Finite Group Databasebeta

← C2×#22626329 #34030258

Subgroups — C2×#22626329 #34030258

Order 18688.

798 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 192 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×D8×#64408C212yesmaximal, complemented
2#22626329C218yesmaximal, direct product factor
3C2×#17989514C211yesmaximal, characteristic, complemented
4C2×#17989499C212yesmaximal, complemented
5C2×#17989474C211yesmaximal, characteristic, complemented
6C2×D16×D73C211yesmaximal, characteristic
7C2×D4×#64408—22no—
8C2×#14556664C2211yescharacteristic
9D8×#64408—24no—
10D8×#64408C2218yescomplemented
11C2×#14556660C2212yes—
12C2×#14556653—22no—
13C2×C8×#64408C2211yescharacteristic
14#17989514C2214yescomplemented
15#17989499C2218yescomplemented
16#17989474C2214yescomplemented
17C2×D8×D73C2212yes—
18C2×D1168C411yescharacteristic, complemented
19C2×#14556532C412yescomplemented
20D16×D73C414yescomplemented
21D16×D73C2214yes—
22C2×C16×D73C2211yescharacteristic
23C2×D16×C73C411yescharacteristic, complemented
24C23×#64408—42no—
25C2×#11924036D411yescharacteristic
26D4×#64408—28no—
27D4×#64408—44no—
28C2×C4⋊#64408—22no—
29C2×C22⋊#64408—42no—
30C2×C4×#64408D411yescharacteristic
31#14556664—21no—
32#14556664C2312yes—
33C2×#11924031—21no—
34#14556660—22no—
35#14556660C2314yes—
36#14556653—28no—
37C8×#64408D412yes—
38C8×#64408C2312yes—
39C2×D4×D73—22no—
40C2×D584C2×C412yescomplemented
41C2×#11924013—22no—
42D8×D73—22no—
43D8×D73—22no—
44D8×D73C2×C414yescomplemented
45D8×D73C2314yes—
46C2×C8×D73C2311yescharacteristic
47D1168C2×C414yescomplemented
48#14556532C2×C418yescomplemented
49C2×#11924003C2×C411yescharacteristic, complemented
50C16×D73C2×C412yescomplemented
51C16×D73C2312yes—
52C2×D8×C73C2×C412yescomplemented
53D16×C73C2×C414yescomplemented
54C2×C16×C73C2×C411yescharacteristic, complemented
55C22×#64408—42no—
56C22×#64408—48no—
57C22×#64408—88no—
58C22×#64408D812yes—
59#11924036—21no—
60#11924036C2×D412yes—
61C2×#10596833—21no—
62C4⋊#64408—24no—
63C4⋊#64408—42no—
64C22⋊#64408—48no—
65C4×#64408D812yes—
66C4×#64408C2×D412yes—
67#11924031—22no—
68C23×D73—42no—
69C2×D292—22no—
70C2×C22⋊D73—42no—
71D4×D73—24no—
72D4×D73—24no—
73D4×D73—42no—
74D4×D73—42no—
75C2×C4×D73C2×D411yescharacteristic
76D584—22no—
77D584C22×C414yescomplemented
78#11924013—24no—
79#11924013—24no—
80C2×#10596831#4111yescharacteristic
81C8×D73C22×C411yescharacteristic
82C8×D73C2×D411yescharacteristic
83C8×D73#4111yescharacteristic
84C8×D73C2411yescharacteristic
85#11924003C22×C412yescomplemented
86C2×D4×C73—22no—
87D8×C73—22no—
88D8×C73C22×C414yescomplemented
89C2×C8×C73C22×C411yescharacteristic
90C16×C73C22×C412yescomplemented
91C23×C73—42no—
92C22×D73—42no—
93C22×D73—44no—
94C22×D73—44no—
95C22×D73—84no—
96C22×D73—84no—
97C22×D73C2×D811yescharacteristic
98C2×#64408—24no—
99C2×#64408—44no—
100C2×#64408—816no—
101C2×#64408—84no—
102C2×#64408C2×D814yes—
103D4×C73—24no—
104D4×C73—42no—
105C2×C4×C73C4×D411yescharacteristic
106C22⋊D73—44no—
107C22⋊D73—44no—
108C2×Dic73#13511yescharacteristic
109D292—24no—
110D292—42no—
111C4×D73C4×D411yescharacteristic
112C4×D73C2×D811yescharacteristic
113C4×D73#13511yescharacteristic
114C4×D73C22×D411yescharacteristic
115#10596833—22no—
116C8×C73C4×D411yescharacteristic
117C8×C73C23×C411yescharacteristic
118#10596831C4×D411yescharacteristic
119#10596831C2×#4111yescharacteristic
120C22×C73—44no—
121C22×C73—84no—
122C22×C73C4×D811yescharacteristic
123C2×D73—44no—
124C2×D73—84no—
125C2×D73—84no—
126C2×D73—84no—
127C2×D73—88no—
128C2×D73C4×D811yescharacteristic
129C2×D73#50914yes—
130C2×D73C22×D811yescharacteristic
131#64408—24no—
132#64408—84no—
133C4×C73C4×D811yescharacteristic
134C4×C73C2×C4×D411yescharacteristic
135Dic73C4×D811yescharacteristic
136Dic73C2×#13511yescharacteristic
137C2×#2177—731nomaximal, Sylow
138C2×C73—84no—
139C2×C73#217712yescomplemented
140C2×C73C2×C4×D811yescharacteristic
141D73—84no—
142D73#217712yescomplemented
143D73C2×#50912yes—
144C22×D16—731no—
145C2×C4×D8—732no—
146#2177—738no—
147C2×#367—731no—
148C2×#357—732no—
149C2×#346—731no—
150C73C2×#217711yescharacteristic, complemented, Sylow
151C22×D8—732no—
152C2×C4×D4—1462no—
153C2×D16—732no—
154C2×D16—734no—
155C2×D16—734no—
156C2×D16—731no—
157C2×D16#6440811yescharacteristic, complemented
158C22×C16—731no—
159C22×C16—731no—
160C4×D8—738no—
161C4×D8—1464no—
162C2×#107—732no—
163C2×#102—1462no—
164C2×C4×C8—731no—
165#367—734no—
166#357—738no—
167#346—734no—
168C22×D4—1462no—
169C23×C4—2922no—
170C2×D8—734no—
171C2×D8—734no—
172C2×D8—732no—
173C2×D8—1462no—
174C2×D8—1462no—
175C2×D8—1462no—
176C2×D8C2×#6440812yescomplemented
177C22×C8—731no—
178C22×C8—731no—
179C4×D4—2924no—
180C4×D4—1468no—
181C2×C4⋊C4—1462no—
182C2×C22⋊C4—2922no—
183C2×C42—731no—
184D16—738no—
185D16—734no—
186D16C2×#6440814yescomplemented
187C2×C16—731no—
188C2×C16—732no—
189C2×C16—732no—
190C2×C16—732no—
191C2×C16—1461no—
192C2×C16—1461no—
193C2×C16C2×#6440811yescharacteristic, complemented
194#107—734no—
195#107—1462no—
196#102—1468no—
197C4×C8—732no—
198C4×C8—732no—
199C24—2922no—
200C2×D4—22no—
201C2×D4—2922no—
202C2×D4—2922no—
203C2×D4—2922no—
204C2×D4—1464no—
205C2×D4—1464no—
206C2×D4—1462no—
207C22×C4—2922no—
208C22×C4—2928no—
209C22×C4—5848no—
210C22×C4—731no—
211C22×C4—732no—
212D8—22no—
213D8—734no—
214D8—1464no—
215D8—1464no—
216D8—1462no—
217D8C22×#6440814yescomplemented
218C2×C8—731no—
219C2×C8—731no—
220C2×C8—731no—
221C2×C8—731no—
222C2×C8—731no—
223C2×C8—732no—
224C2×C8—1461no—
225C2×C8—1461no—
226C2×C8C22×#6440811yescharacteristic
227C4⋊C4—2922no—
228C4⋊C4—1464no—
229C22⋊C4—2928no—
230C42—732no—
231C42—732no—
232C16—732no—
233C16—1462no—
234C16C22×#6440812yescomplemented
235C23—42no—
236C23—2924no—
237C23—2924no—
238C23—2922no—
239C23—5844no—
240C23—5844no—
241C23—731no—
242D4—24no—
243D4—42no—
244D4—2924no—
245D4—2924no—
246D4—2922no—
247D4—1464no—
248C2×C4—2924no—
249C2×C4—5844no—
250C2×C4—58416no—
251C2×C4—731no—
252C2×C4—731no—
253C2×C4—731no—
254C2×C4—731no—
255C2×C4—731no—
256C2×C4—734no—
257C2×C4—1464no—
258C2×C4D4×#6440811yescharacteristic
259C8—731no—
260C8—731no—
261C8—1462no—
262C8D4×#6440811yescharacteristic
263C8C23×#6440811yescharacteristic
264C22—44no—
265C22—84no—
266C22—2924no—
267C22—5844no—
268C22—5844no—
269C22—5848no—
270C22—5844no—
271C22—734no—
272C22—731no—
273C22—731no—
274C22D8×#6440811yescharacteristic
275C4—5844no—
276C4—731no—
277C4—731no—
278C4—1464no—
279C4D8×#6440811yescharacteristic
280C4C2×D4×#6440811yescharacteristic
281C2—84no—
282C2—5844no—
283C2—732no—
284C2—732no—
285C2#2262632912yesdirect product factor
286C2C2×D8×#6440811yescharacteristic
subgroupG/H
centerC22D8×#64408
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC2×D16×C73C4
socleC22×C73C4×D8
prime radicalC2×D16×D73C2
cosocleC8×D73C24
hypercenterC2×D16#64408
hypocenterC73C2×#2177
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D16

