Finite Group Databasebeta

← #11904783

Subgroups — #11904783

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
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10596262C211yesmaximal, characteristic, complemented
4C2×C3×#924C211yesmaximal, characteristic, complemented
5#10595493C214yesmaximal, complemented
6#10595043C211yesmaximal, characteristic, complemented
7#10595005C212yesmaximal, complemented
8#10594986C211yesmaximal, characteristic, complemented
9#10594894C212yesmaximal, complemented
10#10594890C212yesmaximal, complemented
11#10594889C212yesmaximal, complemented
12#10594885C214yesmaximal, complemented
13#10594884C212yesmaximal, complemented
14D3×#924C212yesmaximal, complemented
15#10594855C211yesmaximal, characteristic, complemented
16#10594830C212yesmaximal, complemented
17#10594803C212yesmaximal, complemented
18#87264—31nomaximal
19#85985—31nomaximal
20C23×C32×C4C2211yescharacteristic
21C2×#3828C2211yescharacteristic, complemented
22C22×C3×#67C2212yes—
23C2×C3×#235—28no—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic
26C2×C3×#235C2212yes—
27C2×C3×#235C2212yes—
28C2×C3×#235C2211yescharacteristic
29C2×C3×#235C2211yescharacteristic
30C22×C3×D12C2211yescharacteristic
31C22×C3×C4×D3C2212yes—
32C22×C3×Dic6C2211yescharacteristic
33C22×C3×Dic6C2211yescharacteristic, complemented
34C2×#3804C2214yescomplemented
35C2×#3799C2212yescomplemented
36C2×#3797C2212yescomplemented
37#64297—28no—
38C2×#3796C2212yescomplemented
39C2×D3×Dic6C2212yescomplemented
40#64162C2212yes—
41#64139C2211yescharacteristic
42#64139C2211yescharacteristic, complemented
43#64138C2212yescomplemented
44C4×#638C2212yes—
45C4×#638C2212yescomplemented
46#64135C2211yescharacteristic, complemented
47#64133C2211yescharacteristic
48#64133C2211yescharacteristic, complemented
49C2×C3×#217C2212yes—
50C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
51C3×#924C2212yes—
52C3×#924C2212yes—
53C3×#924C2212yescomplemented
54C3×#924C2212yescomplemented
55C2×C3×Dic3⋊C4C2212yescomplemented
56#63978C2214yescomplemented
57#63977C2214yes—
58Dic3×#67C2214yescomplemented
59#63971C2214yescomplemented
60#63969C2214yescomplemented
61D3×#217C2214yes—
62#63964C2214yes—
63#63961C2214yescomplemented
64#63959C2214yescomplemented
65#63958C2214yescomplemented
66#63952C2214yes—
67#63916C2212yescomplemented
68#63909C2212yescomplemented
69#63904C2214yescomplemented
70#63898C2212yescomplemented
71D3×C4⋊Dic3C2212yescomplemented
72#63888C2214yescomplemented
73#63886C2214yescomplemented
74#63884C2214yescomplemented
75D3×Dic3⋊C4C2214yescomplemented
76#63873C2212yescomplemented
77#63871C2212yescomplemented
78#63863C2212yescomplemented
79#63857C2212yescomplemented
80#63856C2212yescomplemented
81#63856C2212yescomplemented
82#63851C2214yescomplemented
83#63850C2214yescomplemented
84#63843C2212yescomplemented
85#63841C2212yescomplemented
86#63839C2214yescomplemented
87C22×C3×#41—31no—
88C2×#1010—31no—
89C2×#1007—31no—
90C22×#235D311yescharacteristic, complemented
91C2×C3×C22⋊Q8—31no—
