Finite Group Databasebeta

← #22621080

Subgroups — #22621080

Order 9344.

360 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 123 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
1#17989139C211yesmaximal, characteristic
2C2×#14556590C211yesmaximal, characteristic
3#17988991C212yesmaximal, complemented
4#17988936C212yesmaximal, complemented
5#17988923C211yesmaximal, characteristic
6#17988922C211yesmaximal, characteristic
7#17988920C211yesmaximal, characteristic
8#17988881C212yesmaximal, complemented
9#17988880C212yesmaximal, complemented
10#17988637C211yesmaximal, characteristic
11#484×C73C211yesmaximal, characteristic
12C22×Dic146—21no—
13#14556590—21no—
14#14556590—21no—
15#14556590C2212yes—
16#14556590C2212yes—
17#14556590C2211yescharacteristic
18#14556589C2211yescharacteristic
19#14556581—21no—
20#14556570C2211yescharacteristic
21#14556568—21no—
22Q8×Dic73C2211yescharacteristic
23#14556556—21no—
24#14556556C2211yescharacteristic
25#14556547—21no—
26C2×C4⋊Dic73C2211yescharacteristic
27C2×#11924007—21no—
28C2×C4×Dic73C2211yescharacteristic
29#14556525C2212yes—
30#14556524C2212yes—
31#14556524C2212yes—
32#14556520C2212yes—
33#14556516C2212yes—
34#14556515C2212yes—
35#14556514C2212yes—
36C22⋊#10596831C2211yescharacteristic
37C8×Dic73C2212yes—
38C22⋊Q8×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic
40#107×C73C2212yes—
41#103×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146—22no—
45C2×Dic146—22no—
46C2×Dic146—44no—
47C2×Dic146C2311yescharacteristic
48C22×Dic73—21no—
49C22×Dic73D411yescharacteristic
50C22×Dic73D411yescharacteristic
51C2×#10596831C2312yes—
52C4⋊Dic73—21no—
53C4⋊Dic73—21no—
54C4⋊Dic73C2312yes—
55C4⋊Dic73C2311yescharacteristic
56#11924007—21no—
57#11924007—22no—
58#11924007—22no—
59#11924007—21no—
60#11924007—21no—
61#11924007—21no—
62#11924007—21no—
63C22⋊Dic73—21no—
64C4×Dic73—21no—
65C4×Dic73—21no—
66C4×Dic73D411yescharacteristic
67C4×Dic73D411yescharacteristic
68C4×Dic73C2311yescharacteristic
69C4×Dic73C2311yescharacteristic
70C2×Q8×C73C2311yescharacteristic
71C22×C4×C73—21no—
72C22×C4×C73C2311yescharacteristic
73C2×C8×C73C2312yes—
74C4⋊C4×C73—21no—
75C4⋊C4×C73—21no—
76C4⋊C4×C73C2312yes—
77C4⋊C4×C73C2311yescharacteristic
78C22⋊C4×C73—21no—
79C23×C73C2×D411yescharacteristic
80Q8×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—42no—
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2411yescharacteristic
88C2×Dic73—22no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—42no—
93C2×Dic73Q1614yes—
94C2×Dic73C2×D411yescharacteristic
95C2×Dic73C2×D411yescharacteristic
96C2×Dic73C2×D411yescharacteristic
97C2×Dic73C2×D411yescharacteristic
98Dic146—22no—
99Dic146—44no—
100Dic146—42no—
101Dic146—44no—
102C8×C73—22no—
103#10596831—22no—
104C22×C73—21no—
105C22×C73—21no—
106C22×C73C2×Q1612yes—
107C22×C73C22×D411yescharacteristic
108C4×C73—21no—
109C4×C73—41no—
110C4×C73—42no—
