Finite Group Databasebeta

← C2×#10593346 #11857532

Subgroups — C2×#10593346 #11857532

Order 1152.

1398 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1398 conjugacy classes of subgroups — too many to draw. Only its 191 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
3C2×#63849C211yesmaximal, characteristic, complemented
4C2×#63738C214yesmaximal, complemented
5#10593346C218yesmaximal, direct product factor
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C3×#235—21no—
8C2×#3811C2212yes—
9C2×#3805—21no—
10#64306—22no—
11#64306—22no—
12#64306C414yescomplemented
13#64306C2214yes—
14C2×#3802C411yescharacteristic, complemented
15C2×C4×D32C412yescomplemented
16C2×#3798—21no—
17C2×#3797C411yescharacteristic, complemented
18C2×#3796—21no—
19C2×C22⋊#157C2212yes—
20#64286—22no—
21#64286C2214yescomplemented
22C2×C4⋊#157—21no—
23C2×C4×#157—21no—
24C2×C3×C4⋊Dic3—21no—
25C2×#3722C2212yes—
26C2×Dic32—21no—
27#63849—22no—
28#63849C2214yescomplemented
29#63738C22116yescomplemented
30C2×D3×#41—61no—
31C2×#892—61no—
32C23×C3⋊D3C2311yescharacteristic
33C22×D32C2×C412yes—
34C22×#157—22no—
35C22×C32×C4D411yescharacteristic
36C22×C3⋊Dic3D411yescharacteristic
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3C2×C411yescharacteristic
39C2×C4×C3⋊D3C2×C412yes—
40C2×C4×C3⋊D3D412yes—
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D412yes—
44C2×C4×C3⋊D3C2312yes—
45C2×C3×#67—22no—
46C22×C3×Dic3—22no—
47C3×#235—24no—
48C3×#235—24no—
49C2×C3×D12—21no—
50C2×C3×C4×D3—22no—
51C2×C3×Dic6—21no—
52#3811—22no—
53#3811—22no—
54#3811C2×C414yes—
55#3811C2314yes—
56C2×#627—21no—
57C2×#626—22no—
58C2×#625—21no—
59C2×#624C2×C412yes—
60#3805—24no—
61#3805—24no—
62C2×D3×Dic3—22no—
63#3802—22no—
64#3802C2×C414yescomplemented
65C4×D32—24no—
66C4×D32C2×C418yescomplemented
67#3798—24no—
68#3798—24no—
69#3797—22no—
70#3797C2×C414yescomplemented
71#3796—24no—
72#3796—24no—
73C22⋊#157—22no—
74C22⋊#157C2314yes—
75C4⋊#157—24no—
76C4×#157—24no—
77C3×C4⋊Dic3—24no—
78#3722—22no—
79#3722C2314yes—
80Dic32—24no—
81C2×#410—91nomaximal, Sylow
82C2×C3×#41—61no—
83D3×#41—64no—
84D3×#41—64no—
85D3×#41—64no—
86D3×#41—64no—
87C2×#239—61no—
88C2×D3×Q8—61no—
89C2×#237—61no—
90C2×#237—62no—
91C2×D3×D4—61no—
92C2×D3×D4—62no—
93C2×#235—21no—
94C2×#235—62no—
95C22×C4×D3—62no—
96C22×C4×D3—61no—
97C22×C4×D3—61no—
98C2×C3×C4⋊C4—61no—
99C2×(C2×D3)⋊C4—62no—
100C2×C4⋊Dic3—21no—
101C2×C4×Dic3—62no—
102#892—64no—
103#892—64no—
104C23×C32C2×D411yescharacteristic
105C22×C3⋊D3—42no—
106C22×C3⋊D3C22×C411yescharacteristic
107C22×C3⋊D3C22×C411yescharacteristic
108C22×C3⋊D3C2×D411yescharacteristic
109C22×C3⋊D3C2×D411yescharacteristic
110C22×C3⋊D3C2×D411yescharacteristic
111C22×C3⋊D3C2411yescharacteristic
112C22×C3×D3—22no—
113C2×D32—22no—
114C2×D32—44no—