92#5833—31no—
93#5833—32no—
94#5831—32no—
95#5827—31no—
96#5825—31no—
97#5825—32no—
98#5824—32no—
99#5824—34no—
100#5816—31no—
101Q8×#67—32no—
102#5806—34no—
103#5806—32no—
104#5791—31no—
105#5791—31no—
106#5791—32no—
107#5791—61no—
108C2×#924—32no—
109C2×#924D311yescharacteristic, complemented
110#5633—32no—
111#5632—32no—
112#5631—32no—
113#5630—32no—
114#5629—32no—
115#5628—32no—
116#5627—32no—
117D3×C22⋊Q8—32no—
118#5510—31no—
119#5507—34no—
120#5504—31no—
121#5490—34no—
122C24×C32C2311yescharacteristic
123C23×C3×D3C2312yes—
124C22×C32×C4—24no—
125C22×C32×C4C2311yescharacteristic
126C22×C32×C4C2311yescharacteristic
127C22×C32×C4C2311yescharacteristic
128C22×C32×C4C2311yescharacteristic
129C22×C32×C4C2311yescharacteristic
130C22×C32×C4C2311yescharacteristic
131C2×#638C2312yes—
132C2×#638C2312yes—
133C2×#638C2312yes—
134#3828—24no—
135C2×C4⋊(C3⋊D3)C2311yescharacteristic
136C2×C4×C3⋊D3C2312yes—
137C2×#634C2311yescharacteristic
138C2×C3×#67—28no—
139C2×C3×#67C2312yes—
140C2×C3×#67C2312yes—
141C2×C3×#67C2312yes—
142C2×C3×#67C2312yes—
143C22×C3×Dic3C2312yes—
144C22×C3×Dic3C2312yes—
145C22×C3×Dic3C2312yes—
146C3×#235—24no—
147C3×#235—28no—
148C3×#235—24no—
149C3×#235—28no—
150C3×#235—24no—
151C3×#235D418yescomplemented
152C2×C3×D12—24no—
153C2×C3×D12C2311yescharacteristic
154C2×C3×D12C2312yes—
155C2×C3×D12C2311yescharacteristic
156C2×C3×C4×D3—28no—
157C2×C3×C4×D3C2312yes—
158C2×C3×C4×D3C2312yes—
159C2×C3×C4×D3C2312yes—
160C2×C3×C4×D3C2312yes—
161C2×C3×Dic6—24no—
162C2×C3×Dic6—24no—
163C2×C3×Dic6C2312yes—
164C2×C3×Dic6C2312yes—
165C2×C3×Dic6C2312yes—
166C2×C3×Dic6C2311yescharacteristic
167C2×C3×Dic6C2311yescharacteristic
168C2×#627C2314yes—
169C2×#626C2314yes—
170C2×#626C2314yes—
171C2×#624C2314yes—
172#3804—216no—
173C2×D3×Dic3C2314yes—
174C2×D3×Dic3C2314yes—
175#3799—28no—
176#3797—28no—
177#3796—28no—
178D3×Dic6—28no—
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×#217C2314yes—
191C3×C4⋊Dic3C2312yes—
192C3×C4⋊Dic3C2312yes—
193C3×Dic3⋊C4C2314yes—
194C3×Dic3⋊C4C2314yes—
195#3724C2314yes—
196#3724C2314yes—
197Dic3⋊Dic3C2314yes—
198Dic3⋊Dic3C2314yes—
199#3722C2314yes—
200(C2×D3)⋊Dic3C2314yes—
201(C2×D3)⋊Dic3C2314yes—
202(C2×D3)⋊Dic3C2314yes—
203(C2×D3)⋊Dic3C2314yes—
204Dic32C2314yes—
205#3489—91noSylow
206C2×C3×#41—31no—
207C2×C3×#41—31no—
208C2×C3×#41—32no—
209C2×C3×#41—32no—
210C2×C3×#41—31no—
211C2×C3×#41—31no—
212C2×C3×#41—68no—
213C22×C3×Q8—31no—
214C22×C3×Q8—31no—
215C22×C3×D4—32no—
216C22×C3×D4—31no—
217C23×C3×C4—21no—
218C23×C3×C4—32no—
219C23×C3×C4C2×D311yescharacteristic
220C23×C3×C4C2×D311yescharacteristic
221C22×#67C2×D312yes—
222#1010—68no—
223#1007—68no—
224C2×#239—32no—
225C2×#239—32no—
226C2×D3×Q8—32no—
227C2×D3×Q8—32no—
228C2×D3×Q8—32no—
229C2×#237—34no—
230C2×#237—32no—
231C2×#235—28no—
232C2×#235—31no—
233C2×#235—31no—
234C2×#235—34no—
235C2×#235—32no—
236C2×#235—61no—
237C2×#235C2×D311yescharacteristic
238C2×#235C2×D312yes—
239C2×#235C2×D311yescharacteristic
240C2×#235C2×D312yes—
241C2×#235C2×D311yescharacteristic