111C4×C73—41no—
112C4×C732−1+412yes—
113Dic73—21no—
114Dic73—41no—
115Dic73—42no—
116Dic73—41no—
117Dic73C2×Q1612yes—
118Dic73C2×Q1612yes—
119Dic73AGL(1,ℤ/8)12yes—
120C2×C73—22no—
121C2×C73#53611yescharacteristic
122C2×C73C22×Q1611yescharacteristic
123C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
124#3230—731nomaximal, Sylow
125C73#323011yescharacteristic, complemented, Sylow
126#533—731no—
127C2×C4⋊Q8—731no—
128#500—732no—
129#487—732no—
130#484—731no—
131#484—731no—
132#484—731no—
133#484D7311yescharacteristic
134#477—732no—
135#477—732no—
136#431—731no—
137C22×Q8—1461no—
138C4⋊Q8—732no—
139C4⋊Q8—732no—
140C4⋊Q8—731no—
141C4⋊Q8—731no—
142C4⋊Q8—1461no—
143C4⋊Q8—1461no—
144#125—1461no—
145C22⋊Q8—731no—
146C22⋊Q8—1461no—
147C22⋊Q8C2×D7311yescharacteristic
148C4×Q8—731no—
149C4×Q8—731no—
150C4×Q8—1461no—
151#117—1461no—
152C2×C4⋊C4—731no—
153C2×C4⋊C4—1461no—
154C2×C4⋊C4C2×D7311yescharacteristic
155C2×C42—731no—
156#107—732no—
157#107—732no—
158#107—732no—
159#107C2×D7312yes—
160C4⋊C8—732no—
161#103—732no—
162#103—732no—
163#103—732no—
164#103C2×D7312yes—
165C22⋊C8—731no—
166C22⋊C8C2×D7311yescharacteristic
167C4×C8—732no—
168C2×Q8—2924no—
169C2×Q8—731no—
170C2×Q8—1461no—
171C2×Q8—1462no—
172C2×Q8—1462no—
173C2×Q8C22×D7311yescharacteristic
174C22×C4—21no—
175C22×C4—731no—
176C22×C4—731no—
177C22×C4—1461no—
178C22×C4C22×D7311yescharacteristic
179C2×C8—732no—
180C2×C8C22×D7312yes—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—732no—
184C4⋊C4—731no—
185C4⋊C4—1462no—
186C4⋊C4—1462no—
187C4⋊C4—1461no—
188C4⋊C4—1461no—
189C4⋊C4—1461no—
190C4⋊C4—1461no—
191C4⋊C4—1461no—
192C4⋊C4—1461no—
193C4⋊C4—1461no—
194C4⋊C4C22×D7312yes—
195C4⋊C4C22×D7311yescharacteristic
196C22⋊C4—21no—
197C22⋊C4—1461no—
198C42—731no—
199C42—731no—
200C42—731no—
201C42—731no—
202C42—1461no—
203C42—1461no—
204C23D4×D7311yescharacteristic
205Q8—22no—
206Q8—2924no—
207Q8—2922no—
208Q8—2924no—
209Q8—1462no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—42no—
215C2×C4—2922no—
216C2×C4—734no—
217C2×C4—731no—
218C2×C4—731no—
219C2×C4—731no—
220C2×C4—731no—
221C2×C4—1461no—
222C2×C4—1461no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4D4×D7311yescharacteristic
226C2×C4C23×D7311yescharacteristic
227C8—22no—
228C8—1462no—
229C22—21no—
230C22—21no—
231C22Q16×D7312yes—
232C22C2×D4×D7311yescharacteristic
233C4—21no—
234C4—41no—
235C4—42no—
236C4—41no—
237C4—2921no—
238C4—2922no—
239C4—2921no—
240C4—732no—
241C4—732no—
242C4—732no—
243C4—1461no—
244C4#1455663812yes—
245C2—22no—
246C2#1798915911yescharacteristic
247C2C2×Q16×D7311yescharacteristic
248C2AGL(1,ℤ/8)×D7311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#484×C73C2
socleC22×C73C22×D4
hypercenter#484D73
hypocenterC73#3230
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #17988991C2semidirect
4. #17988936C2semidirect
8. #17988881C2semidirect
9. #17988880C2semidirect
125. C73#3230semidirect