Finite Group Databasebeta

← #22620704

Subgroups — #22620704

Order 9344.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14556567C211yesmaximal, characteristic
2C22⋊Q8×D73C211yesmaximal, characteristic
3#17988923C211yesmaximal, characteristic, complemented
4#17988921C212yesmaximal, complemented
5#17988920C211yesmaximal, characteristic, complemented
6#17988827C212yesmaximal, complemented
7#17988825C212yesmaximal, complemented
8#17988743C211yesmaximal, characteristic, complemented
9#17988741C212yesmaximal, complemented
10C22⋊C8×D73C211yesmaximal, characteristic
11#451×C73C211yesmaximal, characteristic, complemented
12C2×Q8×D73C2211yescharacteristic
13C22×C4×D73C2211yescharacteristic
14C2×#11924018C2212yescomplemented
15C2×C8×D73C2212yes—
16#14556571C2211yescharacteristic
17#14556570C2211yescharacteristic
18#14556569—21no—
19#14556568—21no—
20#14556567—21no—
21#14556567—21no—
22#14556567C2212yes—
23#14556567C2211yescharacteristic
24#14556567C2212yes—
25C2×C4⋊Dic73C2211yescharacteristic
26C2×#11924007—21no—
27C4⋊C4×D73—21no—
28C4⋊C4×D73C2211yescharacteristic
29C2×#11924005—21no—
30C22⋊C4×D73—21no—
31#14556525C2212yescomplemented
32#14556524C2212yescomplemented
33#14556516C2212yescomplemented
34#14556515C2212yescomplemented
35#14556515C2212yescomplemented
36C22⋊#10596831C2211yescharacteristic
37#14556503C2212yes—
38C22×Q8×C73C2211yescharacteristic
39C2×Q16×C73C2212yescomplemented
40C22⋊Q8×C73C2211yescharacteristic
41#103×C73C2212yescomplemented
42C22⋊C8×C73C2211yescharacteristic
43C23×D73D411yescharacteristic
44C2×Dic146—21no—
45C2×Dic146C2311yescharacteristic
46Q8×D73—42no—
47C22×Dic73—21no—
48C22×Dic73D411yescharacteristic
49C2×C4×D73—21no—
50C2×C4×D73—21no—
51C2×C4×D73—42no—
52C2×C4×D73D411yescharacteristic
53C2×C4×D73D411yescharacteristic
54C2×C4×D73C2311yescharacteristic
55C2×C4×D73C2311yescharacteristic
56#11924018—42no—
57C2×#10596831C2312yes—
58C8×D73—42no—
59C4⋊Dic73—21no—
60C4⋊Dic73—21no—
61C4⋊Dic73C2311yescharacteristic
62C4⋊Dic73C2312yes—
63#11924007—21no—
64#11924007—21no—
65#11924007—21no—
66#11924007—22no—
67#11924007—22no—
68C22⋊Dic73—21no—
69#11924005—21no—
70#11924005—21no—
71#11924005—22no—
72#11924005—22no—
73C2×Q8×C73—21no—
74C2×Q8×C73—42no—
75C2×Q8×C73C2312yes—
76C2×Q8×C73C2311yescharacteristic
77C22×C4×C73—21no—
78C22×C4×C73C2311yescharacteristic
79Q16×C73—42no—
80C2×C8×C73C2312yes—
81C4⋊C4×C73—21no—
82C4⋊C4×C73C2311yescharacteristic
83C22⋊C4×C73—21no—
84C23×C73C2×D411yescharacteristic
85C22×D73—41no—
86C22×D73—41no—
87C22×D73Q1614yescomplemented
88C22×D73C2×D411yescharacteristic
89C22×D73C2×D411yescharacteristic
90Q8×C73—22no—
91Q8×C73—22no—
92Q8×C73—22no—
93Q8×C73—42no—
94C2×C4×C73—22no—
95C2×C4×C73—21no—
96C2×C4×C73—21no—
97C2×C4×C73—22no—
98C2×C4×C73—42no—
99C2×C4×C73C2×D411yescharacteristic
100C2×C4×C73C2411yescharacteristic
101C2×Dic73—22no—
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73—41no—
105C2×Dic73—42no—
106C2×Dic73C2×D411yescharacteristic
107C2×Dic73C2×D411yescharacteristic
108C4×D73—22no—
109C4×D73—22no—
110C4×D73—41no—
111C4×D73—41no—
112C4×D73—42no—
113C4×D73—42no—
114Dic146—22no—
115Dic146—42no—
116C8×C73—22no—
117#10596831—22no—
118C22×C73—21no—
119C22×C73—21no—
120C22×C73C2×Q1612yes—
121C22×C73C22×D411yescharacteristic
122C2×D73—21no—
123C2×D73—21no—
124C2×D73—21no—
125C2×D73—21no—
126C2×D73—44no—
127C2×D73C2×Q1612yes—
128C2×D73C2×Q1612yes—
129C4×C73—21no—
130C4×C73—41no—
131C4×C73—42no—
132C4×C73—41no—
133C4×C73H(5,𝔽2)12yes—
134Dic73—21no—
135Dic73—21no—
136Dic73—41no—
