Finite Group Databasebeta

← #11904769

Subgroups — #11904769

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×C3×#1010C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3#10596299C211yesmaximal, characteristic, complemented
4C3×#5833C211yesmaximal, characteristic, complemented
5D3×#946C212yesmaximal, complemented
6#10595397C212yesmaximal, complemented
7#10595305C214yesmaximal, complemented
8#10595301C212yesmaximal, complemented
9#10595232C212yesmaximal, complemented
10#10595151C214yesmaximal, complemented
11#10595070C212yesmaximal, complemented
12#10594986C211yesmaximal, characteristic, complemented
13#10594900C212yesmaximal, complemented
14#10594890C212yesmaximal, complemented
15C2×#63871C211yesmaximal, characteristic, complemented
16#10594855C211yesmaximal, characteristic, complemented
17#10594803C212yesmaximal, complemented
18#87295—31nomaximal
19#86380—31nomaximal
20C2×C32×#41C2211yescharacteristic, complemented
21C22×C4×C3⋊D3C2211yescharacteristic
22C3×#1010—28no—
23C2×C3×D3×Q8C2212yescomplemented
24C2×C3×#237C2214yescomplemented
25C2×C3×#237C2212yescomplemented
26C2×C3×#235C2211yescharacteristic
27C2×C3×#235C2211yescharacteristic
28C2×C3×#235C2212yescomplemented
29C22×C3×Dic6C2211yescharacteristic, complemented
30C22×C3×Dic6C2212yescomplemented
31C2×#3811C2212yes—
32C2×#3805C2212yes—
33#64306—28no—
34C2×#3802C2211yescharacteristic
35C2×C4×D32C2212yes—
36C2×#3798C2212yes—
37C2×#3797C2211yescharacteristic
38C2×#3796C2211yescharacteristic
39C2×#3796C2211yescharacteristic
40#64155C2211yescharacteristic
41#64155C2211yescharacteristic, complemented
42#64147C2211yescharacteristic
43#64147C2211yescharacteristic, complemented
44#64146C2212yes—
45#64144C2212yescomplemented
46C4×#638C2212yes—
47C4×#638C2212yescomplemented
48#64135C2211yescharacteristic, complemented
49C3×#946C2212yescomplemented
50C3×#939C2214yescomplemented
51C3×#938C2212yescomplemented
52C3×#930C2212yescomplemented
53C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
54C3×#924C2212yescomplemented
55#63983C2214yes—
56#63978C2214yescomplemented
57Dic3×#67C2214yescomplemented
58Dic3×#67C2214yescomplemented
59#63971C2214yescomplemented
60#63970C2214yescomplemented
61#63969C2214yescomplemented
62C2×Dic3⋊Dic3C2212yescomplemented
63#63964C2214yescomplemented
64C2×#3722C2212yes—
65#63961C2214yescomplemented
66#63952C2214yes—
67D3×(C2×D3)⋊C4C2214yes—
68#63907C2214yescomplemented
69#63905C2214yescomplemented
70#63898C2212yescomplemented
71D3×C4⋊Dic3C2212yescomplemented
72#63888C2214yes—
73#63887C2214yescomplemented
74D3×Dic3⋊C4C2214yescomplemented
75#63873C2212yescomplemented
76#63871C2212yes—
77#63871C2212yes—
78#63871C2212yescomplemented
79#63871C2212yescomplemented
80#63863C2212yescomplemented
81#63856C2212yescomplemented
82#63856C2212yescomplemented
83#63850C2214yescomplemented
84#63843C2212yescomplemented
85#63841C2212yescomplemented
86#63839C2214yescomplemented
87C2×C3×2−1+4—31no—
88C2×#1010D311yescharacteristic, complemented
89C2×D3×#41—31no—
90C2×D3×#41—31no—
91C3×#537—31no—
92#5833—32no—
