Finite Group Databasebeta

← #22613166

Subgroups — #22613166

Order 9344.

696 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 159 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×D4×Dic73C212yesmaximal, complemented
2C2×D4×Dic73C211yesmaximal, characteristic, complemented
3C2×#14556547C211yesmaximal, characteristic, complemented
4#17988519C211yesmaximal, characteristic, complemented
5#17988512C211yesmaximal, characteristic, complemented
6#17988510C212yesmaximal, complemented
7#17988501C212yesmaximal, complemented
8#17988501C211yesmaximal, characteristic, complemented
9#17988438C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic73C212yesmaximal, complemented
11#392×C73C211yesmaximal, characteristic
12C23×Dic73C2212yes—
13C23×Dic73C2211yescharacteristic
14D4×Dic73—28no—
15D4×Dic73—24no—
16#14556547—24no—
17C2×C4⋊Dic73C2212yes—
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2212yes—
25C2×C22⋊Dic73C2212yes—
26C2×C22⋊Dic73C2212yes—
27C2×C4×Dic73C2211yescharacteristic
28C2×C4×Dic73C2212yes—
29C2×C4×Dic73C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2212yes—
32#14556498C2211yescharacteristic
33C22×D4×C73C2211yescharacteristic
34C22×D4×C73C2212yes—
35C2×C22⋊C4×C73C2212yes—
36C2×C22⋊C4×C73C2211yescharacteristic
37#95×C73C2211yescharacteristic
38C22×Dic73—22no—
39C22×Dic73—22no—
40C22×Dic73—24no—
41C22×Dic73—24no—
42C22×Dic73—24no—
43C22×Dic73D414yescomplemented
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2312yes—
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2311yescharacteristic
50C4⋊Dic73—22no—
51C4⋊Dic73—24no—
52#11924007—22no—
53#11924007—24no—
54#11924007—22no—
55C22⋊Dic73—24no—
56C22⋊Dic73—24no—
57C22⋊Dic73—22no—
58C22⋊Dic73—24no—
59C22⋊Dic73—24no—
60C4×Dic73—22no—
61C4×Dic73—24no—
62C4×Dic73D414yescomplemented
63C24×C73C2311yescharacteristic
64C24×C73C2312yes—
65C2×D4×C73—24no—
66C2×D4×C73—24no—
67C2×D4×C73—24no—
68C2×D4×C73—22no—
69C2×D4×C73—24no—
70C22×C4×C73C2311yescharacteristic
71C22×C4×C73C2311yescharacteristic
72C22×C4×C73C2312yes—
73C22⋊C4×C73—22no—
74C22⋊C4×C73—24no—
75C23×C73—21no—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73—22no—
79C23×C73—22no—
80C23×C73—22no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73—21no—
84C23×C73—22no—
85C23×C73C2×D412yes—
86C23×C73#4114yes—
87C23×C73C2411yescharacteristic
88D4×C73—28no—
89D4×C73—216no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73C2×D412yes—
96C2×C4×C73#4114yes—
97C2×Dic73—21no—
98C2×Dic73—22no—
99C2×Dic73—21no—
100C2×Dic73—28no—
101C2×Dic73—22no—
102C2×Dic73—21no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—48no—
110C2×Dic73C2×D412yes—
111C2×Dic73C2×D412yes—
112C2×Dic73C2×D412yes—
113C2×Dic73C2×D412yes—
114C2×Dic73#4112yes—
115C22×C73—22no—
116C22×C73—24no—
117C22×C73—24no—
118C22×C73—24no—
119C22×C73—24no—
120C22×C73—42no—
121C22×C73—41no—
122C22×C73—42no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73—41no—
126C22×C73—42no—
127C22×C73C22×D411yescharacteristic
128C22×C73C22×D411yescharacteristic
129C22×C73C2×#4111yescharacteristic
130C22×C73C2×#4112yes—
131C22×C73C2×#4112yes—
132C4×C73—22no—
133C4×C73—24no—
134C4×C73—41no—
135Dic73—22no—
136Dic73—22no—
137Dic73—42no—
138Dic73—42no—
139Dic73—41no—
140Dic73#12114yes—
141C2×C73—42no—
