Finite Group Databasebeta

← #22620054

Subgroups — #22620054

Order 9344.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#17989137C211yesmaximal, characteristic
2C2×C4×Dic146C211yesmaximal, characteristic, complemented
3#17988901C212yesmaximal, complemented
4#17988883C212yesmaximal, complemented
5#17988788C212yesmaximal, complemented
6#17988728C212yesmaximal, complemented
7#17988689C214yesmaximal, complemented
8#432×C73C211yesmaximal, characteristic, complemented
9C2×#11924028—21no—
10C22×Dic146C2211yescharacteristic
11C2×#11924017C2214yes—
12#14556591C2211yescharacteristic
13#14556588C2211yescharacteristic
14#14556579—21no—
15#14556565—21no—
16#14556565C2212yes—
17C4×Dic146—21no—
18C4×Dic146—21no—
19C4×Dic146C2212yes—
20C4×Dic146C2212yes—
21C4×D292—21no—
22C4×D292C2212yes—
23C2×C4⋊Dic73C2211yescharacteristic
24C2×#11924007—21no—
25C2×C4×Dic73—21no—
26#14556525C2214yes—
27#14556516C2214yes—
28#14556513C2214yes—
29C2×C42×C73C2211yescharacteristic
30C4⋊C8×C73C2212yes—
31C22⋊C8×C73C2212yes—
32#97×C73C2212yes—
33#11924028—44no—
34C2×Dic146—21no—
35C2×Dic146—24no—
36C2×Dic146—21no—
37C2×Dic146C2312yes—
38C2×D292—21no—
39C2×D292—21no—
40C2×D292C2312yes—
41C2×C22⋊D73—22no—
42C22×Dic73—21no—
43C22×Dic73—21no—
44C2×C4×D73—22no—
45#11924017—28no—
46C4⋊Dic73—21no—
47C4⋊Dic73—21no—
48C4⋊Dic73C2312yes—
49C4⋊Dic73C2312yes—
50#11924007—22no—
51#11924007—22no—
52#11924005—22no—
53#11924005—22no—
54C4×Dic73—22no—
55C4×Dic73—22no—
56C22×C4×C73D411yescharacteristic
57C22×C4×C73D411yescharacteristic
58C22×C4×C73C2311yescharacteristic
59C2×C8×C73C2314yes—
60C42×C73D411yescharacteristic
61C42×C73D411yescharacteristic
62C42×C73C2311yescharacteristic
63C42×C73C2311yescharacteristic
64C23×C73C2×D411yescharacteristic
65C22×D73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73C2×D411yescharacteristic
70C2×C4×C73C2×D411yescharacteristic
71C2×C4×C73C2×D411yescharacteristic
72C2×C4×C73C2×D411yescharacteristic
73C2×C4×C73C2×D411yescharacteristic
74C2×C4×C73C2411yescharacteristic
75C22⋊D73—44no—
76C2×Dic73—24no—
77C2×Dic73—22no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—42no—
81D292—24no—
82D292—42no—
83D292—42no—
84C4×D73—44no—
85Dic146—24no—
86Dic146—22no—
87Dic146—42no—
88Dic146#4114yescomplemented
89C8×C73—24no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73AGL(1,ℤ/8)12yes—
93C22×C73C22×D411yescharacteristic
94C2×D73—42no—
95C2×D73—42no—
96C2×D73—42no—
97C4×C73—21no—
98C4×C73—21no—
99C4×C73—21no—
100C4×C73—21no—
101C4×C73#13712yes—
102C4×C73C2×#4112yes—
103Dic73—24no—
104Dic73—42no—
105Dic73—42no—
106C2×C73—22no—
107C2×C73#52511yescharacteristic
108C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
109C2×C73C2×#13711yescharacteristic
110D73—82no—
111#3112—731nomaximal, Sylow
112C73#311211yescharacteristic, complemented, Sylow
113#532—731no—
114C2×C4×Q8—731no—
115#480—732no—
116#477—732no—
117#460—732no—
118#448—732no—
119#440—734no—
120#432D7311yescharacteristic, complemented
121C2×#41—1461no—
122C22×Q8—731no—
123C2×SD16—734no—
124C4⋊Q8—731no—
125#127—731no—
126#124—1461no—
127#121—732no—
128#121—1461no—
129C4×Q8—732no—
130C4×Q8—732no—
131C4×Q8—1461no—
132C4×Q8—1461no—
133C4×D4—732no—
134C4×D4—1461no—
135C2×C4⋊C4—731no—
136C2×C4⋊C4—1461no—
137C2×C42—1461no—
138C2×C42C2×D7311yescharacteristic
139#107—734no—
140C4⋊C8C2×D7312yes—
141#103—734no—
142#102—734no—
143C22⋊C8C2×D7312yes—
144#97C2×D7312yes—
145#41—2924no—
146C2×Q8—732no—
147C2×Q8—1464no—
148C2×Q8—1461no—
149C2×Q8—1461no—
150C2×D4—732no—
151C2×D4—1462no—
152C2×D4—1461no—
153C2×D4—1461no—
154C22×C4—1461no—
155C22×C4—1462no—
156C22×C4—1461no—
157C22×C4D29211yescharacteristic
158C22×C4D29211yescharacteristic
159C22×C4C22×D7311yescharacteristic
160SD16—1468no—
161C2×C8C22×D7314yes—
162C4⋊C4—732no—
163C4⋊C4—732no—
164C4⋊C4—1462no—
165C4⋊C4—1462no—
166C4⋊C4—1461no—
167C4⋊C4—1461no—
168C22⋊C4—1462no—
169C22⋊C4—1462no—
170C42—1462no—
171C42—1462no—
172C42D29211yescharacteristic
173C42D29211yescharacteristic
174C42C22×D7311yescharacteristic
175C42C22×D7311yescharacteristic
176C23—1462no—
177C23C2×D29211yescharacteristic
178Q8—2922no—
179Q8—734no—
180Q8—1464no—
181Q8—1462no—
182D4—2922no—
183D4—2924no—
184D4—2922no—
185D4—1464no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—2924no—
190C2×C4—2922no—
191C2×C4—1462no—
192C2×C4—1462no—
193C2×C4—1464no—
194C2×C4—1462no—
195C2×C4C2×D29211yescharacteristic
196C2×C4C2×D29211yescharacteristic
197C2×C4C2×D29211yescharacteristic
198C2×C4C2×D29211yescharacteristic
199C2×C4C2×D29211yescharacteristic
200C2×C4C23×D7311yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—2922no—
205C22—2922no—
206C22—2922no—
207C22#1455661912yes—
208C22C22×D29211yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—2922no—
214C4—2922no—
215C4—1464no—
216C4#1455662412yes—
217C4#41×D7312yes—
218C2—22no—
219C2—5842no—
220C2#1798909911yescharacteristic
221C2C2×#1455661911yescharacteristic
222C2C2×#1455662411yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#432×C73C2
socleC22×C73C22×D4
hypercenter#432D73
hypocenterC73#3112
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic146C2semidirect
3. #17988901C2semidirect
4. #17988883C2semidirect
5. #17988788C2semidirect
6. #17988728C2semidirect
7. #17988689C2semidirect
8. #432×C73C2semidirect
88. Dic146#41semidirect
112. C73#3112semidirect
120. #432D73semidirect