Finite Group Databasebeta

← C2×#10590236 #11899569

Subgroups — C2×#10590236 #11899569

Order 1152.

845 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 845 conjugacy classes of subgroups — too many to draw. Only its 156 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×#63810C211yesmaximal, characteristic, complemented
2C2×#63797C211yesmaximal, characteristic, complemented
3C2×#63625C211yesmaximal, characteristic, complemented
4C2×C3×#800C211yesmaximal, characteristic, complemented
5C2×C3×D48C211yesmaximal, characteristic, complemented
6C2×#63547C211yesmaximal, characteristic, complemented
7C2×#63545C211yesmaximal, characteristic, complemented
8#10590236C218yesmaximal, direct product factor
9C2×#4914—31nomaximal
10C2×#4911—31nomaximal
11C2×#3802—21no—
12C2×#3796—21no—
13C2×C8×C3⋊D3C2211yescharacteristic
14C2×C3×Dic12C2211yescharacteristic, complemented
15C2×C3×D24C2211yescharacteristic
16C2×C3×D24C2211yescharacteristic
17C2×C3×D24C2211yescharacteristic, complemented
18C2×#3715—21no—
19C2×#3713—21no—
20#63810—22no—
21#63810C2214yescomplemented
22#63797—22no—
23#63797C2214yescomplemented
24C2×C32×C16C2211yescharacteristic, complemented
25C2×C3⋊(C3⋊C16)C2211yescharacteristic, complemented
26#63625C2214yescomplemented
27C3×#800C2214yescomplemented
28C3×D48C2214yescomplemented
29#63547C2214yescomplemented
30#63545C2214yescomplemented
31C2×#919—31no—
32C2×#912—31no—
33C2×D3×D8—31no—
34C2×D3×D8—31no—
35C2×C3×SD32—31no—
36C2×C3×D16—31no—
37C2×#828—31no—
38C2×#827—31no—
39C2×#826—31no—
40C2×#826—31no—
41#4914—38no—
42#4911—38no—
43C2×#800D311yescharacteristic, complemented
44C2×D48D311yescharacteristic, complemented
45C2×#798—31no—
46C2×#798—31no—
47C2×#798—61no—
48C22×D32—41no—
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×Dic6—21no—
54C2×#626—41no—
55C2×#625—41no—
56C2×D3×Dic3—41no—
57#3802—24no—
58#3802—42no—
59#3796—24no—
60#3796—42no—
61C2×C32×C8C2311yescharacteristic
62C2×C3⋊(C3⋊C8)D411yescharacteristic
63C8×C3⋊D3D412yes—
64C8×C3⋊D3C2312yes—
65C3×Dic12—21no—
66C3×Dic12C2312yescomplemented
67C3×D24—21no—
68C3×D24—21no—
69C3×D24—21no—
70C3×D24C2312yes—
71C3×D24C2312yes—
72C3×D24C2312yescomplemented
73#3715—24no—
74#3713—24no—
75C32×C16C2312yescomplemented
76C3⋊(C3⋊C16)C2312yescomplemented
77C2×#509—91noSylow
78C2×#239—61no—
79C2×#237—61no—
80C2×D3×D4—61no—
81C2×D3×D4—61no—
82C2×C3×Q16—31no—
83C2×C3×D8—31no—
84C2×C3×D8—31no—
85C2×C3×D8—31no—
86C2×#215—61no—
87C2×#214—61no—
88C2×#213—61no—
89C2×#213—61no—
90#919—34no—
91#919—62no—
92#912—34no—
93#912—62no—
94D3×D8—34no—
95D3×D8—34no—
96D3×D8—62no—
97D3×D8—62no—
98C2×Dic12C2×D311yescharacteristic, complemented
