Finite Group Databasebeta

← #22614879

Subgroups — #22614879

Order 9344.

676 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 171 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×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556569C212yesmaximal, complemented
3C2×#14556568C212yesmaximal, complemented
4C2×#14556551C211yesmaximal, characteristic
5#17988524C211yesmaximal, characteristic, complemented
6#17988523C211yesmaximal, characteristic, complemented
7#17988522C211yesmaximal, characteristic, complemented
8#17988487C212yesmaximal
9#17988456C212yesmaximal, complemented
10#17988438C211yesmaximal, characteristic, complemented
11#399×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2212yes—
13C22×C22⋊D73C2211yescharacteristic
14C23×Dic73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556590—24no—
17#14556569—28no—
18#14556568—28no—
19#14556551—24no—
20C2×C4⋊Dic73C2211yescharacteristic
21C2×C4⋊Dic73C2212yes—
22C2×#11924007C2212yes—
23C2×#11924007C2211yescharacteristic
24C2×#11924007C2212yes—
25C2×#11924007C2212yes—
26C2×#11924007C2212yes—
27C2×C22⋊Dic73C2212yes—
28C2×#11924005C2212yes—
29C2×#11924005C2212yes—
30C2×#11924005C2211yescharacteristic
31C2×C4×Dic73C2212yes—
32C2×C4×Dic73C2211yescharacteristic
33#14556498C2211yescharacteristic
34C2×C4⋊C4×C73C2211yescharacteristic
35C2×C4⋊C4×C73C2212yes—
36C2×C22⋊C4×C73C2212yes—
37C2×C22⋊C4×C73C2211yescharacteristic
38#95×C73C2211yescharacteristic
39C23×D73C2311yescharacteristic
40C2×Dic146—24no—
41C2×Dic146—24no—
42C2×Dic146—24no—
43C2×C22⋊D73—22no—
44C2×C22⋊D73—22no—
45C2×C22⋊D73Q814yescomplemented
46C22×Dic73—22no—
47C22×Dic73—24no—
48C22×Dic73C2312yes—
49C22×Dic73C2311yescharacteristic
50C22×Dic73C2312yes—
51C22×Dic73C2311yescharacteristic
52C22×Dic73C2311yescharacteristic
53C2×C4×D73—22no—
54C2×C4×D73—24no—
55C4⋊Dic73—24no—
56C4⋊Dic73—22no—
57#11924007—22no—
58#11924007—24no—
59#11924007—24no—
60#11924007—24no—
61#11924007D418yescomplemented
62C22⋊Dic73—24no—
63#11924005—22no—
64#11924005—24no—
65#11924005—24no—
66C4×Dic73—24no—
67C4×Dic73D414yes—
68C24×C73C2311yescharacteristic
69C22×C4×C73C2312yes—
70C22×C4×C73C2311yescharacteristic
71C22×C4×C73C2311yescharacteristic
72C22×C4×C73C2312yes—
73C4⋊C4×C73—24no—
74C4⋊C4×C73—22no—
75C22⋊C4×C73—22no—
76C22⋊C4×C73—24no—
77C23×C73—22no—
78C23×C73—21no—
79C23×C73—21no—
80C23×C73—22no—
81C23×C73C2×Q812yes—
82C23×C73C2411yescharacteristic
83C22×D73—22no—
84C22×D73—21no—
85C22×D73—21no—
86C22×D73—22no—
87C22×D73C2×Q812yes—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73C2×D412yes—
97C2×C4×C73C2×D414yes—
98C22⋊D73—28no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—21no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—44no—
107C2×Dic73C2×D414yes—
108C2×Dic73C2×D412yes—
109C2×Dic73C2×D412yes—
110C2×Dic73C2×D414yes—
111C2×Dic73C2×Q812yes—
112C2×Dic73#4112yes—
113C4×D73—44no—
114Dic146—48no—
115C22×C73—22no—
116C22×C73—24no—
117C22×C73—41no—
118C22×C73—41no—
119C22×C73—42no—
120C22×C73C22×D411yescharacteristic
121C22×C73C22×D412yes—
122C22×C73C22×Q811yescharacteristic
123C22×C73C2×#4111yescharacteristic
124C22×C732−1+412yes—
125C2×D73—22no—
126C2×D73—24no—
127C2×D73—41no—
128C2×D73—41no—
129C2×D73—42no—
130C4×C73—22no—
131C4×C73—24no—
132C4×C73—42no—
133C4×C73—41no—
134Dic73—24no—
135Dic73—42no—
136Dic73—41no—
137Dic73C22⋊Q814yescomplemented