242C2×#235C2×D311yescharacteristic
243C22×D12C2×D311yescharacteristic
244C22×C4×D3C2×D312yes—
245C22×Dic6—32no—
246C22×Dic6C2×D311yescharacteristic
247C22×Dic6C2×D311yescharacteristic, complemented
248C3×C22⋊Q8—32no—
249C3×C22⋊Q8—32no—
250C3×C22⋊Q8—32no—
251C3×C22⋊Q8—32no—
252C2×C3×C4⋊C4—32no—
253C2×C3×C4⋊C4—31no—
254C2×C3×C22⋊C4—32no—
255#953—32no—
256#953—32no—
257#953—34no—
258#953—62no—
259C2×#217—34no—
260C2×#217C2×D312yes—
261#947—32no—
262#946—32no—
263#946—32no—
264#946—32no—
265#946—34no—
266Q8×Dic3—32no—
267#944—32no—
268#944—32no—
269#944—34no—
270#939—34no—
271#939—34no—
272#939—34no—
273#938—34no—
274#938—32no—
275#936—32no—
276#936—34no—
277#935—34no—
278#935—34no—
279#935—34no—
280D4×Dic3—34no—
281D4×Dic3—32no—
282#930—31no—
283#930—31no—
284#930—31no—
285#930—31no—
286#930—34no—
287#930—32no—
288#930—61no—
289#930—61no—
290#929—32no—
291#929—32no—
292#929—34no—
293#929—34no—
294#929—62no—
295C4×#67—32no—
296C4×#67—32no—
297C4×#67—32no—
298C4×#67—32no—
299C4×#67—34no—
300C4×#67—34no—
301C4×#67—34no—
302C4×#67—62no—
303C4×#67—62no—
304#926—31no—
305#926—31no—
306#926—32no—
307#926—61no—
308C2×C4⋊Dic3—32no—
309C2×C4⋊Dic3C2×D311yescharacteristic, complemented
310#924—31no—
311#924—31no—
312#924—31no—
313#924—31no—
314#924—32no—
315#924—32no—
316#924—34no—
317#924—32no—
318#924—34no—
319#924—61no—
320#924—61no—
321#924C2×D312yes—
322#924C2×D312yes—
323#924C2×D312yescomplemented
324#924C2×D312yescomplemented
325C2×Dic3⋊C4—34no—
326C2×Dic3⋊C4C2×D312yescomplemented
327#897—32no—
328#897—32no—
329#896—34no—
330#896—34no—
331#895—32no—
332#895—34no—
333#895—32no—
334#894—34no—
335#894—34no—
336#893—32no—
337#893—34no—
338#892—32no—
339D3×C4⋊C4—32no—
340D3×C4⋊C4—34no—
341#888—34no—
342#887—32no—
343#885—34no—
344#884—34no—
345#884—34no—
346#883—34no—
347#882—34no—
348#67⋊C4—34no—
349D3×C22⋊C4—34no—
350#878—34no—
351C23×C32—22no—
352C23×C32—22no—
353C23×C32—41no—
354C23×C32C2411yescharacteristic
355C23×C32C2411yescharacteristic
356C23×C32C2411yescharacteristic
357C22×C3⋊D3C2412yes—
358C22×C3×D3—24no—
359C22×C3×D3—24no—
360C22×C3×D3—42no—
361C22×C3×D3C2412yes—
362C22×C3×D3C2412yes—
363C2×C32×C4—22no—
364C2×C32×C4—22no—
365C2×C32×C4—22no—
366C2×C32×C4—22no—
367C2×C32×C4—22no—
368C2×C32×C4C2×D414yes—
369C2×C32×C4C2411yescharacteristic
370C2×C32×C4C2411yescharacteristic
371C2×C32×C4C2411yescharacteristic
372C2×C32×C4C2411yescharacteristic
373#638—24no—
374#638—24no—
375#638—42no—
376C2×C3⋊Dic3C2412yes—
377C2×C3⋊Dic3C2412yes—
378C2×C3⋊Dic3C2412yes—
379C4⋊(C3⋊D3)—22no—
380C4×C3⋊D3—24no—
381#634—22no—
382C3×#67—24no—
383C3×#67—24no—
384C3×#67—24no—
385C3×#67C2×D418yes—
386C2×C3×Dic3—24no—
387C2×C3×Dic3—24no—
388C2×C3×Dic3—42no—
389C2×C3×Dic3C2414yes—
390C2×C3×Dic3C2414yes—
391C2×C3×Dic3C2412yes—
392C2×C3×Dic3C2412yes—
393C3×D12—24no—
394C3×D12—22no—
395C3×D12C2×D414yes—
396C3×C4×D3—24no—
397C3×C4×D3—24no—
398C3×C4×D3—24no—
399C3×C4×D3C2×D418yes—
400C3×Dic6—24no—
401C3×Dic6—24no—
402C3×Dic6—22no—
403C3×Dic6—24no—
