Finite Group Databasebeta

← #11904657

Subgroups — #11904657

Order 1152.

3463 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C211yesmaximal, characteristic, complemented
2C2×D3×#235C211yesmaximal, characteristic, complemented
3#10595981C211yesmaximal, characteristic, complemented
4C2×C3×#895C211yesmaximal, characteristic, complemented
5C3×#5504C211yesmaximal, characteristic, complemented
6#10595073C214yesmaximal, complemented
7D12×#67C214yesmaximal, complemented
8#10595042C211yesmaximal, characteristic, complemented
9#10595023C211yesmaximal, characteristic, complemented
10#10594630C212yesmaximal, complemented
11#10594628C212yesmaximal, complemented
12#10594626C212yesmaximal, complemented
13#10594621C212yesmaximal, complemented
14D3×#895C212yesmaximal, complemented
15#10594524C212yesmaximal, complemented
16#10594522C212yesmaximal, complemented
17#10594382C212yesmaximal, complemented
18#85949—31nomaximal
19#85900—31nomaximal
20C2×#3828C2211yescharacteristic, complemented
21C2×#3828C2211yescharacteristic, complemented
22C2×C3×#235C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic, complemented
24C22×C3×D12C2212yescomplemented
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C2×D3×#67C2214yescomplemented
27C2×D3×#67C2212yescomplemented
28C2×#3804C2212yescomplemented
29#64307—28no—
30D3×#235—28no—
31C2×#3802C2212yescomplemented
32C2×D3×D12C2212yescomplemented
33C2×D3×D12C2211yescharacteristic, complemented
34C2×D3×D12C2214yescomplemented
35C2×C4×D32C2212yescomplemented
36C2×#3799C2211yescharacteristic, complemented
37C2×#3798C2212yescomplemented
38C2×#3796C2212yescomplemented
39C2×#3795C2211yescharacteristic, complemented
40C2×#3795C2212yescomplemented
41C2×D3×Dic6C2211yescharacteristic, complemented
42C2×C32×C4⋊C4C2211yescharacteristic, complemented
43#64139C2214yescomplemented
44#64106C2212yescomplemented
45#64106C2212yescomplemented
46#64104C2212yescomplemented
47#64104C2212yescomplemented
48C3×C4×#67C2214yescomplemented
49C2×C3×(C2×D3)⋊C4C2212yescomplemented
50C3×#926C2211yescharacteristic, complemented
51C3×#895C2212yescomplemented
52C3×#895C2212yescomplemented
53C3×#895C2212yescomplemented
54C3×#895C2212yescomplemented
55C3×#893C2212yescomplemented
56C3×#892C2212yescomplemented
57C3×D3×C4⋊C4C2212yescomplemented
58C3×#887C2212yescomplemented
59#63977C2214yescomplemented
60#63977C2212yescomplemented
61#63966C2212yescomplemented
62#63923C2214yescomplemented
63#63922C2214yescomplemented
64#63922C2214yescomplemented
65D3×(C2×D3)⋊C4C2214yescomplemented
66#63916C2212yescomplemented
67#63916C2212yescomplemented
68#63911C2212yescomplemented
69#63911C2214yescomplemented
70#63910C2214yescomplemented
71#63909C2211yescharacteristic, complemented
72#63909C2211yescharacteristic, complemented
73#63908C2214yescomplemented
74#63906C2214yescomplemented
75C4×#626C2212yescomplemented
76C4×#626C2212yescomplemented
77#63893C2214yescomplemented
78Dic3×D12C2214yescomplemented
79#63891C2214yescomplemented
80#63886C2214yescomplemented
81#63886C2214yescomplemented
82#63880C2214yescomplemented
83#63860C2212yescomplemented
84#63857C2211yescharacteristic, complemented
85#63857C2211yescharacteristic, complemented
86#63852C2214yescomplemented
87C2×#1009—31no—
88C2×D3×#41—31no—
89C2×#1004—31no—
90C22×#235—31no—
91C2×C3×#121—31no—
92C3×#520—31no—
93#5805—31no—
94D4×#67—34no—
95#5791—31no—
96#5612—32no—
97#5609—32no—
98#5608—32no—
99#5607—32no—
