Finite Group Databasebeta

← #11904780

Subgroups — #11904780

Order 1152.

3191 conjugacy classes of subgroups.

The subgroup lattice has 1148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#235C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10595981C211yesmaximal, characteristic, complemented
4C2×C3×#897C211yesmaximal, characteristic, complemented
5C3×#5504C211yesmaximal, characteristic, complemented
6#10595073C214yesmaximal, complemented
7#10595023C211yesmaximal, characteristic, complemented
8#10594906C214yesmaximal, complemented
9#10594866C211yesmaximal, characteristic, complemented
10#10594629C212yesmaximal, complemented
11#10594627C212yesmaximal, complemented
12D3×#897C212yesmaximal, complemented
13#10594523C212yesmaximal, complemented
14#10594383C212yesmaximal, complemented
15#10594381C212yesmaximal, complemented
16#10594380C212yesmaximal, complemented
17#10594329C212yesmaximal, complemented
18#85985—31nomaximal
19#85901—31nomaximal
20C2×#3828C2211yescharacteristic
21C2×#3828C2211yescharacteristic, complemented
22C2×C3×#235C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2211yescharacteristic, complemented
25C2×D3×#67C2212yes—
26C2×#3804C2212yes—
27C2×#3804C2214yescomplemented
28D3×#235—28no—
29C2×D3×D12C2211yescharacteristic
30C2×C4×D32C2212yes—
31C2×#3799C2211yescharacteristic
32C2×#3799C2212yescomplemented
33C2×#3798C2212yes—
34C2×#3797C2212yescomplemented
35#64297—28no—
36C2×#3796C2212yescomplemented
37C2×#3795C2211yescharacteristic
38C2×D3×Dic6C2211yescharacteristic
39C2×D3×Dic6C2212yescomplemented
40C2×C32×C4⋊C4C2211yescharacteristic, complemented
41#64139C2214yescomplemented
42#64106C2212yescomplemented
43#64106C2212yescomplemented
44#64104C2212yescomplemented
45#64104C2212yescomplemented
46C3×C4×#67C2214yescomplemented
47C2×C3×(C2×D3)⋊C4C2212yes—
48C3×#926C2211yescharacteristic, complemented
49C2×C3×C4⋊Dic3C2212yescomplemented
50C3×#897C2212yes—
51C3×#897C2212yes—
52C3×#897C2212yescomplemented
53C3×#897C2212yescomplemented
54C3×#893C2212yescomplemented
55C3×#892C2212yescomplemented
56C3×D3×C4⋊C4C2212yescomplemented
57C3×#887C2212yescomplemented
58#63977C2212yes—
59#63966C2214yescomplemented
60#63966C2212yescomplemented
61#63923C2214yes—
62D3×(C2×D3)⋊C4C2214yes—
63#63918C2214yescomplemented
64#63910C2214yescomplemented
65#63909C2211yescharacteristic
66#63909C2214yescomplemented
67#63909C2211yescharacteristic, complemented
68#63906C2214yescomplemented
69C4×#626C2212yes—
70C4×#626C2212yescomplemented
71#63895C2214yescomplemented
72#63895C2214yescomplemented
73#63894C2214yescomplemented
74#63893C2214yes—
75#63891C2214yescomplemented
76#63890C2214yescomplemented
77#63890C2214yescomplemented
78D3×C4⋊Dic3C2214yescomplemented
79#63880C2214yes—
80#63871C2212yescomplemented
81#63871C2212yescomplemented
82#63866C2212yescomplemented
83#63864C2212yescomplemented
84#63857C2211yescharacteristic
85#63857C2211yescharacteristic, complemented
86#63852C2214yescomplemented
87C2×#1010—31no—
88C2×D3×#41—31no—
89C2×#1007—31no—
90C22×#235—31no—
91C2×C3×C22⋊Q8—31no—
92C3×#520—31no—
