C22×D312yes—
602C4⋊Dic3C22×D312yes—
603C4⋊Dic3C22×D312yes—
604Dic3⋊C4—34no—
605Dic3⋊C4—34no—
606Dic3⋊C4—34no—
607Dic3⋊C4C22×D314yes—
608C4×Dic3C22×D314yes—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32C22×D412yes—
612C22×C32C2511yescharacteristic
613C2×C3⋊D3—22no—
614C2×C3⋊D3—22no—
615C2×C3⋊D3—22no—
616C2×C3×D3—21no—
617C2×C3×D3—22no—
618C2×C3×D3—22no—
619C2×C3×D3—21no—
620C2×C3×D3—22no—
621C2×C3×D3—21no—
622C2×C3×D3—22no—
623C2×C3×D3—21no—
624C2×C3×D3—22no—
625C2×C3×D3—21no—
626C2×C3×D3—44no—
627C2×C3×D3C22×D414yes—
628C2×C3×D32−1+412yescomplemented
629D32—48no—
630C32×C4—22no—
631C32×C4—22no—
632C32×C4C22×D412yes—
633C32×C4C22×D412yes—
634C3⋊Dic3—24no—
635C3⋊Dic3—22no—
636C3×Dic3—21no—
637C3×Dic3—22no—
638C3×Dic3—21no—
639C3×Dic3—24no—
640C3×Dic3C22×D414yes—
6412−1+4—188no—
642C2×#41—31no—
643C2×#41—31no—
644C2×#41—92no—
645C2×#41—92no—
646C2×#41—92no—
647C2×#41—92no—
648C2×#41—91no—
649C2×#41—91no—
650C2×#41—94no—
651C2×#41—91no—
652C2×#41—188no—
653C22×Q8—92no—
654C22×Q8—92no—
655C22×Q8—91no—
656C22×Q8—91no—
657C22×D4—91no—
658C22×D4—92no—
659C23×C4—31no—
660C23×C4—92no—
661C4⋊Q8—94no—
662C4⋊Q8—92no—
663#124—94no—
664#124—92no—
665#123—32no—
666#123—94no—
667#123—94no—
668#123—94no—
669#123—94no—
670C22⋊Q8—31no—
671C22⋊Q8—31no—
672C22⋊Q8—94no—
673C22⋊Q8—94no—
674C22⋊Q8—94no—
675C22⋊Q8—92no—
676C22⋊Q8—92no—
677C22⋊Q8—92no—
678C22⋊Q8—92no—
679C22⋊Q8—92no—
680C22⋊Q8—92no—
681C22⋊Q8—92no—
682C22⋊Q8—92no—
683#121—31no—
684#121—31no—
685#121—94no—
686#121—92no—
687#121—92no—
688#121—94no—
689#121—94no—
690#121—94no—
691#120—32no—
692#120—94no—
693C4×Q8—32no—
694C4×D4—34no—
695C4×D4—32no—
696C4×D4—32no—
697C4×D4—32no—
698C4×D4—94no—
699C4×D4—94no—
700#117—32no—
701#117D3211yescharacteristic, complemented
702C2×C4⋊C4—31no—
703C2×C4⋊C4—32no—
704C2×C4⋊C4—94no—
705C2×C4⋊C4—92no—
706C2×C22⋊C4—94no—
707C2×C22⋊C4—92no—
708C23×C3—21no—
709C23×C3—31no—
710C23×C3—32no—
711C23×C3—31no—
712C23×C3—32no—
713C23×C3—62no—
714C23×C3—62no—
715C23×C3—121no—
716C23×C3C23×D311yescharacteristic
717C23×C3C23×D311yescharacteristic
718C22×D3—22no—
719C22×D3—22no—
720C22×D3—32no—
721C22×D3—32no—
722C22×D3—41no—
723C22×D3—62no—
724C22×D3—64no—
725C22×D3—64no—
726C22×D3—64no—
727C22×D3—64no—
728C22×D3—122no—
729C22×D3—122no—
730C22×D3C23×D311yescharacteristic
731C22×D3C23×D312yes—
732C22×D3C23×D312yes—
733C22×D3C23×D311yescharacteristic