100#5606—32no—
101D3×#121—32no—
102#5599—32no—
103#5598—32no—
104#5577—32no—
105#5576—32no—
106#5554—34no—
107#5554—32no—
108D4×D12—34no—
109D4×D12—32no—
110#5525—31no—
111#5525—32no—
112#5524—31no—
113#5524—32no—
114#5510—31no—
115#5510—31no—
116#5510—32no—
117#5510—61no—
118C2×#895—32no—
119C2×#895D311yescharacteristic, complemented
120#5504D311yescharacteristic, complemented
121#5490—34no—
122C23×C3×D3C2311yescharacteristic
123C23×C3×D3C2312yes—
124C22×D32C2312yes—
125C22×D32C2314yes—
126C22×C32×C4C2312yes—
127C22×C32×C4C2311yescharacteristic
128C2×#638C2312yes—
129C2×#638C2312yes—
130#3828—24no—
131#3828—24no—
132C2×C4⋊(C3⋊D3)C2311yescharacteristic
133C2×C4⋊(C3⋊D3)C2311yescharacteristic
134C2×C4⋊(C3⋊D3)C2314yes—
135C2×C4×C3⋊D3C2312yes—
136C2×C4×C3⋊D3C2312yes—
137C2×#634C2311yescharacteristic
138C2×#634C2311yescharacteristic
139C2×C3×#67C2312yes—
140C22×C3×Dic3C2311yescharacteristic
141C3×#235D418yescomplemented
142C2×C3×D12—24no—
143C2×C3×D12—44no—
144C2×C3×D12C2312yes—
145C2×C3×D12C2312yes—
146C2×C3×D12C2314yes—
147C2×C3×D12C2314yes—
148C2×C3×D12C2311yescharacteristic
149C2×C3×C4×D3—24no—
150C2×C3×C4×D3C2311yescharacteristic
151C2×C3×C4×D3C2311yescharacteristic
152C2×C3×C4×D3C2311yescharacteristic
153C2×C3×C4×D3C2311yescharacteristic
154C2×C3×C4×D3C2314yes—
155C2×C3×C4×D3C2312yes—
156C2×C3×Dic6C2311yescharacteristic
157D3×#67—28no—
158D3×#67—216no—
159C2×#627C2312yes—
160C2×#626C2314yes—
161C2×#626C2312yes—
162C2×#626C2312yes—
163C2×#626C2312yes—
164C2×#626C2314yes—
165C2×#626C2314yes—
166C2×#626C2312yes—
167C2×#625C2312yes—
168C2×#625C2314yes—
169C2×#624C2312yes—
170#3804—28no—
171C2×D3×Dic3C2312yes—
172C2×D3×Dic3C2314yes—
173C2×D3×Dic3C2312yes—
174#3802—28no—
175D3×D12—24no—
176D3×D12—28no—
177D3×D12—48no—
178C4×D32—28no—
179#3799—24no—
180#3798—28no—
181#3796—28no—
182#3795—24no—
183#3795—28no—
184D3×Dic6—24no—
185C32×C4⋊C4C2312yes—
186C32×C4⋊C4C2312yes—
187#3752C2314yes—
188#3752C2314yes—
189C4⋊(C3⋊Dic3)C2314yes—
190C3×#217C2312yes—
191C3×(C2×D3)⋊C4C2314yes—
192C3×(C2×D3)⋊C4C2314yes—
193C3×(C2×D3)⋊C4C2314yes—
194C3×C4⋊Dic3C2311yescharacteristic
195C3×C4⋊Dic3C2311yescharacteristic
196C3×Dic3⋊C4C2314yes—
197C3×C4×Dic3C2314yes—
198C3×C4×Dic3C2312yes—
199Dic3⋊Dic3C2312yes—
200Dic3⋊Dic3C2312yes—
201#3722C2312yes—
202#3722C2312yes—
203(C2×D3)⋊Dic3C2314yes—
204(C2×D3)⋊Dic3C2312yes—
205(C2×D3)⋊Dic3C2312yes—
206(C2×D3)⋊Dic3C2314yes—
207#3488—91noSylow
208C2×C3×#41—31no—
209C22×C3×D4—31no—
210C22×C3×D4—32no—
211C23×C3×C4—31no—
212C22×#67—32no—
213C22×#67—34no—
214#1009—68no—
215D3×#41—68no—
216C2×#239—32no—
217C2×#239—31no—
218C2×D3×Q8—31no—
219#1004—68no—
220C2×#237—32no—
221C2×#237—32no—
222C2×#237—31no—
223C2×#237—32no—
224C2×D3×D4—32no—
225C2×D3×D4—34no—
226C2×D3×D4—32no—
227C2×D3×D4—32no—
228C2×D3×D4—32no—
229C2×D3×D4—31no—
230C2×D3×D4—34no—
231C2×#235—31no—
232C2×#235—31no—
233C2×#235—31no—
234C2×#235—31no—
235C2×#235—32no—
236C2×#235—31no—
237C2×#235—32no—
238C2×#235—32no—
239C2×#235—32no—
240C2×#235—31no—
241C2×#235—61no—
242C2×#235—61no—
243C2×#235—68no—
244C2×#235C2×D311yescharacteristic
245C22×D12—31no—
246C22×D12—32no—
247C22×D12—34no—
248C22×D12C2×D311yescharacteristic, complemented
249C22×D12C2×D312yescomplemented
250C22×C4×D3—32no—
251C22×C4×D3—32no—
252C22×C4×D3C2×D311yescharacteristic, complemented
253C22×Dic6—31no—
254C3×#121—32no—
255C3×#121—32no—
256C3×#121—32no—
257C3×#121—32no—
258C3×C4×Q8—32no—