93#5816—31no—
94#5791—31no—
95#5633—32no—
96#5632—32no—
97#5631—32no—
98#5630—32no—
99#5629—32no—
100#5628—32no—
101#5627—32no—
102D3×C22⋊Q8—32no—
103#5576—32no—
104Q8×D12—32no—
105#5555—34no—
106#5555—32no—
107#5554—34no—
108#5554—32no—
109#5526—31no—
110#5526—32no—
111#5524—31no—
112#5524—32no—
113#5510—31no—
114#5510—31no—
115#5510—32no—
116#5510—61no—
117C2×#897—32no—
118C2×#897D311yescharacteristic, complemented
119#5507—34no—
120#5504D311yescharacteristic, complemented
121#5490—34no—
122C23×C3×D3C2311yescharacteristic
123C22×D32C2312yes—
124C22×C32×C4C2312yes—
125C22×C32×C4C2311yescharacteristic
126C2×#638C2312yes—
127C2×#638C2312yes—
128#3828—24no—
129#3828—24no—
130C2×C4⋊(C3⋊D3)C2311yescharacteristic
131C2×C4⋊(C3⋊D3)C2311yescharacteristic
132C2×C4⋊(C3⋊D3)C2314yes—
133C2×C4×C3⋊D3C2312yes—
134C2×C4×C3⋊D3C2312yes—
135C2×#634C2311yescharacteristic
136C2×#634C2311yescharacteristic
137C2×C3×#67C2312yes—
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2312yes—
140C3×#235D418yescomplemented
141C2×C3×D12C2311yescharacteristic
142C2×C3×C4×D3—24no—
143C2×C3×C4×D3C2311yescharacteristic
144C2×C3×C4×D3C2311yescharacteristic
145C2×C3×C4×D3C2311yescharacteristic
146C2×C3×C4×D3C2311yescharacteristic
147C2×C3×C4×D3C2314yes—
148C2×C3×C4×D3C2312yes—
149C2×C3×Dic6—24no—
150C2×C3×Dic6C2312yes—
151C2×C3×Dic6C2312yes—
152C2×C3×Dic6C2311yescharacteristic
153D3×#67—28no—
154C2×#627C2312yes—
155C2×#627C2314yes—
156C2×#626C2314yes—
157C2×#626C2312yes—
158C2×#626C2312yes—
159C2×#626C2312yes—
160C2×#626C2312yes—
161C2×#625C2312yes—
162C2×#624C2314yes—
163C2×#624C2312yes—
164#3804—216no—
165#3804—28no—
166C2×D3×Dic3C2312yes—
167C2×D3×Dic3C2314yes—
168C2×D3×Dic3C2312yes—
169D3×D12—24no—
170C4×D32—28no—
171#3799—28no—
172#3799—24no—
173#3798—28no—
174#3797—28no—
175#3796—28no—
176#3795—24no—
177D3×Dic6—28no—
178D3×Dic6—24no—
179C32×C4⋊C4C2312yes—
180C32×C4⋊C4C2312yes—
181#3752C2314yes—
182#3752C2314yes—
183C4⋊(C3⋊Dic3)C2314yes—
184C3×#217C2312yes—
185C3×(C2×D3)⋊C4C2314yes—
186C3×(C2×D3)⋊C4C2314yes—
187C3×(C2×D3)⋊C4C2314yes—
188C3×C4⋊Dic3C2311yescharacteristic
189C3×C4⋊Dic3C2311yescharacteristic
190C3×C4⋊Dic3C2314yes—
191C3×C4⋊Dic3C2314yes—
192C3×Dic3⋊C4C2314yes—
193C3×C4×Dic3C2314yes—
194C3×C4×Dic3C2312yes—
195Dic3⋊Dic3C2312yes—
196Dic3⋊Dic3C2312yes—
197Dic3⋊Dic3C2314yes—
198Dic3⋊Dic3C2314yes—
199#3722C2314yes—
200#3722C2314yes—
201#3722C2312yes—
202#3722C2312yes—
203(C2×D3)⋊Dic3C2312yes—
204(C2×D3)⋊Dic3C2312yes—
205#3489—91noSylow
206C2×C3×#41—31no—
207C22×C3×Q8—31no—
208C23×C3×C4—31no—
209C22×#67—32no—
210#1010—68no—
211D3×#41—68no—
212#1007—68no—
213C2×#239—32no—
214C2×#239—31no—
215C2×#239—32no—
216C2×D3×Q8—31no—
217C2×D3×Q8—32no—
218C2×D3×Q8—32no—
219C2×D3×Q8—32no—
220C2×#237—32no—
221C2×#237—34no—
222C2×#237—31no—
223C2×#237—32no—
224C2×D3×D4—32no—
225C2×D3×D4—31no—
226C2×#235—31no—
227C2×#235—31no—
228C2×#235—31no—
229C2×#235—31no—
230C2×#235—32no—
231C2×#235—34no—
232C2×#235—31no—
233C2×#235—32no—
234C2×#235—32no—
235C2×#235—31no—
236C2×#235—32no—
237C2×#235—61no—
238C2×#235—61no—
239C2×#235—68no—