Complements

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

NH ≅ G/Ntype
1. C2×D8×#64408C2semidirect
2. #22626329C2direct (N × H)
3. C2×#17989514C2semidirect
4. C2×#17989499C2semidirect
5. C2×#17989474C2semidirect
10. D8×#64408C22semidirect
14. #17989514C22semidirect
15. #17989499C22semidirect
16. #17989474C22semidirect
18. C2×D1168C4semidirect
19. C2×#14556532C4semidirect
20. D16×D73C4semidirect
23. C2×D16×C73C4semidirect
40. C2×D584C2×C4semidirect
44. D8×D73C2×C4semidirect
47. D1168C2×C4semidirect
48. #14556532C2×C4semidirect
49. C2×#11924003C2×C4semidirect
50. C16×D73C2×C4semidirect
52. C2×D8×C73C2×C4semidirect
53. D16×C73C2×C4semidirect
54. C2×C16×C73C2×C4semidirect
77. D584C22×C4semidirect
85. #11924003C22×C4semidirect
88. D8×C73C22×C4semidirect
90. C16×C73C22×C4semidirect
139. C2×C73#2177semidirect
142. D73#2177semidirect
150. C73C2×#2177semidirect
157. C2×D16#64408semidirect
176. C2×D8C2×#64408semidirect
186. D16C2×#64408semidirect
193. C2×C16C2×#64408semidirect
217. D8C22×#64408semidirect
234. C16C22×#64408semidirect
285. C2#22626329direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D8×#644082
#226263292
C2×#179895142
C2×#179894992
C2×#179894742
C2×D16×D732
C2×#217773