Finite Group Databasebeta

← #11904772

Subgroups — #11904772

Order 1152.

3209 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10595995C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C3×#5523C211yesmaximal, characteristic, complemented
6#10595043C211yesmaximal, characteristic, complemented
7C2×#63871C211yesmaximal, characteristic, complemented
8#10594627C212yesmaximal, complemented
9D3×#897C212yesmaximal, complemented
10#10594523C212yesmaximal, complemented
11#10594380C212yesmaximal, complemented
12#10594293C214yesmaximal, complemented
13#10594077C214yesmaximal, complemented
14#10594005C212yesmaximal, complemented
15#10593903C212yesmaximal, complemented
16#10593901C212yesmaximal, complemented
17#10593896C212yesmaximal, complemented
18#86356—31nomaximal
19#85901—31nomaximal
20C2×#3828C2211yescharacteristic, complemented
21C22×C4×C3⋊D3C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23C2×C3×#235C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic, complemented
25C2×#3811C2212yes—
26C2×#3805C2212yes—
27C2×#3804C2214yescomplemented
28#64306—28no—
29C2×#3802C2211yescharacteristic
30C2×C4×D32C2212yes—
31C2×#3799C2212yescomplemented
32C2×#3798C2212yes—
33C2×#3797C2211yescharacteristic
34C2×#3797C2212yescomplemented
35#64297—28no—
36C2×#3796C2211yescharacteristic
37C2×#3796C2211yescharacteristic
38C2×#3796C2212yescomplemented
39C2×D3×Dic6C2212yescomplemented
40C32×#117C2211yescharacteristic, complemented
41#64106C2211yescharacteristic
42#64106C2211yescharacteristic, complemented
43#64104C2211yescharacteristic
44#64104C2211yescharacteristic, complemented
45#64095C2212yescomplemented
46#64091C2212yes—
47C4×C4⋊(C3⋊D3)C2212yes—
48C4×C4⋊(C3⋊D3)C2212yescomplemented
49C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
50C3×#897C2212yescomplemented
51C3×#897C2212yescomplemented
52C3×#892C2212yescomplemented
53C3×D3×C4⋊C4C2212yescomplemented
54C3×#886C2214yescomplemented
55C3×#67⋊C4C2214yescomplemented
56C3×#875C2212yescomplemented
57C3×C4×D12C2212yescomplemented
58C3×#869C2212yescomplemented
59C3×C4×Dic6C2212yescomplemented
60#63978C2214yescomplemented
61C2×Dic3⋊Dic3C2212yescomplemented
62C2×#3722C2212yes—
63#63923C2214yes—
64D3×(C2×D3)⋊C4C2214yes—
65#63918C2214yescomplemented
66#63916C2212yescomplemented
67#63910C2214yescomplemented
68#63909C2212yescomplemented
69#63909C2214yescomplemented
70#63906C2214yescomplemented
71#63895C2214yes—
72#63895C2214yescomplemented
73#63894C2214yes—
74#63893C2214yescomplemented
75#63891C2214yescomplemented
76#63890C2214yescomplemented
77#63890C2214yescomplemented
78D3×C4⋊Dic3C2214yescomplemented
79#63880C2214yescomplemented
80#63871C2212yes—
81#63871C2212yes—
82#63871C2212yescomplemented
83#63871C2212yescomplemented
84#63871C2212yescomplemented
85#63857C2212yescomplemented
86#63852C2214yescomplemented
87C2×#1010—31no—
88C2×D3×#41—31no—
89C2×D3×#41—31no—
90C2×#1007—31no—
91C3×#536—31no—
92C3×#520—31no—
93#5833—31no—
94C2×#946—31no—
95#5727—32no—
96#5726—32no—
97#5677—32no—
98#5676—32no—
99#5655—34no—
100#5654—34no—
101#5629—32no—
102#5628—32no—
103#5627—32no—
104D3×C22⋊Q8—32no—
105#5576—32no—
106Q8×D12—32no—