259C3×C4×D4—34no—
260C3×C4×D4—32no—
261C3×#117—31no—
262C3×#117—32no—
263C2×C3×C4⋊C4—21no—
264C2×C3×C4⋊C4—32no—
265C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
266C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
267C2×C3×C22⋊C4—32no—
268#953—34no—
269#953—32no—
270#940—34no—
271#940—32no—
272#939—34no—
273#939—34no—
274#938—34no—
275#938—32no—
276#938—32no—
277#937—34no—
278#937—34no—
279#936—32no—
280D4×Dic3—34no—
281#930—34no—
282#930—34no—
283#930—34no—
284#930—34no—
285#930—31no—
286#930—31no—
287#930—64no—
288#929—32no—
289C4×#67—32no—
290C4×#67—32no—
291C4×#67C2×D314yescomplemented
292C2×(C2×D3)⋊C4—34no—
293C2×(C2×D3)⋊C4C2×D312yescomplemented
294#926C2×D311yescharacteristic, complemented
295#924—31no—
296#924—31no—
297#897—31no—
298#897—31no—
299#897—32no—
300#897—32no—
301#897—32no—
302#897—32no—
303#897—34no—
304#897—62no—
305#897—62no—
306#895—32no—
307#895—34no—
308#895—34no—
309#895—32no—
310#895—31no—
311#895—31no—
312#895—32no—
313#895—32no—
314#895—32no—
315#895—32no—
316#895—34no—
317#895—62no—
318#895—62no—
319#895C2×D312yescomplemented
320#895C2×D312yescomplemented
321#895C2×D312yescomplemented
322#895C2×D312yescomplemented
323#893C2×D312yescomplemented
324#892C2×D312yescomplemented
325D3×C4⋊C4C2×D312yescomplemented
326#887C2×D312yescomplemented
327#886—32no—
328#886—34no—
329#885—34no—
330#884—34no—
331#884—34no—
332#883—34no—
333#882—32no—
334#882—34no—
335#882—34no—
336#882—34no—
337#882—34no—
338#882—34no—
339#67⋊C4—34no—
340D3×C22⋊C4—34no—
341#878—34no—
342#875—32no—
343#875—34no—
344#874—34no—
345#874—32no—
346C4×D12—34no—
347C4×D12—32no—
348C4×D12—32no—
349C4×D12—34no—
350C23×C32C2411yescharacteristic
351C22×C3⋊D3C2412yes—
352C22×C3⋊D3C2412yes—
353C22×C3×D3—22no—
354C22×C3×D3—24no—
355C22×C3×D3—22no—
356C22×C3×D3—41no—
357C22×C3×D3—42no—
358C22×C3×D3—42no—
359C22×C3×D3C2414yes—
360C22×C3×D3C2411yescharacteristic
361C22×C3×D3C2412yes—
362C22×C3×D3C2411yescharacteristic
363C2×D32—24no—
364C2×D32—24no—
365C2×D32—28no—
366C2×D32—42no—
367C2×D32—44no—
368C2×D32—44no—
369C2×C32×C4—42no—
370C2×C32×C4C2×D414yescomplemented
371C2×C32×C4C2414yes—
372C2×C32×C4C2411yescharacteristic
373C2×C32×C4C2411yescharacteristic
374#638—24no—
375#638—24no—
376C2×C3⋊Dic3C2412yes—
377C2×C3⋊Dic3C2412yes—
378C4⋊(C3⋊D3)—22no—
379C4⋊(C3⋊D3)—22no—
380C4⋊(C3⋊D3)—44no—
381C4×C3⋊D3—24no—
382C4×C3⋊D3—24no—
383#634—22no—
384#634—22no—
385C3×#67C2×D418yescomplemented
386C2×C3×Dic3—22no—
387C2×C3×Dic3C2412yes—
388C2×C3×Dic3C2412yes—
389C2×C3×Dic3C2411yescharacteristic
390C2×C3×Dic3C2411yescharacteristic
391C2×C3×Dic3C2412yes—
392C3×D12—28no—
393C3×D12—24no—
394C3×D12—24no—
395C3×D12—44no—
396C3×D12C2×D414yescomplemented
397C3×C4×D3—22no—
398C3×C4×D3—22no—
399C3×C4×D3—22no—
400C3×C4×D3—22no—
401C3×C4×D3—44no—
402C3×C4×D3C2×D418yescomplemented
403C3×Dic6C2×D414yescomplemented
404#627—24no—
405#626—24no—
406#626—24no—
407#626—28no—
408#626—24no—
409#626—44no—
410#626—42no—
411#626—44no—
412#625—24no—
413#625—28no—
414#624—24no—
415D3×Dic3—24no—
416D3×Dic3—24no—
417D3×Dic3—28no—
418C2×H(5,𝔽2)—91no—
419C22×#41—91no—
420#550—92no—
421#548—92no—
422#546—94no—
423#546—92no—
424D42—92no—
425D42—94no—
426#537—92no—
427#537—91no—
428#535—92no—
429#535—91no—
430#525—92no—
431#525—91no—
432C2×#121—31no—
433C2×#121—92no—
434#520—31no—
435C24×C3—31no—
436C24×C3—32no—
437C23×D3—32no—
438C23×D3—32no—
439C23×D3—34no—
440C23×D3—34no—
