Finite Group Databasebeta

← C2×#19127894 #24916873

Subgroups — C2×#19127894 #24916873

Order 10624.

648 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 165 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
1C22×#13050575C211yesmaximal, characteristic, complemented
2C2×#14581788C211yesmaximal, characteristic, complemented
3C2×D4×Dic83C211yesmaximal, characteristic, complemented
4#19127894C218yesmaximal, direct product factor
5C2×Dic83⋊C8C211yesmaximal, characteristic, complemented
6C2×#14581714C211yesmaximal, characteristic, complemented
7C2×#14581713C211yesmaximal, characteristic, complemented
8C22×D8×C83C211yesmaximal, characteristic, complemented
9C22×D332C2211yescharacteristic
10C22×C22⋊D83—21no—
11C22×C22⋊D83—21no—
12C23×Dic83—21no—
13C2×#13050575—24no—
14C2×#13050575C2214yescomplemented
15C22×C83⋊C8C2211yescharacteristic
16#14581788—22no—
17#14581788C2214yescomplemented
18D4×Dic83—22no—
19D4×Dic83C2214yescomplemented
20C2×C4⋊Dic83C2211yescharacteristic
21C2×C22⋊Dic83—21no—
22C2×C4×Dic83C2211yescharacteristic
23Dic83⋊C8C2214yescomplemented
24#14581714C2214yescomplemented
25#14581713C2214yescomplemented
26C22×D4×C83C2211yescharacteristic
27C22×D4×C83C2211yescharacteristic
28C2×D8×C83—24no—
29C2×D8×C83C2214yescomplemented
30C22×C8×C83C2211yescharacteristic
31C23×D83—21no—
32C2×D332—22no—
33C2×D332—22no—
34C2×D332—21no—
35C2×D332C2312yes—
36C2×C22⋊D83—24no—
37C2×C22⋊D83—24no—
38C2×C22⋊D83—44no—
39C2×C22⋊D83—44no—
40C22×Dic83—21no—
41C22×Dic83—24no—
42C22×Dic83—44no—
43C22×Dic83D411yescharacteristic
44C22×Dic83D411yescharacteristic
45#13050575—28no—
46C2×C83⋊C8—22no—
47C2×C83⋊C8C2312yes—
48C4⋊Dic83—21no—
49C4⋊Dic83C2312yes—
50C22⋊Dic83—24no—
51C4×Dic83D412yes—
52C4×Dic83C2312yes—
53C24×C83—21no—
54C24×C83—21no—
55C2×D4×C83—21no—
56C2×D4×C83—22no—
57C2×D4×C83—21no—
58C2×D4×C83—22no—
59C2×D4×C83—22no—
60C2×D4×C83D414yescomplemented
61C2×D4×C83C2312yes—
62C2×D4×C83C2312yes—
63C22×C4×C83C2311yescharacteristic
64D8×C83—28no—
65C2×C8×C83—22no—
66C2×C8×C83C2312yes—
67C23×C83—24no—
68C23×C83—22no—
69C23×C83—22no—
70C23×C83—42no—
71C23×C83—42no—
72C23×C83—42no—
73C23×C83—42no—
74C23×C83—42no—
75C23×C83C2×D411yescharacteristic
76C22×D83—22no—
77C22×D83—42no—
78C22×D83—42no—
79C22×D83—42no—
80D4×C83—24no—
81D4×C83—22no—
82D4×C83—22no—
83D4×C83—22no—
84D4×C83—42no—
85D4×C83C2×D414yescomplemented
86C2×C4×C83C2×D411yescharacteristic
87C2×C4×C83C2×D412yes—
88C2×C4×C83#4112yes—
89C2×C4×C83C2411yescharacteristic
90C22⋊D83—48no—
91C22⋊D83—48no—
92C2×Dic83—22no—
93C2×Dic83—22no—
94C2×Dic83—42no—
95C2×Dic83—48no—
96C2×Dic83D814yescomplemented
97C2×Dic83C2×D412yes—
98C2×Dic83C2×D412yes—
99D332—22no—
100D332—22no—
101D332—42no—
102C8×C83—22no—
103C83⋊C8—22no—
104C22×C83—24no—
105C22×C83—42no—
106C22×C83—42no—
107C22×C83—48no—
108C22×C83—42no—
109C22×C83—42no—
110C22×C83—42no—
111C22×C83—84no—
112C22×C83#12112yes—
113C22×C83C2×D812yes—
114C22×C83AGL(1,ℤ/8)12yes—
115C22×C83C22×D411yescharacteristic
116C2×D83—42no—
117C2×D83—42no—
118C2×D83—42no—
119C2×D83—84no—
120C4×C83#12112yes—
121C4×C83C22×D411yescharacteristic
122C4×C83C2×#4111yescharacteristic
123Dic83—22no—
124Dic83—42no—
125Dic83C2×D814yescomplemented
126C2×C83—44no—
127C2×C83—82no—
128C2×C83#45914yescomplemented
129C2×C83C2×#12111yescharacteristic
130C2×C83C22×D811yescharacteristic
131C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
132D83—82no—
133C2×#459—831nomaximal, Sylow
134C83C2×#45911yescharacteristic, complemented, Sylow
135C22×D8—831no—