99C2×D24C2×D311yescharacteristic
100C2×D24C2×D311yescharacteristic
101C2×D24C2×D311yescharacteristic, complemented
102C2×D3×C8—31no—
103C2×D3×C8—31no—
104C2×D3×C8—61no—
105C3×SD32—34no—
106C3×D16—34no—
107C2×C3×C16—21no—
108C2×C3×C16C2×D311yescharacteristic, complemented
109C2×C3×C16C2×D311yescharacteristic, complemented
110#828—34no—
111#827—34no—
112#826—34no—
113#826—34no—
114C2×C3⋊C16—31no—
115C2×C3⋊C16—31no—
116C2×C3⋊C16—61no—
117#800C2×D314yescomplemented
118D48C2×D314yescomplemented
119#798—34no—
120#798—34no—
121#798—64no—
122C22×C3⋊D3D811yescharacteristic
123C22×C3×D3—41no—
124C22×C3×D3—41no—
125C22×C3×D3—41no—
126C2×D32—44no—
127C2×D32—84no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C3⋊Dic3D811yescharacteristic
130C4×C3⋊D3D812yes—
131C4×C3⋊D3C2×D412yes—
132C2×C3×Dic3—41no—
133C3×D12—22no—
134C3×D12—22no—
135C3×D12—22no—
136C3×D12—41no—
137C3×D12—41no—
138C3×D12—41no—
139C3×Dic6—22no—
140C3×Dic6—41no—
141#626—44no—
142#625—44no—
143D3×Dic3—44no—
144C32×C8C2×D411yescharacteristic
145C32×C8C2411yescharacteristic
146C3⋊(C3⋊C8)C2×D412yes—
147C2×#135—91no—
148C22×D8—91no—
149#509—98no—
150C2×SD32—31no—
151C2×SD32—91no—
152C2×D16—31no—
153C2×D16—91no—
154C2×M32—91no—
155C23×D3—121no—
156C23×D3—121no—
157C2×C3×Q8—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×#67—121no—
162C2×#67—121no—
163C2×#67—121no—
164C22×Dic3—121no—
165#239—64no—
166#239—122no—
167#237—64no—
168#237—122no—
169D3×D4—64no—
170D3×D4—64no—
171D3×D4—122no—
172D3×D4—122no—
173C2×D12—21no—
174C2×D12—21no—
175C2×D12—21no—
176C2×D12—121no—
177C2×C4×D3—31no—
178C2×C4×D3—31no—
179C2×C4×D3—61no—
180C2×C4×D3—121no—
181C2×Dic6—21no—
182C3×Q16—32no—
183C3×Q16—61no—
184C3×D8—32no—
185C3×D8—32no—
186C3×D8—32no—
187C3×D8—61no—
188C3×D8—61no—
189C3×D8—61no—
190C2×C3×C8—21no—
191C2×C3×C8C22×D311yescharacteristic
192C2×C3×C8C22×D311yescharacteristic
193#215—64no—
194#214—64no—
195#213—64no—
196#213—64no—
197C2×C3⋊C8—31no—
198C2×C3⋊C8—31no—
199C2×C3⋊C8—61no—
200Dic12—21no—
201Dic12C22×D312yescomplemented
202D24—21no—
203D24—21no—
204D24—21no—
205D24C22×D312yes—
206D24C22×D312yes—
207D24C22×D312yescomplemented
208D3×C8—32no—
209D3×C8—32no—
210D3×C8—32no—
211D3×C8—32no—
212D3×C8—62no—
213D3×C8—62no—
214C3×C16—22no—
215C3×C16C22×D312yescomplemented
216C3×C16C22×D312yescomplemented
217C3⋊C16—32no—
218C3⋊C16—32no—
219C3⋊C16—62no—
220C22×C32C2×D811yescharacteristic
221C2×C3⋊D3—22no—
222C2×C3⋊D3C2×D812yes—
223C2×C3×D3—42no—
224C2×C3×D3—42no—
225C2×C3×D3—42no—
226C2×C3×D3—82no—
227C2×C3×D3—82no—
228C2×C3×D3—82no—
229D32—88no—
230C32×C4C2×D811yescharacteristic
231C32×C4C22×D411yescharacteristic
232C3⋊Dic3C2×D812yes—
233C3×Dic3—42no—
234C2×#41—181no—