138Dic73#12714yes—
139C2×C73—42no—
140C2×C73C2×C22⋊Q811yescharacteristic
141C2×C73C2×#12711yescharacteristic
142C2×C73#53611yescharacteristic
143C2×C73#54712yes—
144C2×C73D4×Q812yes—
145D73—42no—
146#2542—731nomaximal, Sylow
147C73#254211yescharacteristic, complemented, Sylow
148C2×C4⋊Q8—731no—
149C2×C22⋊Q8—732no—
150C2×C22⋊Q8—732no—
151C2×C4×D4—731no—
152#399—731no—
153#399—731no—
154#399—731no—
155#399D7311yescharacteristic, complemented
156#390—732no—
157#384—732no—
158C4×C4⋊C4—731no—
159C22×Q8—732no—
160C22×D4—731no—
161C23×C4—731no—
162C23×C4—731no—
163C4⋊Q8—1464no—
164C22⋊Q8—1468no—
165C22⋊Q8—1468no—
166C4×D4—1464no—
167C2×C4⋊C4—732no—
168C2×C4⋊C4—731no—
169C2×C4⋊C4—732no—
170C2×C4⋊C4—732no—
171C2×C4⋊C4—732no—
172C2×C4⋊C4—732no—
173C2×C4⋊C4—731no—
174C2×C4⋊C4C2×D7312yes—
175C2×C4⋊C4C2×D7311yescharacteristic
176C2×C22⋊C4—732no—
177C2×C22⋊C4—731no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4C2×D7311yescharacteristic
181C2×C22⋊C4C2×D7312yes—
182C2×C42—731no—
183C2×C42—732no—
184#95—731no—
185#95C2×D7311yescharacteristic
186C24—731no—
187C24C22×D7311yescharacteristic
188C2×Q8—1464no—
189C2×Q8—1464no—
190C2×Q8—1464no—
191C2×D4—734no—
192C2×D4—1462no—
193C2×D4—1462no—
194C22×C4—731no—
195C22×C4—731no—
196C22×C4—732no—
197C22×C4—732no—
198C22×C4—731no—
199C22×C4—1462no—
200C22×C4—1464no—
201C22×C4—1462no—
202C22×C4—1464no—
203C22×C4C22×D7312yes—
204C22×C4C22×D7311yescharacteristic
205C22×C4C22×D7311yescharacteristic
206C22×C4C22×D7312yes—
207C4⋊C4—24no—
208C4⋊C4—22no—
209C4⋊C4—738no—
210C4⋊C4—1462no—
211C4⋊C4—1464no—
212C4⋊C4—1464no—
213C4⋊C4—1464no—
214C4⋊C4—1464no—
215C4⋊C4—1462no—
216C22⋊C4—22no—
217C22⋊C4—24no—
218C22⋊C4—1464no—
219C22⋊C4—1464no—
220C22⋊C4—1462no—
221C22⋊C4—1464no—
222C42—734no—
223C42—1464no—
224C23—22no—
225C23—21no—
226C23—21no—
227C23—22no—
228C23—732no—
229C23—1462no—
230C23—1461no—
231C23—1461no—
232C23—1462no—
233C23Q8×D7312yes—
234C23C23×D7311yescharacteristic
235Q8—2928no—
236D4—1468no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—2924no—
246C2×C4—2924no—
247C2×C4—732no—
248C2×C4—732no—
249C2×C4—734no—
250C2×C4—732no—
251C2×C4—732no—
252C2×C4—734no—
253C2×C4—1461no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4—1462no—
257C2×C4—1462no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4D4×D7312yes—
261C2×C4D4×D7314yes—
262C22—24no—
263C22—22no—
264C22—41no—
265C22—41no—
266C22—42no—
267C22—2921no—
268C22—2921no—
269C22—2922no—
270C22—1464no—
271C22—1462no—
272C22C2×D4×D7311yescharacteristic
273C22C2×D4×D7312yes—
274C22C2×Q8×D7311yescharacteristic
275C22#41×D7311yescharacteristic
276C22#1455663812yes—
277C4—22no—
278C4—24no—
279C4—41no—
280C4—42no—
281C4—2921no—
282C4—2922no—
283C4—734no—
284C4—734no—
285C4—1464no—
286C2—42no—
287C2—2922no—
288C2C22⋊Q8×D7311yescharacteristic
289C2#127×D7311yescharacteristic
290C2#1798915911yescharacteristic
291C2#1798923512yes—
292C2#1798925012yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2542
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
2. C2×#14556569C2semidirect
3. C2×#14556568C2semidirect
5. #17988524C2semidirect
6. #17988523C2semidirect
7. #17988522C2semidirect
9. #17988456C2semidirect
10. #17988438C2semidirect
11. #399×C73C2semidirect
45. C2×C22⋊D73Q8semidirect
61. #11924007D4semidirect
137. Dic73C22⋊Q8semidirect
147. C73#2542semidirect
155. #399D73semidirect