Finite Group Databasebeta

← C2×#20296065 #28379783

Subgroups — C2×#20296065 #28379783

Order 13952.

544 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 170 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×Q8×#89137C211yesmaximal, characteristic, complemented
2C2×D4×#89137C211yesmaximal, characteristic
3#20296065C218yesmaximal, direct product factor
4C2×#16812768C211yesmaximal, characteristic, complemented
5C2×#16812762C211yesmaximal, characteristic, complemented
6C2×#16812761C211yesmaximal, characteristic
7C2×#16812753C211yesmaximal, characteristic, complemented
8C2×SD16×D109C211yesmaximal, characteristic
9C23×#89137—21no—
10C2×D109⋊C8C2211yescharacteristic
11Q8×#89137—22no—
12Q8×#89137C2214yescomplemented
13D4×#89137—22no—
14D4×#89137C2214yes—
15C2×C4⋊#89137—21no—
16C2×C4⋊#89137C2211yescharacteristic
17C2×C4⋊#89137C2211yescharacteristic
18C2×C22⋊#89137—21no—
19C2×C4×#89137—21no—
20C2×C4×#89137C2211yescharacteristic
21#16812768C2214yescomplemented
22#16812762C2214yescomplemented
23#16812761C2214yes—
24#16812753C2214yescomplemented
25C2×Q8×D109C2211yescharacteristic
26C2×D4×D109C2211yescharacteristic
27C2×#13182018C411yescharacteristic, complemented
28C2×#13182017C411yescharacteristic, complemented
29C2×#13182016C411yescharacteristic, complemented
30SD16×D109C414yescomplemented
31SD16×D109C2214yes—
32C2×C8×D109C2211yescharacteristic
33C2×SD16×C109C411yescharacteristic, complemented
34C22×#89137—21no—
35C22×#89137—21no—
36C22×#89137—24no—
37C22×#89137—44no—
38C22×#89137D411yescharacteristic
39C22×#89137D411yescharacteristic
40D109⋊C8—21no—
41D109⋊C8C2312yes—
42C2×#11724786—21no—
43C4⋊#89137—24no—
44C4⋊#89137—21no—
45C4⋊#89137—21no—
46C4⋊#89137C2312yes—
47C4⋊#89137C2312yes—
48C22⋊#89137—24no—
49C4×#89137—24no—
50C4×#89137D412yes—
51C4×#89137C2312yes—
52C23×D109—21no—
53C2×Dic218—21no—
54C2×Dic218C2×C411yescharacteristic, complemented
55Q8×D109—21no—
56Q8×D109—21no—
57Q8×D109C2×C412yescomplemented
58Q8×D109C2312yes—
59C2×D436C2×C411yescharacteristic
60C2×C22⋊D109—21no—
61D4×D109—21no—
62D4×D109—21no—
63D4×D109C2×C412yes—
64D4×D109C2312yes—
65C2×C4×D109—21no—
66C2×C4×D109C2311yescharacteristic
67#13182018C2×C414yescomplemented
68#13182017C2×C414yescomplemented
69#13182016C2×C414yescomplemented
70C2×#11724784C2×C411yescharacteristic, complemented
71C8×D109C2×C412yescomplemented
72C8×D109C2312yes—
73C2×Q8×C109C2×C411yescharacteristic, complemented
74C2×D4×C109C2×C411yescharacteristic
75SD16×C109C2×C414yescomplemented
76C2×C8×C109C2×C411yescharacteristic, complemented
77C23×C109—21no—
78C22×D109—21no—
79C22×D109—22no—
80C22×D109—22no—
81C22×D109—42no—
82C22×D109—42no—
83C22×D109C2×D411yescharacteristic
84C2×#89137—22no—
85C2×#89137—22no—
86C2×#89137—22no—
87C2×#89137—22no—
88C2×#89137—48no—
89C2×#89137—42no—
90C2×#89137—42no—
91C2×#89137C2×D412yes—