404C3×Dic6C2×D414yes—
405#627—28no—
406#626—28no—
407#626—44no—
408#624—28no—
409D3×Dic3—28no—
410D3×Dic3—44no—
411C2×2−1+4—91no—
412C22×#41—31no—
413D4×Q8—92no—
414#548—92no—
415#547—94no—
416#547—92no—
417#546—94no—
418#546—92no—
419#537—91no—
420#537—92no—
421#536—92no—
422#536—91no—
423#525—92no—
424#525—91no—
425C2×C22⋊Q8—31no—
426C2×C22⋊Q8—92no—
427#520—91no—
428C24×C3—21no—
429C24×C3—32no—
430C24×C3C22×D311yescharacteristic
431C24×C3C22×D311yescharacteristic
432C23×D3C22×D312yes—
433C3×#41—38no—
434C3×#41—68no—
435C3×#41—68no—
436C3×#41—64no—
437C3×#41—64no—
438C3×#41—64no—
439C2×C3×Q8—31no—
440C2×C3×Q8—32no—
441C2×C3×Q8—31no—
442C2×C3×Q8—32no—
443C2×C3×Q8—32no—
444C2×C3×Q8—64no—
445C2×C3×Q8—64no—
446C2×C3×D4—32no—
447C2×C3×D4—32no—
448C2×C3×D4—32no—
449C2×C3×D4—32no—
450C2×C3×D4—31no—
451C2×C3×D4—32no—
452C2×C3×D4—31no—
453C2×C3×D4—64no—
454C2×C3×D4—68no—
455C22×C3×C4—24no—
456C22×C3×C4—24no—
457C22×C3×C4—21no—
458C22×C3×C4—21no—
459C22×C3×C4—21no—
460C22×C3×C4—21no—
461C22×C3×C4—21no—
462C22×C3×C4—21no—
463C22×C3×C4—32no—
464C22×C3×C4—32no—
465C22×C3×C4—32no—
466C22×C3×C4—32no—
467C22×C3×C4—32no—
468C22×C3×C4—32no—
469C22×C3×C4—32no—
470C22×C3×C4—44no—
471C22×C3×C4—68no—
472C22×C3×C4C22×D311yescharacteristic
473C22×C3×C4C22×D311yescharacteristic
474C22×C3×C4C22×D311yescharacteristic
475C22×C3×C4C22×D311yescharacteristic
476C22×C3×C4C22×D311yescharacteristic
477C22×C3×C4C22×D311yescharacteristic
478C22×C3×C4C22×D311yescharacteristic
479C22×C3×C4C22×D311yescharacteristic
480C22×C3×C4C22×D311yescharacteristic
481C22×C3×C4C22×D311yescharacteristic
482C22×C3×C4C22×D311yescharacteristic
483C22×C3×C4C22×D311yescharacteristic
484C2×#67—28no—
485C2×#67—32no—
486C2×#67—32no—
487C2×#67—32no—
488C2×#67—32no—
489C2×#67—32no—
490C2×#67—32no—
491C2×#67—34no—
492C2×#67—34no—
493C2×#67—62no—
494C2×#67—62no—
495C2×#67—62no—
496C2×#67C22×D312yes—
497C2×#67C22×D312yes—
498C2×#67C22×D312yes—
499C2×#67C22×D312yes—
500C22×Dic3—34no—
501C22×Dic3—34no—
502C22×Dic3C22×D312yes—
503C22×Dic3C22×D312yes—
504C22×Dic3C22×D312yes—
505#239—68no—
506#239—68no—
507D3×Q8—68no—
508D3×Q8—68no—
509D3×Q8—68no—
510#237—68no—
511#237—616no—
512#235—24no—
513#235—28no—
514#235—24no—
515#235—28no—
516#235—24no—
517#235—68no—
518#235—64no—
519#235—64no—
520#235—616no—
521#235—124no—
522#235#6718yescomplemented
523C2×D12—24no—
524C2×D12—34no—
525C2×D12—31no—
526C2×D12—31no—
527C2×D12—34no—
528C2×D12—61no—
529C2×D12C22×D312yes—
530C2×D12C22×D311yescharacteristic
531C2×D12C22×D311yescharacteristic
532C2×C4×D3—28no—
533C2×C4×D3—34no—
534C2×C4×D3—32no—
535C2×C4×D3—32no—
536C2×C4×D3—34no—
537C2×C4×D3—34no—
538C2×C4×D3—34no—
539C2×C4×D3—62no—
540C2×C4×D3C22×D312yes—
541C2×C4×D3C22×D312yes—
542C2×C4×D3C22×D312yes—
543C2×C4×D3C22×D312yes—
544C2×Dic6—24no—
545C2×Dic6—24no—
546C2×Dic6—31no—
547C2×Dic6—31no—
548C2×Dic6—34no—
549C2×Dic6—34no—
550C2×Dic6—61no—
551C2×Dic6—68no—
552C2×Dic6C22×D312yes—
553C2×Dic6C22×D311yescharacteristic
554C2×Dic6C22×D312yes—
555C2×Dic6C22×D312yes—