142C2×C73—44no—
143C2×C73C2×#12111yescharacteristic
144C2×C73#52511yescharacteristic
145C2×C73#52512yes—
146C2×C73#52912yes—
147C2×C73#53211yescharacteristic
148#2392—731nomaximal, Sylow
149C73#239211yescharacteristic, complemented, Sylow
150C2×C4×D4—731no—
151C2×C4×D4—732no—
152C2×#117—731no—
153#398—731no—
154#397—731no—
155#396—732no—
156#394—732no—
157#394—731no—
158#392D7311yescharacteristic
159C4×C4⋊C4—731no—
160C4×C22⋊C4—732no—
161C22×D4C2×D7311yescharacteristic
162C22×D4C2×D7312yes—
163C23×C4—731no—
164C23×C4—732no—
165C4×D4—1464no—
166C4×D4—1468no—
167#117—1464no—
168C2×C4⋊C4—731no—
169C2×C4⋊C4—731no—
170C2×C4⋊C4—732no—
171C2×C4⋊C4—731no—
172C2×C4⋊C4—732no—
173C2×C22⋊C4—731no—
174C2×C22⋊C4—732no—
175C2×C22⋊C4—732no—
176C2×C22⋊C4—732no—
177C2×C22⋊C4—732no—
178C2×C22⋊C4C2×D7311yescharacteristic
179C2×C22⋊C4C2×D7312yes—
180C2×C42—731no—
181C2×C42—731no—
182C2×C42—732no—
183#95—732no—
184#95—732no—
185#95—731no—
186#95C2×D7311yescharacteristic
187C24C22×D7311yescharacteristic
188C24C22×D7312yes—
189C2×D4—24no—
190C2×D4—24no—
191C2×D4—24no—
192C2×D4—22no—
193C2×D4—24no—
194C22×C4—731no—
195C22×C4—734no—
196C22×C4—731no—
197C22×C4—731no—
198C22×C4—732no—
199C22×C4—731no—
200C22×C4—732no—
201C22×C4—1464no—
202C22×C4—1464no—
203C22×C4—1464no—
204C22×C4—1462no—
205C22×C4—1462no—
206C22×C4C22×D7311yescharacteristic
207C22×C4C22×D7311yescharacteristic
208C22×C4C22×D7312yes—
209C4⋊C4—1462no—
210C4⋊C4—1464no—
211C4⋊C4—1462no—
212C4⋊C4—1462no—
213C4⋊C4—1464no—
214C22⋊C4—22no—
215C22⋊C4—24no—
216C22⋊C4—1462no—
217C22⋊C4—1464no—
218C22⋊C4—1464no—
219C22⋊C4—1464no—
220C22⋊C4—1464no—
221C42—734no—
222C42—1462no—
223C42—1464no—
224C23—21no—
225C23—22no—
226C23—22no—
227C23—21no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23D4×D7312yes—
235C23#1192402714yes—
236C23C23×D7311yescharacteristic
237D4—28no—
238D4—216no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—2928no—
245C2×C4—732no—
246C2×C4—732no—
247C2×C4—732no—
248C2×C4—732no—
249C2×C4—732no—
250C2×C4—1462no—
251C2×C4—1461no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4—1462no—
257C2×C4—1462no—
258C2×C4—1468no—
259C2×C4—1461no—
260C2×C4—1461no—
261C2×C4—1462no—
262C2×C4D4×D7312yes—
263C2×C4#1192402714yes—
264C22—22no—
265C22—24no—
266C22—24no—
267C22—24no—
268C22—24no—
269C22—41no—
270C22—42no—
271C22—42no—
272C22—41no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22C2×D4×D7311yescharacteristic
277C22C2×D4×D7311yescharacteristic
278C22#41×D7311yescharacteristic
279C22C2×#1192402712yes—
280C22C2×#1192402712yes—
281C4—22no—
282C4—24no—
283C4—41no—
284C4—2922no—
285C4—2922no—
286C4—2921no—
287C4—734no—
288C4—1462no—
289C4—1462no—
290C2—42no—
291C2—44no—
292C2#121×D7311yescharacteristic
293C2#1798909311yescharacteristic
294C2#1798909312yes—
295C2#1798911812yes—
296C2#1798913511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2392
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic73C2semidirect
2. C2×D4×Dic73C2semidirect
3. C2×#14556547C2semidirect
4. #17988519C2semidirect
5. #17988512C2semidirect
6. #17988510C2semidirect
7. #17988501C2semidirect
8. #17988501C2semidirect
9. #17988438C2semidirect
10. C22⋊C4×Dic73C2semidirect
43. C22×Dic73D4semidirect
62. C4×Dic73D4semidirect
149. C73#2392semidirect