115C2×D32C22×C414yes—
116C2×#157—24no—
117C2×#157—44no—
118C2×C32×C4C22⋊C411yescharacteristic
119C2×C32×C4C22⋊C411yescharacteristic
120C2×C32×C4C22⋊C412yes—
121C2×C32×C4C2×D412yes—
122C2×C3⋊Dic3C22⋊C411yescharacteristic
123C2×C3⋊Dic3C22⋊C412yes—
124C2×C3⋊Dic3C22⋊C411yescharacteristic
125C2×C3⋊Dic3C2×D412yes—
126C4×C3⋊D3C22⋊C412yes—
127C4×C3⋊D3C22⋊C412yes—
128C4×C3⋊D3C22⋊C412yes—
129C4×C3⋊D3C22⋊C412yes—
130C4×C3⋊D3C22×C412yes—
131C4×C3⋊D3C22×C412yes—
132C4×C3⋊D3C2×D412yes—
133C4×C3⋊D3C2×D412yes—
134C3×#67—24no—
135C3×#67—24no—
136C2×C3×Dic3—22no—
137C2×C3×Dic3—24no—
138C2×C3×Dic3—44no—
139C3×D12—24no—
140C3×C4×D3—28no—
141C3×Dic6—24no—
142#627—24no—
143#626—24no—
144#626—24no—
145#625—24no—
146#624—22no—
147#624C22×C414yes—
148D3×Dic3—28no—
149C22×#41—91no—
150C2×#117—91no—
151C2×#117—91no—
152#410—98no—
153C2×#99—94no—
154C23×D3—62no—
155C23×D3—61no—
156C23×D3—61no—
157C3×#41—64no—
158C3×#41—64no—
159C2×C3×Q8—61no—
160C2×C3×D4—61no—
161C2×C3×D4—62no—
162C22×C3×C4—21no—
163C22×C3×C4—21no—
164C22×C3×C4—62no—
165C22×C3×C4—62no—
166C2×#67—22no—
167C2×#67—62no—
168C2×#67—62no—
169C22×Dic3—22no—
170C22×Dic3—61no—
171C22×Dic3—61no—
172C22×Dic3—62no—
173#239—64no—
174#239—64no—
175D3×Q8—64no—
176D3×Q8—64no—
177#237—64no—
178#237—64no—
179#237—68no—
180#237—68no—
181D3×D4—64no—
182D3×D4—64no—
183D3×D4—64no—
184D3×D4—64no—
185D3×D4—64no—
186D3×D4—64no—
187#235—24no—
188#235—24no—
189#235—68no—
190#235—68no—
191C2×D12—21no—
192C2×D12—62no—
193C2×C4×D3—22no—
194C2×C4×D3—68no—
195C2×C4×D3—62no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—61no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—61no—
202C2×C4×D3—62no—
203C2×C4×D3—62no—
204C2×C4×D3—62no—
205C2×C4×D3—62no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—62no—
209C2×C4×D3—61no—
210C2×C4×D3—61no—
211C2×C4×D3—62no—
212C2×C4×D3—68no—
213C2×C4×D3—62no—
214C2×Dic6—21no—
215C2×Dic6—62no—
216C3×C4⋊C4—64no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219C4⋊Dic3—24no—
220C4×Dic3—68no—
221C22×C32—22no—
222C22×C32C2×C22⋊C411yescharacteristic
223C22×C32C2×C22⋊C411yescharacteristic
224C22×C32C22×D411yescharacteristic
225C2×C3⋊D3—22no—
226C2×C3⋊D3—22no—
227C2×C3⋊D3—41no—
228C2×C3⋊D3—41no—
229C2×C3⋊D3—41no—
230C2×C3⋊D3—41no—
231C2×C3⋊D3C2×C22⋊C411yescharacteristic
232C2×C3⋊D3C2×C22⋊C411yescharacteristic
233C2×C3⋊D3C23×C411yescharacteristic
234C2×C3⋊D3C22×D411yescharacteristic
235C2×C3×D3—24no—
236C2×C3×D3—44no—
237D32—44no—
238D32—44no—
239#157—44no—
240C32×C4C2×C22⋊C412yes—
241C32×C4C2×C22⋊C412yes—
242C3⋊Dic3C2×C22⋊C412yes—
243C3⋊Dic3C2×C22⋊C412yes—
244C3×Dic3—24no—
245C3×Dic3—44no—
246C2×#41—61no—
247C2×#41—94no—
248C2×#41—94no—
249C2×#41—181no—
250C2×#41—181no—
251C2×#41—181no—
252C2×#41—182no—
253C2×#41—182no—
254C22×Q8—91no—