93#5833D311yescharacteristic, complemented
94#5829—34no—
95#5829—32no—
96#5828—31no—
97#5828—31no—
98#5828—32no—
99#5828—61no—
100#5827—31no—
101#5825—31no—
102#5824—34no—
103#5824—32no—
104#5817—32no—
105#5816—31no—
106#5816—32no—
107Q8×#67—32no—
108C2×#946—32no—
109C2×#946—31no—
110#5632—32no—
111#5631—32no—
112#5628—32no—
113D3×C22⋊Q8—32no—
114#5612—32no—
115#5611—34no—
116#5610—34no—
117#5608—32no—
118#5606—32no—
119#5598—32no—
120C2×#897—31no—
121#5504—31no—
122C23×C3⋊D3C2311yescharacteristic
123C22×D32C2312yes—
124C32×#41—24no—
125C2×C32×Q8C2311yescharacteristic
126C2×C32×D4C2311yescharacteristic
127C2×C32×D4C2312yes—
128C22×C32×C4C2312yes—
129C22×C32×C4C2311yescharacteristic
130C2×#638C2312yes—
131C2×#638C2312yes—
132C22×C3⋊Dic3C2311yescharacteristic
133C2×C4×C3⋊D3—24no—
134C2×C4×C3⋊D3C2311yescharacteristic
135C2×C4×C3⋊D3C2311yescharacteristic
136C2×C4×C3⋊D3C2311yescharacteristic
137C2×C4×C3⋊D3C2311yescharacteristic
138C2×C3×#67C2312yes—
139C2×C3×#67C2314yes—
140C2×C3×#67C2314yes—
141C2×C3×#67C2312yes—
142C22×C3×Dic3C2314yes—
143C22×C3×Dic3C2312yes—
144C22×C3×Dic3C2312yes—
145C3×D3×Q8—28no—
146C3×#237—216no—
147C3×#237—28no—
148C3×#235—24no—
149C3×#235—28no—
150C3×#235D418yescomplemented
151C2×C3×D12C2311yescharacteristic
152C2×C3×D12C2311yescharacteristic
153C2×C3×C4×D3C2312yes—
154C2×C3×C4×D3C2314yes—
155C2×C3×C4×D3C2312yes—
156C2×C3×Dic6—24no—
157C2×C3×Dic6—28no—
158C2×C3×Dic6C2311yescharacteristic
159C2×C3×Dic6C2312yes—
160C2×C3×Dic6C2314yes—
161C2×C3×Dic6C2312yes—
162C2×C3×Dic6C2311yescharacteristic
163#3811—28no—
164C2×#627C2312yes—
165C2×#626C2312yes—
166C2×#626C2312yes—
167C2×#625C2312yes—
168C2×#624C2312yes—
169#3805—28no—
170C2×D3×Dic3C2312yes—
171C2×D3×Dic3C2312yes—
172C2×D3×Dic3C2314yes—
173#3802—24no—
174C4×D32—28no—
175#3798—28no—
176#3797—24no—
177#3796—24no—
178#3796—24no—
179#3757C2312yes—
180#3757C2312yes—
181#3757C2312yes—
182#3752C2312yes—
183#3752C2312yes—
184C4⋊(C3⋊Dic3)C2311yescharacteristic
185C4⋊(C3⋊Dic3)C2311yescharacteristic
186#3750C2312yes—
187#3750C2312yes—
188C4×C3⋊Dic3C2312yes—
189C3×#217C2314yes—
190C3×(C2×D3)⋊C4C2314yes—
191C3×C4⋊Dic3C2312yes—
192C3×C4⋊Dic3C2312yes—
193C3×Dic3⋊C4C2314yes—
194#3724C2314yes—
195#3724C2314yes—
196Dic3⋊Dic3C2314yes—
197Dic3⋊Dic3C2314yes—
198Dic3⋊Dic3C2314yes—
199#3722C2314yes—
200#3722C2314yes—
201(C2×D3)⋊Dic3C2314yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204Dic32C2314yes—
205#3489—91noSylow
206C3×2−1+4—68no—
207C2×C3×#41—21no—
208C2×C3×#41—34no—
209C2×C3×#41—32no—
210C2×C3×#41—31no—
211C2×C3×#41—31no—
212C2×C3×#41—32no—
213C2×C3×#41C2×D311yescharacteristic, complemented
214C2×C3×#41C2×D311yescharacteristic, complemented
215C22×C3×Q8—32no—
216C22×C3×Q8—31no—
217C22×C3×Q8—32no—
218#1010—28no—
219D3×#41—68no—
220D3×#41—68no—
221C2×#239—31no—
222C2×#239—31no—
223C2×D3×Q8—31no—
224C2×D3×Q8—31no—
225C2×D3×Q8C2×D312yescomplemented
226C2×#237—32no—
227C2×#237—32no—
228C2×#237—31no—
229C2×#237—31no—
230C2×#237C2×D312yescomplemented
231C2×#237C2×D314yescomplemented
232C2×D3×D4—32no—
233C2×D3×D4—32no—
234C2×D3×D4—31no—
235C2×D3×D4—31no—