441C23×D3C22×D311yescharacteristic
442C23×D3C22×D312yes—
443C3×#41—38no—
444C2×C3×Q8—31no—
445C2×C3×D4—32no—
446C2×C3×D4—31no—
447C2×C3×D4—34no—
448C2×C3×D4—32no—
449C2×C3×D4—32no—
450C2×C3×D4—34no—
451C2×C3×D4—64no—
452C2×C3×D4—124no—
453C22×C3×C4—21no—
454C22×C3×C4—22no—
455C22×C3×C4—32no—
456C22×C3×C4—31no—
457C22×C3×C4—31no—
458C22×C3×C4—31no—
459C22×C3×C4—31no—
460C22×C3×C4—31no—
461C22×C3×C4—34no—
462C22×C3×C4—64no—
463C22×C3×C4C22×D312yes—
464C22×C3×C4C22×D312yes—
465C22×C3×C4C22×D311yescharacteristic
466C22×C3×C4C22×D311yescharacteristic
467C2×#67—32no—
468C2×#67—32no—
469C2×#67—32no—
470C2×#67—32no—
471C2×#67—32no—
472C2×#67—34no—
473C2×#67—34no—
474C2×#67—32no—
475C2×#67—32no—
476C2×#67—34no—
477C2×#67—32no—
478C2×#67—32no—
479C2×#67—34no—
480C2×#67—34no—
481C2×#67—32no—
482C2×#67—62no—
483C2×#67—62no—
484C2×#67—68no—
485C2×#67—616no—
486C2×#67C22×D312yes—
487C22×Dic3—34no—
488C22×Dic3—32no—
489C22×Dic3—32no—
490C22×Dic3C22×D311yescharacteristic
491#239—64no—
492#239—68no—
493D3×Q8—64no—
494#237—64no—
495#237—68no—
496#237—68no—
497#237—68no—
498D3×D4—64no—
499D3×D4—68no—
500D3×D4—68no—
501D3×D4—616no—
502D3×D4—68no—
503D3×D4—68no—
504D3×D4—128no—
505#235—68no—
506#235—68no—
507#235—64no—
508#235—64no—
509#235—64no—
510#235—64no—
511#235—68no—
512#235—64no—
513#235—68no—
514#235—64no—
515#235—124no—
516#235—124no—
517#235D1218yescomplemented
518C2×D12—24no—
519C2×D12—32no—
520C2×D12—32no—
521C2×D12—34no—
522C2×D12—32no—
523C2×D12—31no—
524C2×D12—31no—
525C2×D12—31no—
526C2×D12—31no—
527C2×D12—32no—
528C2×D12—34no—
529C2×D12—34no—
530C2×D12—34no—
531C2×D12—34no—
532C2×D12—44no—
533C2×D12—61no—
534C2×D12—61no—
535C2×D12—64no—
536C2×D12—68no—
537C2×D12—64no—
538C2×D12—128no—
539C2×D12C22×D314yes—
540C2×D12C22×D312yes—
541C2×D12C22×D312yes—
542C2×D12C22×D314yes—
543C2×D12C22×D311yescharacteristic
544C2×C4×D3—24no—
545C2×C4×D3—32no—
546C2×C4×D3—34no—
547C2×C4×D3—32no—
548C2×C4×D3—32no—
549C2×C4×D3—32no—
550C2×C4×D3—32no—
551C2×C4×D3—32no—
552C2×C4×D3—32no—
553C2×C4×D3—32no—
554C2×C4×D3—62no—
555C2×C4×D3—62no—
556C2×C4×D3—68no—
557C2×C4×D3—68no—
558C2×C4×D3C22×D311yescharacteristic
559C2×C4×D3C22×D311yescharacteristic
560C2×C4×D3C22×D311yescharacteristic
561C2×C4×D3C22×D311yescharacteristic
562C2×C4×D3C22×D314yes—
563C2×C4×D3C22×D312yes—
564C2×Dic6—31no—
565C2×Dic6—31no—
566C2×Dic6—31no—
567C2×Dic6—31no—
568C2×Dic6—32no—
569C2×Dic6—32no—
570C2×Dic6—61no—
571C2×Dic6—61no—
572C2×Dic6—64no—
573C2×Dic6C22×D311yescharacteristic
574C3×C4⋊C4—22no—
575C3×C4⋊C4—22no—
576C3×C4⋊C4—34no—
577C3×C4⋊C4—31no—
578C3×C4⋊C4—31no—
579C3×C4⋊C4C22×D312yes—
580C3×C4⋊C4C22×D312yes—
581C3×C4⋊C4C22×D312yes—
582C3×C4⋊C4C22×D312yes—
583C3×C22⋊C4—32no—
584C3×C22⋊C4—34no—
585C3×C22⋊C4—34no—
586C3×C22⋊C4—34no—
587C3×C42—34no—
588C3×C42—32no—
589#217—34no—
590#217—34no—
591#217—32no—
592#217—32no—
593#217C22×D312yes—
594(C2×D3)⋊C4—32no—
595(C2×D3)⋊C4—34no—
596(C2×D3)⋊C4—32no—
597(C2×D3)⋊C4—34no—
598(C2×D3)⋊C4—34no—
599(C2×D3)⋊C4—34no—
600(C2×D3)⋊C4—34no—
601(C2×D3)⋊C4—34no—
602(C2×D3)⋊C4—32no—
603(C2×D3)⋊C4—32no—
604(C2×D3)⋊C4—32no—
605(C2×D3)⋊C4—32no—
606(C2×D3)⋊C4—64no—
607(C2×D3)⋊C4—64no—
608(C2×D3)⋊C4C22×D314yes—
609(C2×D3)⋊C4C22×D314yes—
610(C2×D3)⋊C4C22×D314yes—
611C4⋊Dic3—34no—
612C4⋊Dic3—34no—
613C4⋊Dic3—32no—
614C4⋊Dic3—32no—
615C4⋊Dic3—64no—
616C4⋊Dic3C22×D311yescharacteristic
617C4⋊Dic3C22×D311yescharacteristic
618Dic3⋊C4—32no—
619Dic3⋊C4—32no—