255C22×D4—92no—
256C22×D4—91no—
257C23×C4—92no—
258C23×C4—91no—
259#117—94no—
260#117—94no—
261#117—182no—
262#117—182no—
263C2×C4⋊C4—61no—
264C2×C4⋊C4—181no—
265C2×C22⋊C4—92no—
266C2×C22⋊C4—92no—
267C2×C42—181no—
268C2×C42—181no—
269#99—916no—
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—62no—
273C22×D3—22no—
274C22×D3—64no—
275C22×D3—61no—
276C22×D3—61no—
277C22×D3—61no—
278C22×D3—61no—
279C22×D3—61no—
280C22×D3—61no—
281C22×D3—61no—
282C22×D3—61no—
283C22×D3—61no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—61no—
287C22×D3—64no—
288C22×D3—128no—
289C22×D3—124no—
290C22×D3—122no—
291C22×D3—122no—
292C3×Q8—64no—
293C3×D4—64no—
294C3×D4—64no—
295C3×D4—64no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—22no—
301C2×C3×C4—22no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—68no—
305C2×C3×C4—62no—
306C2×C3×C4—64no—
307C2×C3×C4—124no—
308#67—24no—
309#67—24no—
310#67—64no—
311#67—64no—
312#67—68no—
313C2×Dic3—22no—
314C2×Dic3—24no—
315C2×Dic3—44no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—62no—
319C2×Dic3—62no—
320C2×Dic3—61no—
321C2×Dic3—61no—
322C2×Dic3—62no—
323C2×Dic3—62no—
324C2×Dic3—68no—
325D12—24no—
326D12—64no—
327D12—64no—
328C4×D3—28no—
329C4×D3—64no—
330C4×D3—62no—
331C4×D3—62no—
332C4×D3—62no—
333C4×D3—62no—
334C4×D3—62no—
335C4×D3—62no—
336C4×D3—62no—
337C4×D3—62no—
338C4×D3—62no—
339C4×D3—62no—
340C4×D3—62no—
341C4×D3—62no—
342C4×D3—62no—
343C4×D3—62no—
344C4×D3—62no—
345C4×D3—62no—
346C4×D3—64no—
347C4×D3—68no—
348Dic6—24no—
349Dic6—68no—
350C2×C32—21no—
351C2×C32—21no—
352C2×C32#41012yescomplemented
353C2×C32C22×C22⋊C411yescharacteristic
354C3⋊D3—21no—
355C3⋊D3—21no—
356C3⋊D3—21no—
357C3⋊D3—21no—
358C3×D3—44no—
359C24—92no—
360C24—91no—
361#41—64no—
362#41—64no—
363#41—184no—
364#41—184no—
365#41—184no—
366#41—184no—
367#41—184no—
368#41—184no—
369C2×Q8—61no—
370C2×Q8—94no—
371C2×Q8—181no—
372C2×Q8—182no—
373C2×D4—62no—
374C2×D4—61no—
375C2×D4—94no—
376C2×D4—94no—
377C2×D4—94no—
378C2×D4—182no—
379C2×D4—182no—
380C2×D4—181no—
381C2×D4—182no—
382C2×D4—182no—
383C22×C4—62no—
384C22×C4—62no—
385C22×C4—92no—
386C22×C4—98no—
387C22×C4—91no—
388C22×C4—92no—
389C22×C4—92no—
390C22×C4—91no—
391C22×C4—91no—
392C22×C4—92no—
393C22×C4—91no—
394C22×C4—91no—
395C22×C4—92no—
396C22×C4—184no—
397C22×C4—182no—
398C22×C4—182no—
399C22×C4GO+(4,𝔽2)11yescharacteristic
400C4⋊C4—64no—
401C4⋊C4—184no—
402C22⋊C4—94no—
403C22⋊C4—94no—
404C22⋊C4—182no—
405C22⋊C4—182no—
406C42—184no—
407C42—184no—
408C22×C3—22no—
409C22×C3—22no—
410C22×C3—21no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—21no—
415C22×C3—21no—
416C22×C3—42no—
417C22×C3—64no—
418C22×C3—124no—
419C2×D3—24no—
420C2×D3—44no—
421C2×D3—61no—
422C2×D3—61no—
423C2×D3—61no—
424C2×D3—61no—
425C2×D3—61no—
