Finite Group Databasebeta

← C2×#10593381 #11858171

Subgroups — C2×#10593381 #11858171

Order 1152.

1382 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 1382 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×#64283C211yesmaximal, characteristic, complemented
3C2×#63849C211yesmaximal, characteristic, complemented
4C2×#63741C214yesmaximal, complemented
5#10593381C218yesmaximal, direct product factor
6C22×C4×C3⋊D3C2211yescharacteristic
7C2×C3×#235—21no—
8C2×#3811—21no—
9C2×#3805C2212yes—
10#64306—22no—
11#64306—22no—
12#64306C414yescomplemented
13#64306C2214yes—
14C2×#3802C411yescharacteristic, complemented
15C2×C4×D32—21no—
16C2×#3798C412yescomplemented
17C2×#3797C411yescharacteristic, complemented
18C2×#3796—21no—
19C2×#3792C2212yescomplemented
20#64283—22no—
21#64283C2214yescomplemented
22C2×#3788—21no—
23C2×#3787—21no—
24C2×C3×C4⋊Dic3—21no—
25C2×#3722—21no—
26C2×Dic32C2212yescomplemented
27#63849—22no—
28#63849C2214yescomplemented
29#63741C22116yescomplemented
30C2×D3×#41—61no—
31C2×#892—61no—
32C23×C3⋊D3D411yescharacteristic
33C22×D32—21no—
34C22×C32×C4D411yescharacteristic
35C22×C3⋊Dic3C2311yescharacteristic
36C2×C4×C3⋊D3C2×C411yescharacteristic
37C2×C4×C3⋊D3C2×C411yescharacteristic
38C2×C4×C3⋊D3C2×C412yes—
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3D411yescharacteristic
41C2×C4×C3⋊D3D411yescharacteristic
42C2×C4×C3⋊D3D412yes—
43C2×C4×C3⋊D3C2312yes—
44C2×C3×#67—22no—
45C22×C3×Dic3—22no—
46C3×#235—24no—
47C3×#235—24no—
48C2×C3×D12—21no—
49C2×C3×C4×D3—22no—
50C2×C3×Dic6—21no—
51#3811—24no—
52#3811—24no—
53C2×#627C2×C412yes—
54C2×#626—22no—
55C2×#625C2×C412yes—
56C2×#624—21no—
57#3805—22no—
58#3805—22no—
59#3805C2×C414yes—
60#3805C2314yes—
61C2×D3×Dic3—22no—
62#3802—22no—
63#3802C2×C414yescomplemented
64C4×D32—24no—
65C4×D32—24no—
66#3798—24no—
67#3798C2×C418yescomplemented
68#3797—22no—
69#3797C2×C414yescomplemented
70#3796—24no—
71#3796—24no—
72#3792—22no—
73#3792C2314yescomplemented
74C2×#622—22no—
75#3788—24no—
76#3787—24no—
77C3×C4⋊Dic3—24no—
78#3722—24no—
79Dic32—22no—
80Dic32C2314yescomplemented
81C2×#421—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—62no—
90C2×#237—61no—
91C2×D3×D4—61no—
92C2×D3×D4—62no—
93C2×#235—21no—
94C2×#235—62no—
95C22×C4×D3—61no—
96C22×C4×D3—61no—
97C22×C4×D3—62no—
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⋊D3C22⋊C412yes—
109C22×C3⋊D3C2×D412yes—
110C22×C3×D3—22no—
111C2×D32—24no—
112C2×D32—44no—
113C2×C32×C4C22⋊C411yescharacteristic
114C2×C32×C4C22⋊C411yescharacteristic
115C2×C32×C4C22⋊C412yes—
116C2×C32×C4C2×D412yes—
117C2×C3⋊Dic3C22×C411yescharacteristic
118C2×C3⋊Dic3C22×C411yescharacteristic