620Dic3⋊C4C22×D314yes—
621C4×Dic3C22×D314yes—
622C4×Dic3C22×D312yes—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32C22×D412yes—
626C22×C32C2511yescharacteristic
627C2×C3⋊D3—22no—
628C2×C3⋊D3—22no—
629C2×C3⋊D3—22no—
630C2×C3⋊D3—22no—
631C2×C3⋊D3—22no—
632C2×C3⋊D3—22no—
633C2×C3×D3—21no—
634C2×C3×D3—22no—
635C2×C3×D3—22no—
636C2×C3×D3—21no—
637C2×C3×D3—24no—
638C2×C3×D3—21no—
639C2×C3×D3—24no—
640C2×C3×D3—21no—
641C2×C3×D3—21no—
642C2×C3×D3—24no—
643C2×C3×D3—44no—
644C2×C3×D3—84no—
645C2×C3×D3C22×D414yes—
646C2×C3×D3H(5,𝔽2)12yescomplemented
647D32—48no—
648D32—88no—
649C32×C4—24no—
650C32×C4C22×D412yes—
651C32×C4C22×D412yes—
652C3⋊Dic3—22no—
653C3⋊Dic3—22no—
654C3×Dic3—21no—
655C3×Dic3—21no—
656C3×Dic3—22no—
657C3×Dic3—22no—
658C3×Dic3C22×D414yes—
659H(5,𝔽2)—188no—
660C2×#41—31no—
661C2×#41—92no—
662C2×#41—92no—
663C2×#41—92no—
664C2×#41—91no—
665C2×#41—91no—
666C2×#41—92no—
667C2×#41—91no—
668C2×#41—91no—
669C2×#41—188no—
670C22×Q8—91no—
671C22×D4—31no—
672C22×D4—32no—
673C22×D4—92no—
674C22×D4—91no—
675C22×D4—94no—
676C22×D4—92no—
677C22×D4—92no—
678C22×D4—94no—
679C23×C4—31no—
680C23×C4—92no—
681#127—92no—
682#127—94no—
683#124—94no—
684#124—92no—
685#123—94no—
686#123—92no—
687C22⋊Q8—94no—
688C22⋊Q8—91no—
689C22⋊Q8—91no—
690C22⋊Q8—92no—
691C22⋊Q8—92no—
692#121—32no—
693#121—32no—
694#121—32no—
695#121—32no—
696#121—94no—
697#121—94no—
698#121—91no—
699#121—91no—
700#121—92no—
701#121—94no—
702#121—92no—
703#121—94no—
704#121—94no—
705#121—94no—
706#121—92no—
707#121—92no—
708#120—94no—
709#120—94no—
710#120—94no—
711#120—92no—
712#120—94no—
713C4×Q8—32no—
714C4×D4—34no—
715C4×D4—32no—
716C4×D4—94no—
717C4×D4—92no—
718C4×D4—92no—
719C4×D4—94no—
720#117—31no—
721#117—32no—
722C2×C4⋊C4—32no—
723C2×C4⋊C4D3211yescharacteristic, complemented
724C2×C22⋊C4—32no—
725C2×C22⋊C4—94no—
726C23×C3—21no—
727C23×C3—31no—
728C23×C3—32no—
729C23×C3—34no—
730C23×C3—31no—
731C23×C3—62no—
732C23×C3—62no—
733C23×C3—64no—
734C23×C3—121no—
735C23×C3—122no—
736C23×C3—122no—
737C23×C3C23×D311yescharacteristic
738C23×C3C23×D311yescharacteristic
739C22×D3—22no—
740C22×D3—24no—
741C22×D3—22no—
742C22×D3—32no—
743C22×D3—32no—
744C22×D3—32no—
745C22×D3—32no—
746C22×D3—41no—
747C22×D3—42no—
748C22×D3—42no—
749C22×D3—62no—
750C22×D3—62no—
751C22×D3—64no—
752C22×D3—64no—
753C22×D3—68no—
754C22×D3—64no—
755C22×D3—64no—
756C22×D3—68no—
757C22×D3—122no—
758C22×D3—122no—
759C22×D3—124no—
760C22×D3—124no—
761C22×D3—124no—
762C22×D3—124no—
763C22×D3C23×D314yes—
764C22×D3C23×D311yescharacteristic
765C22×D3C23×D312yes—
766C22×D3C23×D311yescharacteristic
767C3×Q8—34no—
768C3×D4—38no—
769C3×D4—34no—
770C3×D4—68no—
771C3×D4—64no—
772C3×D4—64no—
773C3×D4—124no—
774C2×C3×C4—21no—
775C2×C3×C4—21no—
776C2×C3×C4—24no—
777C2×C3×C4—24no—
778C2×C3×C4—32no—
779C2×C3×C4—38no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—32no—
783C2×C3×C4—32no—
784C2×C3×C4—42no—
785C2×C3×C4—42no—
786C2×C3×C4—62no—
787C2×C3×C4—62no—
788C2×C3×C4—62no—
789C2×C3×C4—62no—
790C2×C3×C4—62no—
791C2×C3×C4—82no—
792C2×C3×C4—124no—
793C2×C3×C4C2×D1214yescomplemented
794C2×C3×C4D3×D414yescomplemented
795C2×C3×C4C23×D314yes—
796C2×C3×C4C23×D314yes—
797C2×C3×C4C23×D311yescharacteristic
798C2×C3×C4C23×D311yescharacteristic
799C2×C3×C4C23×D311yescharacteristic
800C2×C3×C4C23×D311yescharacteristic
801#67—64no—
802#67—64no—
803#67—68no—
804#67—64no—
805#67—64no—
806#67—64no—
807#67—64no—
808#67—64no—