426C2×D3—61no—
427C2×D3—61no—
428C2×D3—61no—
429C2×D3—64no—
430C2×D3—122no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—128no—
434C2×D3—128no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—122no—
444C2×D3—122no—
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—22no—
449C3×C4—64no—
450C3×C4—124no—
451Dic3—24no—
452Dic3—44no—
453Dic3—62no—
454Dic3—62no—
455Dic3—62no—
456Dic3—62no—
457C32C2×#41011yescharacteristic, complemented, Sylow
458C23—62no—
459C23—94no—
460C23—91no—
461C23—91no—
462C23—91no—
463C23—91no—
464C23—91no—
465C23—91no—
466C23—182no—
467C23—362no—
468C23—364no—
469C23C2×GO+(4,𝔽2)11yescharacteristic
470Q8—64no—
471Q8—184no—
472D4—64no—
473D4—64no—
474D4—64no—
475D4—184no—
476D4—184no—
477D4—184no—
478C2×C4—62no—
479C2×C4—68no—
480C2×C4—64no—
481C2×C4—94no—
482C2×C4—92no—
483C2×C4—92no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—92no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—92no—
494C2×C4—124no—
495C2×C4—182no—
496C2×C4—188no—
497C2×C4—184no—
498C2×C4—364no—
499C2×C4D32⋊C412yes—
500C2×C4D32⋊C411yescharacteristic
501C2×C4D32⋊C411yescharacteristic
502C2×C4C2×GO+(4,𝔽2)12yes—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—22no—
506C2×C3—22no—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—41no—
511C2×C3—41no—
512C2×C3—124no—
513D3—44no—
514D3—62no—
515D3—62no—
516D3—121no—
517D3—121no—
518D3—121no—
519D3—121no—
520D3—121no—
521D3—121no—
522C22—22no—
523C22—64no—
524C22—91no—
525C22—91no—
526C22—91no—
527C22—91no—
528C22—124no—
529C22—182no—
530C22—182no—
531C22—361no—
532C22—361no—
533C22—361no—
534C22—361no—
535C22—364no—
536C22—364no—
537C22C2×D32⋊C411yescharacteristic
538C22C2×D32⋊C411yescharacteristic
539C22C22×GO+(4,𝔽2)11yescharacteristic
540C4—64no—
541C4—92no—
542C4—92no—
543C4—124no—
544C4—364no—
545C4C2×D32⋊C412yes—
546C4C2×D32⋊C412yes—
547C3—21no—
548C3—21no—
549C2—21no—
550C2—21no—
551C2—124no—
552C2—181no—
553C2—181no—
554C2—181no—
555C2—181no—
556C2#1059334612yesdirect product factor
557C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊D3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64306C2
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#410
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64286C2semidirect
3. C2×#63849C2semidirect
4. C2×#63738C2semidirect
5. #10593346C2direct (N × H)
12. #64306C4semidirect
14. C2×#3802C4semidirect
15. C2×C4×D32C4semidirect
17. C2×#3797C4semidirect
21. #64286C22semidirect
28. #63849C22semidirect
29. #63738C22semidirect
64. #3802C2×C4semidirect
66. C4×D32C2×C4semidirect
70. #3797C2×C4semidirect
352. C2×C32#410semidirect
457. C32C2×#410semidirect
556. C2#10593346direct (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
C2×#638492
C2×#637382
#105933462
C2×#4109