Finite Group Databasebeta

← #22619740

Subgroups — #22619740

Order 9344.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C4×#11924028C211yesmaximal, characteristic
2#17988879C212yesmaximal, complemented
3#17988874C212yesmaximal, complemented
4#17988869C212yesmaximal, complemented
5#17988864C212yesmaximal, complemented
6#17988627C212yesmaximal, complemented
7#17988611C211yesmaximal, characteristic, complemented
8#17988586C212yesmaximal
9C2×C4⋊Q8×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C2×#11924012C2212yes—
12C4×Dic146C2211yescharacteristic
13C4×Dic146C2211yescharacteristic
14C4×D292C2211yescharacteristic
15C4×D292C2211yescharacteristic
16C4×C22⋊D73—21no—
17C4×C22⋊D73—21no—
18#14556550C2211yescharacteristic
19#14556548—21no—
20C42×D73—21no—
21#14556524C2214yes—
22#14556522C2214yes—
23C4⋊#10596831C2212yes—
24C4⋊#10596831C2212yes—
25#14556514C2214yes—
26#14556511C2214yes—
27C22×Q8×C73—21no—
28C4⋊Q8×C73—21no—
29C4⋊Q8×C73—21no—
30C4⋊Q8×C73C2212yes—
31C4⋊Q8×C73C2212yes—
32C2×C4⋊C4×C73—21no—
33C2×C4⋊C4×C73C2212yes—
34C2×C42×C73C2211yescharacteristic
35#11924028—22no—
36#11924028Q814yescomplemented
37C2×Dic146C2311yescharacteristic
38C2×D292C2311yescharacteristic
39C2×C22⋊D73—21no—
40C2×C4×D73—21no—
41C2×C4×D73—21no—
42C2×C4×D73—21no—
43#11924012—24no—
44C2×#10596831C2314yes—
45C4⋊Dic73C2311yescharacteristic
46C4⋊Dic73C2311yescharacteristic
47#11924007—21no—
48#11924007—21no—
49C22⋊Dic73—21no—
50#11924005—21no—
51#11924005—21no—
52C4×Dic73—21no—
53C4×Dic73—21no—
54C4×Dic73—21no—
55C2×Q8×C73—22no—
56C2×Q8×C73—22no—
57C2×Q8×C73—44no—
58C22×C4×C73—22no—
59C22×C4×C73D411yescharacteristic
60C22×C4×C73D411yescharacteristic
61C22×C4×C73C2311yescharacteristic
62C4⋊C4×C73—22no—
63C4⋊C4×C73—22no—
64C4⋊C4×C73—22no—
65C4⋊C4×C73C2314yes—
66C42×C73D411yescharacteristic
67C42×C73D411yescharacteristic
68C42×C73C2311yescharacteristic
69C42×C73C2311yescharacteristic
70C23×C73C2×D411yescharacteristic
71C22×D73—21no—
72Q8×C73—44no—
73Q8×C73—44no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—24no—
77C2×C4×C73—44no—
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D411yescharacteristic
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2×Q812yes—
84C2×C4×C73#4112yes—
85C2×C4×C73C2411yescharacteristic
86C22⋊D73—24no—
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—21no—
90D292—21no—
91D292C2×Q812yescomplemented
92C4×D73—24no—
93C4×D73—42no—
94C4×D73—42no—
95Dic146—21no—
96Dic146C2×Q812yescomplemented
97#10596831—24no—
98C22×C73—21no—
99C22×C73—21no—
100C22×C73C22⋊Q812yes—
101C22×C73C22×D411yescharacteristic
102C2×D73—22no—
103C2×D73—41no—
104C2×D73—41no—
105C4×C73—21no—
106C4×C73—21no—
107C4×C73—44no—
108C4×C73C22⋊Q812yes—
109C4×C73AGL(1,ℤ/8)12yes—
110C4×C73#13712yes—
111C4×C73C22×Q811yescharacteristic
112C4×C73C2×#4111yescharacteristic
113Dic73—22no—
114Dic73—41no—
115Dic73—41no—
116C2×C73—22no—
117C2×C73C2×C22⋊Q811yescharacteristic
118C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
119C2×C73C2×#13711yescharacteristic