119C2×C3⋊Dic3C2×D411yescharacteristic
120C2×C3⋊Dic3C2×D411yescharacteristic
121C2×C3⋊Dic3C2×D411yescharacteristic
122C2×C3⋊Dic3C2411yescharacteristic
123C4×C3⋊D3C22⋊C412yes—
124C4×C3⋊D3C22⋊C412yes—
125C4×C3⋊D3C22⋊C412yes—
126C4×C3⋊D3C22⋊C412yes—
127C4×C3⋊D3C22×C412yes—
128C4×C3⋊D3C22×C412yes—
129C4×C3⋊D3C2×D412yes—
130C4×C3⋊D3C2×D412yes—
131C3×#67—24no—
132C3×#67—24no—
133C2×C3×Dic3—22no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3—44no—
136C3×D12—24no—
137C3×C4×D3—28no—
138C3×Dic6—24no—
139#627—22no—
140#627C22×C414yes—
141#626—28no—
142#625—22no—
143#625C22×C414yes—
144#624—24no—
145D3×Dic3—24no—
146D3×Dic3—24no—
147#622—24no—
148C22×#41—91no—
149C22×M16—91no—
150C2×#117—91no—
151#421—98no—
152C2×#104—94no—
153C23×D3—61no—
154C23×D3—61no—
155C23×D3—62no—
156C3×#41—64no—
157C3×#41—64no—
158C2×C3×Q8—61no—
159C2×C3×D4—61no—
160C2×C3×D4—62no—
161C22×C3×C4—21no—
162C22×C3×C4—21no—
163C22×C3×C4—62no—
164C22×C3×C4—62no—
165C2×#67—22no—
166C2×#67—62no—
167C2×#67—62no—
168C22×Dic3—22no—
169C22×Dic3—61no—
170C22×Dic3—61no—
171C22×Dic3—62no—
172#239—64no—
173#239—64no—
174D3×Q8—64no—
175D3×Q8—64no—
176#237—64no—
177#237—64no—
178#237—64no—
179#237—64no—
180#237—64no—
181#237—64no—
182D3×D4—64no—
183D3×D4—64no—
184D3×D4—68no—
185D3×D4—68no—
186#235—24no—
187#235—24no—
188#235—68no—
189#235—68no—
190C2×D12—21no—
191C2×D12—62no—
192C2×C4×D3—22no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×C4×D3—61no—
196C2×C4×D3—61no—
197C2×C4×D3—61no—
198C2×C4×D3—61no—
199C2×C4×D3—62no—
200C2×C4×D3—62no—
201C2×C4×D3—62no—
202C2×C4×D3—62no—
203C2×C4×D3—61no—
204C2×C4×D3—61no—
205C2×C4×D3—62no—
206C2×C4×D3—61no—
207C2×C4×D3—61no—
208C2×C4×D3—62no—
209C2×C4×D3—68no—
210C2×C4×D3—68no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×Dic6—21no—
214C2×Dic6—62no—
215C3×C4⋊C4—64no—
216(C2×D3)⋊C4—68no—
217C4⋊Dic3—24no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C22×C32—22no—
221C22×C32C2×C22⋊C411yescharacteristic
222C22×C32C2×C22⋊C411yescharacteristic
223C22×C32C22×D411yescharacteristic
224C2×C3⋊D3—22no—
225C2×C3⋊D3—22no—
226C2×C3⋊D3—42no—
227C2×C3⋊D3—42no—
228C2×C3⋊D3C2×C22⋊C412yes—
229C2×C3⋊D3C2×C22⋊C412yes—
230C2×C3×D3—24no—
231C2×C3×D3—44no—
232D32—48no—
233C32×C4C2×C22⋊C412yes—
234C32×C4C2×C22⋊C412yes—
235C3⋊Dic3C2×C22⋊C411yescharacteristic
236C3⋊Dic3C2×C22⋊C411yescharacteristic
237C3⋊Dic3C23×C411yescharacteristic
238C3⋊Dic3C22×D411yescharacteristic
239C3×Dic3—24no—
240C3×Dic3—44no—
241C2×#41—61no—
242C2×#41—92no—
243C2×#41—92no—
244C2×#41—94no—
245C2×#41—94no—
246C2×#41—181no—
247C2×#41—182no—
248C2×#41—182no—
249C22×Q8—91no—
250C22×D4—91no—
251C22×D4—181no—
252C23×C4—91no—
