Finite Group Databasebeta

← #22620961

Subgroups — #22620961

Order 9344.

386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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×#14556589C211yesmaximal, characteristic, complemented
2#17989123C211yesmaximal, characteristic
3#17988980C212yesmaximal, complemented
4#17988954C212yesmaximal, complemented
5#17988795C212yesmaximal, complemented
6#17988791C212yesmaximal, complemented
7#17988742C211yesmaximal, characteristic, complemented
8#17988728C211yesmaximal, characteristic
9#17988726C211yesmaximal, characteristic
10#17988641C211yesmaximal, characteristic, complemented
11#451×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924017C2212yes—
15C2×#11924015C2212yes—
16#14556589—21no—
17#14556589—21no—
18#14556589C2212yes—
19#14556589C2212yes—
20#14556586—21no—
21#14556582C2211yescharacteristic
22#14556580C2211yescharacteristic
23#14556575—21no—
24#14556565C2211yescharacteristic
25Q8×Dic73C2211yescharacteristic
26#14556553C2211yescharacteristic
27#14556551—21no—
28#14556549—21no—
29C2×#11924007—21no—
30C2×#11924007—21no—
31C2×C4×Dic73C2211yescharacteristic
32#14556520C2212yes—
33#14556516C2212yes—
34#14556515C2212yes—
35#14556514C2212yes—
36C22⋊#10596831C2211yescharacteristic
37#14556501C2212yes—
38C22×Q8×C73C2211yescharacteristic
39C2×Q16×C73C2212yes—
40C22⋊Q8×C73C2211yescharacteristic
41#103×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146—42no—
45C2×Dic146C2312yes—
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C22×Dic73—21no—
49C22×Dic73D411yescharacteristic
50C22×Dic73D411yescharacteristic
51C2×C4×D73—21no—
52#11924018—42no—
53#11924017—42no—
54#11924015—42no—
55C2×#10596831C2312yes—
56C4⋊Dic73—21no—
57C4⋊Dic73—21no—
58C4⋊Dic73C2311yescharacteristic
59#11924007—22no—
60#11924007—22no—
61#11924007—22no—
62#11924007—22no—
63#11924007—21no—
64#11924005—21no—
65#11924005—21no—
66#11924005—21no—
67#11924005—21no—
68C4×Dic73—21no—
69C4×Dic73D411yescharacteristic
70C4×Dic73D411yescharacteristic
71C4×Dic73C2311yescharacteristic
72C4×Dic73C2311yescharacteristic
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—21no—
86Q8×C73—22no—
87Q8×C73—22no—
88Q8×C73—22no—
89Q8×C73—42no—
90C2×C4×C73—22no—
91C2×C4×C73—21no—
92C2×C4×C73—21no—
93C2×C4×C73—22no—
94C2×C4×C73—42no—
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2411yescharacteristic
97C22⋊D73—42no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—21no—
101C2×Dic73—22no—
102C2×Dic73—42no—
103C2×Dic73C2×D411yescharacteristic
104C2×Dic73C2×D411yescharacteristic
105C2×Dic73C2×D411yescharacteristic
106C2×Dic73C2×D411yescharacteristic
107D292—22no—
108C4×D73—42no—
109Dic146—22no—
110Dic146—22no—
111Dic146—42no—
112C8×C73—22no—
113#10596831—22no—
114C22×C73—21no—
115C22×C73—21no—
116C22×C73#13712yes—
117C22×C73C22×D411yescharacteristic
118C2×D73—41no—
119C2×D73—41no—
120C2×D73—41no—
121C4×C73—21no—
122C4×C73—42no—
123C4×C73—41no—
124C4×C73—41no—
125C4×C73H(5,𝔽2)12yes—
126Dic73—21no—
127Dic73—21no—
128Dic73—21no—
129Dic73—42no—
130Dic73—41no—
131Dic73#13712yes—