235C22×D4—181no—
236#135—94no—
237#135—182no—
238C2×Q16—31no—
239C2×SD16—181no—
240C2×D8—31no—
241C2×D8—31no—
242C2×D8—31no—
243C2×D8—94no—
244C2×D8—182no—
245C2×D8—181no—
246C22×C8—91no—
247SD32—34no—
248SD32—94no—
249D16—34no—
250D16—94no—
251M32—94no—
252C2×C16—91no—
253C2×C16D3211yescharacteristic, complemented
254C23×C3—121no—
255C23×C3—121no—
256C23×C3—121no—
257C22×D3—31no—
258C22×D3—31no—
259C22×D3—41no—
260C22×D3—41no—
261C22×D3—41no—
262C22×D3—61no—
263C22×D3—124no—
264C22×D3—124no—
265C22×D3—244no—
266C22×D3—244no—
267C3×Q8—62no—
268C3×Q8—121no—
269C3×D4—62no—
270C3×D4—62no—
271C3×D4—62no—
272C3×D4—121no—
273C3×D4—121no—
274C3×D4—121no—
275C2×C3×C4—21no—
276C2×C3×C4—121no—
277C2×C3×C4D3×D411yescharacteristic
278C2×C3×C4D3×D411yescharacteristic
279#67—124no—
280#67—124no—
281#67—124no—
282C2×Dic3—31no—
283C2×Dic3—31no—
284C2×Dic3—41no—
285C2×Dic3—61no—
286C2×Dic3—124no—
287D12—22no—
288D12—22no—
289D12—22no—
290D12—41no—
291D12—41no—
292D12—41no—
293D12—124no—
294C4×D3—32no—
295C4×D3—32no—
296C4×D3—32no—
297C4×D3—32no—
298C4×D3—62no—
299C4×D3—62no—
300C4×D3—124no—
301Dic6—22no—
302Dic6—41no—
303C3×C8—21no—
304C3×C8—21no—
305C3×C8D3×D411yescharacteristic
306C3×C8D3×D411yescharacteristic
307C3×C8C23×D311yescharacteristic
308C3×C8C23×D311yescharacteristic
309C3⋊C8—32no—
310C3⋊C8—32no—
311C3⋊C8—62no—
312C2×C32#50912yescomplemented
313C2×C32C22×D811yescharacteristic
314C3⋊D3—22no—
315C3×D3—82no—
316C3×D3—82no—
317C3×D3—82no—
318C24—361no—
319#41—184no—
320#41—362no—
321C2×Q8—61no—
322C2×D4—61no—
323C2×D4—61no—
324C2×D4—61no—
325C2×D4—184no—
326C2×D4—362no—
327C2×D4—361no—
328C2×D4—361no—
329C22×C4—91no—
330C22×C4—361no—
331Q16—32no—
332Q16—61no—
333SD16—184no—
334D8—32no—
335D8—32no—
336D8—32no—
337D8—61no—
338D8—61no—
339D8—61no—
340D8—184no—
341C2×C8—91no—
342C2×C8—92no—
343C2×C8—92no—
344C2×C8C2×D3211yescharacteristic
345C16—92no—
346C16C2×D3212yescomplemented
347C22×C3—21no—
348C22×C3—122no—
349C22×C3—122no—
350C22×C3—122no—
351C22×C3—242no—
352C22×C3—242no—
353C22×C3—242no—
354C22×C3D3×D811yescharacteristic
355C22×C3D3×D811yescharacteristic
356C2×D3—32no—
357C2×D3—32no—
358C2×D3—42no—
359C2×D3—42no—
360C2×D3—42no—
361C2×D3—62no—
362C2×D3—62no—
363C2×D3—62no—
364C2×D3—82no—
365C2×D3—82no—
366C2×D3—82no—
367C2×D3—122no—
368C2×D3—248no—
369C2×D3—248no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—122no—
373C3×C4D3×D811yescharacteristic
374C3×C4D3×D811yescharacteristic
375C3×C4C2×D3×D411yescharacteristic
376C3×C4C2×D3×D411yescharacteristic
377Dic3—32no—
378Dic3—32no—
379Dic3—42no—
380Dic3—62no—
381C32C2×#50911yescharacteristic, complemented, Sylow
382C23—91no—
383C23—121no—
