Finite Group Databasebeta

← #22620843

Subgroups — #22620843

Order 9344.

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

normal subgroups only

This group has 402 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#17989165C212yesmaximal, complemented
2#17988918C212yesmaximal, complemented
3#17988906C212yesmaximal, complemented
4#17988845C211yesmaximal, characteristic, complemented
5#17988840C211yesmaximal, characteristic, complemented
6#17988816C212yesmaximal, complemented
7#17988751C212yesmaximal, complemented
8#17988734C212yesmaximal, complemented
9#408×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2212yes—
11C2×Dic292C2211yescharacteristic
12C2×#11924017C2212yes—
13C2×D584C2211yescharacteristic
14#14556570C2212yes—
15#14556570C2212yes—
16#14556567—22no—
17#14556565C2212yes—
18#14556565C2212yes—
19#14556563—22no—
20#14556563—22no—
21#14556562—22no—
22C2×C4⋊Dic73C2212yes—
23#14556523C2211yescharacteristic
24#14556523C2212yes—
25#14556523C2211yescharacteristic
26#14556516C2212yes—
27#14556516C2212yes—
28#14556513C2212yes—
29#14556513C2212yes—
30C2×#41×C73C2211yescharacteristic
31C2×M16×C73C2211yescharacteristic
32C22×C8×C73C2211yescharacteristic
33C22⋊C8×C73C2212yes—
34C22⋊C8×C73C2212yes—
35#11924028—42no—
36#11924028—42no—
37C2×Dic146C2312yes—
38C2×D292C2312yes—
39C2×C22⋊D73—22no—
40C2×C22⋊D73—22no—
41C2×C22⋊D73—22no—
42C22×Dic73—22no—
43C2×C4×D73—22no—
44Dic292—41no—
45#11924017—42no—
46D584—41no—
47C4⋊Dic73—22no—
48C4⋊Dic73C2312yes—
49C4⋊Dic73C2312yes—
50#11924007—22no—
51#11924007—22no—
52C22⋊Dic73—22no—
53C22⋊Dic73—22no—
54#11924005—22no—
55#11924005—22no—
56#41×C73—41no—
57#41×C73—41no—
58C2×Q8×C73D411yescharacteristic
59C2×D4×C73D412yes—
60C2×D4×C73D411yescharacteristic
61C22×C4×C73C2312yes—
62C22×C4×C73C2311yescharacteristic
63M16×C73—41no—
64C2×C8×C73—41no—
65C2×C8×C73C2312yes—
66C2×C8×C73C2311yescharacteristic
67C2×C8×C73C2311yescharacteristic
68C23×C73C2×D411yescharacteristic
69C23×C73C2×D412yes—
70C22×D73—22no—
71Q8×C73—41no—
72D4×C73—42no—
73D4×C73—41no—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73C2×D411yescharacteristic
79C2×C4×C73C2×D412yes—
80C2×C4×C73C2411yescharacteristic
81C22⋊D73—44no—
82C22⋊D73—82no—
83C22⋊D73—82no—
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—22no—
87C2×Dic73—82no—
88D292—22no—
89D292—22no—
90C4×D73—44no—
91Dic146—22no—
92Dic146—22no—
93C8×C73—22no—
94C8×C73—21no—
95C8×C73—21no—
96C22×C73—22no—
97C22×C73—21no—
98C22×C73—22no—
99C22×C73—22no—
100C22×C73—22no—
101C22×C73C22×D411yescharacteristic
102C2×D73—42no—
103C2×D73—42no—
104C2×D73—42no—
105C4×C73—22no—
106C4×C73—21no—
107C4×C73H(5,𝔽2)11yescharacteristic
108C4×C73H(5,𝔽2)11yescharacteristic
109Dic73—42no—
110Dic73—42no—
111Dic73—42no—
