Finite Group Databasebeta

← C2×#10593784 #11861047

Subgroups — C2×#10593784 #11861047

Order 1152.

730 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 162 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×#64289C211yesmaximal, characteristic, complemented
2C2×#64287C211yesmaximal, characteristic, complemented
3C2×#64125C211yesmaximal, characteristic
4C2×#63785C211yesmaximal, characteristic, complemented
5C2×#63783C211yesmaximal, characteristic, complemented
6#10593784C218yesmaximal, direct product factor
7C2×#63771C211yesmaximal, characteristic, complemented
8C2×#63767C211yesmaximal, characteristic, complemented
9C2×#3832C2211yescharacteristic
10C2×#3830C2211yescharacteristic
11C2×#3792—21no—
12C22×#622—21no—
13#64289—22no—
14#64289C2214yescomplemented
15#64287—22no—
16#64287C2214yescomplemented
17C2×C4×#157C2211yescharacteristic
18C2×#3788—21no—
19C2×#3788C2211yescharacteristic
20C2×#3788C2211yescharacteristic
21C2×#3787—21no—
22C2×#3787C2211yescharacteristic
23C2×C32×SD16C411yescharacteristic, complemented
24C2×#3756C411yescharacteristic, complemented
25C2×#3753C411yescharacteristic, complemented
26#64125C414yescomplemented
27#64125C2214yes—
28C2×#3744C411yescharacteristic, complemented
29C2×C8×C3⋊D3C2211yescharacteristic
30#63785C2214yescomplemented
31#63783C2214yescomplemented
32#63771C2214yescomplemented
33#63767C2214yescomplemented
34C2×#916—62no—
35C22×#157—21no—
36C2×C32×Q8C2×C411yescharacteristic
37C2×C32×D4C2×C411yescharacteristic
38C2×#638—21no—
39C22×C3⋊Dic3—21no—
40#3832—21no—
41#3832—21no—
42#3832C2×C412yes—
43#3832C2312yes—
44#3830—21no—
45#3830—21no—
46#3830C2×C412yes—
47#3830C2312yes—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3C2311yescharacteristic
52C2×#634C2×C411yescharacteristic
53#3792—24no—
54C2×#622—21no—
55C2×#622—21no—
56C2×#622—24no—
57C2×#622D411yescharacteristic
58C2×#622D411yescharacteristic
59C4×#157—21no—
60C4×#157C2312yes—
61#3788—21no—
62#3788—21no—
63#3788—24no—
64#3788C2312yes—
65#3788C2312yes—
66#3787—24no—
67#3787D412yes—
68#3787C2312yes—
69C32×SD16C2×C414yescomplemented
70C2×C32×C8C2×C411yescharacteristic
71#3756C2×C414yescomplemented
72#3753C2×C414yescomplemented
73C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
74#3744C2×C414yescomplemented
75C8×C3⋊D3C2×C412yes—
76C8×C3⋊D3C2312yes—
77C2×#444—91nomaximal, Sylow
78C2×#239—62no—
79C2×#237—62no—
80C2×C3×SD16—22no—
81C2×#216—62no—
82C2×#213—62no—
83#916—68no—
84#916—68no—
85C2×#204—62no—
86C2×D3×C8—62no—
87C23×C32—21no—
88C22×C3⋊D3—21no—
89C22×C3⋊D3#4111yescharacteristic
90C2×#157—22no—
91C2×#157—42no—
92C32×Q8—21no—
93C32×Q8C22×C412yes—
94C32×D4—21no—
95C32×D4C22×C412yes—
96C2×C32×C4—21no—
97C2×C32×C4C22×C411yescharacteristic
98#638—22no—