809#67—64no—
810#67—68no—
811#67—64no—
812#67—68no—
813#67—124no—
814#67—124no—
815#67—124no—
816#67—124no—
817#67—122no—
818#67C2×D1218yescomplemented
819C2×Dic3—22no—
820C2×Dic3—32no—
821C2×Dic3—32no—
822C2×Dic3—32no—
823C2×Dic3—32no—
824C2×Dic3—62no—
825C2×Dic3—62no—
826C2×Dic3—64no—
827C2×Dic3—64no—
828C2×Dic3—68no—
829C2×Dic3C23×D312yes—
830C2×Dic3C23×D312yes—
831C2×Dic3C23×D311yescharacteristic
832C2×Dic3C23×D311yescharacteristic
833C2×Dic3C23×D312yes—
834D12—28no—
835D12—24no—
836D12—24no—
837D12—44no—
838D12—68no—
839D12—64no—
840D12—64no—
841D12—64no—
842D12—62no—
843D12—62no—
844D12—62no—
845D12—62no—
846D12—122no—
847D12—122no—
848D12—124no—
849D12—124no—
850D12—122no—
851D12—124no—
852D12—124no—
853D12—244no—
854D12C2×D1214yescomplemented
855C4×D3—22no—
856C4×D3—22no—
857C4×D3—22no—
858C4×D3—22no—
859C4×D3—44no—
860C4×D3—64no—
861C4×D3—64no—
862C4×D3—68no—
863C4×D3—64no—
864C4×D3—64no—
865C4×D3—64no—
866C4×D3—64no—
867C4×D3—64no—
868C4×D3—64no—
869C4×D3—124no—
870C4×D3—124no—
871C4×D3C2×D1218yescomplemented
872Dic6—64no—
873Dic6—62no—
874Dic6—62no—
875Dic6—62no—
876Dic6—62no—
877Dic6—64no—
878Dic6—122no—
879Dic6—122no—
880Dic6C2×D1214yescomplemented
881C2×C32—22no—
882C2×C32C23×D411yescharacteristic
883C2×C32C2×H(5,𝔽2)11yescharacteristic
884C2×C32#58511yescharacteristic
885C3⋊D3—42no—
886C3⋊D3—42no—
887C3×D3—22no—
888C3×D3—24no—
889C3×D3—44no—
890C3×D3—41no—
891C24—31no—
892C24—32no—
893C24—92no—
894C24—94no—
895#41—38no—
896#41—188no—
897#41—188no—
898#41—188no—
899#41—184no—
900#41—184no—
901#41—188no—
902#41—184no—
903#41—184no—
904C2×Q8—31no—
905C2×Q8—92no—
906C2×Q8—91no—
907C2×Q8—91no—
908C2×Q8—184no—
909C2×D4—32no—
910C2×D4—31no—
911C2×D4—34no—
912C2×D4—32no—
913C2×D4—32no—
914C2×D4—34no—
915C2×D4—64no—
916C2×D4—92no—
917C2×D4—92no—
918C2×D4—94no—
919C2×D4—92no—
920C2×D4—94no—
921C2×D4—92no—
922C2×D4—94no—
923C2×D4—92no—
924C2×D4—94no—
925C2×D4—92no—
926C2×D4—92no—
927C2×D4—91no—
928C2×D4—91no—
929C2×D4—94no—
930C2×D4—124no—
931C2×D4—188no—
932C2×D4—184no—
933C2×D4—188no—
934C2×D4—188no—
935C2×D4—1816no—
936C2×D4—368no—
937C22×C4—32no—
938C22×C4—31no—
939C22×C4—31no—
940C22×C4—31no—
941C22×C4—31no—
942C22×C4—31no—
943C22×C4—34no—
944C22×C4—64no—
945C22×C4—92no—
946C22×C4—92no—
947C22×C4—92no—
948C22×C4—94no—
949C22×C4—92no—
950C22×C4—92no—
951C22×C4—188no—
952C22×C4C2×D3212yes—
953C22×C4C2×D3211yescharacteristic
954C4⋊C4—31no—
955C4⋊C4—34no—
956C4⋊C4—31no—
957C4⋊C4—92no—
958C4⋊C4—92no—
959C4⋊C4—94no—
960C4⋊C4C2×D3212yes—
961C4⋊C4C2×D3212yes—
962C22⋊C4—32no—
963C22⋊C4—34no—
964C22⋊C4—34no—
965C22⋊C4—34no—
966C22⋊C4—92no—
967C22⋊C4—92no—
968C22⋊C4—94no—
969C22⋊C4—92no—
970C22⋊C4—94no—
971C22⋊C4—92no—
972C22⋊C4—94no—
973C22⋊C4—94no—
974C42—34no—
975C42—32no—
976C22×C3—21no—
977C22×C3—21no—
978C22×C3—21no—
979C22×C3—21no—
980C22×C3—22no—
981C22×C3—21no—
982C22×C3—34no—
983C22×C3—32no—
984C22×C3—41no—
985C22×C3—41no—
986C22×C3—61no—
987C22×C3—62no—
988C22×C3—62no—
989C22×C3—61no—
990C22×C3—64no—
991C22×C3—61no—
992C22×C3—64no—
993C22×C3—61no—
994C22×C3—61no—
995C22×C3—64no—
996C22×C3—124no—
997C22×C3—244no—
998C22×C3C22×D1212yes—
999C22×C3C2×D3×D412yes—
1000C22×C3C24×D311yescharacteristic
1001C22×C3C24×D311yescharacteristic
1002C2×D3—21no—
1003C2×D3—21no—
1004C2×D3—22no—
1005C2×D3—22no—
1006C2×D3—21no—
1007C2×D3—24no—
1008C2×D3—24no—
1009C2×D3—21no—
1010C2×D3—21no—
1011C2×D3—24no—
1012C2×D3—44no—
1013C2×D3—62no—
