Finite Group Databasebeta

← #22615696

Subgroups — #22615696

Order 9344.

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

normal subgroups only

This group has 528 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×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556568C212yesmaximal
3C2×#14556547C211yesmaximal, characteristic
4#17988521C212yesmaximal, complemented
5#17988519C211yesmaximal, characteristic, complemented
6#17988518C211yesmaximal, characteristic, complemented
7#17988515C212yesmaximal
8#17988512C211yesmaximal, characteristic
9#17988491C212yesmaximal, complemented
10#17988451C211yesmaximal, characteristic, complemented
11#397×C73C211yesmaximal, characteristic
12C22×Dic146C2212yes—
13C23×Dic73C2211yescharacteristic
14#14556590—24no—
15#14556568—28no—
16#14556547—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2212yes—
19C2×#11924007C2212yes—
20C2×#11924007C2212yes—
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×#11924007C2211yescharacteristic
24C2×C22⋊Dic73C2212yes—
25C2×C22⋊Dic73C2211yescharacteristic
26C2×C4×Dic73C2211yescharacteristic
27C2×C4×Dic73C2211yescharacteristic
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32#14556498C2212yes—
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37#95×C73C2212yes—
38C2×Dic146—24no—
39C2×Dic146—24no—
40C2×Dic146—24no—
41C22×Dic73—22no—
42C22×Dic73—22no—
43C22×Dic73D414yes—
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2312yes—
46C22×Dic73C2312yes—
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2311yescharacteristic
50C4⋊Dic73—22no—
51C4⋊Dic73—24no—
52#11924007—22no—
53#11924007—22no—
54#11924007—24no—
55#11924007—24no—
56#11924007—24no—
57C22⋊Dic73—24no—
58C22⋊Dic73—22no—
59C4×Dic73—22no—
60C4×Dic73D414yes—
61C24×C73C2311yescharacteristic
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C4⋊C4×C73—22no—
67C22⋊C4×C73—24no—
68C22⋊C4×C73—22no—
69C23×C73—21no—
70C23×C73—21no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73C2×D412yes—
74C23×C73C2411yescharacteristic
75C2×C4×C73—22no—
76C2×C4×C73—21no—
77C2×C4×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73C2×D412yes—
85C2×Dic73—21no—
86C2×Dic73—21no—
87C2×Dic73—22no—
88C2×Dic73—28no—
89C2×Dic73—21no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73—22no—
97C2×Dic73C2×D412yes—
98C2×Dic73C2×D412yes—
99C2×Dic73C2×D412yes—
100C2×Dic73C2×D412yes—
101C2×Dic73#4112yes—
102Dic146—48no—
103C22×C73—22no—
104C22×C73—24no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73—42no—
108C22×C73C22×D411yescharacteristic
109C22×C73C22×D411yescharacteristic
110C22×C73C2×#4111yescharacteristic
111C22×C732−1+412yes—
112C22×C732−1+412yes—
113C4×C73—22no—
114C4×C73—42no—
115C4×C73—41no—
116C4×C73—42no—
117Dic73—22no—
118Dic73—22no—
119Dic73—42no—
120Dic73—41no—
121Dic73—42no—
122Dic73#12114yes—
123C2×C73—42no—
124C2×C73C2×#12111yescharacteristic
125C2×C73#53611yescharacteristic
126C2×C73#53611yescharacteristic
127C2×C73#53612yes—
128C2×C73#54112yes—
129#2621—731nomaximal, Sylow
130C73#262111yescharacteristic, complemented, Sylow
131C2×C4⋊Q8—731no—
132C2×C22⋊Q8—732no—
133C2×#117—731no—
134#398—731no—
135#398—731no—
136#398—732no—
137#397—731no—
138#397—732no—
139#397D7311yescharacteristic
140#391—732no—
141#382—731no—
142C22×Q8—732no—
143C23×C4—731no—
144C4⋊Q8—1464no—
145C22⋊Q8—1468no—
146#117—1464no—
147C2×C4⋊C4—731no—
148C2×C4⋊C4—731no—
149C2×C4⋊C4—732no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4—732no—
152C2×C4⋊C4—732no—
153C2×C4⋊C4—731no—
154C2×C4⋊C4C2×D7311yescharacteristic
155C2×C22⋊C4—731no—
156C2×C22⋊C4—732no—
157C2×C22⋊C4C2×D7311yescharacteristic
158C2×C22⋊C4C2×D7312yes—
159C2×C42—731no—
160C2×C42—731no—
161#95—732no—
162#95—731no—
163#95—732no—
164#95—732no—
165#95—732no—
166#95C2×D7311yescharacteristic
167#95C2×D7312yes—
168C24C22×D7311yescharacteristic
169C2×Q8—1464no—
170C2×Q8—1464no—
171C2×Q8—1464no—
172C22×C4—731no—
173C22×C4—734no—
174C22×C4—731no—
175C22×C4—731no—
176C22×C4—731no—
177C22×C4—732no—
178C22×C4—732no—
179C22×C4—1462no—
180C22×C4—1462no—
181C22×C4C22×D7311yescharacteristic
182C22×C4C22×D7312yes—
183C22×C4C22×D7312yes—
184C22×C4C22×D7311yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—1462no—
187C4⋊C4—1464no—
188C4⋊C4—1464no—
189C4⋊C4—1464no—
190C4⋊C4—1464no—
191C4⋊C4—1462no—
192C4⋊C4—1462no—
193C22⋊C4—24no—
194C22⋊C4—22no—
195C22⋊C4—1462no—
196C22⋊C4—1464no—
197C42—734no—
198C42—1462no—
199C23—21no—
200C23—21no—
201C23—22no—
202C23—22no—
203C23D4×D7312yes—
204C23C23×D7311yescharacteristic
205Q8—2928no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—732no—
216C2×C4—732no—
217C2×C4—732no—
218C2×C4—732no—
219C2×C4—732no—
220C2×C4—1461no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4—1462no—
228C2×C4—1468no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4—1462no—
232C2×C4D4×D7312yes—
233C22—24no—
234C22—22no—
235C22—41no—
236C22—41no—
237C22—42no—
238C22C2×D4×D7311yescharacteristic
239C22C2×D4×D7311yescharacteristic
240C22#41×D7311yescharacteristic
241C22#1455663812yes—
242C22#1455663812yes—
243C4—22no—
244C4—41no—
245C4—42no—
246C4—42no—
247C4—2921no—
248C4—2922no—
249C4—2922no—
250C4—734no—
251C4—1462no—
252C4—1462no—
253C2—42no—
254C2#121×D7311yescharacteristic
255C2#1798915711yescharacteristic
256C2#1798915911yescharacteristic
257C2#1798915912yes—
258C2#1798919412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2621
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
4. #17988521C2semidirect
5. #17988519C2semidirect
6. #17988518C2semidirect
9. #17988491C2semidirect
10. #17988451C2semidirect
130. C73#2621semidirect