240C2×#235C2×D311yescharacteristic
241C22×D12—31no—
242C22×C4×D3—32no—
243C22×C4×D3—32no—
244C22×C4×D3C2×D311yescharacteristic
245C22×Dic6—31no—
246C22×Dic6—32no—
247C22×Dic6C2×D311yescharacteristic, complemented
248C3×C22⋊Q8—32no—
249C3×C22⋊Q8—32no—
250C3×C22⋊Q8—32no—
251C3×C22⋊Q8—32no—
252C3×C4×Q8—32no—
253C3×C4×D4—34no—
254C3×C4×D4—32no—
255C3×#117—31no—
256C3×#117—32no—
257C2×C3×C4⋊C4—21no—
258C2×C3×C4⋊C4—32no—
259C2×C3×C4⋊C4—32no—
260C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
261C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
262C2×C3×C22⋊C4—32no—
263#953—32no—
264#947—32no—
265#946—32no—
266#946—32no—
267#944—32no—
268#930—34no—
269#930—34no—
270#930—34no—
271#930—34no—
272#930—31no—
273#930—31no—
274#930—64no—
275#929—34no—
276#929—32no—
277C4×#67—32no—
278C4×#67—32no—
279C4×#67C2×D314yescomplemented
280C2×(C2×D3)⋊C4—34no—
281C2×(C2×D3)⋊C4C2×D312yes—
282#926C2×D311yescharacteristic, complemented
283C2×C4⋊Dic3—34no—
284C2×C4⋊Dic3C2×D312yescomplemented
285#924—31no—
286#924—31no—
287#897—31no—
288#897—31no—
289#897—32no—
290#897—32no—
291#897—32no—
292#897—32no—
293#897—32no—
294#897—32no—
295#897—34no—
296#897—34no—
297#897—34no—
298#897—62no—
299#897—62no—
300#897C2×D312yes—
301#897C2×D312yes—
302#897C2×D312yescomplemented
303#897C2×D312yescomplemented
304#896—34no—
305#896—34no—
306#895—34no—
307#895—31no—
308#895—31no—
309#895—32no—
310#895—32no—
311#895—32no—
312#895—32no—
313#895—34no—
314#895—62no—
315#895—62no—
316#894—34no—
317#894—34no—
318#893—34no—
319#893C2×D312yescomplemented
320#892C2×D312yescomplemented
321D3×C4⋊C4—34no—
322D3×C4⋊C4C2×D312yescomplemented
323#888—34no—
324#887C2×D312yescomplemented
325#886—32no—
326#886—34no—
327#886—34no—
328#886—34no—
329#886—34no—
330#885—34no—
331#884—34no—
332#884—34no—
333#883—34no—
334#882—32no—
335#882—34no—
336#882—34no—
337#67⋊C4—34no—
338D3×C22⋊C4—34no—
339#878—34no—
340#875—32no—
341#875—34no—
342C4×D12—32no—
343C4×D12—32no—
344C4×D12—34no—
345C4×D12—34no—
346#869—32no—
347#869—34no—
348C23×C32C2411yescharacteristic
349C22×C3⋊D3C2412yes—
350C22×C3⋊D3C2412yes—
351C22×C3×D3—22no—
352C22×C3×D3—22no—
353C22×C3×D3—41no—
354C22×C3×D3C2411yescharacteristic
355C22×C3×D3C2412yes—
356C22×C3×D3C2411yescharacteristic
357C2×D32—24no—
358C2×D32—24no—
359C2×D32—42no—
360C2×C32×C4—42no—
361C2×C32×C4C2×D414yes—
362C2×C32×C4C2414yes—
363C2×C32×C4C2411yescharacteristic
364C2×C32×C4C2411yescharacteristic
365#638—24no—
366#638—24no—
367C2×C3⋊Dic3C2412yes—
368C2×C3⋊Dic3C2412yes—
369C4⋊(C3⋊D3)—22no—
370C4⋊(C3⋊D3)—22no—
371C4⋊(C3⋊D3)—44no—
372C4×C3⋊D3—24no—
373C4×C3⋊D3—24no—
374#634—22no—
375#634—22no—
376C3×#67C2×D418yes—
377C2×C3×Dic3—24no—
378C2×C3×Dic3—22no—
379C2×C3×Dic3C2412yes—
380C2×C3×Dic3C2412yes—
381C2×C3×Dic3C2411yescharacteristic
382C2×C3×Dic3C2411yescharacteristic
383C2×C3×Dic3C2414yes—
384C2×C3×Dic3C2412yes—
385C3×D12C2×D414yes—
386C3×C4×D3—22no—
387C3×C4×D3—22no—
388C3×C4×D3—22no—
389C3×C4×D3—22no—
390C3×C4×D3—44no—
391C3×C4×D3C2×D418yes—
392C3×Dic6—24no—
393C3×Dic6—24no—
394C3×Dic6C2×D414yes—
395#627—28no—