107#5555—34no—
108#5555—32no—
109#5554—34no—
110#5554—32no—
111#5526—32no—
112#5526D311yescharacteristic, complemented
113#5524—31no—
114#5524—31no—
115#5524—32no—
116#5524—61no—
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⋊Dic3C2311yescharacteristic
127#3828—24no—
128C2×C4⋊(C3⋊D3)C2311yescharacteristic
129C2×C4⋊(C3⋊D3)C2312yes—
130C2×C4⋊(C3⋊D3)C2312yes—
131C2×C4×C3⋊D3—24no—
132C2×C4×C3⋊D3C2311yescharacteristic
133C2×C4×C3⋊D3C2312yes—
134C2×C4×C3⋊D3C2311yescharacteristic
135C2×C4×C3⋊D3C2311yescharacteristic
136C2×C4×C3⋊D3C2311yescharacteristic
137C2×#634C2311yescharacteristic
138C2×C3×#67C2312yes—
139C2×C3×#67C2312yes—
140C22×C3×Dic3C2312yes—
141C22×C3×Dic3C2312yes—
142C3×#235—24no—
143C3×#235D418yescomplemented
144C2×C3×D12C2311yescharacteristic
145C2×C3×D12C2311yescharacteristic
146C2×C3×C4×D3C2312yes—
147C2×C3×C4×D3C2314yes—
148C2×C3×C4×D3C2312yes—
149C2×C3×Dic6—24no—
150C2×C3×Dic6C2312yes—
151C2×C3×Dic6C2311yescharacteristic
152C2×C3×Dic6C2312yes—
153C2×C3×Dic6C2311yescharacteristic
154#3811—28no—
155C2×#627C2314yes—
156C2×#627C2312yes—
157C2×#626C2312yes—
158C2×#626C2312yes—
159C2×#626C2314yes—
160C2×#626C2314yes—
161C2×#625C2312yes—
162C2×#624C2312yes—
163C2×#624C2314yes—
164#3805—28no—
165#3804—216no—
166C2×D3×Dic3C2314yes—
167C2×D3×Dic3C2312yes—
168C2×D3×Dic3C2312yes—
169#3802—24no—
170C4×D32—28no—
171#3799—28no—
172#3798—28no—
173#3797—28no—
174#3797—24no—
175#3796—24no—
176#3796—28no—
177#3796—24no—
178D3×Dic6—28no—
179C32×C4⋊C4C2311yescharacteristic
180C32×C4⋊C4C2311yescharacteristic
181C32×C22⋊C4C2312yes—
182C32×C42C2312yes—
183#3752C2312yes—
184#3752C2312yes—
185#3752C2312yes—
186#3752C2312yes—
187C4⋊(C3⋊Dic3)C2312yes—
188C4⋊(C3⋊Dic3)C2312yes—
189C3×(C2×D3)⋊C4C2314yes—
190C3×(C2×D3)⋊C4C2314yes—
191C3×(C2×D3)⋊C4C2314yes—
192C3×C4⋊Dic3C2314yes—
193C3×C4⋊Dic3C2314yes—
194C3×C4⋊Dic3C2312yes—
195C3×C4⋊Dic3C2312yes—
196C3×Dic3⋊C4C2314yes—
197C3×C4×Dic3C2314yes—
198Dic3⋊Dic3C2314yes—
199Dic3⋊Dic3C2314yes—
200Dic3⋊Dic3C2314yes—
201#3722C2314yes—
202#3722C2314yes—
203#3722C2314yes—
204(C2×D3)⋊Dic3C2314yes—
205#3489—91noSylow
206C2×C3×#41—31no—
207C2×C3×#41—31no—
208C22×C3×Q8—31no—
209#1010—68no—
210D3×#41—68no—
211D3×#41—68no—
212#1007—68no—
213C2×#239—31no—
214C2×#239—31no—
215C2×#239—32no—
216C2×#239—32no—
217C2×D3×Q8—32no—
218C2×D3×Q8—31no—
219C2×D3×Q8—31no—
220C2×D3×Q8—32no—
221C2×D3×Q8—32no—
222C2×#237—32no—
223C2×#237—32no—
224C2×#237—34no—
225C2×#237—31no—
226C2×#237—31no—
227C2×#237—32no—
228C2×D3×D4—32no—
229C2×D3×D4—32no—
230C2×D3×D4—31no—
231C2×D3×D4—31no—
232C2×#235—31no—
233C2×#235—31no—
234C2×#235—34no—
235C2×#235—32no—
236C2×#235—32no—
237C2×#235—32no—
238C2×#235—61no—
239C2×#235C2×D311yescharacteristic
240C2×#235C2×D311yescharacteristic
241C22×C4×D3—31no—
242C22×C4×D3—31no—
243C22×C4×D3—32no—
244C22×C4×D3—32no—
245C22×C4×D3—61no—
246C22×Dic6—32no—
247C22×Dic6C2×D311yescharacteristic, complemented
248C3×C4⋊Q8—32no—
249C3×#124—32no—
250C3×#123—34no—
251C3×C22⋊Q8—32no—
252C3×C22⋊Q8—32no—
253C3×C4×Q8—32no—
254C3×C4×D4—34no—
255C3×C4×D4—32no—
256C3×#117—21no—
257C3×#117—32no—
258C3×#117C2×D311yescharacteristic, complemented
