Finite Group Databasebeta

← #22616066

Subgroups — #22616066

Order 9344.

598 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14556576C211yesmaximal, characteristic, complemented
2C2×#14556562C211yesmaximal, characteristic, complemented
3#17988517C211yesmaximal, characteristic, complemented
4#17988514C211yesmaximal, characteristic, complemented
5#17988502C212yesmaximal, complemented
6#17988496C212yesmaximal, complemented
7#17988495C211yesmaximal, characteristic, complemented
8#17988487C212yesmaximal, complemented
9#17988475C212yesmaximal, complemented
10#17988434C211yesmaximal, characteristic, complemented
11#394×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×C22⋊D73C2212yes—
14C22×C22⋊D73C2212yes—
15C22×C4×D73C2211yescharacteristic
16#14556576—24no—
17#14556562—24no—
18C2×C4⋊Dic73C2211yescharacteristic
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2212yes—
21C2×C22⋊Dic73C2212yes—
22C2×C22⋊Dic73C2212yes—
23C2×#11924005C2212yes—
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2211yescharacteristic
27C2×#11924005C2212yes—
28C2×C4×Dic73C2212yes—
29#14556498C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2212yes—
32C22×D4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2212yes—
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C23×D73C2311yescharacteristic
39C2×D292—22no—
40C2×D292—42no—
41C2×C22⋊D73—24no—
42C2×C22⋊D73—24no—
43C2×C22⋊D73—42no—
44C2×C22⋊D73—42no—
45C2×C22⋊D73—42no—
46C2×C22⋊D73—42no—
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2312yes—
49C22×Dic73C2311yescharacteristic
50C22×Dic73C2312yes—
51C2×C4×D73—42no—
52C2×C4×D73D414yescomplemented
53C4⋊Dic73—22no—
54#11924007—22no—
55#11924007—42no—
56C22⋊Dic73—24no—
57C22⋊Dic73—24no—
58#11924005—22no—
59#11924005—22no—
60#11924005—22no—
61#11924005—24no—
62#11924005—42no—
63C4×Dic73—42no—
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—21no—
85C22×D73—21no—
86C22×D73—21no—
87C22×D73—22no—
88C22×D73—21no—
89C22×D73—21no—
90C22×D73—22no—
91C22×D73C2×D412yes—
92D4×C73—44no—
93C2×C4×C73—22no—
94C2×C4×C73—21no—
95C2×C4×C73—21no—
96C2×C4×C73—22no—
97C2×C4×C73—21no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—21no—
102C2×C4×C73C2×D412yes—
103C22⋊D73—48no—
104C22⋊D73—48no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—21no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73C2×D412yes—
114C2×Dic73#4114yes—
115D292—44no—
116C4×D73—44no—
117C22×C73—42no—
118C22×C73—42no—
119C22×C73—42no—
120C22×C73—42no—
121C22×C73—42no—
122C22×C73—42no—
123C22×C73—42no—
124C22×C73C22×D411yescharacteristic
125C22×C73C2×#4112yes—
126C22×C73H(5,𝔽2)12yes—
127C22×C73H(5,𝔽2)11yescharacteristic
128C22×C73H(5,𝔽2)11yescharacteristic
129C2×D73—22no—
130C2×D73—22no—
131C2×D73—22no—
132C2×D73—42no—
133C2×D73—42no—
134C2×D73—41no—
135C2×D73—41no—
136C2×D73—41no—
137C2×D73—42no—
138C2×D73—42no—
139C4×C73—22no—
140C4×C73—41no—
141C4×C73—41no—
142C4×C73—42no—
143Dic73—22no—
144Dic73—24no—
145Dic73—41no—
146Dic73—42no—
147C2×C73—82no—
148C2×C73#53211yescharacteristic
149C2×C73#53411yescharacteristic
150C2×C73#53511yescharacteristic
151C2×C73#53812yes—
152C2×C73#54012yes—
153D73—42no—
154D73—81no—