236C2×#235—32no—
237C2×#235—32no—
238C2×#235C2×D311yescharacteristic
239C2×#235C2×D311yescharacteristic
240C2×#235C2×D312yescomplemented
241C22×C4×D3—31no—
242C22×C4×D3—31no—
243C22×C4×D3—32no—
244C22×C4×D3—32no—
245C22×C4×D3—61no—
246C22×Dic6C2×D312yescomplemented
247C22×Dic6C2×D311yescharacteristic, complemented
248C3×C22⋊Q8—32no—
249C3×C22⋊Q8—32no—
250C3×#121—32no—
251C3×#121—34no—
252C3×#121—32no—
253C2×C3×C4⋊C4—31no—
254#947—32no—
255#947—34no—
256#946—31no—
257#946—31no—
258#946—31no—
259#946—31no—
260#946—32no—
261#946—32no—
262#946—34no—
263#946—32no—
264#946—32no—
265#946—32no—
266#946—32no—
267#946—34no—
268#946—61no—
269#946—61no—
270#946C2×D312yescomplemented
271Q8×Dic3—32no—
272#944—32no—
273#944—32no—
274#944—34no—
275#939—34no—
276#939—34no—
277#939—34no—
278#939C2×D314yescomplemented
279#938—31no—
280#938—31no—
281#938—31no—
282#938—31no—
283#938—34no—
284#938—61no—
285#938—61no—
286#938C2×D312yescomplemented
287#937—32no—
288#937—32no—
289#937—34no—
290#937—34no—
291#937—62no—
292#936—32no—
293#935—32no—
294#935—32no—
295#935—34no—
296#935—34no—
297#935—62no—
298D4×Dic3—34no—
299D4×Dic3—34no—
300D4×Dic3—32no—
301#930—34no—
302#930C2×D312yescomplemented
303#929—34no—
304#929—34no—
305#929—34no—
306C4×#67—32no—
307C4×#67—32no—
308C4×#67—32no—
309C4×#67—32no—
310C4×#67—34no—
311C4×#67—34no—
312C4×#67—34no—
313C4×#67—62no—
314C4×#67—62no—
315C2×(C2×D3)⋊C4—32no—
316C2×(C2×D3)⋊C4—32no—
317C2×(C2×D3)⋊C4—34no—
318#926—31no—
319#926—31no—
320#926—32no—
321#926—61no—
322C2×C4⋊Dic3—32no—
323C2×C4⋊Dic3—32no—
324C2×C4⋊Dic3C2×D311yescharacteristic, complemented
325#924—32no—
326#924—32no—
327#924—34no—
328#924C2×D312yescomplemented
329C2×Dic3⋊C4—32no—
330C2×Dic3⋊C4—34no—
331#897—32no—
332#897—32no—
333#897—32no—
334#897—32no—
335#896—34no—
336#894—34no—
337#893—32no—
338#892—32no—
339D3×C4⋊C4—32no—
340D3×C4⋊C4—34no—
341#888—34no—
342#887—32no—
343#885—34no—
344#884—34no—
345#883—34no—
346#883—34no—
347#67⋊C4—34no—
348D3×C22⋊C4—34no—
349#878—34no—
350#878—34no—
351C23×C32C2412yes—
352C23×C32C2411yescharacteristic
353C22×C3⋊D3—22no—
354C22×C3⋊D3—22no—
355C22×C3⋊D3—41no—
356C22×C3⋊D3C2411yescharacteristic
357C22×C3⋊D3C2411yescharacteristic
358C22×C3×D3C2412yes—
359C22×C3×D3C2412yes—
360C2×D32—24no—
361C2×D32—24no—
362C2×D32—42no—
363C32×Q8—22no—
364C32×D4—24no—
365C32×D4—22no—
366C2×C32×C4—24no—
367C2×C32×C4C2×D414yes—
368C2×C32×C4C2412yes—
369C2×C32×C4C2411yescharacteristic
370C2×C32×C4C2411yescharacteristic
371#638—24no—
372#638—42no—
373C2×C3⋊Dic3—22no—
374C2×C3⋊Dic3C2412yes—
375C2×C3⋊Dic3C2412yes—
376C2×C3⋊Dic3C2411yescharacteristic
377C2×C3⋊Dic3C2411yescharacteristic
378C4×C3⋊D3—22no—
379C4×C3⋊D3—22no—
380C4×C3⋊D3—22no—
381C4×C3⋊D3—22no—
382C3×#67—24no—
383C3×#67—28no—
384C3×#67—44no—
385C3×#67C2×D418yes—
386C2×C3×Dic3—24no—
387C2×C3×Dic3—28no—
388C2×C3×Dic3—42no—
389C2×C3×Dic3C2414yes—
390C2×C3×Dic3C2414yes—
391C2×C3×Dic3C2412yes—
392C2×C3×Dic3C2412yes—
393C3×D12—22no—
394C3×D12C2×D414yes—
395C3×C4×D3—28no—
396C3×C4×D3—24no—
397C3×C4×D3C2×D418yes—
398C3×Dic6—22no—
399C3×Dic6—24no—