137Dic73—41no—
138Dic73—42no—
139C2×C73—22no—
140C2×C73#53411yescharacteristic
141C2×C73C22×Q1611yescharacteristic
142C2×C73#57511yescharacteristic
143D73—22no—
144D73—22no—
145#3189—731nomaximal, Sylow
146C73#318911yescharacteristic, complemented, Sylow
147C2×C22⋊Q8—731no—
148C2×C22⋊Q8—731no—
149#484—731no—
150#484—732no—
151#484—731no—
152#467—732no—
153#467—732no—
154#451—731no—
155#451—732no—
156#451D7311yescharacteristic, complemented
157C2×C22⋊C8—731no—
158C22×Q8—731no—
159C22×Q8C2×D7311yescharacteristic
160C23×C4—731no—
161C2×Q16—732no—
162C2×Q16C2×D7312yescomplemented
163C22×C8—732no—
164C22⋊Q8—732no—
165C22⋊Q8—731no—
166C22⋊Q8—732no—
167C22⋊Q8—731no—
168C22⋊Q8—731no—
169C22⋊Q8—1461no—
170C22⋊Q8—1461no—
171C22⋊Q8—1461no—
172C22⋊Q8—1461no—
173C22⋊Q8C2×D7311yescharacteristic
174C2×C4⋊C4—731no—
175C2×C4⋊C4—731no—
176C2×C4⋊C4—1461no—
177C2×C4⋊C4—1461no—
178C2×C22⋊C4—1461no—
179C2×C22⋊C4—1461no—
180#107—732no—
181#107—732no—
182#103—732no—
183#103—732no—
184#103—732no—
185#103C2×D7312yescomplemented
186C22⋊C8—731no—
187C22⋊C8—732no—
188C22⋊C8C2×D7311yescharacteristic
189C24—731no—
190C2×Q8—21no—
191C2×Q8—42no—
192C2×Q8—2922no—
193C2×Q8—731no—
194C2×Q8—1461no—
195C2×Q8C22×D7311yescharacteristic
196C2×Q8C22×D7312yes—
197C22×C4—21no—
198C22×C4—2922no—
199C22×C4—731no—
200C22×C4—731no—
201C22×C4—731no—
202C22×C4—731no—
203C22×C4—731no—
204C22×C4—1461no—
205C22×C4—1461no—
206C22×C4—1461no—
207C22×C4C22×D7311yescharacteristic
208Q16—42no—
209Q16—2922no—
210C2×C8—2922no—
211C2×C8—732no—
212C2×C8C22×D7312yes—
213C4⋊C4—21no—
214C4⋊C4—731no—
215C4⋊C4—732no—
216C4⋊C4—1461no—
217C4⋊C4—1461no—
218C4⋊C4—1462no—
219C4⋊C4—1462no—
220C4⋊C4—1461no—
221C4⋊C4—1461no—
222C4⋊C4—1461no—
223C4⋊C4C22×D7311yescharacteristic
224C22⋊C4—21no—
225C22⋊C4—1461no—
226C22⋊C4—1461no—
227C22⋊C4—1462no—
228C22⋊C4—1462no—
229C22⋊C4—1461no—
230C23—2921no—
231C23—2921no—
232C23—734no—
233C23—731no—
234C23—731no—
235C23D4×D7311yescharacteristic
236Q8—22no—
237Q8—22no—
238Q8—22no—
239Q8—42no—
240Q8—2922no—
241Q8—1462no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—2921no—
248C2×C4—2921no—
249C2×C4—2922no—
250C2×C4—2922no—
251C2×C4—2922no—
252C2×C4—2921no—
253C2×C4—731no—
254C2×C4—731no—
255C2×C4—1462no—
256C2×C4—1461no—
257C2×C4—1461no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4D4×D7311yescharacteristic
261C2×C4C23×D7311yescharacteristic
262C8—22no—
263C8—1462no—
264C22—21no—
265C22—21no—
266C22—2924no—
267C22—732no—
268C22—732no—
269C22—1461no—
270C22—1461no—
271C22—1461no—
272C22—1461no—
273C22Q16×D7312yes—
274C22C2×D4×D7311yescharacteristic
275C4—21no—
276C4—41no—
277C4—42no—
278C4—41no—
279C4—2921no—
280C4—2922no—
281C4—2921no—
282C4—1461no—
283C4—1461no—
284C4#1455663612yes—
285C2—22no—
286C2—1462no—
287C2—1462no—
288C2#1798914711yescharacteristic
289C2C2×Q16×D7311yescharacteristic
290C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73#3189
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #17988923C2semidirect
4. #17988921C2semidirect
5. #17988920C2semidirect
6. #17988827C2semidirect
7. #17988825C2semidirect
8. #17988743C2semidirect
9. #17988741C2semidirect
11. #451×C73C2semidirect
14. C2×#11924018C22semidirect
31. #14556525C22semidirect
32. #14556524C22semidirect
33. #14556516C22semidirect
34. #14556515C22semidirect
35. #14556515C22semidirect
39. C2×Q16×C73C22semidirect
41. #103×C73C22semidirect
87. C22×D73Q16semidirect
146. C73#3189semidirect
156. #451D73semidirect
162. C2×Q16C2×D73semidirect
185. #103C2×D73semidirect