Finite Group Databasebeta

← #22619967

Subgroups — #22619967

Order 9344.

384 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556556C211yesmaximal, characteristic
3#17988922C211yesmaximal, characteristic
4#17988881C212yesmaximal, complemented
5#17988796C212yesmaximal, complemented
6#17988745C211yesmaximal, characteristic
7#17988742C211yesmaximal, characteristic
8#17988681C212yesmaximal, complemented
9#17988679C212yesmaximal, complemented
10#17988637C211yesmaximal, characteristic
11#484×C73C211yesmaximal, characteristic
12C22×Dic146C2211yescharacteristic
13C2×Dic292C2212yes—
14C2×#11924018C2212yes—
15#14556590C2211yescharacteristic
16#14556589C2211yescharacteristic
17#14556581—21no—
18#14556570C2211yescharacteristic
19#14556568—21no—
20Q8×Dic73C2211yescharacteristic
21#14556556—21no—
22#14556556—21no—
23#14556556—21no—
24#14556556C2212yes—
25#14556556C2211yescharacteristic
26#14556556C2212yes—
27#14556547—21no—
28C2×#11924007—21no—
29C2×C4×Dic73—21no—
30C2×C4×Dic73C2211yescharacteristic
31#14556524C2212yes—
32#14556520C2212yes—
33#14556516C2212yes—
34#14556514C2212yes—
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—24no—
45C2×Dic146—21no—
46C2×Dic146C2311yescharacteristic
47C2×Dic146C2312yes—
48C22×Dic73—21no—
49C22×Dic73D411yescharacteristic
50C22×Dic73D411yescharacteristic
51Dic292—24no—
52#11924018—24no—
53C2×#10596831C2312yes—
54C4⋊Dic73—21no—
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—22no—
65C4×Dic73—22no—
66C4×Dic73—21no—
67C4×Dic73—21no—
68C4×Dic73D411yescharacteristic
69C4×Dic73D411yescharacteristic
70C4×Dic73C2311yescharacteristic
71C4×Dic73C2311yescharacteristic
72C2×Q8×C73C2311yescharacteristic
73C22×C4×C73—21no—
74C22×C4×C73C2311yescharacteristic
75C2×C8×C73C2312yes—
76C4⋊C4×C73—21no—
77C4⋊C4×C73—21no—
78C4⋊C4×C73C2312yes—
79C4⋊C4×C73C2311yescharacteristic
80C22⋊C4×C73—21no—
81C23×C73C2×D411yescharacteristic
82Q8×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—42no—
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2411yescharacteristic
90C2×Dic73—24no—
91C2×Dic73—22no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—41no—
95C2×Dic73Q1614yescomplemented
96C2×Dic73C2×D411yescharacteristic
97C2×Dic73C2×D411yescharacteristic
98C2×Dic73C2×D411yescharacteristic
99C2×Dic73C2×D411yescharacteristic
100Dic146—24no—
101Dic146—22no—
102Dic146—22no—
103Dic146—42no—
104Dic146#4114yes—
105C8×C73—22no—
106#10596831—22no—
107C22×C73—21no—
108C22×C73—21no—
109C22×C73C2×Q1612yes—
110C22×C73C22×D411yescharacteristic
111C4×C73—21no—
112C4×C73—41no—
113C4×C73—41no—
114C4×C73—42no—
115C4×C73C2×#4112yes—
116Dic73—24no—
117Dic73—21no—
118Dic73—21no—
119Dic73—41no—
120Dic73—41no—
121Dic73C2×Q1612yes—
122Dic73C2×Q1612yes—
123C2×C73—22no—
124C2×C73#52511yescharacteristic
125C2×C73C22×Q1611yescharacteristic
126C2×C73#57511yescharacteristic
127#3104—731nomaximal, Sylow
128C73#310411yescharacteristic, complemented, Sylow
129#533—731no—
130C2×C4×Q8—731no—
131#484—731no—
132#484D7311yescharacteristic
133#477—732no—
134#462—732no—
135#451—731no—
136#451—731no—
137C4×Q16—732no—
138C4×Q16—732no—
139#431—731no—
140C22×Q8—731no—
141C2×Q16—732no—
142C2×Q16—732no—
143C4⋊Q8—731no—
144C4⋊Q8—731no—
145#125—1461no—
146C22⋊Q8—731no—
147C22⋊Q8—1461no—
148C22⋊Q8C2×D7311yescharacteristic
149C4×Q8—731no—
150C4×Q8—732no—
151C4×Q8—732no—
152C4×Q8—731no—
153C4×Q8—1461no—
154C4×Q8—1461no—
155C4×Q8—1461no—
156#117—1461no—
157C2×C4⋊C4—1461no—
158C2×C4⋊C4C2×D7311yescharacteristic
159C2×C42—731no—
160C2×C42—1461no—
161#107—732no—
162#107C2×D7312yes—
163C4⋊C8—732no—
164#103—732no—
165#103—732no—
166#103—732no—
167#103C2×D7312yes—
168C22⋊C8—731no—
169C22⋊C8C2×D7311yescharacteristic
170C4×C8—732no—
171C2×Q8—732no—
172C2×Q8—731no—
173C2×Q8—1461no—
174C2×Q8—1464no—
175C2×Q8—1461no—
176C2×Q8C22×D7311yescharacteristic
177C22×C4—21no—
178C22×C4—731no—
179C22×C4—731no—
180C22×C4—1461no—
181C22×C4C22×D7311yescharacteristic
182Q16—1464no—
183Q16—1464no—
184C2×C8—732no—
185C2×C8C22×D7312yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—731no—
189C4⋊C4—1462no—
190C4⋊C4—1462no—
191C4⋊C4—1461no—
192C4⋊C4—1461no—
193C4⋊C4—1461no—
194C4⋊C4—1461no—
195C4⋊C4—1461no—
196C4⋊C4—1461no—
197C4⋊C4C22×D7311yescharacteristic
198C4⋊C4C22×D7312yes—
199C22⋊C4—21no—
200C22⋊C4—1461no—
201C42—731no—
202C42—731no—
203C42—731no—
204C42—731no—
205C42—1462no—
206C42—1462no—
207C42—1461no—
208C42—1461no—
209C23D4×D7311yescharacteristic
210Q8—22no—
211Q8—2922no—
212Q8—734no—
213Q8—1464no—
214Q8—1462no—
215Q8—1462no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—2921no—
222C2×C4—734no—
223C2×C4—731no—
224C2×C4—731no—
225C2×C4—731no—
226C2×C4—731no—
227C2×C4—1461no—
228C2×C4—1461no—
229C2×C4—1464no—
230C2×C4—1462no—
231C2×C4D4×D7311yescharacteristic
232C2×C4C23×D7311yescharacteristic
233C8—22no—
234C8—1462no—
235C22—21no—
236C22—21no—
237C22Q16×D7312yes—
238C22C2×D4×D7311yescharacteristic
239C4—21no—
240C4—42no—
241C4—41no—
242C4—41no—
243C4—2921no—
244C4—2921no—
245C4—732no—
246C4—732no—
247C4—1461no—
248C4—1461no—
249C4—1464no—
250C4#41×D7312yes—
251C2—22no—
252C2#1798909511yescharacteristic
253C2C2×Q16×D7311yescharacteristic
254C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#484×C73C2
socleC22×C73C22×D4
hypercenter#484D73
hypocenterC73#3104
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
4. #17988881C2semidirect
5. #17988796C2semidirect
8. #17988681C2semidirect
9. #17988679C2semidirect
95. C2×Dic73Q16semidirect
128. C73#3104semidirect