400C3×Dic6—24no—
401C3×Dic6—28no—
402C3×Dic6C2×D414yes—
403#627—24no—
404#626—24no—
405#626—24no—
406#625—24no—
407#624—24no—
408D3×Dic3—24no—
409D3×Dic3—24no—
410D3×Dic3—44no—
411C2×2−1+4—31no—
412C22×#41—91no—
413D4×Q8—92no—
414#548—92no—
415#547—94no—
416#547—92no—
417#546—94no—
418#546—92no—
419#537—31no—
420#537—92no—
421#536—92no—
422#536—91no—
423#525—92no—
424#525—91no—
425C2×C22⋊Q8—91no—
426C2×C22⋊Q8—92no—
427#520—91no—
428C23×D3—31no—
429C23×D3—31no—
430C23×D3—32no—
431C23×D3—32no—
432C23×D3—61no—
433C3×#41—24no—
434C3×#41—24no—
435C3×#41—38no—
436C3×#41—44no—
437C3×#41—68no—
438C3×#41—68no—
439C3×#41—616no—
440C3×#41—64no—
441C2×C3×Q8—21no—
442C2×C3×Q8—31no—
443C2×C3×Q8—31no—
444C2×C3×Q8—34no—
445C2×C3×Q8—32no—
446C2×C3×Q8—32no—
447C2×C3×Q8—68no—
448C2×C3×Q8—68no—
449C2×C3×Q8—64no—
450C2×C3×Q8C22×D311yescharacteristic
451C2×C3×Q8C22×D311yescharacteristic
452C2×C3×D4—22no—
453C2×C3×D4—21no—
454C2×C3×D4—32no—
455C2×C3×D4—32no—
456C2×C3×D4—34no—
457C2×C3×D4—34no—
458C2×C3×D4—31no—
459C2×C3×D4—31no—
460C2×C3×D4C22×D312yes—
461C2×C3×D4C22×D312yes—
462C2×C3×D4C22×D311yescharacteristic
463C2×C3×D4C22×D311yescharacteristic
464C22×C3×C4—21no—
465C22×C3×C4—22no—
466C22×C3×C4—32no—
467C22×C3×C4—32no—
468C22×C3×C4—34no—
469C22×C3×C4—32no—
470C22×C3×C4—34no—
471C22×C3×C4—32no—
472C22×C3×C4C22×D312yes—
473C22×C3×C4C22×D312yes—
474C22×C3×C4C22×D311yescharacteristic
475C22×C3×C4C22×D311yescharacteristic
476C2×#67—32no—
477C2×#67—32no—
478C2×#67—32no—
479C2×#67—32no—
480C2×#67—32no—
481C2×#67—32no—
482C2×#67—32no—
483C2×#67—32no—
484C2×#67—62no—
485C2×#67—62no—
486C2×#67C22×D314yes—
487C2×#67C22×D312yes—
488C2×#67C22×D314yes—
489C2×#67C22×D312yes—
490C22×Dic3—31no—
491C22×Dic3—31no—
492C22×Dic3—32no—
493C22×Dic3—32no—
494C22×Dic3—34no—
495C22×Dic3—61no—
496C22×Dic3C22×D314yes—
497C22×Dic3C22×D312yes—
498C22×Dic3C22×D312yes—
499#239—64no—
500#239—64no—
501D3×Q8—28no—
502D3×Q8—64no—
503D3×Q8—64no—
504#237—216no—
505#237—28no—
506#237—64no—
507#237—68no—
508#237—68no—
509#237—64no—
510D3×D4—64no—
511D3×D4—68no—
512D3×D4—68no—
513D3×D4—64no—
514#235—24no—
515#235—28no—
516#235—68no—
517#235—68no—
518#235#6718yescomplemented
519C2×D12—32no—
520C2×D12—32no—
521C2×D12C22×D311yescharacteristic
522C2×D12C22×D311yescharacteristic
523C2×C4×D3—32no—
524C2×C4×D3—32no—
525C2×C4×D3—31no—
526C2×C4×D3—31no—
527C2×C4×D3—31no—
528C2×C4×D3—31no—
529C2×C4×D3—31no—
530C2×C4×D3—31no—
531C2×C4×D3—31no—
532C2×C4×D3—31no—
533C2×C4×D3—32no—
534C2×C4×D3—32no—
535C2×C4×D3—34no—
536C2×C4×D3—61no—
537C2×C4×D3—61no—
538C2×C4×D3—61no—
539C2×C4×D3—61no—
540C2×C4×D3—68no—
541C2×C4×D3—64no—
542C2×C4×D3—64no—
543C2×C4×D3—68no—
544C2×C4×D3—124no—
545C2×C4×D3C22×D314yes—
546C2×C4×D3C22×D312yes—
547C2×C4×D3C22×D312yes—
548C2×Dic6—24no—
549C2×Dic6—28no—
550C2×Dic6—32no—
551C2×Dic6—32no—
552C2×Dic6C22×D314yes—
553C2×Dic6C22×D312yes—
554C2×Dic6C22×D312yes—
555C2×Dic6C22×D311yescharacteristic
556C2×Dic6C22×D311yescharacteristic
557C3×C4⋊C4—32no—
558C3×C4⋊C4—34no—
559C3×C4⋊C4—32no—
560C3×C22⋊C4—34no—
561C3×C22⋊C4—34no—
562#217—32no—