396#627—24no—
397#626—28no—
398#626—24no—
399#626—24no—
400#626—24no—
401#626—42no—
402#625—24no—
403#624—28no—
404#624—24no—
405D3×Dic3—28no—
406D3×Dic3—24no—
407D3×Dic3—24no—
408C2×2−1+4—91no—
409C22×#41—91no—
410D4×Q8—92no—
411#548—92no—
412#547—94no—
413#547—92no—
414#546—94no—
415#546—92no—
416#537—92no—
417#537—91no—
418#536—92no—
419#536—91no—
420#525—92no—
421#525—91no—
422C2×C22⋊Q8—31no—
423C2×C22⋊Q8—92no—
424#520—31no—
425C24×C3—31no—
426C23×D3—32no—
427C23×D3—32no—
428C23×D3C22×D311yescharacteristic
429C3×#41—38no—
430C2×C3×Q8—31no—
431C2×C3×Q8—32no—
432C2×C3×Q8—32no—
433C2×C3×Q8—64no—
434C2×C3×D4—32no—
435C2×C3×D4—31no—
436C22×C3×C4—21no—
437C22×C3×C4—22no—
438C22×C3×C4—32no—
439C22×C3×C4—32no—
440C22×C3×C4—31no—
441C22×C3×C4—31no—
442C22×C3×C4—31no—
443C22×C3×C4—31no—
444C22×C3×C4—31no—
445C22×C3×C4—34no—
446C22×C3×C4—64no—
447C22×C3×C4C22×D312yes—
448C22×C3×C4C22×D312yes—
449C22×C3×C4C22×D311yescharacteristic
450C22×C3×C4C22×D311yescharacteristic
451C2×#67—32no—
452C2×#67—32no—
453C2×#67—32no—
454C2×#67—32no—
455C2×#67—32no—
456C2×#67—32no—
457C2×#67—32no—
458C2×#67—34no—
459C2×#67—32no—
460C2×#67—32no—
461C2×#67—32no—
462C2×#67—62no—
463C2×#67—62no—
464C2×#67—68no—
465C2×#67C22×D312yes—
466C22×Dic3—32no—
467C22×Dic3—32no—
468C22×Dic3—34no—
469C22×Dic3C22×D311yescharacteristic
470C22×Dic3C22×D312yes—
471#239—64no—
472#239—68no—
473#239—68no—
474D3×Q8—68no—
475D3×Q8—64no—
476D3×Q8—68no—
477D3×Q8—68no—
478#237—68no—
479#237—64no—
480#237—68no—
481#237—616no—
482D3×D4—64no—
483D3×D4—68no—
484#235—68no—
485#235—68no—
486#235—64no—
487#235—64no—
488#235—64no—
489#235—64no—
490#235—68no—
491#235—616no—
492#235—64no—
493#235—68no—
494#235—64no—
495#235—124no—
496#235—124no—
497#235D1218yescomplemented
498C2×D12—32no—
499C2×D12—32no—
500C2×D12—34no—
501C2×D12—32no—
502C2×D12—31no—
503C2×D12—31no—
504C2×D12—31no—
505C2×D12—31no—
506C2×D12—32no—
507C2×D12—34no—
508C2×D12—34no—
509C2×D12—61no—
510C2×D12—61no—
511C2×D12—64no—
512C2×D12—64no—
513C2×D12C22×D311yescharacteristic
514C2×C4×D3—24no—
515C2×C4×D3—32no—
516C2×C4×D3—34no—
517C2×C4×D3—32no—
518C2×C4×D3—32no—
519C2×C4×D3—32no—
520C2×C4×D3—32no—
521C2×C4×D3—32no—
522C2×C4×D3—34no—
523C2×C4×D3—32no—
524C2×C4×D3—34no—
525C2×C4×D3—32no—
526C2×C4×D3—62no—
527C2×C4×D3—62no—
528C2×C4×D3—68no—
529C2×C4×D3—68no—
530C2×C4×D3C22×D311yescharacteristic
531C2×C4×D3C22×D311yescharacteristic
532C2×C4×D3C22×D311yescharacteristic
533C2×C4×D3C22×D311yescharacteristic
534C2×C4×D3C22×D314yes—
535C2×C4×D3C22×D312yes—
536C2×Dic6—24no—
537C2×Dic6—31no—
538C2×Dic6—31no—
539C2×Dic6—31no—
540C2×Dic6—31no—
541C2×Dic6—32no—
542C2×Dic6—34no—
543C2×Dic6—34no—
544C2×Dic6—32no—
545C2×Dic6—61no—
546C2×Dic6—61no—
547C2×Dic6—68no—
548C2×Dic6—64no—
549C2×Dic6C22×D312yes—
550C2×Dic6C22×D312yes—
551C2×Dic6C22×D311yescharacteristic
552C3×C4⋊C4—22no—
553C3×C4⋊C4—22no—
554C3×C4⋊C4—34no—
555C3×C4⋊C4—34no—
556C3×C4⋊C4—34no—
557C3×C4⋊C4—31no—
558C3×C4⋊C4—31no—
559C3×C4⋊C4C22×D312yes—
560C3×C4⋊C4C22×D312yes—
561C3×C4⋊C4C22×D312yes—
562C3×C4⋊C4C22×D312yes—
563C3×C22⋊C4—32no—