92C2×#89137C2×D412yes—
93Q8×C109—21no—
94Q8×C109C22×C412yescomplemented
95D4×C109—21no—
96D4×C109C22×C412yes—
97C2×C4×C109—21no—
98C2×C4×C109C22×C411yescharacteristic
99C22⋊D109—22no—
100C22⋊D109—22no—
101C2×Dic109—21no—
102C2×Dic109#4111yescharacteristic
103D436—21no—
104D436C22×C412yes—
105C4×D109—22no—
106C4×D109—22no—
107C4×D109C22×C411yescharacteristic
108C4×D109C2×D411yescharacteristic
109C4×D109#4111yescharacteristic
110C4×D109C2411yescharacteristic
111Dic218—21no—
112Dic218—22no—
113Dic218—22no—
114Dic218C22×C412yescomplemented
115#11724786—22no—
116C8×C109C22×C412yescomplemented
117#11724784C22×C412yescomplemented
118C22×C109—22no—
119C22×C109—42no—
120C22×C109C4×D411yescharacteristic
121C2×D109—22no—
122C2×D109—42no—
123C2×D109—42no—
124C2×D109—42no—
125C2×D109—44no—
126C2×D109C4×D411yescharacteristic
127C2×D109AGL(1,ℤ/8)12yes—
128C2×D109#13712yes—
129C2×D109C22×D411yescharacteristic
130#89137—22no—
131#89137—22no—
132#89137—42no—
133#89137—42no—
134C4×C109—22no—
135C4×C109C4×D411yescharacteristic
136C4×C109C23×C411yescharacteristic
137Dic109—22no—
138Dic109C4×D411yescharacteristic
139Dic109C2×#4111yescharacteristic
140C2×C109—42no—
141C2×C109#44012yescomplemented
142C2×C109C2×C4×D411yescharacteristic
143D109—42no—
144D109#44012yescomplemented
145D109C2×AGL(1,ℤ/8)11yescharacteristic
146D109C2×#13711yescharacteristic
147C2×#440—1091nomaximal, Sylow
148C109C2×#44011yescharacteristic, complemented, Sylow
149C22×SD16—1091no—
150C2×C4×Q8—1091no—
151C2×C4×D4—1091no—
152#440—1098no—
153C2×#107—1091no—
154C2×#103—1091no—
155C2×#102—1091no—
156C2×#97—1091no—
157C22×Q8—1091no—
158C22×D4—1091no—
159C23×C4—2181no—
160C2×SD16—1091no—
161C2×SD16—1091no—
162C2×SD16—1094no—
163C2×SD16—1094no—
164C2×SD16—1091no—
165C2×SD16#8913711yescharacteristic, complemented
166C22×C8—1091no—
167C22×C8—1091no—
168C4×Q8—1094no—
169C4×Q8—2182no—
170C4×D4—1094no—
171C4×D4—2182no—
172C2×C4⋊C4—1091no—
173C2×C4⋊C4—1091no—
174C2×C4⋊C4—2181no—
175C2×C22⋊C4—2181no—
176C2×C42—1091no—
177C2×C42—2181no—
178#107—1094no—
179#103—1094no—
180#102—1094no—
181#97—1094no—
182C24—2181no—
183C2×Q8—1092no—
184C2×Q8—1092no—
185C2×Q8—1091no—
186C2×Q8—2181no—
187C2×Q8—2181no—
188C2×Q8—2181no—
189C2×Q8C2×#8913711yescharacteristic, complemented
190C2×D4—1092no—
191C2×D4—1092no—
192C2×D4—1091no—
193C2×D4—2181no—
194C2×D4—2181no—
195C2×D4—2181no—
196C2×D4C2×#8913711yescharacteristic
197C22×C4—1091no—
198C22×C4—1091no—
199C22×C4—1091no—
200C22×C4—4364no—
201C22×C4—2181no—
202C22×C4—2184no—
203C22×C4—2181no—
204C22×C4—2181no—
205SD16—1094no—
206SD16—1094no—
207SD16—1094no—
208SD16C2×#8913714yescomplemented
209C2×C8—1091no—
210C2×C8—1092no—
211C2×C8—1092no—
212C2×C8—1092no—
213C2×C8—2181no—
214C2×C8—2181no—
215C2×C8C2×#8913711yescharacteristic, complemented
216C4⋊C4—1092no—
217C4⋊C4—1092no—
218C4⋊C4—2181no—