384C23—121no—
385C23—121no—
386C23—364no—
387C23—724no—
388Q8—62no—
389Q8—121no—
390D4—62no—
391D4—62no—
392D4—62no—
393D4—121no—
394D4—121no—
395D4—121no—
396D4—364no—
397D4—364no—
398C2×C4—91no—
399C2×C4—92no—
400C2×C4—92no—
401C2×C4—121no—
402C2×C4—364no—
403C2×C4#380211yescharacteristic
404C8—92no—
405C8#380211yescharacteristic
406C8C22×D3211yescharacteristic
407C2×C3—22no—
408C2×C3—21no—
409C2×C3—242no—
410C2×C3—242no—
411C2×C3—242no—
412C2×C3#491112yescomplemented
413C2×C3#491412yescomplemented
414C2×C3C2×D3×D811yescharacteristic
415C2×C3C2×D3×D811yescharacteristic
416D3—62no—
417D3—62no—
418D3—82no—
419D3—82no—
420D3—82no—
421D3—122no—
422C22—92no—
423C22—122no—
424C22—122no—
425C22—122no—
426C22—182no—
427C22—242no—
428C22—242no—
429C22—242no—
430C22—728no—
431C22#6379711yescharacteristic
432C4—92no—
433C4—122no—
434C4#6379711yescharacteristic
435C4C2×#380211yescharacteristic
436C3—21no—
437C3C2×#491111yescharacteristic, complemented
438C3C2×#491411yescharacteristic, complemented
439C2—182no—
440C2—242no—
441C2—242no—
442C2—242no—
443C2#1059023612yesdirect product factor
444C2C2×#6379711yescharacteristic
subgroupG/H
centerC22#63797
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC2×C32×C16C22
socleC22×C32C2×D8
hypercenterC2×C16D32
hypocenterC32C2×#509
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×#63810C2semidirect
2. C2×#63797C2semidirect
3. C2×#63625C2semidirect
4. C2×C3×#800C2semidirect
5. C2×C3×D48C2semidirect
6. C2×#63547C2semidirect
7. C2×#63545C2semidirect
8. #10590236C2direct (N × H)
14. C2×C3×Dic12C22semidirect
17. C2×C3×D24C22semidirect
21. #63810C22semidirect
23. #63797C22semidirect
24. C2×C32×C16C22semidirect
25. C2×C3⋊(C3⋊C16)C22semidirect
26. #63625C22semidirect
27. C3×#800C22semidirect
28. C3×D48C22semidirect
29. #63547C22semidirect
30. #63545C22semidirect
43. C2×#800D3semidirect
44. C2×D48D3semidirect
66. C3×Dic12C23semidirect
72. C3×D24C23semidirect
75. C32×C16C23semidirect
76. C3⋊(C3⋊C16)C23semidirect
98. C2×Dic12C2×D3semidirect
101. C2×D24C2×D3semidirect
108. C2×C3×C16C2×D3semidirect
109. C2×C3×C16C2×D3semidirect
117. #800C2×D3semidirect
118. D48C2×D3semidirect
201. Dic12C22×D3semidirect
207. D24C22×D3semidirect
215. C3×C16C22×D3semidirect
216. C3×C16C22×D3semidirect
253. C2×C16D32semidirect
312. C2×C32#509semidirect
346. C16C2×D32semidirect
381. C32C2×#509semidirect
412. C2×C3#4911semidirect
413. C2×C3#4914semidirect
437. C3C2×#4911semidirect
438. C3C2×#4914semidirect
443. C2#10590236direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#638102
C2×#637972
C2×#636252
C2×C3×#8002
C2×C3×D482
C2×#635472
C2×#635452
#105902362
C2×#49143
C2×#49113