564C3×C22⋊C4—34no—
565C3×C22⋊C4—34no—
566C3×C22⋊C4—34no—
567C3×C42—34no—
568C3×C42—32no—
569#217—32no—
570#217—32no—
571#217C22×D312yes—
572(C2×D3)⋊C4—32no—
573(C2×D3)⋊C4—32no—
574(C2×D3)⋊C4—34no—
575(C2×D3)⋊C4—34no—
576(C2×D3)⋊C4—34no—
577(C2×D3)⋊C4—34no—
578(C2×D3)⋊C4—32no—
579(C2×D3)⋊C4—34no—
580(C2×D3)⋊C4—32no—
581(C2×D3)⋊C4—34no—
582(C2×D3)⋊C4—34no—
583(C2×D3)⋊C4—34no—
584(C2×D3)⋊C4—32no—
585(C2×D3)⋊C4—32no—
586(C2×D3)⋊C4—64no—
587(C2×D3)⋊C4—64no—
588(C2×D3)⋊C4C22×D314yes—
589(C2×D3)⋊C4C22×D314yes—
590(C2×D3)⋊C4C22×D314yes—
591C4⋊Dic3—34no—
592C4⋊Dic3—34no—
593C4⋊Dic3—34no—
594C4⋊Dic3—32no—
595C4⋊Dic3—34no—
596C4⋊Dic3—32no—
597C4⋊Dic3—64no—
598C4⋊Dic3C22×D314yes—
599C4⋊Dic3C22×D314yes—
600C4⋊Dic3C22×D311yescharacteristic
601C4⋊Dic3C22×D311yescharacteristic
602Dic3⋊C4—34no—
603Dic3⋊C4—34no—
604Dic3⋊C4—32no—
605Dic3⋊C4—32no—
606Dic3⋊C4C22×D314yes—
607C4×Dic3C22×D314yes—
608C4×Dic3C22×D312yes—
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—22no—
617C2×C3⋊D3—22no—
618C2×C3⋊D3—22no—
619C2×C3×D3—21no—
620C2×C3×D3—22no—
621C2×C3×D3—22no—
622C2×C3×D3—21no—
623C2×C3×D3—21no—
624C2×C3×D3—21no—
625C2×C3×D3—21no—
626C2×C3×D3—44no—
627C2×C3×D3C22×D414yes—
628C2×C3×D32−1+412yescomplemented
629D32—48no—
630C32×C4—24no—
631C32×C4C22×D412yes—
632C32×C4C22×D412yes—
633C3⋊Dic3—22no—
634C3⋊Dic3—22no—
635C3×Dic3—21no—
636C3×Dic3—24no—
637C3×Dic3—21no—
638C3×Dic3—22no—
639C3×Dic3—22no—
640C3×Dic3C22×D414yes—
6412−1+4—188no—
642C2×#41—31no—
643C2×#41—92no—
644C2×#41—94no—
645C2×#41—92no—
646C2×#41—91no—
647C2×#41—92no—
648C2×#41—91no—
649C2×#41—92no—
650C2×#41—91no—
651C2×#41—91no—
652C2×#41—188no—
653C22×Q8—31no—
654C22×Q8—92no—
655C22×Q8—91no—
656C22×Q8—92no—
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—94no—
666#123—94no—
667#123—94no—
668#123—92no—
669#123—94no—
670C22⋊Q8—32no—
671C22⋊Q8—32no—
672C22⋊Q8—32no—
673C22⋊Q8—32no—
674C22⋊Q8—94no—
675C22⋊Q8—94no—
676C22⋊Q8—94no—
677C22⋊Q8—91no—
678C22⋊Q8—91no—
679C22⋊Q8—92no—
680C22⋊Q8—92no—
681C22⋊Q8—92no—
682C22⋊Q8—92no—
683#121—94no—
684#121—94no—
685#121—91no—
686#121—91no—
687#121—94no—
688#121—94no—
689#121—92no—
690#121—92no—
691#120—94no—
692#120—92no—
693C4×Q8—32no—
694C4×D4—34no—
695C4×D4—32no—
696C4×D4—94no—
697C4×D4—94no—
698C4×D4—92no—
699C4×D4—92no—
700#117—31no—
701#117—32no—
702C2×C4⋊C4—32no—
703C2×C4⋊C4—32no—
704C2×C4⋊C4—94no—
705C2×C4⋊C4D3211yescharacteristic, complemented
706C2×C22⋊C4—32no—
707C2×C22⋊C4—94no—
708C23×C3—21no—
709C23×C3—31no—
710C23×C3—32no—
711C23×C3—31no—
712C23×C3—62no—
713C23×C3—62no—
714C23×C3—121no—
715C23×C3C23×D311yescharacteristic
716C23×C3C23×D311yescharacteristic
717C22×D3—22no—
718C22×D3—22no—
719C22×D3—32no—
720C22×D3—32no—
721C22×D3—32no—
722C22×D3—32no—
723C22×D3—41no—
724C22×D3—62no—
725C22×D3—62no—
726C22×D3—64no—
727C22×D3—64no—
728C22×D3—64no—
729C22×D3—64no—
730C22×D3—122no—
731C22×D3—122no—
732C22×D3C23×D311yescharacteristic
733C22×D3C23×D312yes—
734C22×D3C23×D311yescharacteristic
735C3×Q8—34no—
736C3×Q8—64no—
737C3×Q8—64no—
738C3×D4—38no—
739C3×D4—34no—
740C2×C3×C4—21no—
