Finite Group Databasebeta

← C2×#10593317 #11857811

Subgroups — C2×#10593317 #11857811

Order 1152.

1406 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 1406 conjugacy classes of subgroups — too many to draw. Only its 199 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic
2C2×#64286C211yesmaximal, characteristic, complemented
3C22×#3710C211yesmaximal, characteristic, complemented
4C2×#63730C212yesmaximal, complemented
5#10593317C218yesmaximal, direct product factor
6C2×#63729C212yesmaximal, complemented
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C3×#235—21no—
9C2×#3811—21no—
10C2×#3805C412yescomplemented
11#64306—22no—
12#64306—22no—
13#64306C414yescomplemented
14#64306C2214yes—
15C2×#3802C2211yescharacteristic
16C2×C4×D32—21no—
17C2×#3798C412yescomplemented
18C2×#3797C2211yescharacteristic
19C2×#3796—21no—
20C2×C22⋊#157—21no—
21#64286—22no—
22#64286C2214yescomplemented
23C2×C4⋊#157C2212yes—
24C2×C4×#157—21no—
25C22×C3×C3⋊C8—21no—
26C2×#3710—22no—
27C2×#3710—21no—
28C2×#3710C2212yes—
29C2×#3710C2214yescomplemented
30#63730C2218yescomplemented
31#63729C2218yescomplemented
32C2×D3×#41—61no—
33C22×D3×C8—61no—
34C23×C3⋊D3D411yescharacteristic
35C22×D32—21no—
36C22×#157—22no—
37C22×C32×C4D411yescharacteristic
38C22×C3⋊Dic3C2×C411yescharacteristic
39C2×C4×C3⋊D3C2×C411yescharacteristic
40C2×C4×C3⋊D3C2×C412yes—
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3D412yes—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C4×C3⋊D3C2312yes—
47C2×C3×#67—22no—
48C3×#235—24no—
49C3×#235—24no—
50C2×C3×D12—21no—
51C2×C3×C4×D3—22no—
52C2×C3×Dic6—21no—
53#3811—24no—
54#3811—24no—
55C2×#627C2×C412yes—
56C2×#626—22no—
57C2×#625C2×C412yes—
58C2×#624—21no—
59#3805—24no—
60#3805C2×C418yescomplemented
61C2×D3×Dic3—22no—
62#3802—21no—
63#3802—21no—
64#3802C2×C412yes—
65#3802C2312yes—
66C4×D32—24no—
67C4×D32—24no—
68#3798—24no—
69#3798C2×C418yescomplemented
70#3797—21no—
71#3797—21no—
72#3797C2×C412yes—
73#3797C2312yes—
74#3796—24no—
75#3796—24no—
76C22⋊#157—24no—
77C4⋊#157—22no—
78C4⋊#157C2314yes—
79C4×#157—24no—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8—24no—
82#3710—22no—
83#3710—24no—
84#3710C2314yes—
85C2×#416—91nomaximal, Sylow
86C2×C3×#41—61no—
87D3×#41—64no—
88D3×#41—64no—
89D3×#41—64no—
90D3×#41—64no—
91C2×#239—61no—
92C2×D3×Q8—61no—
93C2×#237—62no—
94C2×#237—61no—
95C2×D3×D4—61no—
96C2×D3×D4—62no—
97C2×#235—21no—
98C2×#235—62no—
99C22×C4×D3—61no—
100C22×C4×D3—61no—
101C22×C4×D3—62no—
102C22×C3×C8—61no—
103C22×C3⋊C8—21no—
104C2×D3×C8—62no—
105C2×D3×C8—64no—
106C2×D3×C8—64no—
107C2×D3×C8—62no—
108C23×C32C22⋊C411yescharacteristic
109C22×C3⋊D3—24no—
110C22×C3⋊D3C22⋊C411yescharacteristic
111C22×C3⋊D3C22⋊C412yes—
112C22×C3⋊D3C2×D412yes—