99#638—22no—
100C2×C3⋊Dic3—21no—
101C2×C3⋊Dic3—22no—
102C2×C3⋊Dic3—22no—
103C2×C3⋊Dic3C2×D411yescharacteristic
104C4⋊(C3⋊D3)—22no—
105C4⋊(C3⋊D3)—22no—
106C4⋊(C3⋊D3)—21no—
107C4⋊(C3⋊D3)C22×C412yes—
108C4×C3⋊D3—22no—
109C4×C3⋊D3—22no—
110C4×C3⋊D3C22×C411yescharacteristic
111C4×C3⋊D3C2×D411yescharacteristic
112C4×C3⋊D3#4111yescharacteristic
113C4×C3⋊D3C2411yescharacteristic
114#634—21no—
115#634C22×C412yes—
116#622—22no—
117#622—22no—
118#622C2×D412yes—
119#622C2×D412yes—
120C32×C8C22×C412yes—
121C3⋊(C3⋊C8)C22×C412yes—
122C2×#135—91no—
123C2×#131—91no—
124C2×#131—91no—
125#444—98no—
126C2×#108—91no—
127C2×#104—91no—
128C2×#104—91no—
129C2×#97—91no—
130C2×C3×Q8—22no—
131C2×C3×D4—22no—
132C2×#67—122no—
133C22×Dic3—122no—
134#239—64no—
135#239—64no—
136#239—122no—
137#239—122no—
138#237—64no—
139#237—64no—
140#237—122no—
141#237—122no—
142C2×D12—62no—
143C2×D12—122no—
144C2×C4×D3—62no—
145C2×C4×D3—122no—
146C2×Dic6—62no—
147C3×SD16—28no—
148C2×C3×C8—22no—
149#216—68no—
150#213—68no—
151C2×C3⋊C8—62no—
152#204—68no—
153D3×C8—64no—
154D3×C8—64no—
155C22×C32—22no—
156C22×C32—42no—
157C22×C32C4×D411yescharacteristic
158C2×C3⋊D3—22no—
159C2×C3⋊D3—22no—
160C2×C3⋊D3—42no—
161C2×C3⋊D3C4×D411yescharacteristic
162C2×C3⋊D3C2×#4111yescharacteristic
163#157—42no—
164C32×C4—22no—
165C32×C4C4×D411yescharacteristic
166C32×C4C23×C411yescharacteristic
167C3⋊Dic3—22no—
168C3⋊Dic3C4×D411yescharacteristic
169C3⋊Dic3C22×D411yescharacteristic
170C2×#41—91no—
171C2×#41—91no—
172#135—94no—
173#135—94no—
174C2×Q16—91no—
175C2×SD16—91no—
176C2×SD16#15711yescharacteristic, complemented
177C2×D8—91no—
178#131—94no—
179#131—94no—
180#131—182no—
181#131—182no—
182C2×M16—91no—
183C2×M16—91no—
184C2×M16—181no—
185C2×M16—181no—
186C22×C8—91no—
187C22×C8—91no—
188C22×C8—181no—
189C22×C8—181no—
190C2×C42—91no—
191#108—94no—
192#104—94no—
193#104—94no—
194#97—94no—
195C23×C3—42no—
196C22×D3—62no—
197C22×D3—122no—
198C3×Q8—24no—
199C3×Q8—42no—
200C3×D4—24no—
201C3×D4—42no—
202C2×C3×C4—22no—
203C2×C3×C4—42no—
204#67—124no—
205#67—124no—
206C2×Dic3—62no—
207C2×Dic3—124no—
208C2×Dic3—124no—
209C2×Dic3—122no—
210D12—64no—
211D12—122no—
212D12—124no—
213D12—124no—
214C4×D3—62no—
215C4×D3—62no—
216C4×D3—62no—
217C4×D3—62no—
218C4×D3—124no—
219C4×D3—124no—
220Dic6—64no—
221Dic6—122no—
222C3×C8—24no—
223C3⋊C8—64no—
224C2×C32—42no—
225C2×C32#44412yescomplemented
226C2×C32C2×C4×D411yescharacteristic
227C3⋊D3—21no—
228C3⋊D3—21no—
229C3⋊D3—42no—
230#41—92no—
231#41—92no—
232#41—92no—
233#41—92no—
234#41—181no—
235#41—181no—
236#41—181no—
237#41—181no—
238C2×Q8—91no—
239C2×Q8C2×#15711yescharacteristic
240C2×D4—91no—
241C2×D4—181no—
242C2×D4—181no—
243C2×D4C2×#15711yescharacteristic
244C22×C4—91no—
245C22×C4—181no—