741C2×C3×C4—21no—
742C2×C3×C4—24no—
743C2×C3×C4—24no—
744C2×C3×C4—32no—
745C2×C3×C4—38no—
746C2×C3×C4—34no—
747C2×C3×C4—31no—
748C2×C3×C4—31no—
749C2×C3×C4—32no—
750C2×C3×C4—32no—
751C2×C3×C4—42no—
752C2×C3×C4—42no—
753C2×C3×C4—62no—
754C2×C3×C4—64no—
755C2×C3×C4—62no—
756C2×C3×C4—62no—
757C2×C3×C4—62no—
758C2×C3×C4—62no—
759C2×C3×C4—82no—
760C2×C3×C4—124no—
761C2×C3×C4C2×D1214yes—
762C2×C3×C4D3×D414yes—
763C2×C3×C4C23×D314yes—
764C2×C3×C4C23×D314yes—
765C2×C3×C4C23×D311yescharacteristic
766C2×C3×C4C23×D311yescharacteristic
767C2×C3×C4C23×D311yescharacteristic
768C2×C3×C4C23×D311yescharacteristic
769#67—64no—
770#67—68no—
771#67—64no—
772#67—64no—
773#67—64no—
774#67—64no—
775#67—64no—
776#67—64no—
777#67—64no—
778#67—64no—
779#67—124no—
780#67—124no—
781#67—122no—
782#67C2×D1218yes—
783C2×Dic3—24no—
784C2×Dic3—22no—
785C2×Dic3—32no—
786C2×Dic3—32no—
787C2×Dic3—32no—
788C2×Dic3—32no—
789C2×Dic3—62no—
790C2×Dic3—62no—
791C2×Dic3—68no—
792C2×Dic3—64no—
793C2×Dic3—64no—
794C2×Dic3C23×D312yes—
795C2×Dic3C23×D312yes—
796C2×Dic3C23×D311yescharacteristic
797C2×Dic3C23×D311yescharacteristic
798C2×Dic3C23×D314yes—
799C2×Dic3C23×D312yes—
800D12—64no—
801D12—64no—
802D12—68no—
803D12—64no—
804D12—62no—
805D12—62no—
806D12—62no—
807D12—62no—
808D12—122no—
809D12—122no—
810D12—124no—
811D12—124no—
812D12—122no—
813D12—244no—
814D12C2×D1214yes—
815C4×D3—22no—
816C4×D3—22no—
817C4×D3—22no—
818C4×D3—22no—
819C4×D3—44no—
820C4×D3—64no—
821C4×D3—68no—
822C4×D3—64no—
823C4×D3—64no—
824C4×D3—68no—
825C4×D3—64no—
826C4×D3—64no—
827C4×D3—64no—
828C4×D3—64no—
829C4×D3—64no—
830C4×D3—68no—
831C4×D3—124no—
832C4×D3—124no—
833C4×D3C2×D1218yes—
834Dic6—24no—
835Dic6—24no—
836Dic6—68no—
837Dic6—64no—
838Dic6—62no—
839Dic6—62no—
840Dic6—62no—
841Dic6—62no—
842Dic6—64no—
843Dic6—68no—
844Dic6—122no—
845Dic6—122no—
846Dic6C2×D1214yes—
847C2×C32—22no—
848C2×C32C23×D411yescharacteristic
849C2×C32C2×2−1+411yescharacteristic
850C2×C32#58511yescharacteristic
851C3⋊D3—42no—
852C3⋊D3—42no—
853C3×D3—22no—
854C3×D3—24no—
855C3×D3—41no—
856C24—31no—
857C24—92no—
858#41—38no—
859#41—188no—
860#41—188no—
861#41—188no—
862#41—184no—
863#41—1816no—
864#41—184no—
865#41—188no—
866#41—184no—
867#41—184no—
868C2×Q8—31no—
869C2×Q8—32no—
870C2×Q8—32no—
871C2×Q8—64no—
872C2×Q8—94no—
873C2×Q8—92no—
874C2×Q8—91no—
875C2×Q8—91no—
876C2×Q8—188no—
877C2×Q8—184no—
878C2×Q8—188no—
879C2×D4—32no—
880C2×D4—31no—
881C2×D4—92no—
882C2×D4—94no—
883C2×D4—92no—
884C2×D4—92no—
885C2×D4—92no—
886C2×D4—92no—
887C2×D4—92no—
888C2×D4—92no—
889C2×D4—91no—
890C2×D4—91no—
891C2×D4—94no—
892C2×D4—184no—
893C2×D4—188no—
894C22×C4—32no—
895C22×C4—32no—
896C22×C4—31no—
897C22×C4—31no—
898C22×C4—31no—
899C22×C4—31no—
900C22×C4—31no—
901C22×C4—34no—
902C22×C4—64no—
903C22×C4—94no—
904C22×C4—92no—
905C22×C4—94no—
906C22×C4—92no—
907C22×C4—92no—
908C22×C4—92no—
909C22×C4—92no—
910C22×C4—188no—
911C22×C4C2×D3212yes—
912C22×C4C2×D3211yescharacteristic
913C4⋊C4—31no—
914C4⋊C4—34no—
915C4⋊C4—34no—
916C4⋊C4—34no—
917C4⋊C4—31no—
918C4⋊C4—92no—
919C4⋊C4—94no—
920C4⋊C4—94no—
