Finite Group Databasebeta

← #22622811

Subgroups — #22622811

Order 9344.

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

normal subgroups only

This group has 338 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#17989312C211yesmaximal, characteristic, complemented
2#17989298C211yesmaximal, characteristic
3#17988987C212yesmaximal, complemented
4#17988897C212yesmaximal, complemented
5#17988886C212yesmaximal
6#17988879C211yesmaximal, characteristic, complemented
7#17988864C211yesmaximal, characteristic
8C8×Dic146C211yesmaximal, characteristic, complemented
9C4×#11924017C211yesmaximal, characteristic
10#17988674C212yesmaximal
11#498×C73C211yesmaximal, characteristic, complemented
12C2×#11924017C2211yescharacteristic
13#14556589—21no—
14#14556582C2212yes—
15#14556582C2212yes—
16#14556581—22no—
17#14556571—21no—
18#14556567—22no—
19Q8×Dic73—21no—
20C4×Dic146C2211yescharacteristic
21C4×Dic146C2211yescharacteristic
22#14556556C2212yes—
23C4×D292C2211yescharacteristic
24#14556553C2212yes—
25C4⋊C4×D73—21no—
26#14556524C2212yes—
27#14556524C2212yes—
28#14556523C2211yescharacteristic
29C4⋊#10596831C2211yescharacteristic
30#14556520C2212yes—
31#14556516C2211yescharacteristic
32#14556514C2212yes—
33#14556513C2211yescharacteristic
34#14556511C2212yes—
35C8×Dic73C2212yes—
36C4⋊Q8×C73C2211yescharacteristic
37C4⋊Q8×C73C2211yescharacteristic
38#106×C73C2212yes—
39#106×C73C2212yes—
40C4×C8×C73C2211yescharacteristic
41C2×Dic146D411yescharacteristic
42C2×Dic146C2311yescharacteristic
43C2×D292C2311yescharacteristic
44C2×C4×D73—21no—
45C2×C4×D73—22no—
46#11924017Q814yescomplemented
47C2×#10596831C2312yes—
48C4⋊Dic73—22no—
49C4⋊Dic73—22no—
50C4⋊Dic73D411yescharacteristic
51C4⋊Dic73C2311yescharacteristic
52C4⋊Dic73C2311yescharacteristic
53#11924007—21no—
54#11924007—22no—
55#11924007—22no—
56#11924007—22no—
57#11924007D412yes—
58#11924005—21no—
59#11924005—22no—
60C4×Dic73—21no—
61C4×Dic73—22no—
62C4×Dic73C2312yes—
63C2×Q8×C73—21no—
64C2×Q8×C73—21no—
65C2×C8×C73C2311yescharacteristic
66C2×C8×C73C2311yescharacteristic
67C4⋊C4×C73—21no—
68C4⋊C4×C73—21no—
69C4⋊C4×C73C2312yes—
70C4⋊C4×C73C2312yes—
71C42×C73C2311yescharacteristic
72C22×D73—21no—
73Q8×C73—42no—
74Q8×C73—81no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2411yescharacteristic
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—21no—
83C2×Dic73C2×D412yes—
84C2×Dic73C2×D412yes—
85D292—21no—
86D292C2×Q812yes—
87C4×D73—42no—
88C4×D73—82no—
89Dic146—22no—
90Dic146—21no—
91Dic146C2×Q812yes—
92C8×C73—21no—
93C8×C73C2×Q812yes—
94#10596831—22no—
95C22×C73C22×D411yescharacteristic
96C2×D73—22no—
97C2×D73—41no—
98C2×D73—41no—
99C4×C73—21no—
100C4×C73—42no—
101C4×C73—42no—
102C4×C73#13512yes—
103C4×C73C22×Q811yescharacteristic
104C4×C732−1+411yescharacteristic
105Dic73—22no—
106Dic73—22no—
107Dic73—22no—
108Dic73—41no—
109Dic73—41no—
110C2×C73D4×Q811yescharacteristic
111C2×C73C2×#13511yescharacteristic
112C2×C73#57711yescharacteristic
113D73—42no—
114#3381—731nomaximal, Sylow
115C73#338111yescharacteristic, complemented, Sylow
116#557—731no—
117#554—731no—
118#499—732no—
119#498D7311yescharacteristic, complemented
120#479—732no—
121#478—732no—
122#477—731no—
123#474—731no—
124C8×Q8—731no—
125C4×SD16—732no—
126C4×SD16—731no—
127C2×SD16—731no—
128C4⋊Q8—1461no—
129C4⋊Q8C2×D7311yescharacteristic
130C4⋊Q8C2×D7311yescharacteristic
131#125—732no—
132#125—732no—
133#125—1462no—
134C22⋊Q8—1461no—
135C22⋊Q8—1462no—
136C4×Q8—731no—
137C4×Q8—732no—
138C4×Q8—731no—
139C4×Q8—1461no—
140C4×D4—732no—
141C4×D4—731no—
142C2×C4⋊C4—1461no—
143#107—732no—
144#107—732no—
145#106—731no—
146#106C2×D7312yes—
147#106C2×D7312yes—
148C4⋊C8—732no—
149C4⋊C8—731no—
150#103—731no—
151#103—732no—
152#102—731no—
153#102—732no—
154C4×C8—732no—
155C4×C8C2×D7311yescharacteristic
156C2×Q8—21no—
157C2×Q8—21no—
158C2×Q8—731no—
159C2×Q8—731no—
160C2×D4—731no—
161C22×C4—1462no—
162C22×C4—1461no—
163SD16—734no—
164C2×C8—732no—
165C2×C8C22×D7311yescharacteristic
166C2×C8C22×D7311yescharacteristic
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—732no—
170C4⋊C4—731no—
171C4⋊C4—731no—
172C4⋊C4—731no—
173C4⋊C4—1462no—
174C4⋊C4—1462no—
175C4⋊C4—1462no—
176C4⋊C4—1462no—
177C4⋊C4—1462no—
178C4⋊C4—1461no—
179C4⋊C4C22×D7312yes—
180C4⋊C4C22×D7312yes—
181C22⋊C4—1462no—
182C22⋊C4—1461no—
183C42—732no—
184C42—1462no—
185C42—1461no—
186C42C22×D7311yescharacteristic
187C23—1461no—
188Q8—42no—
189Q8—81no—
190Q8—732no—
191Q8—1462no—
192Q8—1461no—
193D4—732no—
194D4—1461no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—2922no—
198C2×C4—5842no—
199C2×C4—732no—
200C2×C4—732no—
201C2×C4—1461no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4D4×D7311yescharacteristic
205C2×C4D4×D7311yescharacteristic
206C2×C4C23×D7311yescharacteristic
207C8—21no—
208C8—1462no—
209C8Q8×D7312yes—
210C22—2921no—
211C22—2921no—
212C22—1462no—
213C22C2×D4×D7311yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—2921no—
218C4—2921no—
219C4—1462no—
220C4—1462no—
221C4—1462no—
222C4#1455661212yes—
223C4C2×Q8×D7311yescharacteristic
224C4#1455663911yescharacteristic
225C2—2922no—
226C2#1798925211yescharacteristic
227C2C2×#1455661211yescharacteristic
228C2#1798939311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#498×C73C2
socleC22×C73C22×D4
hypercenter#498D73
hypocenterC73#3381
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #17989312C2semidirect
3. #17988987C2semidirect
4. #17988897C2semidirect
6. #17988879C2semidirect
8. C8×Dic146C2semidirect
11. #498×C73C2semidirect
46. #11924017Q8semidirect
115. C73#3381semidirect
119. #498D73semidirect