Finite Group Databasebeta

← #22615873

Subgroups — #22615873

Order 9344.

584 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14556587C211yesmaximal, characteristic
2C2×#14556581C211yesmaximal, characteristic, complemented
3#17988505C211yesmaximal, characteristic, complemented
4#17988504C211yesmaximal, characteristic, complemented
5#17988503C212yesmaximal, complemented
6#17988502C212yesmaximal, complemented
7#17988501C211yesmaximal, characteristic, complemented
8#17988487C212yesmaximal, complemented
9#17988487C212yesmaximal, complemented
10#17988432C211yesmaximal, characteristic, complemented
11#394×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×C22⋊D73C2212yes—
14C22×C22⋊D73C2212yes—
15#14556587—24no—
16#14556581—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×C4×Dic73C2212yes—
29C2×C4×Dic73C2211yescharacteristic
30#14556498C2211yescharacteristic
31#14556498C2212yes—
32C22×D4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2212yes—
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2312yes—
38C2×D292—22no—
39C2×D292—42no—
40C2×C22⋊D73—24no—
41C2×C22⋊D73—24no—
42C2×C22⋊D73—24no—
43C2×C22⋊D73—24no—
44C2×C22⋊D73—42no—
45C2×C22⋊D73—42no—
46C22×Dic73C2312yes—
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2311yescharacteristic
50C22×Dic73C2311yescharacteristic
51C4⋊Dic73—22no—
52#11924007—22no—
53#11924007—22no—
54#11924007—22no—
55#11924007—22no—
56C22⋊Dic73—42no—
57C22⋊Dic73—42no—
58#11924005—42no—
59#11924005—42no—
60#11924005—42no—
61#11924005—42no—
62C4×Dic73—24no—
63C4×Dic73D414yes—
64C24×C73C2312yes—
65C2×D4×C73—22no—
66C2×D4×C73—42no—
67C22×C4×C73C2312yes—
68C22×C4×C73C2311yescharacteristic
69C22×C4×C73C2311yescharacteristic
70C22×C4×C73C2311yescharacteristic
71C4⋊C4×C73—22no—
72C22⋊C4×C73—42no—
73C22⋊C4×C73—42no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73—22no—
79C23×C73—22no—
80C23×C73—22no—
81C23×C73C2411yescharacteristic
82C22×D73—22no—
83C22×D73—22no—
84C22×D73—22no—
85C22×D73—22no—
86C22×D73—22no—
87C22×D73—22no—
88C22×D73—22no—
89D4×C73—44no—
90C2×C4×C73—22no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—22no—
94C2×C4×C73—21no—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—21no—
99C2×C4×C73C2×D412yes—
100C22⋊D73—48no—
101C22⋊D73—48no—
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73—21no—
105C2×Dic73—21no—
106C2×Dic73—22no—
107C2×Dic73—21no—
108C2×Dic73—22no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—21no—
112C2×Dic73C2×D412yes—
113C2×Dic73C2×D412yes—
114C2×Dic73#4114yes—
115D292—44no—
116C22×C73—42no—
117C22×C73—42no—
118C22×C73—42no—
119C22×C73—42no—
120C22×C73—42no—
121C22×C73—42no—
122C22×C73—42no—
123C22×C73C22×D411yescharacteristic
124C22×C73C2×#4112yes—
125C22×C73H(5,𝔽2)12yes—
126C22×C73H(5,𝔽2)11yescharacteristic
127C22×C73H(5,𝔽2)11yescharacteristic
128C2×D73—42no—
129C2×D73—42no—
130C2×D73—42no—
131C2×D73—42no—
132C2×D73—42no—
133C2×D73—42no—
134C2×D73—42no—
135C4×C73—22no—
136C4×C73—41no—
137C4×C73—41no—
138C4×C73—42no—
139Dic73—22no—
140Dic73—41no—
141Dic73—41no—
142Dic73—42no—
143Dic73#12414yes—
144C2×C73—82no—
145C2×C73C2×#12411yescharacteristic