113C22×C3⋊D3C2×D411yescharacteristic
114C22×C3×D3—22no—
115C2×D32—22no—
116C2×D32—22no—
117C2×D32—44no—
118C2×#157—24no—
119C2×#157—44no—
120C2×C32×C4C22⋊C411yescharacteristic
121C2×C32×C4C22⋊C412yes—
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D412yes—
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C2×C3⋊Dic3C22⋊C412yes—
126C2×C3⋊Dic3C22×C412yes—
127C2×C3⋊Dic3C22×C411yescharacteristic
128C4×C3⋊D3C22⋊C412yes—
129C4×C3⋊D3C22⋊C412yes—
130C4×C3⋊D3C22⋊C412yes—
131C4×C3⋊D3C22×C411yescharacteristic
132C4×C3⋊D3C22×C412yes—
133C4×C3⋊D3C2×D412yes—
134C4×C3⋊D3C2×D411yescharacteristic
135C4×C3⋊D3C2×D412yes—
136C4×C3⋊D3C2×D411yescharacteristic
137C4×C3⋊D3C2411yescharacteristic
138C3×#67—28no—
139C2×C3×Dic3—22no—
140C3×D12—22no—
141C3×D12—22no—
142C3×C4×D3—28no—
143C3×Dic6—22no—
144C3×Dic6—22no—
145#627—22no—
146#627C22×C414yes—
147#626—28no—
148#625—22no—
149#625C22×C414yes—
150#624—22no—
151#624—22no—
152D3×Dic3—28no—
153C3×C3⋊C8—24no—
154C22×#41—91no—
155C23×C8—91no—
156C2×#117—91no—
157#416—98no—
158C2×#103—92no—
159C2×#102—92no—
160C23×D3—61no—
161C23×D3—61no—
162C23×D3—62no—
163C3×#41—64no—
164C3×#41—64no—
165C2×C3×Q8—61no—
166C2×C3×D4—61no—
167C2×C3×D4—62no—
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—62no—
171C2×#67—22no—
172C2×#67—62no—
173C2×#67—62no—
174C22×Dic3—61no—
175C22×Dic3—61no—
176C22×Dic3—62no—
177#239—64no—
178#239—64no—
179D3×Q8—62no—
180D3×Q8—62no—
181D3×Q8—62no—
182D3×Q8—62no—
183#237—68no—
184#237—64no—
185#237—64no—
186#237—68no—
187D3×D4—62no—
188D3×D4—62no—
189D3×D4—62no—
190D3×D4—62no—
191D3×D4—68no—
192D3×D4—68no—
193#235—24no—
194#235—24no—
195#235—68no—
196#235—68no—
197C2×D12—21no—
198C2×D12—62no—
199C2×C4×D3—22no—
200C2×C4×D3—61no—
201C2×C4×D3—62no—
202C2×C4×D3—61no—
203C2×C4×D3—62no—
204C2×C4×D3—61no—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—62no—
209C2×C4×D3—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3—61no—
216C2×C4×D3—68no—
217C2×C4×D3—68no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×Dic6—21no—
221C2×Dic6—62no—
222C2×C3×C8—62no—
223C2×C3×C8—64no—
224C2×C3⋊C8—22no—
225C2×C3⋊C8—24no—
226D3×C8—64no—
227D3×C8—64no—
228D3×C8—68no—
229C22×C32—22no—
230C22×C32C2×C22⋊C412yes—
231C22×C32C2×C22⋊C411yescharacteristic
232C2×C3⋊D3—22no—
233C2×C3⋊D3—24no—
234C2×C3⋊D3—24no—
235C2×C3⋊D3C2×C22⋊C412yes—
236C2×C3⋊D3C2×C22⋊C411yescharacteristic
237C2×C3⋊D3#13514yes—
238C2×C3⋊D3C22×D411yescharacteristic
239C2×C3×D3—24no—
240C2×C3×D3—44no—
241D32—44no—
242D32—44no—
243#157—44no—
244C32×C4C2×C22⋊C411yescharacteristic
245C32×C4C2×C22⋊C412yes—
246C32×C4C22×D411yescharacteristic
247C3⋊Dic3C2×C22⋊C412yes—
248C3⋊Dic3C2×C22⋊C411yescharacteristic
249C3⋊Dic3C23×C411yescharacteristic
250C3×Dic3—24no—
251C2×#41—61no—
252C2×#41—92no—