563#217—32no—
564#217—32no—
565#217—32no—
566#217—32no—
567#217—32no—
568#217—34no—
569#217—34no—
570#217—34no—
571#217—62no—
572#217—62no—
573#217—62no—
574#217C22×D314yes—
575(C2×D3)⋊C4—34no—
576(C2×D3)⋊C4—34no—
577(C2×D3)⋊C4—34no—
578(C2×D3)⋊C4—32no—
579(C2×D3)⋊C4—32no—
580(C2×D3)⋊C4—32no—
581(C2×D3)⋊C4—32no—
582(C2×D3)⋊C4—34no—
583(C2×D3)⋊C4—34no—
584(C2×D3)⋊C4—34no—
585(C2×D3)⋊C4—34no—
586(C2×D3)⋊C4—62no—
587(C2×D3)⋊C4—62no—
588(C2×D3)⋊C4C22×D314yes—
589C4⋊Dic3—31no—
590C4⋊Dic3—31no—
591C4⋊Dic3—31no—
592C4⋊Dic3—31no—
593C4⋊Dic3—34no—
594C4⋊Dic3—34no—
595C4⋊Dic3—34no—
596C4⋊Dic3—61no—
597C4⋊Dic3—61no—
598C4⋊Dic3C22×D312yes—
599C4⋊Dic3C22×D312yes—
600Dic3⋊C4—32no—
601Dic3⋊C4—32no—
602Dic3⋊C4—32no—
603Dic3⋊C4—32no—
604Dic3⋊C4—34no—
605Dic3⋊C4—34no—
606Dic3⋊C4—34no—
607Dic3⋊C4—34no—
608Dic3⋊C4—34no—
609Dic3⋊C4—34no—
610Dic3⋊C4—34no—
611Dic3⋊C4—62no—
612Dic3⋊C4—62no—
613Dic3⋊C4C22×D314yes—
614C4×Dic3—32no—
615C4×Dic3—32no—
616C4×Dic3—34no—
617C4×Dic3—34no—
618C4×Dic3—62no—
619C22×C32—21no—
620C22×C32—21no—
621C22×C32—22no—
622C22×C32—22no—
623C22×C32—22no—
624C22×C32C22×D412yes—
625C22×C32C2511yescharacteristic
626C2×C3⋊D3—21no—
627C2×C3⋊D3—21no—
628C2×C3⋊D3—21no—
629C2×C3⋊D3—21no—
630C2×C3⋊D3—21no—
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×C4C22×D412yes—
642C32×C4C22×D412yes—
643C3⋊Dic3—21no—
644C3⋊Dic3—21no—
645C3⋊Dic3—22no—
646C3⋊Dic3—22no—
647C3×Dic3—22no—
648C3×Dic3—24no—
649C3×Dic3—24no—
650C3×Dic3C22×D414yes—
6512−1+4—68no—
652C2×#41—32no—
653C2×#41—34no—
654C2×#41—31no—
655C2×#41—31no—
656C2×#41—32no—
657C2×#41—92no—
658C2×#41—92no—
659C2×#41—91no—
660C2×#41—91no—
661C2×#41—188no—
662C2×#41D3211yescharacteristic, complemented
663C22×Q8—32no—
664C22×Q8—31no—
665C22×Q8—32no—
666C22×Q8—91no—
667C22×D4—92no—
668C22×D4—91no—
669C23×C4—92no—
670C23×C4—91no—
671C4⋊Q8—94no—
672C4⋊Q8—92no—
673#124—94no—
674#124—92no—
675#123—94no—
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—92no—
685C22⋊Q8—92no—
686C22⋊Q8—94no—
687C22⋊Q8—92no—
688C22⋊Q8—92no—
689C22⋊Q8—92no—
690C22⋊Q8—92no—
691C22⋊Q8—91no—
692C22⋊Q8—91no—
693#121—32no—
694#121—34no—
695#121—32no—
696#121—94no—
697#121—94no—
698#121—94no—
699#121—91no—
700#121—91no—
701#120—94no—
702#120—92no—
703C4×Q8—92no—
704C4×D4—94no—
705C4×D4—92no—
706C4×D4—94no—
707C4×D4—94no—
708C4×D4—92no—
709C4×D4—92no—
710#117—92no—
711#117—91no—
712C2×C4⋊C4—31no—
713C2×C4⋊C4—92no—
714C2×C4⋊C4—94no—
715C2×C4⋊C4—92no—
716C2×C22⋊C4—94no—
717C2×C22⋊C4—92no—
718C23×C3—21no—
719C23×C3—22no—
720C23×C3—32no—
721C23×C3—32no—
722C23×C3C23×D312yes—
723C23×C3C23×D312yes—
724C23×C3C23×D311yescharacteristic
725C23×C3C23×D311yescharacteristic
726C22×D3—31no—
727C22×D3—31no—
728C22×D3—31no—
729C22×D3—31no—
730C22×D3—61no—
731C22×D3—61no—
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—22no—
750C3×Q8—22no—
751C3×Q8—34no—
752C3×Q8—42no—
753C3×Q8—68no—
754C3×Q8—64no—
755C3×Q8—64no—
756C3×Q8—62no—
757C3×D4—24no—
758C3×D4—24no—
759C3×D4—22no—
760C3×D4—22no—
761C3×D4—38no—
762C3×D4—34no—
763C3×D4—42no—
764C3×D4—44no—
765C3×D4—68no—
766C3×D4—64no—