556C2×Dic6C22×D311yescharacteristic
557C3×C4⋊C4—32no—
558C3×C4⋊C4—34no—
559C3×C4⋊C4—32no—
560C3×C4⋊C4—34no—
561C3×C22⋊C4—34no—
562C3×C22⋊C4—34no—
563#217—32no—
564#217—32no—
565#217—32no—
566#217—32no—
567#217—32no—
568#217—32no—
569#217—34no—
570#217—34no—
571#217—34no—
572#217—34no—
573#217—62no—
574#217—62no—
575#217—62no—
576#217C22×D314yes—
577#217C22×D314yes—
578(C2×D3)⋊C4—34no—
579(C2×D3)⋊C4—34no—
580(C2×D3)⋊C4—34no—
581(C2×D3)⋊C4—34no—
582(C2×D3)⋊C4—32no—
583(C2×D3)⋊C4—32no—
584(C2×D3)⋊C4—32no—
585(C2×D3)⋊C4—32no—
586(C2×D3)⋊C4—34no—
587(C2×D3)⋊C4—34no—
588(C2×D3)⋊C4—62no—
589(C2×D3)⋊C4—62no—
590C4⋊Dic3—31no—
591C4⋊Dic3—31no—
592C4⋊Dic3—31no—
593C4⋊Dic3—31no—
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—62no—
611Dic3⋊C4—62no—
612Dic3⋊C4C22×D314yes—
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—21no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—44no—
627C22×C32C22×D412yes—
628C22×C322−1+412yescomplemented
629C22×C32C2511yescharacteristic
630C2×C3⋊D3—22no—
631C2×C3⋊D3—22no—
632C2×C3⋊D3—22no—
633C2×C3×D3—22no—
634C2×C3×D3—22no—
635C2×C3×D3—22no—
636C2×C3×D3—22no—
637C2×C3×D3—22no—
638C2×C3×D3—48no—
639C2×C3×D3C22×D414yes—
640C32×C4—21no—
641C32×C4—21no—
642C32×C4C22×D412yes—
643C32×C4C22×D412yes—
644C3⋊Dic3—22no—
645C3⋊Dic3—22no—
646C3⋊Dic3—22no—
647C3×Dic3—24no—
648C3×Dic3—22no—
649C3×Dic3—24no—
650C3×Dic3C22×D414yes—
6512−1+4—188no—
652C2×#41—31no—
653C2×#41—32no—
654C2×#41—31no—
655C2×#41—31no—
656C2×#41—32no—
657C2×#41—31no—
658C2×#41—68no—
659C2×#41—94no—
660C2×#41—92no—
661C2×#41—92no—
662C2×#41—91no—
663C22×Q8—31no—
664C22×Q8—31no—
665C22×Q8—92no—
666C22×Q8—92no—
667C22×D4—32no—
668C22×D4—31no—
669C23×C4—32no—
670C23×C4D3211yescharacteristic
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—32no—
683C22⋊Q8—32no—
684C22⋊Q8—94no—
685C22⋊Q8—92no—
686C22⋊Q8—94no—
687C22⋊Q8—94no—
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—92no—
704C4×D4—94no—
705C4×D4—94no—
706C4×D4—92no—
707C4×D4—94no—
708C4×D4—92no—
709C4×D4—92no—
710#117—92no—
711#117—91no—
712C2×C4⋊C4—31no—
713C2×C4⋊C4—32no—
714C2×C4⋊C4—92no—
715C2×C4⋊C4—94no—
716C2×C22⋊C4—32no—
717C2×C22⋊C4—94no—
718C23×C3—22no—
719C23×C3—22no—
720C23×C3—22no—
721C23×C3—22no—
722C23×C3—21no—
723C23×C3—21no—
724C23×C3—21no—
725C23×C3—32no—
726C23×C3—32no—
727C23×C3—42no—
728C23×C3—42no—
729C23×C3—41no—
730C23×C3—41no—
731C23×C3—42no—
732C23×C3—64no—
733C23×C3—64no—
734C23×C3—122no—
735C23×C3C23×D311yescharacteristic
736C23×C3C23×D311yescharacteristic
737C23×C3C23×D311yescharacteristic
738C23×C3C23×D311yescharacteristic
739C23×C3C23×D311yescharacteristic
740C23×C3C23×D311yescharacteristic
741C22×D3—24no—
742C22×D3—24no—
743C22×D3—32no—
744C22×D3—32no—
745C22×D3—42no—
746C22×D3—62no—
747C22×D3C23×D312yes—
748C22×D3C23×D312yes—
749C3×Q8—34no—
750C3×Q8—64no—
751C3×Q8—62no—
752C3×Q8—64no—
753C3×Q8—64no—
754C3×D4—38no—
755C3×D4—34no—
756C3×D4—64no—
757C3×D4—64no—
758C3×D4—64no—
759C3×D4—64no—
760C3×D4—62no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—22no—
