Finite Group Databasebeta

← #22615745

Subgroups — #22615745

Order 9344.

508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14556571C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic
3#17988525C211yesmaximal, characteristic, complemented
4#17988521C212yesmaximal, complemented
5#17988519C212yesmaximal, complemented
6#17988508C211yesmaximal, characteristic, complemented
7#17988507C211yesmaximal, characteristic, complemented
8#17988461C212yesmaximal
9#17988449C212yesmaximal
10#17988446C211yesmaximal, characteristic
11#400×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556571—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2212yes—
19C2×C4⋊Dic73C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×#11924007C2212yes—
24C4⋊C4×D73—24no—
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27#14556498C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34#95×C73C2211yescharacteristic
35#95×C73C2212yes—
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—42no—
40C22×Dic73C2312yes—
41C22×Dic73C2312yes—
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2311yescharacteristic
45C2×C4×D73—22no—
46C2×C4×D73—22no—
47C2×C4×D73—22no—
48C2×C4×D73—42no—
49C2×C4×D73—42no—
50C2×C4×D73D414yes—
51C2×C4×D73Q814yescomplemented
52C4⋊Dic73—22no—
53C4⋊Dic73—24no—
54C4⋊Dic73—42no—
55#11924007—22no—
56#11924007—22no—
57#11924007—42no—
58#11924007—42no—
59#11924005—24no—
60#11924005—24no—
61C22×C4×C73C2312yes—
62C22×C4×C73C2312yes—
63C22×C4×C73C2311yescharacteristic
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2311yescharacteristic
66C4⋊C4×C73—22no—
67C4⋊C4×C73—22no—
68C23×C73C2411yescharacteristic
69C22×D73—22no—
70C22×D73—22no—
71C22×D73C2×D412yes—
72C22×D73C2×Q812yes—
73C22×D73#4112yes—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—24no—
83C2×C4×C73—22no—
84C2×C4×C73C2×D412yes—
85C2×C4×C73C2×Q812yes—
86C2×Dic73—21no—
87C2×Dic73—21no—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73C2×D412yes—
98C2×Dic73C2×Q812yes—
99C4×D73—28no—
100C4×D73—44no—
101C4×D73—44no—
102Dic146—44no—
103C22×C73C22×D411yescharacteristic
104C22×C73C22×Q811yescharacteristic
105C22×C73C2×#4111yescharacteristic
106C22×C73H(5,𝔽2)12yes—
107C22×C732−1+412yes—
108C2×D73—22no—
109C2×D73—22no—
110C2×D73—24no—
111C2×D73—24no—
112C2×D73C22⋊Q814yes—
113C4×C73—22no—
114C4×C73—22no—
115C4×C73—41no—
116C4×C73—42no—
117C4×C73—42no—
118Dic73—22no—
119Dic73—22no—
120Dic73—42no—
121Dic73—41no—
122Dic73—42no—
123C2×C73C2×C22⋊Q811yescharacteristic
124C2×C73#53411yescharacteristic
125C2×C73#53611yescharacteristic
126C2×C73#53912yes—
127C2×C73#54412yes—
128D73—24no—
129#2627—731nomaximal, Sylow
130C73#262711yescharacteristic, complemented, Sylow
131C2×C22⋊Q8—731no—
132C22×C4⋊C4—731no—
133#400—731no—
134#400D7311yescharacteristic, complemented
135#398—732no—
136#398—732no—
137#395—731no—
138#395—731no—
139#385—732no—
140#381—732no—
141#380—731no—
142C22×Q8—731no—
143C23×C4—731no—
144C23×C4—731no—
145C23×C4—731no—
146C22⋊Q8—1464no—
147C2×C4⋊C4—732no—
148C2×C4⋊C4—732no—
149C2×C4⋊C4—732no—
150C2×C4⋊C4—731no—
151C2×C4⋊C4—731no—
152C2×C4⋊C4—731no—
153C2×C4⋊C4—732no—
154C2×C4⋊C4—1464no—
155C2×C4⋊C4C2×D7311yescharacteristic
156C2×C4⋊C4C2×D7311yescharacteristic
157C2×C22⋊C4—732no—
158C2×C22⋊C4—732no—
159#95—731no—
160#95—732no—
161#95—732no—
162#95—732no—
163#95—732no—
164#95C2×D7311yescharacteristic
165#95C2×D7312yes—
166#95C2×D7312yes—
167C24—731no—
168C2×Q8—2922no—
169C2×Q8—1462no—
170C22×C4—2922no—
171C22×C4—2922no—
172C22×C4—734no—
173C22×C4—731no—
174C22×C4—731no—
175C22×C4—734no—
176C22×C4—732no—
177C22×C4—732no—
178C22×C4—731no—
179C22×C4—1462no—
180C22×C4—1462no—
181C22×C4—1462no—
182C22×C4C22×D7312yes—
183C22×C4C22×D7312yes—
184C22×C4C22×D7311yescharacteristic
185C22×C4C22×D7311yescharacteristic
186C22×C4C22×D7311yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—2922no—
190C4⋊C4—2922no—
191C4⋊C4—2922no—
192C4⋊C4—1462no—
193C4⋊C4—1462no—
194C4⋊C4—1464no—
195C4⋊C4—1462no—
196C22⋊C4—1464no—
197C22⋊C4—1464no—
198C23—732no—
199C23—732no—
200C23—732no—
201C23—1462no—
202C23—1462no—
203C23C23×D7311yescharacteristic
204Q8—2924no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—24no—
214C2×C4—22no—
215C2×C4—2924no—
216C2×C4—2924no—
217C2×C4—732no—
218C2×C4—732no—
219C2×C4—1468no—
220C2×C4—1462no—
221C2×C4—1461no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4—1462no—
228C2×C4—1461no—
229C2×C4—1461no—
230C2×C4—1462no—
231C2×C4D4×D7312yes—
232C2×C4Q8×D7312yes—
233C22—734no—
234C22—1462no—
235C22—1462no—
236C22—1464no—
237C22—1464no—
238C22C2×D4×D7311yescharacteristic
239C22C2×Q8×D7311yescharacteristic
240C22#41×D7311yescharacteristic
241C22#1455663712yes—
242C22#1455663812yes—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—42no—
247C4—42no—
248C4—2921no—
249C4—2922no—
250C4—2922no—
251C4—1462no—
252C4—1462no—
253C2—1464no—
254C2C22⋊Q8×D7311yescharacteristic
255C2#1798914811yescharacteristic
256C2#1798915711yescharacteristic
257C2#1798917812yes—
258C2#1798921712yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2627
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #17988525C2semidirect
4. #17988521C2semidirect
5. #17988519C2semidirect
6. #17988508C2semidirect
7. #17988507C2semidirect
11. #400×C73C2semidirect
51. C2×C4×D73Q8semidirect
130. C73#2627semidirect
134. #400D73semidirect