253C23×C4—181no—
254C2×M16—94no—
255C2×M16—92no—
256C2×M16—181no—
257C2×M16—182no—
258C22×C8—181no—
259#117—94no—
260#117—182no—
261C2×C4⋊C4—61no—
262C2×C22⋊C4—181no—
263C2×C42—92no—
264#104—916no—
265C23×C3—21no—
266C23×C3—21no—
267C23×C3—62no—
268C22×D3—22no—
269C22×D3—61no—
270C22×D3—61no—
271C22×D3—62no—
272C22×D3—61no—
273C22×D3—61no—
274C22×D3—62no—
275C22×D3—62no—
276C22×D3—62no—
277C22×D3—68no—
278C22×D3—128no—
279C22×D3—124no—
280C22×D3—122no—
281C22×D3—122no—
282C3×Q8—64no—
283C3×D4—64no—
284C3×D4—64no—
285C3×D4—64no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—22no—
291C2×C3×C4—22no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—68no—
295C2×C3×C4—62no—
296C2×C3×C4—64no—
297C2×C3×C4—124no—
298#67—24no—
299#67—24no—
300#67—64no—
301#67—68no—
302#67—64no—
303C2×Dic3—22no—
304C2×Dic3—24no—
305C2×Dic3—44no—
306C2×Dic3—61no—
307C2×Dic3—61no—
308C2×Dic3—61no—
309C2×Dic3—61no—
310C2×Dic3—61no—
311C2×Dic3—61no—
312C2×Dic3—61no—
313C2×Dic3—61no—
314C2×Dic3—61no—
315C2×Dic3—61no—
316C2×Dic3—61no—
317C2×Dic3—61no—
318C2×Dic3—64no—
319C2×Dic3—64no—
320D12—24no—
321D12—68no—
322C4×D3—28no—
323C4×D3—62no—
324C4×D3—62no—
325C4×D3—62no—
326C4×D3—62no—
327C4×D3—62no—
328C4×D3—62no—
329C4×D3—62no—
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—68no—
340C4×D3—64no—
341C4×D3—64no—
342Dic6—24no—
343Dic6—64no—
344Dic6—64no—
345C2×C32—21no—
346C2×C32—21no—
347C2×C32#42112yescomplemented
348C2×C32C22×C22⋊C411yescharacteristic
349C3⋊D3—22no—
350C3⋊D3—22no—
351C3×D3—44no—
352C24—91no—
353C24—181no—
354#41—64no—
355#41—64no—
356#41—98no—
357#41—94no—
358#41—94no—
359#41—184no—
360#41—182no—
361#41—182no—
362#41—184no—
363#41—184no—
364C2×Q8—61no—
365C2×Q8—92no—
366C2×Q8—94no—
367C2×Q8—182no—
368C2×D4—62no—
369C2×D4—61no—
370C2×D4—94no—
371C2×D4—92no—
372C2×D4—182no—
373C2×D4—182no—
374C2×D4—184no—
375C2×D4—184no—
376C22×C4—62no—
377C22×C4—62no—
378C22×C4—91no—
379C22×C4—92no—
380C22×C4—92no—
381C22×C4—91no—
382C22×C4—91no—
383C22×C4—92no—
384C22×C4—91no—
385C22×C4—92no—
386C22×C4—91no—
387C22×C4—184no—
388C22×C4—184no—
389C22×C4—181no—
390C22×C4—182no—
391C22×C4GO+(4,𝔽2)11yescharacteristic
392M16—94no—
393M16—184no—
394M16—182no—
395C2×C8—184no—
396C2×C8—182no—
397C4⋊C4—64no—
398C22⋊C4—184no—
399C42—94no—
400C42—182no—
401C22×C3—22no—
402C22×C3—22no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—42no—
410C22×C3—64no—
411C22×C3—124no—
412C2×D3—24no—
413C2×D3—44no—
414C2×D3—62no—
415C2×D3—62no—
416C2×D3—62no—
417C2×D3—62no—
418C2×D3—64no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—1216no—
423C2×D3—124no—
424C2×D3—124no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—124no—