136C22×D8D8311yescharacteristic, complemented
137C2×#127—831no—
138C2×C4×D4—831no—
139#459—838no—
140C2×C4⋊C8—831no—
141C2×#102—831no—
142C2×#102—831no—
143C22×D4—831no—
144C22×D4—1661no—
145C22×D4—1661no—
146C22×D4C2×D8311yescharacteristic
147C22×D4C2×D8311yescharacteristic
148C23×C4—1661no—
149C2×D8—24no—
150C2×D8—834no—
151C2×D8—1664no—
152C2×D8C2×D8314yescomplemented
153C22×C8—831no—
154C22×C8C2×D8311yescharacteristic
155#127—834no—
156#127—1662no—
157C4×D4—834no—
158C4×D4—1662no—
159C2×C4⋊C4—831no—
160C2×C22⋊C4—1661no—
161C2×C42—831no—
162C4⋊C8—834no—
163#102—834no—
164#102—834no—
165C24—21no—
166C24—21no—
167C24—1661no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—22no—
171C2×D4—22no—
172C2×D4—22no—
173C2×D4—3324no—
174C2×D4—3324no—
175C2×D4—832no—
176C2×D4—1664no—
177C2×D4—1664no—
178C2×D4—1661no—
179C2×D4—1662no—
180C2×D4—1662no—
181C2×D4C22⋊D8314yescomplemented
182C2×D4C22×D8312yes—
183C2×D4C22×D8312yes—
184C22×C4—3324no—
185C22×C4—831no—
186C22×C4—831no—
187C22×C4—1664no—
188C22×C4—1661no—
189C22×C4C22×D8311yescharacteristic
190D8—28no—
191D8—1668no—
192C2×C8—22no—
193C2×C8—832no—
194C2×C8—1662no—
195C2×C8C22×D8312yes—
196C4⋊C4—832no—
197C4⋊C4—1661no—
198C22⋊C4—1664no—
199C42—832no—
200C42—832no—
201C23—24no—
202C23—22no—
203C23—22no—
204C23—42no—
205C23—42no—
206C23—42no—
207C23—42no—
208C23—42no—
209C23—3322no—
210C23—3322no—
211C23—3322no—
212C23—1662no—
213C23D4×D8311yescharacteristic
214D4—24no—
215D4—22no—
216D4—22no—
217D4—22no—
218D4—42no—
219D4—3328no—
220D4—3328no—
221D4—3322no—
222D4—1662no—
223D4—1662no—
224D4C2×C22⋊D8314yescomplemented
225C2×C4—3322no—
226C2×C4—3328no—
227C2×C4—834no—
228C2×C4—832no—
229C2×C4—832no—
230C2×C4—1662no—
231C2×C4—1662no—
232C2×C4D4×D8311yescharacteristic
233C2×C4C2×C22⋊D8312yes—
234C2×C4#1305058912yes—
235C2×C4C23×D8311yescharacteristic
236C8—22no—
237C8—1662no—
238C22—24no—
239C22—48no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—84no—
246C22—3322no—
247C22—3322no—
248C22—3322no—
249C22—6644no—
250C22#1458176412yes—
251C22D8×D8312yes—
252C22#1458181612yes—
253C22C2×D4×D8311yescharacteristic
254C4—3322no—
255C4—834no—
256C4—1662no—
257C4#1458176412yes—
258C4C22×C22⋊D8311yescharacteristic
259C4C2×#1305058911yescharacteristic
260C2—44no—
261C2—82no—
262C2—6642no—
263C2#1912789414yesdirect product factor
264C2C2×#1458176411yescharacteristic
265C2C2×D8×D8311yescharacteristic
266C2C2×#1458181611yescharacteristic
subgroupG/H
centerC23D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC22×D8×C83C2
socleC23×C83C2×D4
hypercenterC22×D8D83
hypocenterC83C2×#459
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#13050575C2semidirect
2. C2×#14581788C2semidirect
3. C2×D4×Dic83C2semidirect
4. #19127894C2direct (N × H)
5. C2×Dic83⋊C8C2semidirect
6. C2×#14581714C2semidirect
7. C2×#14581713C2semidirect
8. C22×D8×C83C2semidirect
14. C2×#13050575C22semidirect
17. #14581788C22semidirect
19. D4×Dic83C22semidirect
23. Dic83⋊C8C22semidirect
24. #14581714C22semidirect
25. #14581713C22semidirect
29. C2×D8×C83C22semidirect
60. C2×D4×C83D4semidirect
85. D4×C83C2×D4semidirect
96. C2×Dic83D8semidirect
125. Dic83C2×D8semidirect
128. C2×C83#459semidirect
134. C83C2×#459semidirect
136. C22×D8D83semidirect
152. C2×D8C2×D83semidirect
181. C2×D4C22⋊D83semidirect
224. D4C2×C22⋊D83semidirect
263. C2#19127894direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130505752
C2×#145817882
C2×D4×Dic832
#191278942
C2×Dic83⋊C82
C2×#145817142
C2×#145817132
C22×D8×C832
C2×#45983