Finite Group Databasebeta

← #22615674

Subgroups — #22615674

Order 9344.

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

normal subgroups only

This group has 632 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×#14556576C212yesmaximal, complemented
2C2×#14556566C211yesmaximal, characteristic
3C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
4#17988518C211yesmaximal, characteristic, complemented
5#17988511C212yesmaximal, complemented
6#17988509C212yesmaximal, complemented
7#17988505C211yesmaximal, characteristic, complemented
8#17988504C211yesmaximal, characteristic, complemented
9#17988465C212yesmaximal, complemented
10#17988446C211yesmaximal, characteristic, complemented
11#398×C73C211yesmaximal, characteristic, complemented
12C22×D292C2212yes—
13C22×D292C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16C22×C4×D73C2211yescharacteristic
17#14556576—28no—
18#14556566—24no—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×#11924007C2212yes—
24C4⋊C4×D73—24no—
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×#11924005C2212yes—
29C2×#11924005C2212yes—
30C2×#11924005C2212yes—
31#14556498C2211yescharacteristic
32#14556498C2212yes—
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35C2×C4⋊C4×C73C2211yescharacteristic
36#95×C73C2211yescharacteristic
37#95×C73C2212yes—
38C23×D73C2312yes—
39C23×D73C2311yescharacteristic
40C2×D292—24no—
41C2×D292—24no—
42C2×D292—24no—
43C2×D292—22no—
44C2×D292—42no—
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C2×C4×D73—22no—
50C2×C4×D73—22no—
51C2×C4×D73—22no—
52C2×C4×D73—42no—
53C2×C4×D73—42no—
54C2×C4×D73D414yes—
55C2×C4×D73D414yescomplemented
56C4⋊Dic73—22no—
57#11924007—22no—
58#11924007—22no—
59#11924007—24no—
60#11924007—42no—
61#11924005—24no—
62#11924005—24no—
63#11924005—24no—
64#11924005—24no—
65#11924005—42no—
66#11924005—42no—
67C22×C4×C73C2312yes—
68C22×C4×C73C2311yescharacteristic
69C22×C4×C73C2312yes—
70C22×C4×C73C2311yescharacteristic
71C22×C4×C73C2311yescharacteristic
72C4⋊C4×C73—22no—
73C4⋊C4×C73—22no—
74C4⋊C4×C73—24no—
75C23×C73C2411yescharacteristic
76C22×D73—22no—
77C22×D73—22no—
78C22×D73—22no—
79C22×D73—22no—
80C22×D73—22no—
81C22×D73—22no—
82C22×D73—22no—
83C22×D73—22no—
84C22×D73—22no—
85C22×D73C2×D412yes—
86C22×D73C2×D412yes—
87C22×D73#4112yes—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73C2×D412yes—
100C2×C4×C73C2×D412yes—
101C2×Dic73—21no—
102C2×Dic73—21no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—21no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73C2×D412yes—
110C2×Dic73C2×D412yes—
111D292—44no—
112D292—48no—
113C4×D73—28no—
114C4×D73—44no—
115C4×D73—44no—
116C22×C73C22×D411yescharacteristic
117C22×C73C22×D411yescharacteristic
118C22×C73C2×#4111yescharacteristic
119C22×C73H(5,𝔽2)12yes—
120C22×C732−1+412yes—
121C2×D73—22no—
122C2×D73—22no—
123C2×D73—24no—
124C2×D73—24no—
125C2×D73—42no—
126C2×D73—42no—
127C2×D73—42no—
128C2×D73—42no—
129C2×D73—42no—
130C2×D73—42no—
131C2×D73—42no—
132C2×D73#12114yes—
133C4×C73—22no—
134C4×C73—22no—
135C4×C73—42no—
136C4×C73—41no—
137C4×C73—42no—
138Dic73—22no—
139Dic73—22no—
140Dic73—41no—
141Dic73—42no—
142C2×C73C2×#12111yescharacteristic
143C2×C73#53411yescharacteristic
144C2×C73#53611yescharacteristic