246C22×C4—181no—
247C22×C4—181no—
248Q16—94no—
249SD16—94no—
250SD16C2×#15714yescomplemented
251D8—94no—
252M16—92no—
253M16—92no—
254M16—184no—
255M16—184no—
256M16—181no—
257M16—181no—
258C2×C8—92no—
259C2×C8—91no—
260C2×C8—91no—
261C2×C8—92no—
262C2×C8—91no—
263C2×C8—92no—
264C2×C8—92no—
265C2×C8—184no—
266C2×C8—184no—
267C2×C8—181no—
268C2×C8—181no—
269C2×C8C2×#15711yescharacteristic
270C42—92no—
271C42—181no—
272C22×C3—22no—
273C22×C3—44no—
274C22×C3—84no—
275C2×D3—62no—
276C2×D3—62no—
277C2×D3—124no—
278C2×D3—124no—
279C2×D3—244no—
280C3×C4—22no—
281C3×C4—22no—
282C3×C4—44no—
283Dic3—62no—
284Dic3—62no—
285Dic3—124no—
286C32C2×#44411yescharacteristic, complemented, Sylow
287C23—21no—
288C23—91no—
289C23—181no—
290Q8—21no—
291Q8—92no—
292Q8—181no—
293Q8C22×#15712yes—
294D4—21no—
295D4—92no—
296D4—182no—
297D4—182no—
298D4—182no—
299D4—182no—
300D4—181no—
301D4C22×#15712yes—
302C2×C4—21no—
303C2×C4—91no—
304C2×C4—91no—
305C2×C4—91no—
306C2×C4—91no—
307C2×C4—91no—
308C2×C4—182no—
309C2×C4—182no—
310C2×C4—182no—
311C2×C4—182no—
312C2×C4—181no—
313C2×C4—182no—
314C2×C4—362no—
315C2×C4C22×#15711yescharacteristic
316C8—92no—
317C8—92no—
318C8—92no—
319C8—182no—
320C8—182no—
321C8C22×#15712yes—
322C2×C3—22no—
323C2×C3—24no—
324C2×C3—84no—
325D3—122no—
326D3—122no—
327D3—244no—
328C22—22no—
329C22—42no—
330C22—91no—
331C22—91no—
332C22—182no—
333C22—182no—
334C22—362no—
335C22D4×#15711yescharacteristic
336C4—22no—
337C4—91no—
338C4—91no—
339C4—182no—
340C4—362no—
341C4D4×#15711yescharacteristic
342C4C23×#15711yescharacteristic
343C3—22no—
344C2—42no—
345C2—181no—
346C2—181no—
347C2—362no—
348C2#1059378412yesdirect product factor
349C2C2×D4×#15711yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC2×C32×SD16C4
socleC22×C32C4×D4
prime radicalC2×#64125C2
cosocleC4×C3⋊D3C24
hypercenterC2×SD16#157
hypocenterC32C2×#444
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#64289C2semidirect
2. C2×#64287C2semidirect
4. C2×#63785C2semidirect
5. C2×#63783C2semidirect
6. #10593784C2direct (N × H)
7. C2×#63771C2semidirect
8. C2×#63767C2semidirect
14. #64289C22semidirect
16. #64287C22semidirect
23. C2×C32×SD16C4semidirect
24. C2×#3756C4semidirect
25. C2×#3753C4semidirect
26. #64125C4semidirect
28. C2×#3744C4semidirect
30. #63785C22semidirect
31. #63783C22semidirect
32. #63771C22semidirect
33. #63767C22semidirect
69. C32×SD16C2×C4semidirect
71. #3756C2×C4semidirect
72. #3753C2×C4semidirect
74. #3744C2×C4semidirect
176. C2×SD16#157semidirect
225. C2×C32#444semidirect
250. SD16C2×#157semidirect
286. C32C2×#444semidirect
348. C2#10593784direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642892
C2×#642872
C2×#641252
C2×#637852
C2×#637832
#105937842
C2×#637712
C2×#637672
C2×#4449