Finite Group Databasebeta

← #22615862

Subgroups — #22615862

Order 9344.

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

normal subgroups only

This group has 576 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×#14556569C211yesmaximal, characteristic, complemented
2C2×#14556562C211yesmaximal, characteristic
3#17988527C211yesmaximal, characteristic, complemented
4#17988526C211yesmaximal, characteristic, complemented
5#17988515C212yesmaximal, complemented
6#17988501C211yesmaximal, characteristic, complemented
7#17988499C212yesmaximal, complemented
8#17988463C212yesmaximal, complemented
9#17988463C212yesmaximal, complemented
10#95×D73C211yesmaximal, characteristic, complemented
11#394×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C22⋊D73C2212yes—
14C22×C4×D73C2212yes—
15C22×C4×D73C2211yescharacteristic
16#14556569—24no—
17#14556562—24no—
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2211yescharacteristic
21C2×C22⋊Dic73C2212yes—
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26#14556498C2212yes—
27#14556498C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×D4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2212yes—
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C2×Dic146—22no—
39C2×Dic146—42no—
40C2×C22⋊D73—24no—
41C2×C22⋊D73—24no—
42C2×C22⋊D73—24no—
43C22×Dic73C2312yes—
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C2×C4×D73—24no—
49C2×C4×D73—42no—
50C2×C4×D73—42no—
51C2×C4×D73—42no—
52C2×C4×D73D414yes—
53C4⋊Dic73—22no—
54#11924007—22no—
55#11924007—22no—
56C22⋊Dic73—24no—
57C22⋊Dic73—42no—
58C22⋊Dic73—42no—
59#11924005—22no—
60#11924005—22no—
61C24×C73C2312yes—
62C2×D4×C73—22no—
63C2×D4×C73—42no—
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2311yescharacteristic
67C22×C4×C73C2311yescharacteristic
68C4⋊C4×C73—22no—
69C22⋊C4×C73—42no—
70C22⋊C4×C73—42no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73—22no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73C2411yescharacteristic
79C22×D73—22no—
80C22×D73—21no—
81C22×D73—21no—
82C22×D73C2×D412yes—
83C22×D73#4114yes—
84D4×C73—44no—
85C2×C4×C73—22no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—22no—
89C2×C4×C73—21no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73C2×D412yes—
95C22⋊D73—48no—
96C2×Dic73—22no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—21no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—21no—
108C2×Dic73C2×D412yes—
109C4×D73—44no—
110C4×D73—48no—
111Dic146—44no—
112C22×C73—42no—
113C22×C73—42no—
114C22×C73—42no—
115C22×C73—42no—
116C22×C73—42no—
117C22×C73—42no—
118C22×C73—42no—
119C22×C73C22×D411yescharacteristic
120C22×C73C2×#4112yes—
121C22×C73H(5,𝔽2)12yes—
122C22×C73H(5,𝔽2)11yescharacteristic
123C22×C732−1+411yescharacteristic
124C2×D73—22no—
125C2×D73—22no—
126C2×D73—24no—
127C2×D73—24no—
128C2×D73#12414yes—
129C4×C73—22no—
130C4×C73—41no—
131C4×C73—41no—
132C4×C73—42no—
133Dic73—22no—
134Dic73—42no—
135Dic73—41no—
136Dic73—41no—
137Dic73—42no—
138C2×C73—82no—
139C2×C73C2×#12411yescharacteristic
140C2×C73#53411yescharacteristic
141C2×C73#53711yescharacteristic
142C2×C73#53812yes—
143C2×C73#53912yes—
144D73—24no—
145#2639—731nomaximal, Sylow
146C73#263911yescharacteristic, complemented, Sylow
147C2×C22⋊Q8—731no—
148C2×#121—731no—
149#400—731no—
150#400—731no—
151#397—732no—
152#394—731no—
153#394D7311yescharacteristic, complemented
154#393—732no—
155#386—732no—
156#386—732no—
157C2×#95—731no—
158C22×Q8—731no—
159C22×D4—732no—
160C22×D4C2×D7311yescharacteristic
161C23×C4—731no—
162C23×C4—732no—
163C22⋊Q8—1464no—
164#121—1464no—
165C2×C4⋊C4—731no—
166C2×C4⋊C4—731no—
167C2×C4⋊C4—731no—
168C2×C4⋊C4C2×D7311yescharacteristic
169C2×C22⋊C4—732no—
170C2×C22⋊C4—732no—
171C2×C22⋊C4—732no—
172C2×C22⋊C4—731no—
173C2×C22⋊C4—731no—
174C2×C22⋊C4C2×D7312yes—
175C2×C22⋊C4C2×D7312yes—
176#95—732no—
177#95—731no—
178#95—732no—
179#95—732no—
180#95—732no—
181#95—732no—
182#95C2×D7311yescharacteristic
183C24—731no—
184C24C22×D7312yes—
185C2×Q8—2922no—
186C2×Q8—1462no—
187C2×D4—22no—
188C2×D4—42no—
189C2×D4—1464no—
190C2×D4—1464no—
191C2×D4—1464no—
192C22×C4—2922no—
193C22×C4—2922no—
194C22×C4—2922no—
195C22×C4—734no—
196C22×C4—731no—
197C22×C4—732no—
198C22×C4—732no—
199C22×C4—731no—
200C22×C4—731no—
201C22×C4—1464no—
202C22×C4C22×D7312yes—
203C22×C4C22×D7311yescharacteristic
204C22×C4C22×D7311yescharacteristic
205C22×C4C22×D7311yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—1462no—
208C4⋊C4—1462no—
209C4⋊C4—1462no—
210C22⋊C4—42no—
211C22⋊C4—42no—
212C22⋊C4—2922no—
213C22⋊C4—2922no—
214C22⋊C4—1462no—
215C22⋊C4—1462no—
216C22⋊C4—1464no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—732no—
225C23—734no—
226C23—1462no—
227C23—1461no—
228C23—1461no—
229C23C23×D7311yescharacteristic
230Q8—2924no—
231D4—44no—
232D4—2928no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—2924no—
243C2×C4—2928no—
244C2×C4—732no—
245C2×C4—1461no—
246C2×C4—1462no—
247C2×C4—1461no—
248C2×C4—1462no—
249C2×C4—1462no—
250C2×C4—1462no—
251C2×C4—1461no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1461no—
256C2×C4—1462no—
257C2×C4D4×D7312yes—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—734no—
266C22—1462no—
267C22—1462no—
268C22—1464no—
269C22—1464no—
270C22C2×D4×D7311yescharacteristic
271C22#41×D7312yes—
272C22#1455663612yes—
273C22#1455663611yescharacteristic
274C22#1455663811yescharacteristic
275C4—22no—
276C4—41no—
277C4—41no—
278C4—42no—
279C4—2921no—
280C4—2921no—
281C4—2922no—
282C4—2922no—
283C4—1462no—
284C2—82no—
285C2—1464no—
286C2#124×D7311yescharacteristic
287C2#1798914711yescharacteristic
288C2#1798916611yescharacteristic
289C2#1798916912yes—
290C2#1798918012yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2639
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14556569C2semidirect
3. #17988527C2semidirect
4. #17988526C2semidirect
5. #17988515C2semidirect
6. #17988501C2semidirect
7. #17988499C2semidirect
8. #17988463C2semidirect
9. #17988463C2semidirect
10. #95×D73C2semidirect
11. #394×C73C2semidirect
146. C73#2639semidirect
153. #394D73semidirect