734C3×Q8—34no—
735C3×Q8—62no—
736C3×D4—38no—
737C3×D4—34no—
738C3×D4—64no—
739C3×D4—64no—
740C3×D4—62no—
741C3×D4—122no—
742C2×C3×C4—21no—
743C2×C3×C4—21no—
744C2×C3×C4—22no—
745C2×C3×C4—22no—
746C2×C3×C4—24no—
747C2×C3×C4—32no—
748C2×C3×C4—38no—
749C2×C3×C4—31no—
750C2×C3×C4—31no—
751C2×C3×C4—32no—
752C2×C3×C4—34no—
753C2×C3×C4—62no—
754C2×C3×C4—62no—
755C2×C3×C4—64no—
756C2×C3×C4—62no—
757C2×C3×C4—62no—
758C2×C3×C4—62no—
759C2×C3×C4—124no—
760C2×C3×C4—122no—
761C2×C3×C4C2×D1214yes—
762C2×C3×C4D3×D414yes—
763C2×C3×C4C23×D312yes—
764C2×C3×C4C23×D312yes—
765C2×C3×C4C23×D312yes—
766C2×C3×C4C23×D312yes—
767C2×C3×C4C23×D311yescharacteristic
768C2×C3×C4C23×D311yescharacteristic
769C2×C3×C4C23×D311yescharacteristic
770C2×C3×C4C23×D311yescharacteristic
771#67—24no—
772#67—64no—
773#67—64no—
774#67—68no—
775#67—64no—
776#67—64no—
777#67—64no—
778#67—68no—
779#67—64no—
780#67—124no—
781#67—124no—
782#67C2×D1218yes—
783C2×Dic3—22no—
784C2×Dic3—32no—
785C2×Dic3—34no—
786C2×Dic3—32no—
787C2×Dic3—34no—
788C2×Dic3—42no—
789C2×Dic3—62no—
790C2×Dic3—64no—
791C2×Dic3—68no—
792C2×Dic3—64no—
793C2×Dic3—64no—
794C2×Dic3—64no—
795C2×Dic3—64no—
796C2×Dic3—68no—
797C2×Dic3—124no—
798C2×Dic3C23×D314yes—
799C2×Dic3C23×D311yescharacteristic
800C2×Dic3C23×D311yescharacteristic
801C2×Dic3C23×D312yes—
802C2×Dic3C23×D312yes—
803D12—24no—
804D12—22no—
805D12—42no—
806D12—64no—
807D12—64no—
808D12—62no—
809D12—62no—
810D12—122no—
811D12—124no—
812D12C2×D1214yes—
813C4×D3—22no—
814C4×D3—22no—
815C4×D3—22no—
816C4×D3—22no—
817C4×D3—24no—
818C4×D3—44no—
819C4×D3—64no—
820C4×D3—64no—
821C4×D3—68no—
822C4×D3—64no—
823C4×D3—68no—
824C4×D3—64no—
825C4×D3—64no—
826C4×D3—64no—
827C4×D3—124no—
828C4×D3C2×D1218yes—
829Dic6—22no—
830Dic6—68no—
831Dic6—64no—
832Dic6—64no—
833Dic6—62no—
834Dic6—64no—
835Dic6—64no—
836Dic6—64no—
837Dic6—62no—
838Dic6—64no—
839Dic6—68no—
840Dic6—124no—
841Dic6—124no—
842Dic6—122no—
843Dic6C2×D1214yes—
844C2×C32—22no—
845C2×C32C23×D411yescharacteristic
846C2×C32C2×2−1+411yescharacteristic
847C2×C32#58511yescharacteristic
848C3⋊D3—42no—
849C3×D3—22no—
850C3×D3—24no—
851C3×D3—42no—
852C3×D3—41no—
853C24—31no—
854C24—92no—
855#41—38no—
856#41—64no—
857#41—188no—
858#41—188no—
859#41—188no—
860#41—184no—
861#41—188no—
862#41—184no—
863#41—1816no—
864#41—184no—
865C2×Q8—31no—
866C2×Q8—31no—
867C2×Q8—94no—
868C2×Q8—92no—