259C3×#117C2×D311yescharacteristic, complemented
260C2×C3×C4⋊C4—31no—
261C2×C3×C4⋊C4—32no—
262#946—32no—
263#946—32no—
264#946—32no—
265#946—32no—
266#946—32no—
267#939—34no—
268#938—32no—
269#930—34no—
270#930—34no—
271#930—34no—
272#930—32no—
273C2×(C2×D3)⋊C4—32no—
274C2×(C2×D3)⋊C4—32no—
275C2×(C2×D3)⋊C4—34no—
276C2×C4⋊Dic3—32no—
277C2×C4⋊Dic3—34no—
278C2×C4⋊Dic3C2×D311yescharacteristic, complemented
279#924—32no—
280C2×Dic3⋊C4—32no—
281#897—32no—
282#897—32no—
283#897—32no—
284#897—32no—
285#897—32no—
286#897—32no—
287#897—31no—
288#897—31no—
289#897—31no—
290#897—31no—
291#897—34no—
292#897—34no—
293#897—34no—
294#897—61no—
295#897—61no—
296#897C2×D312yescomplemented
297#897C2×D312yescomplemented
298#896—34no—
299#896—34no—
300#895—32no—
301#895—34no—
302#895—32no—
303#895—31no—
304#895—31no—
305#895—31no—
306#895—31no—
307#895—34no—
308#895—61no—
309#895—61no—
310#894—34no—
311#894—34no—
312#893—34no—
313#892C2×D312yescomplemented
314D3×C4⋊C4—34no—
315D3×C4⋊C4C2×D312yescomplemented
316#888—34no—
317#886—32no—
318#886—32no—
319#886—34no—
320#886—34no—
321#886—34no—
322#886—62no—
323#886C2×D314yescomplemented
324#885—34no—
325#884—34no—
326#884—34no—
327#883—34no—
328#882—32no—
329#882—32no—
330#882—34no—
331#882—34no—
332#882—62no—
333#67⋊C4—34no—
334#67⋊C4C2×D314yescomplemented
335D3×C22⋊C4—34no—
336#878—34no—
337#875—34no—
338#875C2×D312yescomplemented
339C4×D12—32no—
340C4×D12—32no—
341C4×D12—32no—
342C4×D12—32no—
343C4×D12—34no—
344C4×D12—34no—
345C4×D12—62no—
346C4×D12—62no—
347C4×D12C2×D312yescomplemented
348#869—34no—
349#869C2×D312yescomplemented
350C4×Dic6C2×D312yescomplemented
351C23×C32C2411yescharacteristic
352C22×C3⋊D3—22no—
353C22×C3⋊D3—22no—
354C22×C3⋊D3—41no—
355C22×C3⋊D3C2411yescharacteristic
356C22×C3⋊D3C2412yes—
357C22×C3⋊D3C2411yescharacteristic
358C22×C3×D3C2412yes—
359C22×C3×D3C2412yes—
360C2×D32—24no—
361C2×D32—24no—
362C2×D32—42no—
363C2×C32×C4C2×D414yes—
364C2×C32×C4C2412yes—
365C2×C32×C4C2412yes—
366C2×C32×C4C2411yescharacteristic
367C2×C32×C4C2411yescharacteristic
368#638—24no—
369C2×C3⋊Dic3—22no—
370C2×C3⋊Dic3C2412yes—
371C2×C3⋊Dic3C2411yescharacteristic
372C2×C3⋊Dic3C2411yescharacteristic
373C4⋊(C3⋊D3)—24no—
374C4⋊(C3⋊D3)—22no—
375C4⋊(C3⋊D3)—42no—
376C4×C3⋊D3—22no—
377C4×C3⋊D3—24no—
378C4×C3⋊D3—22no—
379C4×C3⋊D3—22no—
380C4×C3⋊D3—22no—
381#634—22no—
382C3×#67—24no—
383C3×#67C2×D418yes—
384C2×C3×Dic3—24no—
385C2×C3×Dic3—42no—
386C2×C3×Dic3C2414yes—
387C2×C3×Dic3C2412yes—
388C2×C3×Dic3C2414yes—
389C2×C3×Dic3C2412yes—
390C3×D12—22no—
391C3×D12C2×D414yes—
392C3×C4×D3—24no—
393C3×C4×D3—44no—
394C3×C4×D3C2×D418yes—
395C3×Dic6—24no—
396C3×Dic6—24no—
397C3×Dic6—22no—
398C3×Dic6C2×D414yes—
399#627—28no—
400#627—24no—
401#626—24no—
402#626—28no—
403#626—24no—
404#626—44no—
405#625—24no—
406#624—28no—
407#624—24no—
408D3×Dic3—28no—
409D3×Dic3—24no—
410D3×Dic3—24no—
411C2×2−1+4—91no—
412C22×#41—91no—
413D4×Q8—92no—
414#548—92no—
415#547—94no—
416#547—92no—
417#546—94no—
418#546—92no—
419#537—92no—
420#537—91no—
421#536—31no—
422#536—92no—
423#525—92no—
424#525—91no—
425C2×C22⋊Q8—92no—
426C2×C22⋊Q8—91no—
427#520—31no—