253C2×#41—92no—
254C2×#41—94no—
255C2×#41—94no—
256C2×#41—181no—
257C2×#41—182no—
258C2×#41—182no—
259C22×Q8—91no—
260C22×D4—91no—
261C22×D4—181no—
262C23×C4—91no—
263C23×C4—181no—
264C22×C8—61no—
265C22×C8—92no—
266C22×C8—94no—
267C22×C8—181no—
268C22×C8—182no—
269#117—94no—
270#117—182no—
271C2×C4⋊C4—92no—
272C2×C22⋊C4—181no—
273C2×C42—181no—
274#103—98no—
275#102—98no—
276C23×C3—21no—
277C23×C3—21no—
278C23×C3—62no—
279C22×D3—22no—
280C22×D3—61no—
281C22×D3—62no—
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—62no—
285C22×D3—61no—
286C22×D3—62no—
287C22×D3—62no—
288C22×D3—64no—
289C22×D3—64no—
290C22×D3—68no—
291C22×D3—124no—
292C22×D3—128no—
293C3×Q8—62no—
294C3×Q8—62no—
295C3×D4—62no—
296C3×D4—62no—
297C3×D4—68no—
298C2×C3×C4—21no—
299C2×C3×C4—22no—
300C2×C3×C4—21no—
301C2×C3×C4—22no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—68no—
307C2×C3×C4—62no—
308#67—28no—
309#67—64no—
310#67—68no—
311#67—64no—
312C2×Dic3—22no—
313C2×Dic3—61no—
314C2×Dic3—62no—
315C2×Dic3—61no—
316C2×Dic3—62no—
317C2×Dic3—61no—
318C2×Dic3—62no—
319C2×Dic3—61no—
320C2×Dic3—62no—
321C2×Dic3—68no—
322D12—22no—
323D12—22no—
324D12—68no—
325C4×D3—28no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—61no—
333C4×D3—62no—
334C4×D3—62no—
335C4×D3—61no—
336C4×D3—61no—
337C4×D3—62no—
338C4×D3—62no—
339C4×D3—61no—
340C4×D3—62no—
341C4×D3—61no—
342C4×D3—61no—
343C4×D3—62no—
344C4×D3—61no—
345C4×D3—61no—
346C4×D3—64no—
347C4×D3—64no—
348C4×D3—68no—
349Dic6—22no—
350Dic6—22no—
351Dic6—64no—
352Dic6—64no—
353C3×C8—64no—
354C3⋊C8—24no—
355C2×C32—22no—
356C2×C32#41612yescomplemented
357C2×C32C22×C22⋊C411yescharacteristic
358C3⋊D3—22no—
359C3⋊D3#41612yescomplemented
360C3⋊D3C2×#13512yes—
361C3×D3—44no—
362C24—91no—
363C24—181no—
364#41—64no—
365#41—64no—
366#41—98no—
367#41—98no—
368#41—184no—
369#41—184no—
370#41—184no—
371#41—184no—
372C2×Q8—61no—
373C2×Q8—92no—
374C2×Q8—92no—
375C2×Q8—92no—
376C2×Q8—181no—
377C2×Q8—181no—
378C2×D4—62no—
379C2×D4—61no—
380C2×D4—92no—
381C2×D4—92no—
382C2×D4—92no—
383C2×D4—182no—
384C2×D4—181no—
385C2×D4—181no—
386C2×D4—184no—
387C2×D4—184no—
388C22×C4—62no—
389C22×C4—91no—
390C22×C4—91no—
391C22×C4—92no—
392C22×C4—91no—
393C22×C4—92no—
394C22×C4—92no—
395C22×C4—92no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—184no—
399C22×C4—184no—
400C22×C4—181no—
401C22×C4—182no—
402C22×C4—182no—
403C22×C4GO+(4,𝔽2)11yescharacteristic
404C2×C8—62no—
405C2×C8—64no—
406C2×C8—94no—
407C2×C8—182no—
408C2×C8—184no—
409C4⋊C4—94no—
410C4⋊C4—182no—
411C22⋊C4—184no—
412C42—184no—
413C22×C3—24no—
414C22×C3—21no—
415C22×C3—22no—
416C22×C3—21no—
417C22×C3—22no—
418C22×C3—42no—
419C22×C3—64no—
420C22×C3—124no—
421C2×D3—24no—
422C2×D3—44no—
423C2×D3—61no—