1014C2×D3—62no—
1015C2×D3—62no—
1016C2×D3—62no—
1017C2×D3—62no—
1018C2×D3—62no—
1019C2×D3—62no—
1020C2×D3—62no—
1021C2×D3—62no—
1022C2×D3—62no—
1023C2×D3—62no—
1024C2×D3—62no—
1025C2×D3—84no—
1026C2×D3—122no—
1027C2×D3—122no—
1028C2×D3—122no—
1029C2×D3—122no—
1030C2×D3—122no—
1031C2×D3—122no—
1032C2×D3—128no—
1033C2×D3—128no—
1034C2×D3—248no—
1035C2×D3—248no—
1036C2×D3C22×D1214yes—
1037C2×D3#100412yescomplemented
1038C3×C4—24no—
1039C3×C4—24no—
1040C3×C4—22no—
1041C3×C4—22no—
1042C3×C4—34no—
1043C3×C4—44no—
1044C3×C4—61no—
1045C3×C4—61no—
1046C3×C4—62no—
1047C3×C4—62no—
1048C3×C4C22×D1212yes—
1049C3×C4C22×D1212yes—
1050C3×C4C2×D3×D412yes—
1051C3×C4C2×D3×D412yes—
1052Dic3—21no—
1053Dic3—21no—
1054Dic3—22no—
1055Dic3—22no—
1056Dic3—62no—
1057Dic3—62no—
1058Dic3—62no—
1059Dic3—62no—
1060Dic3—122no—
1061Dic3—122no—
1062Dic3C22×D1214yes—
1063C32#348811yescharacteristic, complemented, Sylow
1064C23—32no—
1065C23—31no—
1066C23—34no—
1067C23—31no—
1068C23—62no—
1069C23—62no—
1070C23—64no—
1071C23—92no—
1072C23—92no—
1073C23—121no—
1074C23—122no—
1075C23—122no—
1076C23—184no—
1077C23—184no—
1078C23—188no—
1079C23—362no—
1080C23—364no—
1081C23—364no—
1082C23C22×D3211yescharacteristic
1083Q8—34no—
1084Q8—184no—
1085Q8—182no—
1086Q8—182no—
1087D4—38no—
1088D4—34no—
1089D4—68no—
1090D4—64no—
1091D4—64no—
1092D4—124no—
1093D4—188no—
1094D4—184no—
1095D4—184no—
1096D4—184no—
1097D4—188no—
1098D4—184no—
1099D4—184no—
1100D4—184no—
1101D4—182no—
1102D4—182no—
1103D4—364no—
1104D4—364no—
1105D4—362no—
1106D4—364no—
1107C2×C4—32no—
1108C2×C4—38no—
1109C2×C4—32no—
1110C2×C4—32no—
1111C2×C4—31no—
1112C2×C4—31no—
1113C2×C4—42no—
1114C2×C4—62no—
1115C2×C4—62no—
1116C2×C4—62no—
1117C2×C4—62no—
1118C2×C4—62no—
1119C2×C4—92no—
1120C2×C4—92no—
1121C2×C4—124no—
1122C2×C4—184no—
1123C2×C4—184no—
1124C2×C4—188no—
1125C2×C4—184no—
1126C2×C4—184no—
1127C2×C4—184no—
1128C2×C4D3×D1214yescomplemented
1129C2×C4C22×D3214yes—
1130C2×C4C22×D3211yescharacteristic
1131C2×C4C22×D3211yescharacteristic
1132C2×C3—22no—
1133C2×C3—22no—
1134C2×C3—21no—
1135C2×C3—21no—
1136C2×C3—21no—
1137C2×C3—42no—
1138C2×C3—62no—
1139C2×C3—64no—
1140C2×C3—124no—
1141C2×C3—121no—
1142C2×C3C23×D1211yescharacteristic
1143C2×C3C22×D3×D411yescharacteristic
1144C2×C3C2×#100411yescharacteristic
1145C2×C3#596411yescharacteristic
1146C2×C3D3×H(5,𝔽2)11yescharacteristic
1147C2×C3#596811yescharacteristic
1148D3—24no—
1149D3—22no—
1150D3—41no—
1151D3—44no—
1152D3—122no—
1153D3—122no—
1154D3—122no—
1155D3—122no—
1156D3—242no—
1157D3—242no—
1158C22—21no—
1159C22—21no—
1160C22—34no—
1161C22—32no—
1162C22—61no—
1163C22—62no—
1164C22—61no—
1165C22—62no—
1166C22—61no—
1167C22—64no—
1168C22—64no—
1169C22—61no—
1170C22—61no—
1171C22—64no—
1172C22—124no—
1173C22—182no—
1174C22—182no—
1175C22—182no—
1176C22—182no—
1177C22—182no—
1178C22—182no—
1179C22—244no—
1180C22—368no—
1181C22—728no—
1182C22C2×D3×D1212yes—
1183C22C23×D3211yescharacteristic
1184C4—24no—
1185C4—34no—
1186C4—61no—
1187C4—61no—
1188C4—62no—
1189C4—62no—
1190C4—182no—
1191C4—182no—
1192C4C2×D3×D1212yes—
1193C4C2×D3×D1212yes—
1194C3—21no—
1195C3#8590011yescharacteristic, complemented
1196C3#8594911yescharacteristic, complemented
1197C2—22no—
1198C2—62no—
1199C2—64no—
1200C2—121no—
1201C2—124no—
1202C2—362no—
1203C2—362no—
1204C2C22×D3×D1211yescharacteristic
1205C2D3×#100411yescharacteristic
1206C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3488