764C2×C3×C4—22no—
765C2×C3×C4—22no—
766C2×C3×C4—22no—
767C2×C3×C4—22no—
768C2×C3×C4—22no—
769C2×C3×C4—22no—
770C2×C3×C4—22no—
771C2×C3×C4—21no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—21no—
775C2×C3×C4—24no—
776C2×C3×C4—32no—
777C2×C3×C4—38no—
778C2×C3×C4—34no—
779C2×C3×C4—32no—
780C2×C3×C4—34no—
781C2×C3×C4—42no—
782C2×C3×C4—42no—
783C2×C3×C4—42no—
784C2×C3×C4—42no—
785C2×C3×C4—42no—
786C2×C3×C4—64no—
787C2×C3×C4—64no—
788C2×C3×C4—64no—
789C2×C3×C4—64no—
790C2×C3×C4—64no—
791C2×C3×C4—122no—
792C2×C3×C4D3×D414yes—
793C2×C3×C4C2×#6714yes—
794C2×C3×C4C23×D311yescharacteristic
795C2×C3×C4C23×D311yescharacteristic
796C2×C3×C4C23×D311yescharacteristic
797C2×C3×C4C23×D311yescharacteristic
798C2×C3×C4C23×D311yescharacteristic
799C2×C3×C4C23×D311yescharacteristic
800C2×C3×C4C23×D311yescharacteristic
801C2×C3×C4C23×D311yescharacteristic
802#67—24no—
803#67—24no—
804#67—24no—
805#67—68no—
806#67—64no—
807#67—64no—
808#67—64no—
809#67—64no—
810#67—124no—
811#67—124no—
812#67—124no—
813#67—122no—
814#67—122no—
815#67—124no—
816#67C2×#6718yes—
817C2×Dic3—24no—
818C2×Dic3—24no—
819C2×Dic3—32no—
820C2×Dic3—32no—
821C2×Dic3—32no—
822C2×Dic3—32no—
823C2×Dic3—32no—
824C2×Dic3—32no—
825C2×Dic3—42no—
826C2×Dic3—62no—
827C2×Dic3—62no—
828C2×Dic3—62no—
829C2×Dic3—68no—
830C2×Dic3—124no—
831C2×Dic3C23×D314yes—
832C2×Dic3C23×D312yes—
833C2×Dic3C23×D314yes—
834C2×Dic3C23×D312yes—
835D12—24no—
836D12—22no—
837D12—68no—
838D12—62no—
839D12—62no—
840D12—122no—
841D12—124no—
842D12C2×#6714yes—
843C4×D3—24no—
844C4×D3—24no—
845C4×D3—24no—
846C4×D3—68no—
847C4×D3—68no—
848C4×D3—64no—
849C4×D3—64no—
850C4×D3—68no—
851C4×D3—124no—
852C4×D3—124no—
853C4×D3C2×#6718yes—
854Dic6—24no—
855Dic6—24no—
856Dic6—22no—
857Dic6—24no—
858Dic6—68no—
859Dic6—62no—
860Dic6—62no—
861Dic6—68no—
862Dic6—122no—
863Dic6C2×#6714yes—
864C2×C32—22no—
865C2×C32—22no—
866C2×C32—41no—
867C2×C32C23×D411yescharacteristic
868C2×C32C2×2−1+411yescharacteristic
869C2×C32#58511yescharacteristic
870C3⋊D3—42no—
871C3×D3—24no—
872C3×D3—42no—
873C24—32no—
874C24C2×D3211yescharacteristic
875#41—38no—
876#41—68no—
877#41—68no—
878#41—64no—
879#41—64no—
880#41—64no—
881#41—188no—
882#41—1816no—
883#41—188no—
884#41—184no—
885C2×Q8—31no—
886C2×Q8—32no—
887C2×Q8—32no—
888C2×Q8—32no—
889C2×Q8—31no—
890C2×Q8—64no—
891C2×Q8—64no—
892C2×Q8—94no—
893C2×Q8—91no—
894C2×Q8—188no—
895C2×Q8—188no—
896C2×D4—32no—
897C2×D4—32no—
898C2×D4—32no—
899C2×D4—32no—
900C2×D4—31no—
901C2×D4—32no—
902C2×D4—31no—
903C2×D4—64no—
904C2×D4—68no—
905C2×D4—94no—
906C2×D4—94no—
907C2×D4—92no—
908C2×D4—92no—
909C2×D4—92no—
910C2×D4—91no—
911C22×C4—24no—
912C22×C4—32no—
913C22×C4—32no—
914C22×C4—32no—
915C22×C4—32no—
916C22×C4—32no—
917C22×C4—32no—
918C22×C4—32no—
919C22×C4—68no—
920C22×C4—94no—
921C22×C4—94no—
922C22×C4—94no—
923C22×C4—92no—
924C22×C4C2×D3211yescharacteristic
925C22×C4C2×D3211yescharacteristic
926C22×C4C2×D3211yescharacteristic
927C22×C4C2×D3211yescharacteristic
928C22×C4C2×D3211yescharacteristic