869C2×Q8—92no—
870C2×Q8—92no—
871C2×Q8—91no—
872C2×Q8—188no—
873C2×Q8—184no—
874C2×Q8—188no—
875C2×Q8—184no—
876C2×D4—32no—
877C2×D4—32no—
878C2×D4—31no—
879C2×D4—32no—
880C2×D4—31no—
881C2×D4—32no—
882C2×D4—92no—
883C2×D4—92no—
884C2×D4—94no—
885C2×D4—94no—
886C2×D4—92no—
887C2×D4—92no—
888C2×D4—91no—
889C2×D4—184no—
890C2×D4—188no—
891C22×C4—32no—
892C22×C4—31no—
893C22×C4—32no—
894C22×C4—32no—
895C22×C4—31no—
896C22×C4—31no—
897C22×C4—31no—
898C22×C4—31no—
899C22×C4—34no—
900C22×C4—64no—
901C22×C4—92no—
902C22×C4—94no—
903C22×C4—92no—
904C22×C4—94no—
905C22×C4—92no—
906C22×C4—92no—
907C22×C4—92no—
908C22×C4—188no—
909C22×C4C2×D3211yescharacteristic
910C4⋊C4—32no—
911C4⋊C4—34no—
912C4⋊C4—32no—
913C4⋊C4—32no—
914C4⋊C4—32no—
915C4⋊C4—94no—
916C4⋊C4—94no—
917C4⋊C4—94no—
918C4⋊C4—94no—
919C4⋊C4—94no—
920C4⋊C4C2×D3211yescharacteristic
921C4⋊C4C2×D3211yescharacteristic
922C22⋊C4—32no—
923C22⋊C4—34no—
924C22⋊C4—32no—
925C22⋊C4—32no—
926C22⋊C4—32no—
927C22⋊C4—94no—
928C22⋊C4—94no—
929C22⋊C4—94no—
930C22⋊C4—94no—
931C22⋊C4—94no—
932C22⋊C4—94no—
933C22⋊C4C2×D3212yes—
934C42—34no—
935C42C2×D3212yes—
936C22×C3—21no—
937C22×C3—21no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—22no—
941C22×C3—21no—
942C22×C3—34no—
943C22×C3—32no—
944C22×C3—41no—
945C22×C3—41no—
946C22×C3—61no—
947C22×C3—62no—
948C22×C3—62no—
949C22×C3—61no—
950C22×C3—62no—
951C22×C3—61no—
952C22×C3—62no—
953C22×C3—61no—
954C22×C3—62no—
955C22×C3—61no—
956C22×C3—124no—
957C22×C3C22×D1212yes—
958C22×C3C2×D3×D412yes—
959C22×C3C24×D311yescharacteristic
960C22×C3C24×D311yescharacteristic
961C2×D3—21no—
962C2×D3—21no—
963C2×D3—22no—
964C2×D3—22no—
965C2×D3—21no—
966C2×D3—22no—
967C2×D3—22no—
968C2×D3—21no—
969C2×D3—21no—
970C2×D3—22no—
971C2×D3—44no—
972C2×D3—62no—
973C2×D3—62no—
974C2×D3—62no—
975C2×D3—62no—
976C2×D3—62no—
977C2×D3—62no—
978C2×D3—122no—
979C2×D3—122no—
980C2×D3—122no—
981C2×D3—128no—
982C2×D3—128no—
983C2×D3C22×D1214yes—
984C2×D3#101012yescomplemented
985C3×C4—22no—
986C3×C4—22no—
987C3×C4—22no—
988C3×C4—22no—
989C3×C4—22no—
990C3×C4—22no—
991C3×C4—34no—
992C3×C4—42no—
993C3×C4—42no—
994C3×C4—62no—
995C3×C4—61no—
996C3×C4—61no—
997C3×C4—64no—
998C3×C4C22×D1212yes—
999C3×C4C22×D1212yes—
1000C3×C4C2×D3×D412yes—
1001C3×C4C2×D3×D412yes—
1002Dic3—22no—
1003Dic3—21no—
1004Dic3—21no—
1005Dic3—24no—
1006Dic3—64no—
1007Dic3—62no—
1008Dic3—64no—