921C4⋊C4—92no—
922C4⋊C4—94no—
923C4⋊C4C2×D3212yes—
924C4⋊C4C2×D3212yes—
925C22⋊C4—32no—
926C22⋊C4—34no—
927C22⋊C4—34no—
928C22⋊C4—34no—
929C22⋊C4—94no—
930C22⋊C4—92no—
931C22⋊C4—94no—
932C22⋊C4—92no—
933C22⋊C4—92no—
934C22⋊C4—92no—
935C22⋊C4—94no—
936C22⋊C4—94no—
937C42—34no—
938C42—32no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—22no—
944C22×C3—21no—
945C22×C3—34no—
946C22×C3—32no—
947C22×C3—41no—
948C22×C3—41no—
949C22×C3—61no—
950C22×C3—62no—
951C22×C3—62no—
952C22×C3—61no—
953C22×C3—61no—
954C22×C3—61no—
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—21no—
967C2×D3—21no—
968C2×D3—44no—
969C2×D3—62no—
970C2×D3—62no—
971C2×D3—62no—
972C2×D3—62no—
973C2×D3—62no—
974C2×D3—62no—
975C2×D3—62no—
976C2×D3—62no—
977C2×D3—62no—
978C2×D3—62no—
979C2×D3—62no—
980C2×D3—62no—
981C2×D3—122no—
982C2×D3—122no—
983C2×D3—122no—
984C2×D3—122no—
985C2×D3—122no—
986C2×D3—122no—
987C2×D3—128no—
988C2×D3—128no—
989C2×D3C22×D1214yes—
990C2×D3#100712yescomplemented
991C3×C4—24no—
992C3×C4—24no—
993C3×C4—22no—
994C3×C4—22no—
995C3×C4—34no—
996C3×C4—44no—
997C3×C4—61no—
998C3×C4—64no—
999C3×C4—61no—
1000C3×C4—62no—
1001C3×C4—62no—
1002C3×C4C22×D1212yes—
1003C3×C4C22×D1212yes—
1004C3×C4C2×D3×D412yes—
1005C3×C4C2×D3×D412yes—
1006Dic3—24no—
1007Dic3—21no—
1008Dic3—21no—
1009Dic3—22no—
1010Dic3—22no—
1011Dic3—62no—
1012Dic3—62no—
1013Dic3—62no—
1014Dic3—62no—
1015Dic3—122no—
1016Dic3—122no—
1017Dic3C22×D1214yes—
1018C32#348911yescharacteristic, complemented, Sylow
1019C23—31no—
1020C23—32no—
1021C23—31no—
1022C23—62no—
1023C23—62no—
1024C23—92no—
1025C23—92no—
1026C23—121no—
1027C23—184no—
1028C23—184no—
1029C23—362no—
1030C23C22×D3211yescharacteristic
1031Q8—34no—
1032Q8—64no—
1033Q8—64no—
1034Q8—188no—
1035Q8—184no—
1036Q8—182no—
1037Q8—182no—
1038D4—38no—
1039D4—34no—
1040D4—184no—
1041D4—184no—
1042D4—188no—
1043D4—184no—
1044D4—184no—
1045D4—184no—
1046D4—184no—
1047D4—182no—
1048D4—182no—
1049D4—364no—
1050D4—362no—
1051C2×C4—32no—
1052C2×C4—38no—
1053C2×C4—32no—
1054C2×C4—32no—
1055C2×C4—34no—
1056C2×C4—31no—
1057C2×C4—31no—
1058C2×C4—42no—
1059C2×C4—62no—
1060C2×C4—64no—
1061C2×C4—62no—
1062C2×C4—62no—
1063C2×C4—62no—
1064C2×C4—62no—
1065C2×C4—92no—
1066C2×C4—92no—
1067C2×C4—124no—
1068C2×C4—184no—
1069C2×C4—188no—
1070C2×C4—184no—
1071C2×C4—184no—
1072C2×C4—188no—
1073C2×C4—184no—
1074C2×C4—184no—
1075C2×C4D3×D1214yes—
1076C2×C4C22×D3214yes—
1077C2×C4C22×D3211yescharacteristic
1078C2×C4C22×D3211yescharacteristic
1079C2×C3—22no—
1080C2×C3—22no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—42no—
1085C2×C3—62no—
1086C2×C3—64no—
1087C2×C3—121no—
1088C2×C3C23×D1211yescharacteristic
1089C2×C3C22×D3×D411yescharacteristic
1090C2×C3C2×#100711yescharacteristic
1091C2×C3#596411yescharacteristic
1092C2×C3#596611yescharacteristic
1093C2×C3D3×2−1+411yescharacteristic
1094D3—24no—
1095D3—22no—
1096D3—41no—
1097D3—122no—
1098D3—122no—
1099D3—122no—
1100D3—122no—
1101D3—242no—
1102D3—242no—
1103C22—21no—
1104C22—21no—
1105C22—34no—
1106C22—32no—
1107C22—61no—
1108C22—62no—
1109C22—61no—
1110C22—62no—