428C23×D3—31no—
429C23×D3—31no—
430C23×D3—32no—
431C23×D3—32no—
432C23×D3—61no—
433C3×#41—38no—
434C3×#41—64no—
435C2×C3×Q8—31no—
436C2×C3×Q8—32no—
437C2×C3×Q8—32no—
438C2×C3×Q8—31no—
439C2×C3×Q8—64no—
440C2×C3×D4—32no—
441C2×C3×D4—32no—
442C2×C3×D4—31no—
443C2×C3×D4—31no—
444C22×C3×C4—21no—
445C22×C3×C4—32no—
446C22×C3×C4—32no—
447C22×C3×C4—32no—
448C22×C3×C4—32no—
449C22×C3×C4—34no—
450C22×C3×C4C22×D311yescharacteristic
451C22×C3×C4C22×D311yescharacteristic
452C2×#67—32no—
453C2×#67—32no—
454C2×#67—32no—
455C2×#67—32no—
456C2×#67—34no—
457C2×#67—32no—
458C2×#67—32no—
459C2×#67—34no—
460C2×#67—62no—
461C2×#67C22×D312yes—
462C2×#67C22×D312yes—
463C22×Dic3—31no—
464C22×Dic3—31no—
465C22×Dic3—32no—
466C22×Dic3—32no—
467C22×Dic3—34no—
468C22×Dic3—61no—
469C22×Dic3C22×D312yes—
470C22×Dic3C22×D312yes—
471#239—64no—
472#239—68no—
473#239—64no—
474#239—68no—
475D3×Q8—64no—
476D3×Q8—68no—
477D3×Q8—68no—
478D3×Q8—68no—
479D3×Q8—64no—
480#237—64no—
481#237—68no—
482#237—616no—
483#237—68no—
484#237—68no—
485#237—64no—
486D3×D4—64no—
487D3×D4—68no—
488D3×D4—68no—
489D3×D4—64no—
490#235—24no—
491#235—68no—
492#235—68no—
493#235—64no—
494#235—64no—
495#235—616no—
496#235—68no—
497#235—124no—
498#235D1218yescomplemented
499C2×D12—32no—
500C2×D12—34no—
501C2×D12—32no—
502C2×D12—32no—
503C2×D12—32no—
504C2×D12—31no—
505C2×D12—31no—
506C2×D12—34no—
507C2×D12—32no—
508C2×D12—32no—
509C2×D12—62no—
510C2×D12—62no—
511C2×D12—61no—
512C2×D12C22×D311yescharacteristic
513C2×D12C22×D311yescharacteristic
514C2×C4×D3—32no—
515C2×C4×D3—34no—
516C2×C4×D3—32no—
517C2×C4×D3—32no—
518C2×C4×D3—31no—
519C2×C4×D3—31no—
520C2×C4×D3—32no—
521C2×C4×D3—31no—
522C2×C4×D3—31no—
523C2×C4×D3—31no—
524C2×C4×D3—31no—
525C2×C4×D3—31no—
526C2×C4×D3—31no—
527C2×C4×D3—34no—
528C2×C4×D3—32no—
529C2×C4×D3—34no—
530C2×C4×D3—32no—
531C2×C4×D3—61no—
532C2×C4×D3—61no—
533C2×C4×D3—62no—
534C2×C4×D3—61no—
535C2×C4×D3—61no—
536C2×C4×D3—68no—
537C2×C4×D3—64no—
538C2×C4×D3—64no—
539C2×C4×D3—68no—
540C2×C4×D3—124no—
541C2×C4×D3C22×D312yes—
542C2×C4×D3C22×D314yes—
543C2×C4×D3C22×D312yes—
544C2×Dic6—24no—
545C2×Dic6—31no—
546C2×Dic6—31no—
547C2×Dic6—32no—
548C2×Dic6—34no—
549C2×Dic6—34no—
550C2×Dic6—32no—
551C2×Dic6—61no—
552C2×Dic6—68no—
553C2×Dic6C22×D311yescharacteristic
554C2×Dic6C22×D312yes—
555C2×Dic6C22×D312yes—
556C2×Dic6C22×D311yescharacteristic
557C3×C4⋊C4—21no—
558C3×C4⋊C4—21no—
559C3×C4⋊C4—34no—
560C3×C4⋊C4—34no—
561C3×C4⋊C4—34no—
562C3×C4⋊C4—32no—
563C3×C4⋊C4—32no—
564C3×C4⋊C4C22×D311yescharacteristic
565C3×C4⋊C4C22×D311yescharacteristic
566C3×C4⋊C4C22×D311yescharacteristic
567C3×C4⋊C4C22×D311yescharacteristic
568C3×C22⋊C4—22no—
569C3×C22⋊C4—34no—
570C3×C22⋊C4—34no—
571C3×C22⋊C4—34no—
572C3×C22⋊C4C22×D312yes—
573C3×C22⋊C4C22×D312yes—
574C3×C42—22no—
575C3×C42—34no—
576C3×C42C22×D312yes—
577C3×C42C22×D312yes—
578#217—34no—
579(C2×D3)⋊C4—34no—
580(C2×D3)⋊C4—32no—
581(C2×D3)⋊C4—32no—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—32no—
585(C2×D3)⋊C4—32no—
586(C2×D3)⋊C4—32no—
587(C2×D3)⋊C4—32no—
588(C2×D3)⋊C4—34no—
589(C2×D3)⋊C4—34no—
590(C2×D3)⋊C4—34no—
591(C2×D3)⋊C4—34no—
592(C2×D3)⋊C4—34no—