132C2×C73—22no—
133C2×C73#53511yescharacteristic
134C2×C73C2×#13711yescharacteristic
135C2×C73C2×#13711yescharacteristic
136D73—81no—
137#3218—731nomaximal, Sylow
138C73#321811yescharacteristic, complemented, Sylow
139C2×C4⋊Q8—731no—
140#529—731no—
141#497—732no—
142#491—732no—
143#462—732no—
144#461—732no—
145#451—731no—
146#451D7311yescharacteristic, complemented
147#448—731no—
148#448—731no—
149#432—731no—
150C22×Q8—731no—
151C22×Q8C2×D7311yescharacteristic
152C2×Q16—732no—
153C2×Q16C2×D7312yes—
154C2×SD16—732no—
155C2×SD16—732no—
156C4⋊Q8—732no—
157C4⋊Q8—732no—
158C4⋊Q8—1461no—
159C4⋊Q8—1461no—
160#126—1461no—
161#125—731no—
162#124—731no—
163#123—1461no—
164C22⋊Q8C2×D7311yescharacteristic
165#121—731no—
166C4×Q8—731no—
167C4×D4—731no—
168C4×D4—1461no—
169#117—1461no—
170C2×C4⋊C4—1461no—
171C2×C4⋊C4—1461no—
172C2×C42—731no—
173C4⋊C8—732no—
174#103—732no—
175#103—732no—
176#103—732no—
177#103C2×D7312yes—
178C22⋊C8—731no—
179C22⋊C8C2×D7311yescharacteristic
180#97—732no—
181C2×Q8—21no—
182C2×Q8—42no—
183C2×Q8—2922no—
184C2×Q8—732no—
185C2×Q8—1461no—
186C2×Q8C22×D7312yes—
187C2×Q8C22×D7311yescharacteristic
188C2×D4—731no—
189C2×D4—1461no—
190C22×C4—21no—
191C22×C4—731no—
192C22×C4—731no—
193C22×C4—1461no—
194C22×C4—1461no—
195C22×C4C22×D7311yescharacteristic
196Q16—42no—
197Q16—2922no—
198SD16—2922no—
199SD16—2922no—
200C2×C8—732no—
201C2×C8C22×D7312yes—
202C4⋊C4—21no—
203C4⋊C4—731no—
204C4⋊C4—1462no—
205C4⋊C4—1462no—
206C4⋊C4—1462no—
207C4⋊C4—1462no—
208C4⋊C4—1461no—
209C4⋊C4—1461no—
210C4⋊C4—1461no—
211C4⋊C4C22×D7311yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—1461no—
214C22⋊C4—1461no—
215C22⋊C4—1461no—
216C22⋊C4—1461no—
217C42—731no—
218C42—731no—
219C42—731no—
220C42—731no—
221C42—1461no—
222C23—1461no—
223C23D4×D7311yescharacteristic
224Q8—22no—
225Q8—22no—
226Q8—22no—
227Q8—42no—
228Q8—2922no—
229Q8—1462no—
230Q8—1462no—
231D4—2922no—
232D4—1462no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—42no—
238C2×C4—2922no—
239C2×C4—2922no—
240C2×C4—731no—
241C2×C4—731no—
242C2×C4—731no—
243C2×C4—731no—
244C2×C4—1461no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4—1462no—
248C2×C4D4×D7311yescharacteristic
249C2×C4C23×D7311yescharacteristic
250C8—22no—
251C8—1462no—
252C22—21no—
253C22—21no—
254C22—2921no—
255C22—2921no—
256C22—2921no—
257C22#1455662312yes—
258C22C2×D4×D7311yescharacteristic
259C4—21no—
260C4—41no—
261C4—42no—
262C4—41no—
263C4—2921no—
264C4—2922no—
265C4—732no—
266C4—1461no—
267C4—1461no—
268C4—1461no—
269C4#1455663612yes—
270C2—22no—
271C2—5841no—
272C2#1798915211yescharacteristic
273C2#137×D7311yescharacteristic
274C2C2×#1455662311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#451×C73C2
socleC22×C73C22×D4
hypercenter#451D73
hypocenterC73#3218
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
1. C2×#14556589C2semidirect
3. #17988980C2semidirect
4. #17988954C2semidirect
5. #17988795C2semidirect
6. #17988791C2semidirect
7. #17988742C2semidirect
10. #17988641C2semidirect
11. #451×C73C2semidirect
138. C73#3218semidirect
146. #451D73semidirect