929C22×C4C2×D3211yescharacteristic
930C4⋊C4—32no—
931C4⋊C4—34no—
932C4⋊C4—32no—
933C4⋊C4—34no—
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—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—22no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—21no—
971C22×C3—22no—
972C22×C3—22no—
973C22×C3—21no—
974C22×C3—34no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—41no—
979C22×C3—41no—
980C22×C3—41no—
981C22×C3—44no—
982C22×C3—44no—
983C22×C3—48no—
984C22×C3—62no—
985C22×C3—62no—
986C22×C3—62no—
987C22×C3—62no—
988C22×C3—62no—
989C22×C3—128no—
990C22×C3C2×D3×D412yes—
991C22×C3#100712yescomplemented
992C22×C3#101012yescomplemented
993C22×C3C22×#6712yes—
994C22×C3C24×D311yescharacteristic
995C22×C3C24×D311yescharacteristic
996C2×D3—22no—
997C2×D3—22no—
998C2×D3—22no—
999C2×D3—22no—
1000C2×D3—22no—
1001C2×D3—48no—
1002C2×D3—62no—
1003C2×D3—62no—
1004C2×D3—62no—
1005C2×D3—62no—
1006C2×D3—62no—
1007C2×D3—62no—
1008C2×D3—122no—
1009C2×D3—122no—
1010C2×D3—122no—
1011C2×D3C22×#6714yes—
1012C3×C4—21no—
1013C3×C4—21no—
1014C3×C4—21no—
1015C3×C4—21no—
1016C3×C4—22no—
1017C3×C4—22no—
1018C3×C4—34no—
1019C3×C4—41no—
1020C3×C4—41no—
1021C3×C4—62no—
1022C3×C4—64no—
1023C3×C4—64no—
1024C3×C4C2×D3×D412yes—
1025C3×C4C2×D3×D412yes—
1026C3×C4C22×#6712yes—
1027C3×C4C22×#6712yes—
1028Dic3—24no—
1029Dic3—24no—
1030Dic3—22no—
1031Dic3—62no—
1032Dic3—62no—
1033Dic3—62no—
1034Dic3—62no—
1035Dic3—62no—
1036Dic3—62no—
1037Dic3—122no—
1038Dic3—122no—
1039Dic3—122no—
1040Dic3C22×#6714yes—
1041C32#348911yescharacteristic, complemented, Sylow
1042C23—22no—
1043C23—22no—
1044C23—32no—
1045C23—32no—
1046C23—41no—
1047C23—64no—
1048C23—64no—
1049C23—92no—
1050C23—122no—
1051C23C22×D3211yescharacteristic
1052C23C22×D3211yescharacteristic
1053C23C22×D3211yescharacteristic
1054Q8—34no—
1055Q8—64no—
1056Q8—64no—
1057Q8—64no—
1058Q8—62no—
1059Q8—188no—
1060Q8—182no—
1061D4—38no—
1062D4—34no—
1063D4—64no—
1064D4—64no—
1065D4—64no—
1066D4—64no—
1067D4—62no—
1068D4—188no—
1069D4—184no—
1070D4—184no—
1071D4—182no—
1072D4—364no—
1073D4—362no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—32no—
1080C2×C4—38no—
1081C2×C4—34no—
1082C2×C4—34no—
1083C2×C4—32no—
1084C2×C4—64no—
1085C2×C4—64no—
1086C2×C4—64no—
1087C2×C4—64no—
1088C2×C4—64no—
1089C2×C4—92no—
1090C2×C4—92no—
1091C2×C4—92no—
1092C2×C4—122no—
1093C2×C4—188no—
1094C2×C4—188no—
1095C2×C4—184no—
1096C2×C4—364no—
1097C2×C4D3×#6714yes—
1098C2×C4C22×D3211yescharacteristic
1099C2×C4C22×D3211yescharacteristic
1100C2×C4C22×D3211yescharacteristic
1101C2×C4C22×D3211yescharacteristic
1102C2×C3—22no—
1103C2×C3—22no—
1104C2×C3—22no—
1105C2×C3—22no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—42no—
1110C2×C3—42no—
1111C2×C3—42no—
1112C2×C3—41no—
1113C2×C3—41no—
1114C2×C3—64no—
1115C2×C3—122no—
1116C2×C3C22×D3×D411yescharacteristic
1117C2×C3C2×#100711yescharacteristic
1118C2×C3C2×#101011yescharacteristic
1119C2×C3#596411yescharacteristic
1120C2×C3#596411yescharacteristic
1121C2×C3C23×#6711yescharacteristic