593(C2×D3)⋊C4—34no—
594(C2×D3)⋊C4—62no—
595(C2×D3)⋊C4—62no—
596(C2×D3)⋊C4—62no—
597(C2×D3)⋊C4—62no—
598(C2×D3)⋊C4C22×D314yes—
599(C2×D3)⋊C4C22×D314yes—
600(C2×D3)⋊C4C22×D314yes—
601C4⋊Dic3—32no—
602C4⋊Dic3—32no—
603C4⋊Dic3—32no—
604C4⋊Dic3—32no—
605C4⋊Dic3—34no—
606C4⋊Dic3—34no—
607C4⋊Dic3—34no—
608C4⋊Dic3—62no—
609C4⋊Dic3—62no—
610C4⋊Dic3C22×D312yes—
611C4⋊Dic3C22×D314yes—
612C4⋊Dic3C22×D314yes—
613C4⋊Dic3C22×D312yes—
614Dic3⋊C4—34no—
615Dic3⋊C4—34no—
616Dic3⋊C4—34no—
617Dic3⋊C4C22×D314yes—
618C4×Dic3C22×D314yes—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32C22×D412yes—
622C22×C32C2511yescharacteristic
623C2×C3⋊D3—21no—
624C2×C3⋊D3—21no—
625C2×C3⋊D3—21no—
626C2×C3⋊D3—22no—
627C2×C3⋊D3—21no—
628C2×C3⋊D3—22no—
629C2×C3⋊D3—21no—
630C2×C3⋊D3—22no—
631C2×C3⋊D3—44no—
632C2×C3⋊D32−1+412yescomplemented
633C2×C3×D3—22no—
634C2×C3×D3—22no—
635C2×C3×D3—22no—
636C2×C3×D3—22no—
637C2×C3×D3—22no—
638C2×C3×D3C22×D414yes—
639D32—48no—
640C32×C4—22no—
641C32×C4—22no—
642C32×C4C22×D412yes—
643C32×C4C22×D412yes—
644C3⋊Dic3—21no—
645C3⋊Dic3—22no—
646C3⋊Dic3—21no—
647C3×Dic3—24no—
648C3×Dic3—22no—
649C3×Dic3—24no—
650C3×Dic3C22×D414yes—
6512−1+4—188no—
652C2×#41—31no—
653C2×#41—31no—
654C2×#41—92no—
655C2×#41—94no—
656C2×#41—92no—
657C2×#41—92no—
658C2×#41—92no—
659C2×#41—91no—
660C2×#41—91no—
661C2×#41—91no—
662C2×#41—188no—
663C22×Q8—31no—
664C22×Q8—92no—
665C22×Q8—92no—
666C22×Q8—91no—
667C22×D4—92no—
668C22×D4—91no—
669C23×C4—92no—
670C23×C4—91no—
671C4⋊Q8—32no—
672C4⋊Q8—94no—
673#124—32no—
674#124—94no—
675#123—34no—
676#123—94no—
677#123—94no—
678#123—94no—
679#123—92no—
680C22⋊Q8—32no—
681C22⋊Q8—32no—
682C22⋊Q8—94no—
683C22⋊Q8—94no—
684C22⋊Q8—94no—
685C22⋊Q8—92no—
686C22⋊Q8—92no—
687C22⋊Q8—92no—
688C22⋊Q8—92no—
689C22⋊Q8—92no—
690C22⋊Q8—92no—
691C22⋊Q8—91no—
692C22⋊Q8—91no—
693#121—94no—
694#121—94no—
695#121—92no—
696#121—94no—
697#121—92no—
698#121—94no—
699#121—91no—
700#121—91no—
701#120—94no—
702#120—92no—
703C4×Q8—32no—
704C4×D4—34no—
705C4×D4—32no—
706C4×D4—94no—
707C4×D4—94no—
708C4×D4—92no—
709C4×D4—92no—
710#117—32no—
711#117D3211yescharacteristic, complemented
712C2×C4⋊C4—31no—
713C2×C4⋊C4—32no—
714C2×C4⋊C4—94no—
715C2×C4⋊C4—92no—
716C2×C22⋊C4—94no—
717C2×C22⋊C4—92no—
718C23×C3—21no—
719C23×C3—32no—
720C23×C3—32no—
721C23×C3C23×D311yescharacteristic
722C23×C3C23×D311yescharacteristic
723C22×D3—31no—
724C22×D3—31no—
725C22×D3—31no—
726C22×D3—31no—
727C22×D3—32no—
728C22×D3—32no—
729C22×D3—61no—
730C22×D3—61no—
731C22×D3—62no—
732C22×D3—64no—
733C22×D3—64no—
734C22×D3—64no—
735C22×D3—62no—
736C22×D3—62no—
737C22×D3—62no—
738C22×D3—62no—
739C22×D3—64no—
740C22×D3—122no—
741C22×D3—122no—
742C22×D3—122no—
743C22×D3—122no—
744C22×D3—121no—
745C22×D3—121no—
746C22×D3—122no—
747C22×D3C23×D312yes—
748C22×D3C23×D312yes—
749C3×Q8—34no—
750C3×Q8—64no—
751C3×Q8—64no—
752C3×Q8—62no—
753C3×D4—38no—
754C3×D4—34no—
755C3×D4—64no—
756C3×D4—62no—
757C2×C3×C4—21no—
758C2×C3×C4—21no—
759C2×C3×C4—22no—
760C2×C3×C4—22no—
761C2×C3×C4—24no—
762C2×C3×C4—32no—
763C2×C3×C4—38no—
764C2×C3×C4—34no—
765C2×C3×C4—32no—
766C2×C3×C4—34no—
767C2×C3×C4—64no—
768C2×C3×C4—64no—