767C3×D4—62no—
768C3×D4—124no—
769C2×C3×C4—24no—
770C2×C3×C4—24no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—22no—
774C2×C3×C4—24no—
775C2×C3×C4—32no—
776C2×C3×C4—38no—
777C2×C3×C4—34no—
778C2×C3×C4—34no—
779C2×C3×C4—32no—
780C2×C3×C4—44no—
781C2×C3×C4—68no—
782C2×C3×C4—68no—
783C2×C3×C4—64no—
784C2×C3×C4—64no—
785C2×C3×C4—122no—
786C2×C3×C4D3×D414yes—
787C2×C3×C4C2×#6714yes—
788C2×C3×C4C23×D312yes—
789C2×C3×C4C23×D312yes—
790C2×C3×C4C23×D311yescharacteristic
791C2×C3×C4C23×D311yescharacteristic
792C2×C3×C4C23×D311yescharacteristic
793C2×C3×C4C23×D311yescharacteristic
794#67—24no—
795#67—28no—
796#67—44no—
797#67—64no—
798#67—64no—
799#67—64no—
800#67—64no—
801#67—64no—
802#67—64no—
803#67—124no—
804#67—122no—
805#67—122no—
806#67—124no—
807#67C2×#6718yes—
808C2×Dic3—24no—
809C2×Dic3—28no—
810C2×Dic3—32no—
811C2×Dic3—32no—
812C2×Dic3—32no—
813C2×Dic3—32no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—42no—
819C2×Dic3—62no—
820C2×Dic3—62no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—64no—
824C2×Dic3—62no—
825C2×Dic3—62no—
826C2×Dic3—64no—
827C2×Dic3—122no—
828C2×Dic3—124no—
829C2×Dic3C23×D314yes—
830C2×Dic3C23×D312yes—
831C2×Dic3C23×D314yes—
832C2×Dic3C23×D312yes—
833D12—22no—
834D12—64no—
835D12—64no—
836D12C2×#6714yes—
837C4×D3—28no—
838C4×D3—24no—
839C4×D3—64no—
840C4×D3—64no—
841C4×D3—64no—
842C4×D3—62no—
843C4×D3—62no—
844C4×D3—62no—
845C4×D3—62no—
846C4×D3—62no—
847C4×D3—62no—
848C4×D3—62no—
849C4×D3—62no—
850C4×D3—64no—
851C4×D3—122no—
852C4×D3—122no—
853C4×D3—122no—
854C4×D3—122no—
855C4×D3—124no—
856C4×D3C2×#6718yes—
857Dic6—22no—
858Dic6—24no—
859Dic6—24no—
860Dic6—28no—
861Dic6—64no—
862Dic6—64no—
863Dic6C2×#6714yes—
864C2×C32—22no—
865C2×C32—42no—
866C2×C32C23×D411yescharacteristic
867C2×C32C2×2−1+411yescharacteristic
868C2×C32#58511yescharacteristic
869C3⋊D3—22no—
870C3⋊D3—41no—
871C3×D3—24no—
872C3×D3—42no—
873C24—92no—
874C24—91no—
875#41—24no—
876#41—38no—
877#41—68no—
878#41—68no—
879#41—616no—
880#41—64no—
881#41—188no—
882#41—188no—
883#41—184no—
884#41—184no—
885C2×Q8—31no—
886C2×Q8—31no—
887C2×Q8—32no—
888C2×Q8—34no—
889C2×Q8—32no—
890C2×Q8—68no—
891C2×Q8—68no—
892C2×Q8—64no—
893C2×Q8—92no—
894C2×Q8—184no—
895C2×Q8C2×D3211yescharacteristic
896C2×D4—32no—
897C2×D4—34no—
898C2×D4—32no—
899C2×D4—34no—
900C2×D4—31no—
901C2×D4—31no—
902C2×D4—92no—
903C2×D4—92no—
904C2×D4—92no—
905C2×D4—92no—
906C2×D4—92no—
907C2×D4—188no—
908C2×D4—184no—
909C2×D4C2×D3212yes—
910C2×D4C2×D3211yescharacteristic
911C22×C4—32no—
912C22×C4—32no—
913C22×C4—34no—
914C22×C4—32no—
915C22×C4—34no—
916C22×C4—32no—
917C22×C4—92no—
918C22×C4—92no—
919C22×C4—92no—
920C22×C4—94no—
921C22×C4—91no—
922C22×C4—91no—
923C22×C4—91no—
924C22×C4—91no—
925C22×C4—91no—
926C22×C4—188no—
927C22×C4—184no—
928C22×C4C2×D3212yes—
929C22×C4C2×D3211yescharacteristic
930C4⋊C4—32no—
931C4⋊C4—32no—
932C4⋊C4—34no—
933C4⋊C4—94no—
934C4⋊C4—94no—
935C4⋊C4—94no—
936C4⋊C4—94no—
937C4⋊C4—94no—
938C4⋊C4—91no—
939C4⋊C4—92no—
940C4⋊C4—91no—
941C4⋊C4—92no—
942C22⋊C4—34no—
943C22⋊C4—34no—
944C22⋊C4—94no—
