Finite Group Databasebeta

← #22617985

Subgroups — #22617985

Order 9344.

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

normal subgroups only

This group has 464 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×#14556582C211yesmaximal, characteristic, complemented
2C2×#14556577C211yesmaximal, characteristic
3#17988522C211yesmaximal, characteristic, complemented
4#17988514C211yesmaximal, characteristic, complemented
5#17988512C211yesmaximal, characteristic, complemented
6#17988510C212yesmaximal, complemented
7#17988509C212yesmaximal, complemented
8#17988507C212yesmaximal, complemented
9#17988502C212yesmaximal
10#17988451C211yesmaximal, characteristic, complemented
11#399×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C22⋊D73C2211yescharacteristic
14#14556582—24no—
15#14556577—24no—
16C2×C4⋊Dic73C2212yes—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×#11924007C2212yes—
21C2×C22⋊Dic73C2211yescharacteristic
22C2×C22⋊Dic73C2212yes—
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27C2×C4×Dic73C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—42no—
40C2×C22⋊D73—22no—
41C2×C22⋊D73—42no—
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2311yescharacteristic
47C4⋊Dic73—22no—
48C4⋊Dic73—24no—
49#11924007—24no—
50#11924007—42no—
51#11924007—42no—
52C22⋊Dic73—22no—
53C22⋊Dic73—42no—
54#11924005—22no—
55#11924005—22no—
56#11924005—42no—
57#11924005—42no—
58C4×Dic73D414yes—
59C24×C73C2311yescharacteristic
60C22×C4×C73C2312yes—
61C22×C4×C73C2311yescharacteristic
62C22×C4×C73C2312yes—
63C22×C4×C73C2311yescharacteristic
64C4⋊C4×C73—22no—
65C4⋊C4×C73—42no—
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—21no—
76C22×D73—22no—
77C22×D73—22no—
78C22×D73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
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×C73C2×D412yes—
89C22⋊D73—44no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73C2×D412yes—
102C2×Dic73C2×D412yes—
103Dic146—44no—
104C22×C73—41no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73—42no—
108C22×C73—42no—
109C22×C73C22×D411yescharacteristic
110C22×C73H(5,𝔽2)12yes—
111C22×C73H(5,𝔽2)11yescharacteristic
112C22×C732−1+412yes—
113C22×C732−1+411yescharacteristic
114C2×D73—41no—
115C2×D73—41no—
116C2×D73—41no—
117C2×D73—42no—
118C2×D73—42no—
119C4×C73—22no—
120C4×C73—41no—
121C4×C73—42no—
122C4×C73—42no—
123Dic73—22no—
124Dic73—22no—
125Dic73—41no—
126Dic73—42no—
127Dic73—42no—
128C2×C73—81no—
129C2×C73#53511yescharacteristic
130C2×C73#53611yescharacteristic
131C2×C73#53711yescharacteristic
132C2×C73#56212yes—
133C2×C73#56312yes—
134D73—81no—
135#2820—731nomaximal, Sylow
136C73#282011yescharacteristic, complemented, Sylow
137C2×#125—731no—
138C2×#124—731no—
139#399—731no—
140#399D7311yescharacteristic, complemented
141#397—731no—
142#397—731no—
143#396—732no—
144#396—732no—
145#395—732no—
146#394—732no—
147#382—731no—
148C22×Q8—731no—
149C22×D4—731no—
150#125—1464no—
151#124—1464no—
152C2×C4⋊C4—732no—
153C2×C4⋊C4—732no—
154C2×C4⋊C4—732no—
155C2×C4⋊C4—732no—
156C2×C4⋊C4—731no—
157C2×C4⋊C4C2×D7311yescharacteristic
158C2×C4⋊C4C2×D7312yes—
159C2×C22⋊C4—732no—
160C2×C22⋊C4—732no—
161C2×C22⋊C4—732no—
162C2×C22⋊C4—731no—
163C2×C22⋊C4—731no—
164C2×C22⋊C4—731no—
165C2×C22⋊C4C2×D7311yescharacteristic
166C2×C22⋊C4C2×D7312yes—
167C2×C42—731no—
168#95—732no—
169#95—731no—
170#95—732no—
171#95—732no—
172#95C2×D7311yescharacteristic
173C24—731no—
174C24C22×D7311yescharacteristic
175C2×Q8—2922no—
176C2×Q8—1462no—
177C2×D4—2922no—
178C2×D4—1462no—
179C22×C4—731no—
180C22×C4—731no—
181C22×C4—732no—
182C22×C4—732no—
183C22×C4—731no—
184C22×C4C22×D7312yes—
185C22×C4C22×D7311yescharacteristic
186C22×C4C22×D7312yes—
187C22×C4C22×D7311yescharacteristic
188C4⋊C4—22no—
189C4⋊C4—42no—
190C4⋊C4—2922no—
191C4⋊C4—2922no—
192C4⋊C4—1464no—
193C4⋊C4—1464no—
194C4⋊C4—1462no—
195C22⋊C4—22no—
196C22⋊C4—42no—
197C22⋊C4—2922no—
198C22⋊C4—2922no—
199C22⋊C4—2922no—
200C22⋊C4—1462no—
201C22⋊C4—1462no—
202C22⋊C4—1462no—
203C42—734no—
204C23—21no—
205C23—22no—
206C23—21no—
207C23—22no—
208C23—21no—
209C23—1461no—
210C23—1462no—
211C23—1461no—
212C23—1462no—
213C23—1461no—
214C23C23×D7311yescharacteristic
215Q8—2924no—
216D4—2924no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—732no—
227C2×C4—732no—
228C2×C4—1461no—
229C2×C4—1462no—
230C2×C4—1462no—
231C2×C4—1462no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1462no—
235C2×C4—1462no—
236C2×C4—1462no—
237C2×C4—1461no—
238C2×C4—1461no—
239C2×C4D4×D7312yes—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—2921no—
246C22—2921no—
247C22—2921no—
248C22—2922no—
249C22—2922no—
250C22C2×D4×D7311yescharacteristic
251C22#1455663612yes—
252C22#1455663711yescharacteristic
253C22#1455663812yes—
254C22#1455663911yescharacteristic
255C4—22no—
256C4—41no—
257C4—42no—
258C4—42no—
259C4—2921no—
260C4—2922no—
261C4—2922no—
262C4—1462no—
263C4—1462no—
264C2—81no—
265C2—5841no—
266C2#1798915011yescharacteristic
267C2#1798915911yescharacteristic
268C2#1798916711yescharacteristic
269C2#1798933412yes—
270C2#1798933812yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2820
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14556582C2semidirect
3. #17988522C2semidirect
4. #17988514C2semidirect
5. #17988512C2semidirect
6. #17988510C2semidirect
7. #17988509C2semidirect
8. #17988507C2semidirect
10. #17988451C2semidirect
11. #399×C73C2semidirect
136. C73#2820semidirect
140. #399D73semidirect