769C2×C3×C4—124no—
770C2×C3×C4—122no—
771C2×C3×C4C2×D1214yes—
772C2×C3×C4D3×D414yes—
773C2×C3×C4C23×D312yes—
774C2×C3×C4C23×D312yes—
775C2×C3×C4C23×D312yes—
776C2×C3×C4C23×D312yes—
777C2×C3×C4C23×D311yescharacteristic
778C2×C3×C4C23×D311yescharacteristic
779C2×C3×C4C23×D311yescharacteristic
780C2×C3×C4C23×D311yescharacteristic
781#67—24no—
782#67—64no—
783#67—68no—
784#67—64no—
785#67—64no—
786#67—64no—
787#67—64no—
788#67—64no—
789#67—124no—
790#67—124no—
791#67C2×D1218yes—
792C2×Dic3—24no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—32no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—32no—
799C2×Dic3—42no—
800C2×Dic3—62no—
801C2×Dic3—61no—
802C2×Dic3—61no—
803C2×Dic3—68no—
804C2×Dic3—64no—
805C2×Dic3—62no—
806C2×Dic3—62no—
807C2×Dic3—64no—
808C2×Dic3—122no—
809C2×Dic3C23×D314yes—
810C2×Dic3C23×D312yes—
811C2×Dic3C23×D314yes—
812C2×Dic3C23×D312yes—
813D12—22no—
814D12—64no—
815D12—64no—
816D12—64no—
817D12—64no—
818D12—68no—
819D12—62no—
820D12—62no—
821D12—122no—
822D12—124no—
823D12—122no—
824D12—122no—
825D12—124no—
826D12—124no—
827D12C2×D1214yes—
828C4×D3—24no—
829C4×D3—44no—
830C4×D3—64no—
831C4×D3—68no—
832C4×D3—64no—
833C4×D3—64no—
834C4×D3—68no—
835C4×D3—62no—
836C4×D3—62no—
837C4×D3—62no—
838C4×D3—62no—
839C4×D3—64no—
840C4×D3—62no—
841C4×D3—62no—
842C4×D3—62no—
843C4×D3—62no—
844C4×D3—64no—
845C4×D3—64no—
846C4×D3—68no—
847C4×D3—122no—
848C4×D3—122no—
849C4×D3—122no—
850C4×D3—122no—
851C4×D3—124no—
852C4×D3C2×D1218yes—
853Dic6—24no—
854Dic6—24no—
855Dic6—22no—
856Dic6—68no—
857Dic6—64no—
858Dic6—62no—
859Dic6—62no—
860Dic6—64no—
861Dic6—68no—
862Dic6—122no—
863Dic6C2×D1214yes—
864C2×C32—22no—
865C2×C32C23×D411yescharacteristic
866C2×C32C2×2−1+411yescharacteristic
867C2×C32#58511yescharacteristic
868C3⋊D3—22no—
869C3⋊D3—41no—
870C3⋊D3—42no—
871C3×D3—24no—
872C3×D3—42no—
873C24—92no—
874C24—91no—
875#41—38no—
876#41—64no—
877#41—188no—
878#41—188no—
879#41—1816no—
880#41—188no—
881#41—184no—
882#41—188no—
883#41—184no—
884#41—184no—
885C2×Q8—31no—
886C2×Q8—32no—
887C2×Q8—32no—
888C2×Q8—31no—
889C2×Q8—64no—
890C2×Q8—94no—
891C2×Q8—92no—
892C2×Q8—91no—
893C2×Q8—188no—
894C2×Q8—184no—
895C2×Q8—188no—
896C2×D4—32no—
897C2×D4—32no—
898C2×D4—31no—
899C2×D4—31no—
900C2×D4—94no—
901C2×D4—92no—
902C2×D4—92no—
903C2×D4—94no—
904C2×D4—92no—
905C2×D4—92no—
906C2×D4—92no—
907C2×D4—91no—
908C2×D4—92no—
909C2×D4—188no—
910C2×D4—184no—
911C22×C4—32no—
912C22×C4—32no—
913C22×C4—32no—
914C22×C4—32no—
915C22×C4—34no—
916C22×C4—94no—
917C22×C4—92no—
918C22×C4—94no—
919C22×C4—92no—
920C22×C4—92no—
921C22×C4—91no—
922C22×C4—92no—
923C22×C4—91no—
924C22×C4—91no—
925C22×C4—91no—
926C22×C4—91no—
927C22×C4—188no—
928C22×C4—184no—
929C22×C4C2×D3211yescharacteristic
930C4⋊C4—32no—
931C4⋊C4—34no—
932C4⋊C4—32no—
933C4⋊C4—34no—
934C4⋊C4—34no—
935C4⋊C4—94no—
936C4⋊C4—94no—
937C4⋊C4—94no—
938C4⋊C4—92no—
939C4⋊C4—92no—
940C4⋊C4C2×D3211yescharacteristic
941C4⋊C4C2×D3211yescharacteristic
942C22⋊C4—34no—
943C22⋊C4—34no—
944C22⋊C4—34no—
945C22⋊C4—94no—
946C22⋊C4—94no—
947C22⋊C4—94no—
948C22⋊C4—94no—
949C22⋊C4—92no—
950C22⋊C4—92no—
951C22⋊C4—92no—
952C22⋊C4—92no—