1009Dic3—62no—
1010Dic3—124no—
1011Dic3—122no—
1012Dic3C22×D1214yes—
1013C32#348911yescharacteristic, complemented, Sylow
1014C23—31no—
1015C23—32no—
1016C23—31no—
1017C23—32no—
1018C23—62no—
1019C23—62no—
1020C23—92no—
1021C23—121no—
1022C23—184no—
1023C23—184no—
1024C23—362no—
1025C23C22×D3211yescharacteristic
1026Q8—34no—
1027Q8—62no—
1028Q8—188no—
1029Q8—184no—
1030Q8—184no—
1031Q8—184no—
1032Q8—182no—
1033D4—38no—
1034D4—34no—
1035D4—64no—
1036D4—64no—
1037D4—62no—
1038D4—122no—
1039D4—184no—
1040D4—184no—
1041D4—184no—
1042D4—188no—
1043D4—184no—
1044D4—182no—
1045D4—364no—
1046C2×C4—32no—
1047C2×C4—38no—
1048C2×C4—34no—
1049C2×C4—32no—
1050C2×C4—31no—
1051C2×C4—31no—
1052C2×C4—62no—
1053C2×C4—62no—
1054C2×C4—62no—
1055C2×C4—62no—
1056C2×C4—62no—
1057C2×C4—64no—
1058C2×C4—94no—
1059C2×C4—92no—
1060C2×C4—124no—
1061C2×C4—122no—
1062C2×C4—184no—
1063C2×C4—184no—
1064C2×C4—188no—
1065C2×C4—184no—
1066C2×C4—188no—
1067C2×C4—184no—
1068C2×C4—184no—
1069C2×C4D3×D1214yes—
1070C2×C4C22×D3212yes—
1071C2×C4C22×D3212yes—
1072C2×C4C22×D3211yescharacteristic
1073C2×C4C22×D3211yescharacteristic
1074C2×C3—22no—
1075C2×C3—22no—
1076C2×C3—21no—
1077C2×C3—21no—
1078C2×C3—21no—
1079C2×C3—42no—
1080C2×C3—64no—
1081C2×C3—62no—
1082C2×C3—121no—
1083C2×C3—122no—
1084C2×C3C23×D1211yescharacteristic
1085C2×C3C22×D3×D411yescharacteristic
1086C2×C3C2×#101011yescharacteristic
1087C2×C3#596411yescharacteristic
1088C2×C3#596611yescharacteristic
1089C2×C3D3×2−1+411yescharacteristic
1090D3—22no—
1091D3—24no—
1092D3—41no—
1093D3—42no—
1094D3—122no—
1095D3—122no—
1096D3—242no—
1097C22—21no—
1098C22—21no—
1099C22—34no—
1100C22—32no—
1101C22—61no—
1102C22—62no—
1103C22—62no—
1104C22—61no—
1105C22—61no—
1106C22—62no—
1107C22—62no—
1108C22—61no—
1109C22—61no—
1110C22—62no—
1111C22—124no—
1112C22—182no—
1113C22—182no—
1114C22—182no—
1115C22—368no—
1116C22C2×D3×D1212yes—
1117C22C23×D3211yescharacteristic
1118C4—22no—
1119C4—22no—
1120C4—34no—
1121C4—61no—
1122C4—61no—
1123C4—62no—
1124C4—64no—
1125C4—182no—
1126C4—184no—
1127C4C2×D3×D1212yes—
1128C4C2×D3×D1212yes—
1129C3—21no—
1130C3#8590111yescharacteristic, complemented
1131C3#8604211yescharacteristic, complemented
1132C2—22no—
1133C2—62no—
1134C2—64no—
1135C2—121no—
1136C2—122no—
1137C2—362no—
1138C2C22×D3×D1211yescharacteristic
1139C2D3×#101011yescharacteristic