1122D3—24no—
1123D3—42no—
1124D3—122no—
1125D3—122no—
1126D3—242no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—34no—
1135C22—44no—
1136C22—62no—
1137C22—62no—
1138C22—62no—
1139C22—62no—
1140C22—62no—
1141C22—128no—
1142C22—182no—
1143C22—182no—
1144C22—182no—
1145C22#6429712yescomplemented
1146C22C2×D3×#6712yes—
1147C22C23×D3211yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—34no—
1151C4—64no—
1152C4—62no—
1153C4—64no—
1154C4—182no—
1155C4—182no—
1156C4—182no—
1157C4C2×D3×#6712yes—
1158C4C2×D3×#6712yes—
1159C3—21no—
1160C3#8598511yescharacteristic, complemented
1161C3#8726411yescharacteristic, complemented
1162C2—22no—
1163C2—22no—
1164C2—41no—
1165C2—64no—
1166C2—122no—
1167C2—362no—
1168C2C2×#6429711yescharacteristic
1169C2#1059666911yescharacteristic
1170C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C2×#64297C2semidirect
3. #10596262C2semidirect
4. C2×C3×#924C2semidirect
5. #10595493C2semidirect
6. #10595043C2semidirect
7. #10595005C2semidirect
8. #10594986C2semidirect
9. #10594894C2semidirect
10. #10594890C2semidirect
11. #10594889C2semidirect
12. #10594885C2semidirect
13. #10594884C2semidirect
14. D3×#924C2semidirect
15. #10594855C2semidirect
16. #10594830C2semidirect
17. #10594803C2semidirect
21. C2×#3828C22semidirect
33. C22×C3×Dic6C22semidirect
34. C2×#3804C22semidirect
35. C2×#3799C22semidirect
36. C2×#3797C22semidirect
38. C2×#3796C22semidirect
39. C2×D3×Dic6C22semidirect
42. #64139C22semidirect
43. #64138C22semidirect
45. C4×#638C22semidirect
46. #64135C22semidirect
48. #64133C22semidirect
50. C2×C3×C4⋊Dic3C22semidirect
53. C3×#924C22semidirect
54. C3×#924C22semidirect
55. C2×C3×Dic3⋊C4C22semidirect
56. #63978C22semidirect
58. Dic3×#67C22semidirect
59. #63971C22semidirect
60. #63969C22semidirect
63. #63961C22semidirect
64. #63959C22semidirect
65. #63958C22semidirect
67. #63916C22semidirect
68. #63909C22semidirect
69. #63904C22semidirect
70. #63898C22semidirect
71. D3×C4⋊Dic3C22semidirect
72. #63888C22semidirect
73. #63886C22semidirect
74. #63884C22semidirect
75. D3×Dic3⋊C4C22semidirect
76. #63873C22semidirect
77. #63871C22semidirect
78. #63863C22semidirect
79. #63857C22semidirect
80. #63856C22semidirect
81. #63856C22semidirect
82. #63851C22semidirect
83. #63850C22semidirect
84. #63843C22semidirect
85. #63841C22semidirect
86. #63839C22semidirect
90. C22×#235D3semidirect
109. C2×#924D3semidirect
151. C3×#235D4semidirect
247. C22×Dic6C2×D3semidirect
309. C2×C4⋊Dic3C2×D3semidirect
323. #924C2×D3semidirect
324. #924C2×D3semidirect
326. C2×Dic3⋊C4C2×D3semidirect
522. #235#67semidirect
628. C22×C322−1+4semidirect
991. C22×C3#1007semidirect
992. C22×C3#1010semidirect
1041. C32#3489semidirect
1145. C22#64297semidirect
1160. C3#85985semidirect
1161. C3#87264semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#642972
#105962622
C2×C3×#9242
#105954932
#105950432
#105950052
#105949862
#105948942
#105948902
#105948892
#105948852
#105948842
D3×#9242
#105948552
#105948302
#105948032
#872643
#859853