953C22⋊C4C2×D3212yes—
954C42—34no—
955C42C2×D3212yes—
956C22×C3—21no—
957C22×C3—21no—
958C22×C3—21no—
959C22×C3—21no—
960C22×C3—22no—
961C22×C3—21no—
962C22×C3—34no—
963C22×C3—41no—
964C22×C3—41no—
965C22×C3—62no—
966C22×C3—62no—
967C22×C3—62no—
968C22×C3—62no—
969C22×C3—62no—
970C22×C3C22×D1212yes—
971C22×C3C2×D3×D412yes—
972C22×C3C24×D311yescharacteristic
973C22×C3C24×D311yescharacteristic
974C2×D3—22no—
975C2×D3—22no—
976C2×D3—22no—
977C2×D3—22no—
978C2×D3—22no—
979C2×D3—32no—
980C2×D3—32no—
981C2×D3—62no—
982C2×D3—61no—
983C2×D3—61no—
984C2×D3—61no—
985C2×D3—61no—
986C2×D3—62no—
987C2×D3—62no—
988C2×D3—61no—
989C2×D3—62no—
990C2×D3—61no—
991C2×D3—61no—
992C2×D3—62no—
993C2×D3—62no—
994C2×D3—62no—
995C2×D3—61no—
996C2×D3—61no—
997C2×D3—62no—
998C2×D3—61no—
999C2×D3—121no—
1000C2×D3—121no—
1001C2×D3—121no—
1002C2×D3—121no—
1003C2×D3—122no—
1004C2×D3—122no—
1005C2×D3—122no—
1006C2×D3—128no—
1007C2×D3—128no—
1008C2×D3—124no—
1009C2×D3—124no—
1010C2×D3—128no—
1011C2×D3C22×D1214yes—
1012C3×C4—22no—
1013C3×C4—22no—
1014C3×C4—22no—
1015C3×C4—22no—
1016C3×C4—22no—
1017C3×C4—22no—
1018C3×C4—34no—
1019C3×C4—42no—
1020C3×C4—42no—
1021C3×C4—62no—
1022C3×C4—64no—
1023C3×C4—64no—
1024C3×C4C22×D1212yes—
1025C3×C4C22×D1212yes—
1026C3×C4C2×D3×D412yes—
1027C3×C4C2×D3×D412yes—
1028Dic3—24no—
1029Dic3—22no—
1030Dic3—24no—
1031Dic3—62no—
1032Dic3—61no—
1033Dic3—61no—
1034Dic3—62no—
1035Dic3—61no—
1036Dic3—61no—
1037Dic3—122no—
1038Dic3—121no—
1039Dic3—121no—
1040Dic3C22×D1214yes—
1041C32#348911yescharacteristic, complemented, Sylow
1042C23—32no—
1043C23—32no—
1044C23—91no—
1045C23—91no—
1046C23—92no—
1047C23—182no—
1048C23—184no—
1049C23—184no—
1050C23—182no—
1051C23—361no—
1052C23—362no—
1053C23C22×D3211yescharacteristic
1054Q8—34no—
1055Q8—64no—
1056Q8—64no—
1057Q8—62no—
1058Q8—188no—
1059Q8—184no—
1060Q8—182no—
1061D4—38no—
1062D4—34no—
1063D4—64no—
1064D4—62no—
1065D4—184no—
1066D4—184no—
1067D4—184no—
1068D4—188no—
1069D4—184no—
1070D4—184no—
1071D4—182no—
1072D4—362no—
1073D4—364no—
1074C2×C4—32no—
1075C2×C4—38no—
1076C2×C4—34no—
1077C2×C4—34no—
1078C2×C4—32no—
1079C2×C4—64no—
1080C2×C4—64no—
1081C2×C4—92no—
1082C2×C4—91no—
1083C2×C4—91no—
1084C2×C4—124no—
1085C2×C4—122no—
1086C2×C4—184no—
1087C2×C4—188no—
1088C2×C4—184no—
1089C2×C4—184no—
1090C2×C4—188no—
1091C2×C4—182no—
1092C2×C4—182no—
1093C2×C4—182no—
1094C2×C4—182no—
1095C2×C4—182no—
1096C2×C4—184no—
1097C2×C4D3×D1214yes—
1098C2×C4C22×D3212yes—
1099C2×C4C22×D3212yes—
1100C2×C4C22×D3211yescharacteristic
1101C2×C4C22×D3211yescharacteristic
1102C2×C3—22no—
1103C2×C3—22no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—42no—
1108C2×C3—64no—
1109C2×C3—122no—
1110C2×C3C23×D1211yescharacteristic
1111C2×C3C22×D3×D411yescharacteristic
1112C2×C3#596611yescharacteristic
1113C2×C3D3×2−1+411yescharacteristic
1114C2×C3D3×2−1+411yescharacteristic
1115C2×C3#596811yescharacteristic
1116D3—24no—
1117D3—42no—
1118D3—62no—
1119D3—62no—
1120D3—122no—
1121D3—122no—
1122D3—121no—
1123D3—122no—
1124D3—121no—
1125D3—122no—
1126D3—242no—
1127C22—21no—
1128C22—21no—
1129C22—34no—
1130C22—62no—
1131C22—62no—
1132C22—62no—
1133C22—62no—