1140C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. C2×#64298C2semidirect
3. #10595997C2semidirect
4. C3×#5524C2semidirect
5. C3×#5523C2semidirect
6. #10595043C2semidirect
7. C2×#63857C2semidirect
8. #10594626C2semidirect
9. D3×#897C2semidirect
10. #10594522C2semidirect
11. #10594380C2semidirect
12. #10594292C2semidirect
13. #10594077C2semidirect
14. #10594003C2semidirect
15. #10593899C2semidirect
16. Dic6×D12C2semidirect
17. #10593895C2semidirect
21. C22×#634C22semidirect
23. C2×C3×#235C22semidirect
26. C2×#3805C22semidirect
35. C2×#3795C22semidirect
36. C2×#3795C22semidirect
38. C2×D3×Dic6C22semidirect
39. C2×D3×Dic6C22semidirect
40. C32×#117C22semidirect
41. #64106C22semidirect
42. #64106C22semidirect
43. #64095C22semidirect
44. #64084C22semidirect
45. #64078C22semidirect
46. C2×C3×C4⋊Dic3C22semidirect
48. C3×#897C22semidirect
50. C3×#895C22semidirect
51. C3×#892C22semidirect
52. C3×D3×C4⋊C4C22semidirect
53. C3×#886C22semidirect
55. C3×#67⋊C4C22semidirect
57. C3×C4×D12C22semidirect
58. C3×C4×D12C22semidirect
59. C3×C4×Dic6C22semidirect
60. #63978C22semidirect
61. C2×Dic3⋊Dic3C22semidirect
65. #63918C22semidirect
66. #63916C22semidirect
67. #63909C22semidirect
68. #63908C22semidirect
69. #63906C22semidirect
70. #63895C22semidirect
72. #63893C22semidirect
74. #63891C22semidirect
75. #63891C22semidirect
76. #63890C22semidirect
77. D3×C4⋊Dic3C22semidirect
78. #63886C22semidirect
79. #63880C22semidirect
80. #63871C22semidirect
83. #63857C22semidirect
84. #63857C22semidirect
85. #63857C22semidirect
86. #63852C22semidirect
116. #5524D3semidirect
117. #5523D3semidirect
139. C3×#235D4semidirect
237. C2×#235C2×D3semidirect
261. C3×#117C2×D3semidirect
262. C3×#117C2×D3semidirect
281. C2×C4⋊Dic3C2×D3semidirect
304. #897C2×D3semidirect
310. #895C2×D3semidirect
312. #892C2×D3semidirect
314. D3×C4⋊C4C2×D3semidirect
322. #886C2×D3semidirect
330. #67⋊C4C2×D3semidirect
341. C4×D12C2×D3semidirect
342. C4×D12C2×D3semidirect
347. C4×Dic6C2×D3semidirect
497. #235D12semidirect
628. C2×C3×D32−1+4semidirect
701. #117D32semidirect
984. C2×D3#1010semidirect
1013. C32#3489semidirect
1130. C3#85901semidirect
1131. C3#86042semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×#642982
#105959972
C3×#55242
C3×#55232
#105950432
C2×#638572
#105946262
D3×#8972
#105945222
#105943802
#105942922
#105940772
#105940032
#105938992
Dic6×D122
#105938952
#860423
#859013