145C2×C73#53712yes—
146C2×C73#53912yes—
147D73—24no—
148D73—82no—
149#2618—731nomaximal, Sylow
150C73#261811yescharacteristic, complemented, Sylow
151C2×#123—732no—
152C2×#121—731no—
153C22×C4⋊C4—731no—
154#398—731no—
155#398D7311yescharacteristic, complemented
156#396—732no—
157#396—732no—
158#394—731no—
159#394—731no—
160#386—732no—
161#380—731no—
162C22×D4—731no—
163C22×D4—732no—
164C23×C4—731no—
165C23×C4—731no—
166C23×C4—731no—
167#123—1468no—
168#121—1464no—
169C2×C4⋊C4—732no—
170C2×C4⋊C4—731no—
171C2×C4⋊C4—731no—
172C2×C4⋊C4—731no—
173C2×C4⋊C4—732no—
174C2×C4⋊C4—1464no—
175C2×C4⋊C4C2×D7311yescharacteristic
176C2×C4⋊C4C2×D7311yescharacteristic
177C2×C4⋊C4C2×D7312yes—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—732no—
183C2×C22⋊C4—732no—
184#95—731no—
185#95—732no—
186#95C2×D7311yescharacteristic
187#95C2×D7312yes—
188C24—731no—
189C24—732no—
190C2×D4—2922no—
191C2×D4—1464no—
192C2×D4—1464no—
193C2×D4—1464no—
194C2×D4—1462no—
195C22×C4—2922no—
196C22×C4—2922no—
197C22×C4—734no—
198C22×C4—731no—
199C22×C4—731no—
200C22×C4—734no—
201C22×C4—732no—
202C22×C4—731no—
203C22×C4—1462no—
204C22×C4—1462no—
205C22×C4—1462no—
206C22×C4C22×D7312yes—
207C22×C4C22×D7312yes—
208C22×C4C22×D7311yescharacteristic
209C22×C4C22×D7311yescharacteristic
210C22×C4C22×D7311yescharacteristic
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—24no—
214C4⋊C4—2922no—
215C4⋊C4—1462no—
216C4⋊C4—1464no—
217C4⋊C4—1462no—
218C4⋊C4—1462no—
219C22⋊C4—2922no—
220C22⋊C4—2922no—
221C22⋊C4—1464no—
222C22⋊C4—1464no—
223C22⋊C4—1464no—
224C22⋊C4—1464no—
225C23—732no—
226C23—732no—
227C23—732no—
228C23—1462no—
229C23—1462no—
230C23—1462no—
231C23—1462no—
232C23—1462no—
233C23—1462no—
234C23—1462no—
235C23—1462no—
236C23—1462no—
237C23C23×D7311yescharacteristic
238D4—2924no—
239D4—2928no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—2924no—
252C2×C4—2924no—
253C2×C4—732no—
254C2×C4—732no—
255C2×C4—1468no—
256C2×C4—1462no—
257C2×C4—1461no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4—1462no—
261C2×C4—1461no—
262C2×C4—1461no—
263C2×C4—1462no—
264C2×C4D4×D7312yes—
265C2×C4D4×D7312yes—
266C22—2922no—
267C22—2922no—
268C22—2922no—
269C22—2922no—
270C22—2922no—
271C22—2922no—
272C22—2922no—
273C22—734no—
274C22—1462no—
275C22—1462no—
276C22—1464no—
277C22—1464no—
278C22C2×D4×D7311yescharacteristic
279C22C2×D4×D7311yescharacteristic
280C22#41×D7311yescharacteristic
281C22#1455663712yes—
282C22#1455663912yes—
283C4—22no—
284C4—22no—
285C4—41no—
286C4—42no—
287C4—42no—
288C4—2921no—
289C4—2922no—
290C4—1462no—
291C4—1462no—
292C2—5842no—
293C2—1464no—
294C2#121×D7311yescharacteristic
295C2#1798914811yescharacteristic
296C2#1798916211yescharacteristic
297C2#1798916712yes—
298C2#1798918512yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#398×C73C2
hypercenter#398D73
hypocenterC73#2618
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14556576C2semidirect
3. C2×C4⋊C4×D73C2semidirect
4. #17988518C2semidirect
5. #17988511C2semidirect
6. #17988509C2semidirect
7. #17988505C2semidirect
8. #17988504C2semidirect
9. #17988465C2semidirect
10. #17988446C2semidirect
11. #398×C73C2semidirect
55. C2×C4×D73D4semidirect
150. C73#2618semidirect
155. #398D73semidirect