Finite Group Databasebeta

← #22616044

Subgroups — #22616044

Order 9344.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14556569C211yesmaximal, characteristic
2C2×#14556567C211yesmaximal, characteristic
3#17988521C212yesmaximal, complemented
4#17988519C211yesmaximal, characteristic, complemented
5#17988517C211yesmaximal, characteristic, complemented
6#17988507C212yesmaximal, complemented
7#17988506C211yesmaximal, characteristic, complemented
8#17988446C212yesmaximal
9#17988444C212yesmaximal
10#95×D73C211yesmaximal, characteristic
11#395×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14C22×C4×D73C2212yes—
15#14556569—24no—
16#14556567—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2212yes—
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×#11924007C2212yes—
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C2×#11924005C2211yescharacteristic
27#14556498C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×Q8×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—42no—
40C22×Dic73C2311yescharacteristic
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45C2×C4×D73—42no—
46C2×C4×D73—42no—
47C2×C4×D73—42no—
48C2×C4×D73D414yes—
49C2×C4×D73Q818yescomplemented
50C4⋊Dic73—22no—
51C4⋊Dic73—42no—
52#11924007—22no—
53#11924007—24no—
54#11924007—22no—
55#11924007—42no—
56#11924007—42no—
57#11924005—24no—
58#11924005—22no—
59#11924005—22no—
60C2×Q8×C73—22no—
61C2×Q8×C73—42no—
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2312yes—
67C4⋊C4×C73—22no—
68C4⋊C4×C73—42no—
69C23×C73C2411yescharacteristic
70C22×D73—22no—
71C22×D73—21no—
72C22×D73—21no—
73C22×D73C2×D412yes—
74C22×D73C2×Q814yes—
75Q8×C73—44no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73C2×D412yes—
88C2×C4×C73C2×Q814yes—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—22no—
100C2×Dic73C2×D412yes—
101C2×Dic73C2×Q814yes—
102C4×D73—44no—
103C4×D73—48no—
104Dic146—44no—
105C22×C73C22×D411yescharacteristic
106C22×C73C22×Q812yes—
107C22×C73H(5,𝔽2)12yes—
108C22×C73H(5,𝔽2)11yescharacteristic
109C22×C732−1+411yescharacteristic
110C2×D73—22no—
111C2×D73—22no—
112C2×D73—24no—
113C2×D73—24no—
114C2×D73C4⋊Q814yes—
115C4×C73—22no—
116C4×C73—24no—
117C4×C73—41no—
118C4×C73—42no—
119C4×C73—41no—
120Dic73—22no—
121Dic73—24no—
122Dic73—41no—
123Dic73—41no—
124Dic73—42no—
125C2×C73C2×C4⋊Q811yescharacteristic
126C2×C73#53411yescharacteristic
127C2×C73#53711yescharacteristic
128C2×C73#54312yes—
129C2×C73#54412yes—
130D73—24no—
131#2659—731nomaximal, Sylow
132C73#265911yescharacteristic, complemented, Sylow
133C2×C22⋊Q8—731no—
134C2×C22⋊Q8—731no—
135#398—731no—
136#398—731no—
137#398—732no—
138#395—731no—
139#395—732no—
140#395D7311yescharacteristic, complemented
141#380—732no—
142#380—732no—
143C2×#95—731no—
144C22×Q8—731no—
145C22×Q8C2×D7311yescharacteristic
146C23×C4—731no—
147C23×C4—732no—
148C22⋊Q8—1464no—
149C22⋊Q8—1464no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—732no—
152C2×C4⋊C4—732no—
153C2×C4⋊C4—732no—
154C2×C4⋊C4—731no—
155C2×C4⋊C4—731no—
156C2×C4⋊C4—731no—
157C2×C4⋊C4C2×D7311yescharacteristic
158C2×C4⋊C4C2×D7312yes—
159C2×C22⋊C4—731no—
160C2×C22⋊C4—732no—
161C2×C22⋊C4—731no—
162#95—731no—
163#95—732no—
164#95—732no—
165#95—732no—
166#95—732no—
167#95C2×D7311yescharacteristic
168#95C2×D7312yes—
169C24—731no—
170C2×Q8—22no—
171C2×Q8—42no—
172C2×Q8—2922no—
173C2×Q8—1462no—
174C22×C4—2922no—
175C22×C4—2922no—
176C22×C4—2922no—
177C22×C4—734no—
178C22×C4—738no—
179C22×C4—732no—
180C22×C4—731no—
181C22×C4—732no—
182C22×C4—731no—
183C22×C4—731no—
184C22×C4C22×D7311yescharacteristic
185C22×C4C22×D7312yes—
186C22×C4C22×D7311yescharacteristic
187C22×C4C22×D7311yescharacteristic
188C22×C4C22×D7312yes—
189C4⋊C4—22no—
190C4⋊C4—42no—
191C4⋊C4—2922no—
192C4⋊C4—2922no—
193C4⋊C4—2922no—
194C4⋊C4—1462no—
195C4⋊C4—1464no—
196C4⋊C4—1462no—
197C4⋊C4—1462no—
198C22⋊C4—1462no—
199C22⋊C4—1462no—
200C22⋊C4—1464no—
201C23—732no—
202C23—734no—
203C23—1462no—
204C23—1461no—
205C23—1461no—
206C23C23×D7311yescharacteristic
207Q8—44no—
208Q8—2924no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—2924no—
221C2×C4—2928no—
222C2×C4—732no—
223C2×C4—734no—
224C2×C4—1461no—
225C2×C4—1462no—
226C2×C4—1461no—
227C2×C4—1462no—
228C2×C4—1462no—
229C2×C4—1461no—
230C2×C4—1462no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4D4×D7312yes—
236C2×C4Q8×D7314yes—
237C22—734no—
238C22—1462no—
239C22—1462no—
240C22—1464no—
241C22—1464no—
242C22C2×D4×D7311yescharacteristic
243C22C2×Q8×D7312yes—
244C22#1455663612yes—
245C22#1455663711yescharacteristic
246C22#1455663911yescharacteristic
247C4—22no—
248C4—24no—
249C4—42no—
250C4—41no—
251C4—41no—
252C4—2921no—
253C4—2921no—
254C4—2922no—
255C4—1462no—
256C4—1464no—
257C2—1464no—
258C2C4⋊Q8×D7311yescharacteristic
259C2#1798914711yescharacteristic
260C2#1798916711yescharacteristic
261C2#1798921212yes—
262C2#1798921412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#395×C73C2
hypercenter#395D73
hypocenterC73#2659
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #17988521C2semidirect
4. #17988519C2semidirect
5. #17988517C2semidirect
6. #17988507C2semidirect
7. #17988506C2semidirect
11. #395×C73C2semidirect
49. C2×C4×D73Q8semidirect
132. C73#2659semidirect
140. #395D73semidirect