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⋊C4—92no—
954C42—94no—
955C42—92no—
956C22×C3—21no—
957C22×C3—21no—
958C22×C3—21no—
959C22×C3—21no—
960C22×C3—22no—
961C22×C3—22no—
962C22×C3—22no—
963C22×C3—22no—
964C22×C3—22no—
965C22×C3—22no—
966C22×C3—22no—
967C22×C3—21no—
968C22×C3—34no—
969C22×C3—41no—
970C22×C3—41no—
971C22×C3—42no—
972C22×C3—42no—
973C22×C3—42no—
974C22×C3—62no—
975C22×C3—62no—
976C22×C3—62no—
977C22×C3—62no—
978C22×C3—62no—
979C22×C3C2×D3×D412yes—
980C22×C3C22×#6712yes—
981C22×C3C24×D311yescharacteristic
982C22×C3C24×D311yescharacteristic
983C2×D3—22no—
984C2×D3—22no—
985C2×D3—22no—
986C2×D3—22no—
987C2×D3—22no—
988C2×D3—32no—
989C2×D3—32no—
990C2×D3—62no—
991C2×D3—61no—
992C2×D3—61no—
993C2×D3—61no—
994C2×D3—61no—
995C2×D3—62no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—61no—
999C2×D3—61no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—121no—
1003C2×D3—121no—
1004C2×D3—121no—
1005C2×D3—121no—
1006C2×D3—128no—
1007C2×D3—128no—
1008C2×D3—124no—
1009C2×D3—124no—
1010C2×D3—128no—
1011C2×D3C22×#6714yes—
1012C3×C4—22no—
1013C3×C4—22no—
1014C3×C4—22no—
1015C3×C4—22no—
1016C3×C4—34no—
1017C3×C4—42no—
1018C3×C4—64no—
1019C3×C4—64no—
1020C3×C4—62no—
1021C3×C4C2×D3×D412yes—
1022C3×C4C2×D3×D412yes—
1023C3×C4C22×#6712yes—
1024C3×C4C22×#6712yes—
1025Dic3—22no—
1026Dic3—24no—
1027Dic3—24no—
1028Dic3—61no—
1029Dic3—61no—
1030Dic3—62no—
1031Dic3—62no—
1032Dic3—62no—
1033Dic3—62no—
1034Dic3—61no—
1035Dic3—61no—
1036Dic3—121no—
1037Dic3—121no—
1038Dic3—122no—
1039Dic3—122no—
1040Dic3C22×#6714yes—
1041C32#348911yescharacteristic, complemented, Sylow
1042C23—32no—
1043C23—32no—
1044C23—91no—
1045C23—91no—
1046C23—182no—
1047C23—184no—
1048C23—184no—
1049C23—182no—
1050C23—361no—
1051C23—362no—
1052C23C22×D3212yes—
1053C23C22×D3211yescharacteristic
1054Q8—22no—
1055Q8—34no—
1056Q8—68no—
1057Q8—64no—
1058Q8—64no—
1059Q8—62no—
1060Q8—184no—
1061D4—24no—
1062D4—22no—
1063D4—38no—
1064D4—34no—
1065D4—68no—
1066D4—64no—
1067D4—62no—
1068D4—124no—
1069D4—184no—
1070D4—184no—
1071D4—184no—
1072D4—184no—
1073D4—362no—
1074C2×C4—24no—
1075C2×C4—32no—
1076C2×C4—38no—
1077C2×C4—34no—
1078C2×C4—32no—
1079C2×C4—34no—
1080C2×C4—68no—
1081C2×C4—68no—
1082C2×C4—64no—
1083C2×C4—64no—
1084C2×C4—92no—
1085C2×C4—92no—
1086C2×C4—91no—
1087C2×C4—91no—
1088C2×C4—122no—
1089C2×C4—184no—
1090C2×C4—184no—
1091C2×C4—184no—
1092C2×C4—182no—
1093C2×C4—182no—
1094C2×C4—182no—
1095C2×C4—182no—
1096C2×C4—182no—
1097C2×C4—364no—
1098C2×C4D3×#6714yes—
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—42no—
1109C2×C3—42no—
1110C2×C3—64no—
1111C2×C3—82no—
1112C2×C3—122no—
1113C2×C3C22×D3×D411yescharacteristic
1114C2×C3#596611yescharacteristic
1115C2×C3D3×2−1+411yescharacteristic
1116C2×C3D3×2−1+411yescharacteristic
1117C2×C3#596811yescharacteristic
1118C2×C3C23×#6711yescharacteristic
1119D3—24no—
1120D3—42no—
1121D3—62no—
1122D3—62no—
1123D3—122no—
1124D3—122no—
1125D3—121no—
1126D3—121no—
1127C22—21no—
1128C22—21no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—34no—
1133C22—62no—
1134C22—62no—