112C2×C73—42no—
113C2×C73—41no—
114C2×C73#53411yescharacteristic
115C2×C73#57712yes—
116D73—82no—
117#3204—731nomaximal, Sylow
118C73#320411yescharacteristic, complemented, Sylow
119#537—732no—
120#483—732no—
121#481—732no—
122#470—731no—
123#469—731no—
124#465—732no—
125#452—732no—
126#449—732no—
127#408D7311yescharacteristic, complemented
128C2×#41—732no—
129C2×#41C2×D7311yescharacteristic
130C2×Q16—731no—
131C2×SD16—732no—
132C2×D8—731no—
133C2×M16C2×D7311yescharacteristic
134C22×C8C2×D7311yescharacteristic
135C22⋊Q8—732no—
136C22⋊Q8—732no—
137C22⋊Q8—1462no—
138#121—732no—
139#121—732no—
140#121—1462no—
141#121—1462no—
142#121—1462no—
143C2×C4⋊C4—732no—
144#106—732no—
145#106—731no—
146#106—731no—
147#103—732no—
148#103—732no—
149#102—732no—
150#102—732no—
151C22⋊C8C2×D7312yes—
152C22⋊C8C2×D7312yes—
153#41—41no—
154#41—41no—
155#41—2922no—
156#41—2922no—
157C2×Q8—732no—
158C2×Q8D29211yescharacteristic
159C2×D4—732no—
160C2×D4—1462no—
161C2×D4—1462no—
162C2×D4—1462no—
163C2×D4D29211yescharacteristic
164C2×D4D29212yes—
165C22×C4—1462no—
166C22×C4—1462no—
167C22×C4C22×D7312yes—
168C22×C4C22×D7311yescharacteristic
169Q16—2921no—
170SD16—2922no—
171D8—2921no—
172M16—41no—
173C2×C8—41no—
174C2×C8C22×D7311yescharacteristic
175C2×C8C22×D7312yes—
176C2×C8C22×D7311yescharacteristic
177C4⋊C4—732no—
178C4⋊C4—732no—
179C4⋊C4—1462no—
180C4⋊C4—1462no—
181C4⋊C4—1462no—
182C22⋊C4—1462no—
183C22⋊C4—1462no—
184C22⋊C4—1462no—
185C22⋊C4—1462no—
186C23—1462no—
187C23C2×D29211yescharacteristic
188C23C2×D29212yes—
189Q8—41no—
190Q8—1462no—
191Q8—1462no—
192D4—42no—
193D4—41no—
194D4—2924no—
195D4—5842no—
196D4—5842no—
197D4—1462no—
198D4—1462no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—2924no—
204C2×C4—5842no—
205C2×C4—1462no—
206C2×C4—1462no—
207C2×C4—1462no—
208C2×C4C2×D29211yescharacteristic
209C2×C4C2×D29212yes—
210C2×C4C23×D7311yescharacteristic
211C8—22no—
212C8—21no—
213C8—21no—
214C22—22no—
215C22—22no—
216C22—22no—
217C22—22no—
218C22—21no—
219C22—2922no—
220C22—2922no—
221C22—2922no—
222C22C22×D29211yescharacteristic
223C4—22no—
224C4—21no—
225C4—2922no—
226C4—2922no—
227C4—2922no—
228C4#1455663611yescharacteristic
229C4#1455663611yescharacteristic
230C2—42no—
231C2—41no—
232C2—5842no—
233C2#1798914911yescharacteristic
234C2#1798939912yes—
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#408×C73C2
socleC22×C73C22×D4
hypercenter#408D73
hypocenterC73#3204
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #17989165C2semidirect
2. #17988918C2semidirect
3. #17988906C2semidirect
4. #17988845C2semidirect
5. #17988840C2semidirect
6. #17988816C2semidirect
7. #17988751C2semidirect
8. #17988734C2semidirect
9. #408×C73C2semidirect
118. C73#3204semidirect
127. #408D73semidirect