1134C22—62no—
1135C22—92no—
1136C22—181no—
1137C22—181no—
1138C22—182no—
1139C22—181no—
1140C22—182no—
1141C22—181no—
1142C22—182no—
1143C22—181no—
1144C22—364no—
1145C22—368no—
1146C22C2×D3×D1212yes—
1147C22C23×D3211yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—34no—
1151C4—62no—
1152C4—64no—
1153C4—64no—
1154C4—181no—
1155C4—181no—
1156C4—182no—
1157C4C2×D3×D1212yes—
1158C4C2×D3×D1212yes—
1159C3—21no—
1160C3#8590111yescharacteristic, complemented
1161C3#8635611yescharacteristic, complemented
1162C2—22no—
1163C2—64no—
1164C2—122no—
1165C2—182no—
1166C2—361no—
1167C2—362no—
1168C2C22×D3×D1211yescharacteristic
1169C2#1059669411yescharacteristic
1170C2#1059669811yescharacteristic
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×#64306C2semidirect
2. C2×#64297C2semidirect
3. #10595995C2semidirect
4. C3×#5526C2semidirect
5. C3×#5523C2semidirect
6. #10595043C2semidirect
7. C2×#63871C2semidirect
8. #10594627C2semidirect
9. D3×#897C2semidirect
10. #10594523C2semidirect
11. #10594380C2semidirect
12. #10594293C2semidirect
13. #10594077C2semidirect
14. #10594005C2semidirect
15. #10593903C2semidirect
16. #10593901C2semidirect
17. #10593896C2semidirect
20. C2×#3828C22semidirect
24. C22×C3×Dic6C22semidirect
27. C2×#3804C22semidirect
31. C2×#3799C22semidirect
34. C2×#3797C22semidirect
38. C2×#3796C22semidirect
39. C2×D3×Dic6C22semidirect
40. C32×#117C22semidirect
42. #64106C22semidirect
44. #64104C22semidirect
45. #64095C22semidirect
48. C4×C4⋊(C3⋊D3)C22semidirect
49. C2×C3×C4⋊Dic3C22semidirect
50. C3×#897C22semidirect
51. C3×#897C22semidirect
52. C3×#892C22semidirect
53. C3×D3×C4⋊C4C22semidirect
54. C3×#886C22semidirect
55. C3×#67⋊C4C22semidirect
56. C3×#875C22semidirect
57. C3×C4×D12C22semidirect
58. C3×#869C22semidirect
59. C3×C4×Dic6C22semidirect
60. #63978C22semidirect
61. C2×Dic3⋊Dic3C22semidirect
65. #63918C22semidirect
66. #63916C22semidirect
67. #63910C22semidirect
68. #63909C22semidirect
69. #63909C22semidirect
70. #63906C22semidirect
72. #63895C22semidirect
74. #63893C22semidirect
75. #63891C22semidirect
76. #63890C22semidirect
77. #63890C22semidirect
78. D3×C4⋊Dic3C22semidirect
79. #63880C22semidirect
82. #63871C22semidirect
83. #63871C22semidirect
84. #63871C22semidirect
85. #63857C22semidirect
86. #63852C22semidirect
112. #5526D3semidirect
117. #5523D3semidirect
143. C3×#235D4semidirect
247. C22×Dic6C2×D3semidirect
258. C3×#117C2×D3semidirect
259. C3×#117C2×D3semidirect
278. C2×C4⋊Dic3C2×D3semidirect
296. #897C2×D3semidirect
297. #897C2×D3semidirect
313. #892C2×D3semidirect
315. D3×C4⋊C4C2×D3semidirect
323. #886C2×D3semidirect
334. #67⋊C4C2×D3semidirect
338. #875C2×D3semidirect
347. C4×D12C2×D3semidirect
349. #869C2×D3semidirect
350. C4×Dic6C2×D3semidirect
498. #235D12semidirect
632. C2×C3⋊D32−1+4semidirect
711. #117D32semidirect
1041. C32#3489semidirect
1160. C3#85901semidirect
1161. C3#86356semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#642972
#105959952
C3×#55262
C3×#55232
#105950432
C2×#638712
#105946272
D3×#8972
#105945232
#105943802
#105942932
#105940772
#105940052
#105939032
#105939012
#105938962
#863563
#859013