120D73—42no—
121#3079—731nomaximal, Sylow
122C73#307911yescharacteristic, complemented, Sylow
123C2×C4⋊Q8D7311yescharacteristic, complemented
124C4×#41—731no—
125#477—732no—
126#476—732no—
127#475—732no—
128#474—732no—
129#428—732no—
130#423—731no—
131#417—732no—
132C2×#41—731no—
133C22×Q8—21no—
134C2×M16—732no—
135C4⋊Q8—21no—
136C4⋊Q8—21no—
137C4⋊Q8C2×D7312yes—
138C4⋊Q8C2×D7312yes—
139C4×Q8—731no—
140C4×Q8—731no—
141C4×D4—731no—
142C4×D4—731no—
143C4×D4—1461no—
144C4×D4—1461no—
145#117—731no—
146#117—1461no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4C2×D7312yes—
149C2×C42—1461no—
150C2×C42C2×D7311yescharacteristic
151#107—734no—
152#106—734no—
153C4⋊C8—732no—
154C4⋊C8—732no—
155#103—734no—
156#102—734no—
157#41—734no—
158#41—1462no—
159C2×Q8—22no—
160C2×Q8—22no—
161C2×Q8—44no—
162C2×Q8—731no—
163C2×D4—731no—
164C2×D4—1461no—
165C22×C4—22no—
166C22×C4—1461no—
167C22×C4—1461no—
168C22×C4—1461no—
169C22×C4C22⋊D7311yescharacteristic
170C22×C4C22⋊D7311yescharacteristic
171C22×C4C22×D7311yescharacteristic
172M16—1464no—
173C2×C8—734no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—731no—
178C4⋊C4—731no—
179C4⋊C4—1461no—
180C4⋊C4—1461no—
181C4⋊C4C22×D7314yes—
182C22⋊C4—1461no—
183C22⋊C4—1461no—
184C22⋊C4—1461no—
185C42—1461no—
186C42—1461no—
187C42—1461no—
188C42C22⋊D7311yescharacteristic
189C42C22⋊D7311yescharacteristic
190C42C22×D7311yescharacteristic
191C42C22×D7311yescharacteristic
192C23—1461no—
193C23C2×C22⋊D7311yescharacteristic
194Q8—44no—
195Q8—44no—
196Q8—732no—
197Q8—1461no—
198D4—732no—
199D4—1464no—
200D4—1461no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—24no—
204C2×C4—44no—
205C2×C4—2922no—
206C2×C4—2922no—
207C2×C4—1461no—
208C2×C4—1461no—
209C2×C4—1461no—
210C2×C4—1464no—
211C2×C4C2×C22⋊D7311yescharacteristic
212C2×C4C2×C22⋊D7311yescharacteristic
213C2×C4C2×C22⋊D7311yescharacteristic
214C2×C4C2×C22⋊D7311yescharacteristic
215C2×C4C2×C22⋊D7311yescharacteristic
216C2×C4Q8×D7312yes—
217C2×C4#1192402912yes—
218C2×C4C23×D7311yescharacteristic
219C8—1464no—
220C22—21no—
221C22—21no—
222C22—2921no—
223C22—2921no—
224C22—1462no—
225C22#1455656712yes—
226C22C22×C22⋊D7311yescharacteristic
227C4—21no—
228C4—21no—
229C4—44no—
230C4—2921no—
231C4—2921no—
232C4—1462no—
233C4#1455656712yes—
234C4#1455661712yes—
235C4#1455662212yes—
236C4C2×Q8×D7311yescharacteristic
237C4C2×#1192402911yescharacteristic
238C2—22no—
239C2—2922no—
240C2C2×#1455656711yescharacteristic
241C2C2×#1455661711yescharacteristic
242C2C2×#1455662211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×C4⋊Q8×C73C2
socleC22×C73C22×D4
hypercenterC2×C4⋊Q8D73
hypocenterC73#3079
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #17988879C2semidirect
3. #17988874C2semidirect
4. #17988869C2semidirect
5. #17988864C2semidirect
6. #17988627C2semidirect
7. #17988611C2semidirect
9. C2×C4⋊Q8×C73C2semidirect
36. #11924028Q8semidirect
91. D292C2×Q8semidirect
96. Dic146C2×Q8semidirect
122. C73#3079semidirect
123. C2×C4⋊Q8D73semidirect