1111C22—61no—
1112C22—61no—
1113C22—61no—
1114C22—124no—
1115C22—182no—
1116C22—182no—
1117C22—182no—
1118C22—182no—
1119C22—182no—
1120C22—182no—
1121C22—368no—
1122C22C2×D3×D1212yes—
1123C22C23×D3211yescharacteristic
1124C4—24no—
1125C4—34no—
1126C4—61no—
1127C4—61no—
1128C4—64no—
1129C4—62no—
1130C4—62no—
1131C4—182no—
1132C4—182no—
1133C4C2×D3×D1212yes—
1134C4C2×D3×D1212yes—
1135C3—21no—
1136C3#8590111yescharacteristic, complemented
1137C3#8598511yescharacteristic, complemented
1138C2—22no—
1139C2—62no—
1140C2—64no—
1141C2—121no—
1142C2—362no—
1143C2—362no—
1144C2C22×D3×D1211yescharacteristic
1145C2#1059667811yescharacteristic
1146C2D3×#100711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#235C2semidirect
2. C2×#64297C2semidirect
3. #10595981C2semidirect
4. C2×C3×#897C2semidirect
5. C3×#5504C2semidirect
6. #10595073C2semidirect
7. #10595023C2semidirect
8. #10594906C2semidirect
9. #10594866C2semidirect
10. #10594629C2semidirect
11. #10594627C2semidirect
12. D3×#897C2semidirect
13. #10594523C2semidirect
14. #10594383C2semidirect
15. #10594381C2semidirect
16. #10594380C2semidirect
17. #10594329C2semidirect
21. C2×#3828C22semidirect
24. C22×C3×Dic6C22semidirect
27. C2×#3804C22semidirect
32. C2×#3799C22semidirect
34. C2×#3797C22semidirect
36. C2×#3796C22semidirect
39. C2×D3×Dic6C22semidirect
40. C2×C32×C4⋊C4C22semidirect
41. #64139C22semidirect
42. #64106C22semidirect
43. #64106C22semidirect
44. #64104C22semidirect
45. #64104C22semidirect
46. C3×C4×#67C22semidirect
48. C3×#926C22semidirect
49. C2×C3×C4⋊Dic3C22semidirect
52. C3×#897C22semidirect
53. C3×#897C22semidirect
54. C3×#893C22semidirect
55. C3×#892C22semidirect
56. C3×D3×C4⋊C4C22semidirect
57. C3×#887C22semidirect
59. #63966C22semidirect
60. #63966C22semidirect
63. #63918C22semidirect
64. #63910C22semidirect
66. #63909C22semidirect
67. #63909C22semidirect
68. #63906C22semidirect
70. C4×#626C22semidirect
71. #63895C22semidirect
72. #63895C22semidirect
73. #63894C22semidirect
75. #63891C22semidirect
76. #63890C22semidirect
77. #63890C22semidirect
78. D3×C4⋊Dic3C22semidirect
80. #63871C22semidirect
81. #63871C22semidirect
82. #63866C22semidirect
83. #63864C22semidirect
85. #63857C22semidirect
86. #63852C22semidirect
118. C2×#897D3semidirect
120. #5504D3semidirect
140. C3×#235D4semidirect
247. C22×Dic6C2×D3semidirect
260. C2×C3×C4⋊C4C2×D3semidirect
261. C2×C3×C4⋊C4C2×D3semidirect
279. C4×#67C2×D3semidirect
282. #926C2×D3semidirect
284. C2×C4⋊Dic3C2×D3semidirect
302. #897C2×D3semidirect
303. #897C2×D3semidirect
319. #893C2×D3semidirect
320. #892C2×D3semidirect
322. D3×C4⋊C4C2×D3semidirect
324. #887C2×D3semidirect
497. #235D12semidirect
628. C2×C3×D32−1+4semidirect
705. C2×C4⋊C4D32semidirect
990. C2×D3#1007semidirect
1018. C32#3489semidirect
1136. C3#85901semidirect
1137. C3#85985semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2352
C2×#642972
#105959812
C2×C3×#8972
C3×#55042
#105950732
#105950232
#105949062
#105948662
#105946292
#105946272
D3×#8972
#105945232
#105943832
#105943812
#105943802
#105943292
#859853
#859013