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×#64307C2semidirect
2. C2×D3×#235C2semidirect
3. #10595981C2semidirect
4. C2×C3×#895C2semidirect
5. C3×#5504C2semidirect
6. #10595073C2semidirect
7. D12×#67C2semidirect
8. #10595042C2semidirect
9. #10595023C2semidirect
10. #10594630C2semidirect
11. #10594628C2semidirect
12. #10594626C2semidirect
13. #10594621C2semidirect
14. D3×#895C2semidirect
15. #10594524C2semidirect
16. #10594522C2semidirect
17. #10594382C2semidirect
20. C2×#3828C22semidirect
21. C2×#3828C22semidirect
23. C22×C3×D12C22semidirect
24. C22×C3×D12C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C2×D3×#67C22semidirect
27. C2×D3×#67C22semidirect
28. C2×#3804C22semidirect
31. C2×#3802C22semidirect
32. C2×D3×D12C22semidirect
33. C2×D3×D12C22semidirect
34. C2×D3×D12C22semidirect
35. C2×C4×D32C22semidirect
36. C2×#3799C22semidirect
37. C2×#3798C22semidirect
38. C2×#3796C22semidirect
39. C2×#3795C22semidirect
40. C2×#3795C22semidirect
41. C2×D3×Dic6C22semidirect
42. C2×C32×C4⋊C4C22semidirect
43. #64139C22semidirect
44. #64106C22semidirect
45. #64106C22semidirect
46. #64104C22semidirect
47. #64104C22semidirect
48. C3×C4×#67C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C3×#926C22semidirect
51. C3×#895C22semidirect
52. C3×#895C22semidirect
53. C3×#895C22semidirect
54. C3×#895C22semidirect
55. C3×#893C22semidirect
56. C3×#892C22semidirect
57. C3×D3×C4⋊C4C22semidirect
58. C3×#887C22semidirect
59. #63977C22semidirect
60. #63977C22semidirect
61. #63966C22semidirect
62. #63923C22semidirect
63. #63922C22semidirect
64. #63922C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63916C22semidirect
67. #63916C22semidirect
68. #63911C22semidirect
69. #63911C22semidirect
70. #63910C22semidirect
71. #63909C22semidirect
72. #63909C22semidirect
73. #63908C22semidirect
74. #63906C22semidirect
75. C4×#626C22semidirect
76. C4×#626C22semidirect
77. #63893C22semidirect
78. Dic3×D12C22semidirect
79. #63891C22semidirect
80. #63886C22semidirect
81. #63886C22semidirect
82. #63880C22semidirect
83. #63860C22semidirect
84. #63857C22semidirect
85. #63857C22semidirect
86. #63852C22semidirect
119. C2×#895D3semidirect
120. #5504D3semidirect
141. C3×#235D4semidirect
248. C22×D12C2×D3semidirect
249. C22×D12C2×D3semidirect
252. C22×C4×D3C2×D3semidirect
265. C2×C3×C4⋊C4C2×D3semidirect
266. C2×C3×C4⋊C4C2×D3semidirect
291. C4×#67C2×D3semidirect
293. C2×(C2×D3)⋊C4C2×D3semidirect
294. #926C2×D3semidirect
319. #895C2×D3semidirect
320. #895C2×D3semidirect
321. #895C2×D3semidirect
322. #895C2×D3semidirect
323. #893C2×D3semidirect
324. #892C2×D3semidirect
325. D3×C4⋊C4C2×D3semidirect
326. #887C2×D3semidirect
370. C2×C32×C4C2×D4semidirect
385. C3×#67C2×D4semidirect
396. C3×D12C2×D4semidirect
402. C3×C4×D3C2×D4semidirect
403. C3×Dic6C2×D4semidirect
517. #235D12semidirect
646. C2×C3×D3H(5,𝔽2)semidirect
723. C2×C4⋊C4D32semidirect
793. C2×C3×C4C2×D12semidirect
794. C2×C3×C4D3×D4semidirect
818. #67C2×D12semidirect
854. D12C2×D12semidirect
871. C4×D3C2×D12semidirect
880. Dic6C2×D12semidirect
1037. C2×D3#1004semidirect
1063. C32#3488semidirect
1128. C2×C4D3×D12semidirect
1195. C3#85900semidirect
1196. C3#85949semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C2×D3×#2352
#105959812
C2×C3×#8952
C3×#55042
#105950732
D12×#672
#105950422
#105950232
#105946302
#105946282
#105946262
#105946212
D3×#8952
#105945242
#105945222
#105943822
#859493
#859003