155#2661—731nomaximal, Sylow
156C73#266111yescharacteristic, complemented, Sylow
157C2×#123—731no—
158C2×#121—731no—
159#398—731no—
160#397—731no—
161#394—732no—
162#394D7311yescharacteristic, complemented
163#392—731no—
164#392—732no—
165#390—732no—
166#388—732no—
167C4×C22⋊C4—731no—
168C22×D4—732no—
169C22×D4—732no—
170C22×D4—731no—
171C22×D4C2×D7311yescharacteristic
172C23×C4—731no—
173#123—1464no—
174#121—1464no—
175C2×C4⋊C4—732no—
176C2×C4⋊C4—731no—
177C2×C4⋊C4—731no—
178C2×C4⋊C4C2×D7311yescharacteristic
179C2×C22⋊C4—732no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—731no—
183C2×C22⋊C4—731no—
184C2×C22⋊C4—731no—
185C2×C22⋊C4—732no—
186C2×C22⋊C4C2×D7312yes—
187C2×C22⋊C4C2×D7312yes—
188C2×C42—732no—
189#95—731no—
190#95—732no—
191#95—732no—
192#95C2×D7311yescharacteristic
193C24—731no—
194C24—731no—
195C24C22×D7312yes—
196C2×D4—22no—
197C2×D4—42no—
198C2×D4—2922no—
199C2×D4—2922no—
200C2×D4—2922no—
201C2×D4—2922no—
202C2×D4—2922no—
203C2×D4—1462no—
204C2×D4—1464no—
205C2×D4—1464no—
206C22×C4—2922no—
207C22×C4—734no—
208C22×C4—732no—
209C22×C4—731no—
210C22×C4—731no—
211C22×C4—732no—
212C22×C4C22×D7311yescharacteristic
213C22×C4C22×D7312yes—
214C22×C4C22×D7311yescharacteristic
215C22×C4C22×D7311yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—2922no—
218C4⋊C4—1462no—
219C4⋊C4—1462no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—2922no—
223C22⋊C4—1464no—
224C22⋊C4—1462no—
225C22⋊C4—1462no—
226C22⋊C4—1464no—
227C22⋊C4—1464no—
228C22⋊C4—1462no—
229C42—2922no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—732no—
238C23—1461no—
239C23—1462no—
240C23—1461no—
241C23—1462no—
242C23—1461no—
243C23—1462no—
244C23—1462no—
245C23—1461no—
246C23—1461no—
247C23C23×D7311yescharacteristic
248D4—44no—
249D4—2924no—
250D4—2928no—
251D4—2928no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—2924no—
262C2×C4—732no—
263C2×C4—734no—
264C2×C4—1461no—
265C2×C4—1462no—
266C2×C4—1462no—
267C2×C4—1462no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4—1462no—
271C2×C4—1462no—
272C2×C4D4×D7312yes—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—2922no—
281C22—2922no—
282C22—2921no—
283C22—2921no—
284C22—2921no—
285C22—2922no—
286C22—2922no—
287C22—1462no—
288C22—1462no—
289C22—1462no—
290C22C2×D4×D7311yescharacteristic
291C22#41×D7312yes—
292C22#1455663612yes—
293C22#1455663611yescharacteristic
294C22#1455663711yescharacteristic
295C4—22no—
296C4—41no—
297C4—41no—
298C4—42no—
299C4—2921no—
300C4—2922no—
301C4—1462no—
302C4—1464no—
303C2—82no—
304C2—2922no—
305C2—5841no—
306C2#1798913611yescharacteristic
307C2#1798914711yescharacteristic
308C2#1798915311yescharacteristic
309C2#1798917312yes—
310C2#1798918712yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2661
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14556576C2semidirect
2. C2×#14556562C2semidirect
3. #17988517C2semidirect
4. #17988514C2semidirect
5. #17988502C2semidirect
6. #17988496C2semidirect
7. #17988495C2semidirect
8. #17988487C2semidirect
9. #17988475C2semidirect
10. #17988434C2semidirect
11. #394×C73C2semidirect
52. C2×C4×D73D4semidirect
156. C73#2661semidirect
162. #394D73semidirect