Finite Group Databasebeta

← #22617941

Subgroups — #22617941

Order 9344.

478 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556573C211yesmaximal, characteristic
2C2×#14556567C211yesmaximal, characteristic, complemented
3#17988521C212yesmaximal, complemented
4#17988519C211yesmaximal, characteristic, complemented
5#17988514C212yesmaximal, complemented
6#17988512C211yesmaximal, characteristic, complemented
7#17988510C212yesmaximal, complemented
8#17988506C211yesmaximal, characteristic, complemented
9#17988502C212yesmaximal
10#17988446C211yesmaximal, characteristic, complemented
11#393×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14#14556573—24no—
15#14556567—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2212yes—
21C2×#11924007C2212yes—
22C2×#11924007C2212yes—
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2212yes—
25C2×#11924005C2212yes—
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×Q8×C73C2211yescharacteristic
33C2×C22⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—22no—
39C2×C22⋊D73—42no—
40C22×Dic73C2312yes—
41C22×Dic73C2311yescharacteristic
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2311yescharacteristic
45C2×C4×D73—42no—
46C2×C4×D73D414yes—
47C4⋊Dic73—22no—
48C4⋊Dic73—22no—
49C4⋊Dic73—42no—
50#11924007—22no—
51#11924007—24no—
52#11924007—42no—
53#11924007—42no—
54C22⋊Dic73—22no—
55C22⋊Dic73—42no—
56#11924005—24no—
57#11924005—22no—
58#11924005—42no—
59C24×C73C2311yescharacteristic
60C2×Q8×C73—22no—
61C2×Q8×C73—42no—
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C22⋊C4×C73—22no—
67C22⋊C4×C73—42no—
68C23×C73—21no—
69C23×C73—22no—
70C23×C73—21no—
71C23×C73—22no—
72C23×C73—21no—
73C23×C73C2411yescharacteristic
74C22×D73—21no—
75C22×D73—22no—
76C22×D73—22no—
77C22×D73—21no—
78C22×D73C2×D412yes—
79Q8×C73—44no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73C2×D412yes—
90C22⋊D73—44no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—21no—
100C2×Dic73—22no—
101C2×Dic73—21no—
102C2×Dic73—22no—
103C2×Dic73C2×D412yes—
104C4×D73—44no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73—41no—
108C22×C73—42no—
109C22×C73—42no—
110C22×C73C22×D411yescharacteristic
111C22×C73H(5,𝔽2)12yes—
112C22×C73H(5,𝔽2)11yescharacteristic
113C22×C732−1+412yes—
114C22×C732−1+411yescharacteristic
115C2×D73—22no—
116C2×D73—22no—
117C2×D73—22no—
118C2×D73—42no—
119C2×D73—42no—
120C4×C73—22no—
121C4×C73—42no—
122C4×C73—41no—
123C4×C73—42no—
124Dic73—22no—
125Dic73—41no—
126Dic73—41no—
127Dic73—42no—
128Dic73—42no—
129C2×C73—81no—
130C2×C73#53411yescharacteristic
131C2×C73#53611yescharacteristic
132C2×C73#53711yescharacteristic
133C2×C73#56212yes—
134C2×C73#56312yes—
135D73—42no—
136#2814—731nomaximal, Sylow
137C73#281411yescharacteristic, complemented, Sylow
138C2×#123—731no—
139C2×C22⋊Q8—731no—
140#398—731no—
141#398—732no—
142#397—731no—
143#397—732no—
144#396—732no—
145#395—731no—
146#394—732no—
147#393D7311yescharacteristic, complemented
148#380—731no—
149C22×Q8C2×D7311yescharacteristic
150C22×D4—731no—
151C23×C4—731no—
152#123—1464no—
153C22⋊Q8—1464no—
154C2×C4⋊C4—732no—
155C2×C4⋊C4—732no—
156C2×C4⋊C4—732no—
157C2×C4⋊C4—732no—
158C2×C4⋊C4—731no—
159C2×C4⋊C4—731no—
160C2×C4⋊C4—731no—
161C2×C22⋊C4—732no—
162C2×C22⋊C4—732no—
163C2×C22⋊C4—731no—
164C2×C22⋊C4—732no—
165C2×C22⋊C4—731no—
166C2×C22⋊C4C2×D7311yescharacteristic
167C2×C22⋊C4C2×D7312yes—
168#95—731no—
169#95—732no—
170#95—732no—
171#95—732no—
172#95C2×D7311yescharacteristic
173#95C2×D7312yes—
174C24—731no—
175C24C22×D7311yescharacteristic
176C2×Q8—22no—
177C2×Q8—42no—
178C2×D4—2922no—
179C2×D4—1462no—
180C22×C4—2922no—
181C22×C4—734no—
182C22×C4—731no—
183C22×C4—732no—
184C22×C4—731no—
185C22×C4—732no—
186C22×C4—731no—
187C22×C4C22×D7311yescharacteristic
188C22×C4C22×D7312yes—
189C22×C4C22×D7312yes—
190C22×C4C22×D7311yescharacteristic
191C4⋊C4—2922no—
192C4⋊C4—2922no—
193C4⋊C4—2922no—
194C4⋊C4—1464no—
195C4⋊C4—1462no—
196C4⋊C4—1462no—
197C4⋊C4—1462no—
198C22⋊C4—22no—
199C22⋊C4—42no—
200C22⋊C4—2922no—
201C22⋊C4—2922no—
202C22⋊C4—1464no—
203C22⋊C4—1462no—
204C22⋊C4—1462no—
205C23—21no—
206C23—22no—
207C23—21no—
208C23—22no—
209C23—21no—
210C23—732no—
211C23—1462no—
212C23—1461no—
213C23—1462no—
214C23—1461no—
215C23C23×D7311yescharacteristic
216Q8—44no—
217D4—2924no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—2924no—
228C2×C4—732no—
229C2×C4—1461no—
230C2×C4—1462no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4—1461no—
237C2×C4—1462no—
238C2×C4—1461no—
239C2×C4—1462no—
240C2×C4—1462no—
241C2×C4D4×D7312yes—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—2922no—
248C22—2922no—
249C22—1462no—
250C22—1462no—
251C22—1462no—
252C22C2×D4×D7311yescharacteristic
253C22#1455663612yes—
254C22#1455663711yescharacteristic
255C22#1455663812yes—
256C22#1455663911yescharacteristic
257C4—22no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—2921no—
262C4—2921no—
263C4—2922no—
264C4—2922no—
265C4—1462no—
266C2—81no—
267C2—2922no—
268C2#1798914711yescharacteristic
269C2#1798915711yescharacteristic
270C2#1798916711yescharacteristic
271C2#1798933112yes—
272C2#1798933812yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#393×C73C2
hypercenter#393D73
hypocenterC73#2814
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. C2×#14556567C2semidirect
3. #17988521C2semidirect
4. #17988519C2semidirect
5. #17988514C2semidirect
6. #17988512C2semidirect
7. #17988510C2semidirect
8. #17988506C2semidirect
10. #17988446C2semidirect
11. #393×C73C2semidirect
137. C73#2814semidirect
147. #393D73semidirect