1135C22—62no—
1136C22—62no—
1137C22—62no—
1138C22—92no—
1139C22—181no—
1140C22—181no—
1141C22—181no—
1142C22—181no—
1143C22—181no—
1144C22—364no—
1145C22—368no—
1146C22C2×D3×#6712yes—
1147C22C23×D3211yescharacteristic
1148C4—22no—
1149C4—34no—
1150C4—64no—
1151C4—64no—
1152C4—62no—
1153C4—182no—
1154C4—182no—
1155C4—181no—
1156C4—181no—
1157C4C2×D3×#6712yes—
1158C4C2×D3×#6712yes—
1159C3—21no—
1160C3#8638011yescharacteristic, complemented
1161C3#8729511yescharacteristic, complemented
1162C2—22no—
1163C2—42no—
1164C2—64no—
1165C2—122no—
1166C2—182no—
1167C2—361no—
1168C2#1059669411yescharacteristic
1169C2#1059669811yescharacteristic
1170C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×#64306C2semidirect
3. #10596299C2semidirect
4. C3×#5833C2semidirect
5. D3×#946C2semidirect
6. #10595397C2semidirect
7. #10595305C2semidirect
8. #10595301C2semidirect
9. #10595232C2semidirect
10. #10595151C2semidirect
11. #10595070C2semidirect
12. #10594986C2semidirect
13. #10594900C2semidirect
14. #10594890C2semidirect
15. C2×#63871C2semidirect
16. #10594855C2semidirect
17. #10594803C2semidirect
20. C2×C32×#41C22semidirect
23. C2×C3×D3×Q8C22semidirect
24. C2×C3×#237C22semidirect
25. C2×C3×#237C22semidirect
28. C2×C3×#235C22semidirect
29. C22×C3×Dic6C22semidirect
30. C22×C3×Dic6C22semidirect
41. #64155C22semidirect
43. #64147C22semidirect
45. #64144C22semidirect
47. C4×#638C22semidirect
48. #64135C22semidirect
49. C3×#946C22semidirect
50. C3×#939C22semidirect
51. C3×#938C22semidirect
52. C3×#930C22semidirect
53. C2×C3×C4⋊Dic3C22semidirect
54. C3×#924C22semidirect
56. #63978C22semidirect
57. Dic3×#67C22semidirect
58. Dic3×#67C22semidirect
59. #63971C22semidirect
60. #63970C22semidirect
61. #63969C22semidirect
62. C2×Dic3⋊Dic3C22semidirect
63. #63964C22semidirect
65. #63961C22semidirect
68. #63907C22semidirect
69. #63905C22semidirect
70. #63898C22semidirect
71. D3×C4⋊Dic3C22semidirect
73. #63887C22semidirect
74. D3×Dic3⋊C4C22semidirect
75. #63873C22semidirect
78. #63871C22semidirect
79. #63871C22semidirect
80. #63863C22semidirect
81. #63856C22semidirect
82. #63856C22semidirect
83. #63850C22semidirect
84. #63843C22semidirect
85. #63841C22semidirect
86. #63839C22semidirect
88. C2×#1010D3semidirect
93. #5833D3semidirect
150. C3×#235D4semidirect
213. C2×C3×#41C2×D3semidirect
214. C2×C3×#41C2×D3semidirect
225. C2×D3×Q8C2×D3semidirect
230. C2×#237C2×D3semidirect
231. C2×#237C2×D3semidirect
240. C2×#235C2×D3semidirect
246. C22×Dic6C2×D3semidirect
247. C22×Dic6C2×D3semidirect
270. #946C2×D3semidirect
278. #939C2×D3semidirect
286. #938C2×D3semidirect
302. #930C2×D3semidirect
324. C2×C4⋊Dic3C2×D3semidirect
328. #924C2×D3semidirect
518. #235#67semidirect
632. C2×C3⋊D32−1+4semidirect
662. C2×#41D32semidirect
1041. C32#3489semidirect
1160. C3#86380semidirect
1161. C3#87295semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×#643062
#105962992
C3×#58332
D3×#9462
#105953972
#105953052
#105953012
#105952322
#105951512
#105950702
#105949862
#105949002
#105948902
C2×#638712
#105948552
#105948032
#872953
#863803