146C2×C73#53511yescharacteristic
147C2×C73#53511yescharacteristic
148C2×C73#54012yes—
149C2×C73#54012yes—
150D73—82no—
151#2641—731nomaximal, Sylow
152C73#264111yescharacteristic, complemented, Sylow
153C2×#127—731no—
154C2×#125—731no—
155#394—731no—
156#394—731no—
157#394—732no—
158#394—732no—
159#394—731no—
160#394D7311yescharacteristic, complemented
161#390—732no—
162#390—732no—
163#376—731no—
164C22×D4—732no—
165C22×D4—732no—
166C22×D4—731no—
167C22×D4C2×D7311yescharacteristic
168#127—1464no—
169#125—1464no—
170C2×C4⋊C4—731no—
171C2×C4⋊C4—731no—
172C2×C4⋊C4—731no—
173C2×C4⋊C4—731no—
174C2×C4⋊C4—731no—
175C2×C4⋊C4C2×D7311yescharacteristic
176C2×C22⋊C4—732no—
177C2×C22⋊C4—732no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4C2×D7312yes—
183C2×C22⋊C4C2×D7312yes—
184C2×C42—731no—
185C2×C42—732no—
186#95—732no—
187#95—731no—
188#95C2×D7311yescharacteristic
189C24—732no—
190C24C22×D7312yes—
191C2×D4—22no—
192C2×D4—42no—
193C2×D4—2922no—
194C2×D4—2922no—
195C2×D4—2922no—
196C2×D4—1464no—
197C2×D4—1464no—
198C2×D4—1464no—
199C2×D4—1464no—
200C2×D4—1462no—
201C22×C4—731no—
202C22×C4—731no—
203C22×C4—732no—
204C22×C4—731no—
205C22×C4—731no—
206C22×C4C22×D7312yes—
207C22×C4C22×D7311yescharacteristic
208C22×C4C22×D7311yescharacteristic
209C22×C4C22×D7311yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—1462no—
212C4⋊C4—1462no—
213C4⋊C4—1462no—
214C4⋊C4—1462no—
215C4⋊C4—1462no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—2922no—
219C22⋊C4—2922no—
220C22⋊C4—2922no—
221C22⋊C4—2922no—
222C22⋊C4—2922no—
223C22⋊C4—2922no—
224C42—734no—
225C42—1464no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—1462no—
234C23—1462no—
235C23—1462no—
236C23—1462no—
237C23—1462no—
238C23—1462no—
239C23—1462no—
240C23C23×D7311yescharacteristic
241D4—44no—
242D4—2924no—
243D4—2928no—
244D4—2928no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—732no—
255C2×C4—734no—
256C2×C4—732no—
257C2×C4—1461no—
258C2×C4—1461no—
259C2×C4—1462no—
260C2×C4—1462no—
261C2×C4—1461no—
262C2×C4—1462no—
263C2×C4—1461no—
264C2×C4—1462no—
265C2×C4—1461no—
266C2×C4—1461no—
267C2×C4D4×D7312yes—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—2922no—
276C22—2922no—
277C22—2922no—
278C22—2922no—
279C22—2922no—
280C22—2922no—
281C22—2922no—
282C22C2×D4×D7311yescharacteristic
283C22#41×D7312yes—
284C22#1455663612yes—
285C22#1455663611yescharacteristic
286C22#1455663711yescharacteristic
287C4—22no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—2921no—
292C4—2921no—
293C4—2922no—
294C4—734no—
295C4—1462no—
296C2—82no—
297C2—5842no—
298C2#124×D7311yescharacteristic
299C2#1798915211yescharacteristic
300C2#1798915311yescharacteristic
301C2#1798918712yes—
302C2#1798918912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2641
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14556581C2semidirect
3. #17988505C2semidirect
4. #17988504C2semidirect
5. #17988503C2semidirect
6. #17988502C2semidirect
7. #17988501C2semidirect
8. #17988487C2semidirect
9. #17988487C2semidirect
10. #17988432C2semidirect
11. #394×C73C2semidirect
152. C73#2641semidirect
160. #394D73semidirect