219C4⋊C4—2181no—
220C4⋊C4—2184no—
221C22⋊C4—2184no—
222C42—1092no—
223C42—1092no—
224C42—2184no—
225C23—21no—
226C23—1091no—
227C23—4362no—
228C23—4362no—
229C23—2182no—
230C23—2182no—
231C23—2181no—
232Q8—21no—
233Q8—1092no—
234Q8—2182no—
235Q8—2182no—
236Q8—2181no—
237Q8C22×#8913712yescomplemented
238D4—21no—
239D4—1092no—
240D4—2182no—
241D4—2182no—
242D4—2181no—
243D4C22×#8913712yes—
244C2×C4—21no—
245C2×C4—1091no—
246C2×C4—1091no—
247C2×C4—1091no—
248C2×C4—1091no—
249C2×C4—1091no—
250C2×C4—1092no—
251C2×C4—1092no—
252C2×C4—4362no—
253C2×C4—4362no—
254C2×C4—4368no—
255C2×C4—2182no—
256C2×C4—2182no—
257C2×C4—2182no—
258C2×C4—2182no—
259C2×C4—2182no—
260C2×C4—2182no—
261C2×C4—2181no—
262C2×C4C22×#8913711yescharacteristic
263C8—1092no—
264C8—2182no—
265C8C22×#8913712yescomplemented
266C22—22no—
267C22—42no—
268C22—1092no—
269C22—1092no—
270C22—1091no—
271C22—1091no—
272C22—4362no—
273C22—4362no—
274C22—4364no—
275C22—4362no—
276C22—2182no—
277C22D4×#8913711yescharacteristic
278C4—22no—
279C4—1091no—
280C4—1091no—
281C4—4362no—
282C4—4362no—
283C4—2182no—
284C4—2182no—
285C4—2182no—
286C4D4×#8913711yescharacteristic
287C4C23×#8913711yescharacteristic
288C2—42no—
289C2—1091no—
290C2—1091no—
291C2—1092no—
292C2—4362no—
293C2#2029606512yesdirect product factor
294C2C2×D4×#8913711yescharacteristic
subgroupG/H
centerC22D4×#89137
commutatorC4×C109C23×C4
FrattiniC4C23×#89137
FittingC2×SD16×C109C4
socleC22×C109C4×D4
prime radicalC2×D4×D109C22
cosocleC4×D109C24
hypercenterC2×SD16#89137
hypocenterC109C2×#440
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C2×Q8×#89137C2semidirect
3. #20296065C2direct (N × H)
4. C2×#16812768C2semidirect
5. C2×#16812762C2semidirect
7. C2×#16812753C2semidirect
12. Q8×#89137C22semidirect
21. #16812768C22semidirect
22. #16812762C22semidirect
24. #16812753C22semidirect
27. C2×#13182018C4semidirect
28. C2×#13182017C4semidirect
29. C2×#13182016C4semidirect
30. SD16×D109C4semidirect
33. C2×SD16×C109C4semidirect
54. C2×Dic218C2×C4semidirect
57. Q8×D109C2×C4semidirect
67. #13182018C2×C4semidirect
68. #13182017C2×C4semidirect
69. #13182016C2×C4semidirect
70. C2×#11724784C2×C4semidirect
71. C8×D109C2×C4semidirect
73. C2×Q8×C109C2×C4semidirect
75. SD16×C109C2×C4semidirect
76. C2×C8×C109C2×C4semidirect
94. Q8×C109C22×C4semidirect
114. Dic218C22×C4semidirect
116. C8×C109C22×C4semidirect
117. #11724784C22×C4semidirect
141. C2×C109#440semidirect
144. D109#440semidirect
148. C109C2×#440semidirect
165. C2×SD16#89137semidirect
189. C2×Q8C2×#89137semidirect
208. SD16C2×#89137semidirect
215. C2×C8C2×#89137semidirect
237. Q8C22×#89137semidirect
265. C8C22×#89137semidirect
293. C2#20296065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×#891372
C2×D4×#891372
#202960652
C2×#168127682
C2×#168127622
C2×#168127612
C2×#168127532
C2×SD16×D1092
C2×#440109