428C3×C4—22no—
429C3×C4—22no—
430C3×C4—22no—
431C3×C4—22no—
432C3×C4—64no—
433C3×C4—124no—
434Dic3—24no—
435Dic3—44no—
436Dic3—61no—
437Dic3—61no—
438Dic3—61no—
439Dic3—61no—
440Dic3—61no—
441Dic3—61no—
442Dic3—61no—
443Dic3—61no—
444C32C2×#42111yescharacteristic, complemented, Sylow
445C23—62no—
446C23—91no—
447C23—91no—
448C23—92no—
449C23—92no—
450C23—184no—
451C23—362no—
452C23—364no—
453C23C2×GO+(4,𝔽2)11yescharacteristic
454Q8—64no—
455Q8—94no—
456Q8—182no—
457D4—64no—
458D4—64no—
459D4—64no—
460D4—94no—
461D4—188no—
462D4—182no—
463C2×C4—62no—
464C2×C4—68no—
465C2×C4—64no—
466C2×C4—91no—
467C2×C4—91no—
468C2×C4—91no—
469C2×C4—91no—
470C2×C4—91no—
471C2×C4—91no—
472C2×C4—92no—
473C2×C4—92no—
474C2×C4—92no—
475C2×C4—92no—
476C2×C4—92no—
477C2×C4—92no—
478C2×C4—92no—
479C2×C4—92no—
480C2×C4—124no—
481C2×C4—184no—
482C2×C4—184no—
483C2×C4—184no—
484C2×C4D32⋊C412yes—
485C2×C4D32⋊C411yescharacteristic
486C2×C4D32⋊C411yescharacteristic
487C2×C4C2×GO+(4,𝔽2)12yes—
488C8—184no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—22no—
492C2×C3—22no—
493C2×C3—22no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—41no—
497C2×C3—41no—
498C2×C3—124no—
499D3—44no—
500D3—64no—
501D3—122no—
502D3—122no—
503D3—122no—
504C22—22no—
505C22—64no—
506C22—92no—
507C22—92no—
508C22—124no—
509C22—182no—
510C22—182no—
511C22—362no—
512C22—362no—
513C22—368no—
514C22C2×D32⋊C411yescharacteristic
515C22C2×D32⋊C411yescharacteristic
516C22C22×GO+(4,𝔽2)11yescharacteristic
517C4—64no—
518C4—91no—
519C4—91no—
520C4—91no—
521C4—91no—
522C4—124no—
523C4C2×D32⋊C412yes—
524C4C2×D32⋊C412yes—
525C3—21no—
526C3—21no—
527C2—21no—
528C2—21no—
529C2—124no—
530C2—182no—
531C2—182no—
532C2#1059338112yesdirect product factor
533C2C22×D32⋊C411yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC3⋊Dic3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64306C2
cosocleC2×C3⋊Dic3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C2×#421
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×#64283C2semidirect
3. C2×#63849C2semidirect
4. C2×#63741C2semidirect
5. #10593381C2direct (N × H)
12. #64306C4semidirect
14. C2×#3802C4semidirect
16. C2×#3798C4semidirect
17. C2×#3797C4semidirect
19. C2×#3792C22semidirect
21. #64283C22semidirect
26. C2×Dic32C22semidirect
28. #63849C22semidirect
29. #63741C22semidirect
63. #3802C2×C4semidirect
67. #3798C2×C4semidirect
69. #3797C2×C4semidirect
73. #3792C23semidirect
80. Dic32C23semidirect
347. C2×C32#421semidirect
444. C32C2×#421semidirect
532. C2#10593381direct (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×#642832
C2×#638492
C2×#637412
#105933812
C2×#4219