424C2×D3—61no—
425C2×D3—61no—
426C2×D3—62no—
427C2×D3—61no—
428C2×D3—64no—
429C2×D3—64no—
430C2×D3—62no—
431C2×D3—68no—
432C2×D3—68no—
433C2×D3—64no—
434C2×D3—124no—
435C2×D3—124no—
436C2×D3—122no—
437C2×D3—128no—
438C2×D3—128no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—21no—
445C3×C4—64no—
446Dic3—24no—
447Dic3—61no—
448Dic3—61no—
449Dic3—62no—
450Dic3—62no—
451Dic3—61no—
452Dic3—61no—
453C32C2×#41611yescharacteristic, complemented, Sylow
454C23—62no—
455C23—91no—
456C23—92no—
457C23—92no—
458C23—91no—
459C23—184no—
460C23—182no—
461C23—182no—
462C23—364no—
463C23D32⋊C411yescharacteristic
464Q8—62no—
465Q8—62no—
466Q8—94no—
467Q8—182no—
468D4—68no—
469D4—62no—
470D4—62no—
471D4—94no—
472D4—188no—
473D4—182no—
474C2×C4—62no—
475C2×C4—68no—
476C2×C4—91no—
477C2×C4—91no—
478C2×C4—92no—
479C2×C4—92no—
480C2×C4—91no—
481C2×C4—91no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—91no—
485C2×C4—92no—
486C2×C4—91no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—182no—
491C2×C4—182no—
492C2×C4—188no—
493C2×C4—184no—
494C2×C4—364no—
495C2×C4D32⋊C412yes—
496C2×C4D32⋊C411yescharacteristic
497C2×C4C2×GO+(4,𝔽2)11yescharacteristic
498C2×C4C2×GO+(4,𝔽2)12yes—
499C8—64no—
500C2×C3—24no—
501C2×C3—22no—
502C2×C3—22no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—42no—
506C2×C3—124no—
507D3—44no—
508D3—62no—
509D3—62no—
510D3—62no—
511D3—62no—
512D3—64no—
513D3—122no—
514C22—22no—
515C22—64no—
516C22—94no—
517C22—91no—
518C22—91no—
519C22—92no—
520C22—124no—
521C22—184no—
522C22—184no—
523C22—182no—
524C22—364no—
525C22—364no—
526C22C2×D32⋊C412yes—
527C22C2×D32⋊C411yescharacteristic
528C4—64no—
529C4—92no—
530C4—91no—
531C4—91no—
532C4—364no—
533C4C2×D32⋊C412yes—
534C4C2×D32⋊C411yescharacteristic
535C4C22×GO+(4,𝔽2)11yescharacteristic
536C3—21no—
537C3—21no—
538C2—22no—
539C2—92no—
540C2—92no—
541C2—124no—
542C2—182no—
543C2#1059331712yesdirect product factor
544C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC3⋊Dic3C23×C4
FrattiniC4C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64306C2
cosocleC4×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#416
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64286C2semidirect
3. C22×#3710C2semidirect
4. C2×#63730C2semidirect
5. #10593317C2direct (N × H)
6. C2×#63729C2semidirect
10. C2×#3805C4semidirect
13. #64306C4semidirect
17. C2×#3798C4semidirect
22. #64286C22semidirect
29. C2×#3710C22semidirect
30. #63730C22semidirect
31. #63729C22semidirect
60. #3805C2×C4semidirect
69. #3798C2×C4semidirect
356. C2×C32#416semidirect
359. C3⋊D3#416semidirect
453. C32C2×#416semidirect
543. C2#10593317direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C2×#642862
C22×#37102
C2×#637302
#105933172
C2×#637292
C2×#4169