Finite Group Databasebeta

← #22621068

Subgroups — #22621068

Order 9344.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#17989142C211yesmaximal, characteristic, complemented
2#17989138C211yesmaximal, characteristic
3#17988990C211yesmaximal, characteristic, complemented
4#17988935C211yesmaximal, characteristic, complemented
5#17988934C211yesmaximal, characteristic, complemented
6#17988913C214yesmaximal, complemented
7#17988886C214yesmaximal, complemented
8#17988638C211yesmaximal, characteristic, complemented
9#498×C73C211yesmaximal, characteristic, complemented
10C2×#11924029—21no—
11#14556591C2211yescharacteristic
12#14556588C2211yescharacteristic
13#14556582C2212yes—
14#14556580—21no—
15#14556571—21no—
16#14556567—21no—
17#14556566—21no—
18#14556566C2212yes—
19Q8×Dic73—21no—
20#14556556—21no—
21#14556553—21no—
22#14556553C2212yes—
23#14556549C2212yes—
24C42×D73C2211yescharacteristic
25#14556524C2214yes—
26#14556520C2212yes—
27#14556513C2214yes—
28#14556511C2214yes—
29#14556503C2212yes—
30C4×#10596831C2211yescharacteristic
31C4⋊Q8×C73C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33#106×C73C2214yes—
34C4×C8×C73C2211yescharacteristic
35#11924029—44no—
36C2×Dic146—21no—
37C2×D292—22no—
38C2×D292—21no—
39C2×D292—21no—
40C2×D292C2312yes—
41C2×C4×D73—22no—
42C2×C4×D73D411yescharacteristic
43C2×C4×D73D411yescharacteristic
44C2×C4×D73C2311yescharacteristic
45C2×#10596831C2312yes—
46C4⋊Dic73—21no—
47C4⋊Dic73—22no—
48C4⋊Dic73C2312yes—
49#11924007—22no—
50#11924005—22no—
51#11924005—22no—
52#11924005—22no—
53C4×Dic73—22no—
54C4×Dic73D411yescharacteristic
55C4×Dic73D411yescharacteristic
56C4×Dic73C2311yescharacteristic
57C2×Q8×C73—21no—
58C2×Q8×C73—21no—
59C2×C8×C73C2312yes—
60C4⋊C4×C73—21no—
61C4⋊C4×C73—21no—
62C4⋊C4×C73C2312yes—
63C4⋊C4×C73C2312yes—
64C42×C73C2311yescharacteristic
65C22×D73—22no—
66C22×D73C2×D411yescharacteristic
67Q8×C73—42no—
68Q8×C73—42no—
69C2×C4×C73—22no—
70C2×C4×C73—22no—
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2411yescharacteristic
74C2×Dic73—22no—
75C2×Dic73C2×D411yescharacteristic
76C2×Dic73C2×D411yescharacteristic
77C2×Dic73C2×D411yescharacteristic
78D292—24no—
79D292—44no—
80D292—42no—
81D292—42no—
82C4×D73—22no—
83C4×D73—22no—
84C4×D73—22no—
85C4×D73—44no—
86Dic146—42no—
87C8×C73—22no—
88#10596831—22no—
89C22×C73C22×D411yescharacteristic
90C2×D73—21no—
91C2×D73—21no—
92C2×D73—21no—
93C2×D73—42no—
94C2×D73—42no—
95C2×D73—42no—
96C4×C73—42no—
97C4×C73—42no—
98C4×C73#13512yes—
99C4×C73AGL(1,ℤ/8)12yes—
100C4×C732−1+412yes—
101Dic73—21no—
102Dic73—21no—
103Dic73—21no—
104Dic73—42no—
105C2×C73#53611yescharacteristic
106C2×C73C2×#13511yescharacteristic
107C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
108D73—41no—
109D73—82no—
110#3228—731nomaximal, Sylow
111C73#322811yescharacteristic, complemented, Sylow
112#533—731no—
113#532—731no—
114#500—731no—
115#498D7311yescharacteristic, complemented
116#486—731no—
117#486—731no—
118#482—734no—
119#478—734no—
120#431—731no—
121C2×#41—1461no—
122C4⋊Q8—731no—
123C4⋊Q8C2×D7311yescharacteristic
124C4⋊Q8C2×D7311yescharacteristic
125#127—731no—
126#125—732no—
127#124—1461no—
128C22⋊Q8—1461no—
129C22⋊Q8—1461no—
130#121—732no—
131#121—1461no—
132C4×Q8—1461no—
133C4×Q8—1461no—
134C4×D4—732no—
135C4×D4—1461no—
136#117—732no—
137C2×C42—731no—
138#107—734no—
139#106C2×D7314yes—
140C4⋊C8—732no—
141#102—734no—
142#102—734no—
143C22⋊C8—732no—
144C4×C8—731no—
145C4×C8C2×D7311yescharacteristic
146#41—2924no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—1461no—
150C2×D4—732no—
151C2×D4—1462no—
152C2×D4—1461no—
153C2×D4—1461no—
154C22×C4—731no—
155C22×C4—731no—
156C22×C4—731no—
157C22×C4—1462no—
158C2×C8—732no—
159C2×C8C22×D7312yes—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—732no—
163C4⋊C4—1462no—
164C4⋊C4—1462no—
165C4⋊C4—1461no—
166C4⋊C4C22×D7312yes—
167C4⋊C4C22×D7312yes—
168C22⋊C4—1462no—
169C22⋊C4—1462no—
170C22⋊C4—1462no—
171C42—731no—
172C42—731no—
173C42—731no—
174C42—1462no—
175C42C22×D7311yescharacteristic
176C23—731no—
177C23—1462no—
178Q8—42no—
179Q8—42no—
180Q8—2922no—
181D4—2924no—
182D4—2922no—
183D4—2922no—
184D4—1464no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—2924no—
188C2×C4—731no—
189C2×C4—731no—
190C2×C4—731no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1462no—
194C2×C4—1462no—
195C2×C4D4×D7311yescharacteristic
196C2×C4D4×D7311yescharacteristic
197C2×C4C23×D7311yescharacteristic
198C8—22no—
199C8—1462no—
200C22—2922no—
201C22—2922no—
202C22—2922no—
203C22—1461no—
204C22—1461no—
205C22—1461no—
206C22C2×D4×D7311yescharacteristic
207C4—42no—
208C4—42no—
209C4—2922no—
210C4—1461no—
211C4—1461no—
212C4—1461no—
213C4#1455661212yes—
214C4#1455661812yes—
215C4#1455663912yes—
216C2—2921no—
217C2—5842no—
218C2#1798916211yescharacteristic
219C2C2×#1455661211yescharacteristic
220C2C2×#1455661811yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#498×C73C2
socleC22×C73C22×D4
hypercenter#498D73
hypocenterC73#3228
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. #17989142C2semidirect
3. #17988990C2semidirect
4. #17988935C2semidirect
5. #17988934C2semidirect
6. #17988913C2semidirect
7. #17988886C2semidirect
8. #17988638C2semidirect
9. #498×C73C2semidirect
111. C73#3228semidirect
115. #498D73semidirect