Finite Group Databasebeta

← #22620823

Subgroups — #22620823

Order 9344.

378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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#17989160C212yesmaximal
2#17988931C212yesmaximal, complemented
3#17988926C212yesmaximal, complemented
4#17988845C211yesmaximal, characteristic, complemented
5#17988826C212yesmaximal, complemented
6#17988744C212yesmaximal, complemented
7#17988741C212yesmaximal, complemented
8#17988555C211yesmaximal, characteristic
9#470×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C2×Q8×D73C2212yes—
12C2×Dic292C2211yescharacteristic
13C2×#11924018C2212yes—
14C22×#10596831C2211yescharacteristic
15#14556590—22no—
16#14556577—22no—
17#14556576—22no—
18#14556573—22no—
19#14556571C2212yes—
20#14556570C2212yes—
21#14556567C2212yes—
22#14556549C2212yes—
23#14556524C2212yes—
24#14556523C2211yescharacteristic
25#14556516C2212yes—
26#14556515C2212yes—
27#14556514C2212yes—
28#14556503C2212yes—
29#14556503C2212yes—
30C2×Q16×C73C2211yescharacteristic
31C2×M16×C73C2211yescharacteristic
32C22⋊Q8×C73C2212yes—
33#106×C73C2211yescharacteristic
34#103×C73C2212yes—
35#11924028—41no—
36#11924028—41no—
37C2×Dic146—22no—
38C2×Dic146D411yescharacteristic
39C2×Dic146C2312yes—
40Q8×D73—42no—
41Q8×D73—42no—
42C2×D292D411yescharacteristic
43C2×C22⋊D73D412yes—
44C2×C4×D73—22no—
45C2×C4×D73C2312yes—
46Dic292—41no—
47#11924018—42no—
48C2×#10596831—41no—
49C2×#10596831C2312yes—
50C4⋊Dic73—22no—
51C4⋊Dic73C2312yes—
52#11924007—22no—
53#11924007—22no—
54C22⋊Dic73—22no—
55#11924005—22no—
56#11924005—22no—
57#11924005—22no—
58C4×Dic73—22no—
59C2×Q8×C73C2312yes—
60C22×C4×C73C2311yescharacteristic
61Q16×C73—41no—
62M16×C73—41no—
63C2×C8×C73C2311yescharacteristic
64C2×C8×C73C2311yescharacteristic
65C4⋊C4×C73—22no—
66C4⋊C4×C73C2312yes—
67C22⋊C4×C73—22no—
68C23×C73C2×D411yescharacteristic
69C22×D73C2×D412yes—
70Q8×C73—22no—
71Q8×C73—22no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73C2×D411yescharacteristic
77C2×C4×C73C2411yescharacteristic
78C22⋊D73—42no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73C2×D412yes—
82D292—41no—
83C4×D73—22no—
84C4×D73—22no—
85C4×D73—44no—
86Dic146—22no—
87Dic146—22no—
88Dic146—41no—
89Dic146—44no—
90C8×C73—21no—
91C8×C73—21no—
92#10596831—22no—
93C22×C73—21no—
94C22×C73—22no—
95C22×C73C22×D411yescharacteristic
96C2×D73—22no—
97C2×D73—24no—
98C4×C73—21no—
99C4×C73—42no—
100C4×C73—42no—
101C4×C73H(5,𝔽2)11yescharacteristic
102C4×C73H(5,𝔽2)11yescharacteristic
103Dic73—22no—
104Dic73—42no—
105Dic73—42no—
106C2×C73—41no—
107C2×C73#53411yescharacteristic
108C2×C73#57812yes—
109D73—42no—
110#3202—731nomaximal, Sylow
111C73#320211yescharacteristic, complemented, Sylow
112#536—732no—
113#485—732no—
114#485—732no—
115#470—731no—
116#470D7311yescharacteristic, complemented
117#467—732no—
118#451—732no—
119#451—732no—
120#408—731no—
121C2×#41—731no—
122C22×Q8—732no—
123C2×Q16—732no—
124C2×Q16—731no—
125C2×Q16C2×D7311yescharacteristic
126C2×M16C2×D7311yescharacteristic
127C22×C8—731no—
128C4⋊Q8—1462no—
129#124—1462no—
130#123—1462no—
131#123—1462no—
132C22⋊Q8—732no—
133C22⋊Q8—732no—
134C22⋊Q8—732no—
135C22⋊Q8C2×D7312yes—
136#117—732no—
137#107—732no—
138#106—731no—
139#106C2×D7311yescharacteristic
140#103—732no—
141#103—732no—
142#103—732no—
143#103C2×D7312yes—
144C22⋊C8—732no—
145C22⋊C8—732no—
146#41—2921no—
147#41—2921no—
148C2×Q8—2922no—
149C2×Q8—2922no—
150C2×Q8—731no—
151C2×Q8—732no—
152C2×Q8—1462no—
153C2×Q8C22×D7312yes—
154C2×D4—732no—
155C2×D4—731no—
156C22×C4—732no—
157C22×C4—1462no—
158C22×C4C22×D7311yescharacteristic
159Q16—41no—
160Q16—2921no—
161Q16—2922no—
162M16—41no—
163C2×C8—2921no—
164C2×C8—732no—
165C2×C8C22×D7311yescharacteristic
166C2×C8C22×D7311yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—732no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1462no—
172C4⋊C4C22×D7312yes—
173C22⋊C4—22no—
174C22⋊C4—1462no—
175C22⋊C4—1462no—
176C22⋊C4—1462no—
177C22⋊C4—1462no—
178C42—1462no—
179C23—732no—
180C23D4×D7311yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—2921no—
184Q8—2924no—
185Q8—1462no—
186Q8—1462no—
187D4—2921no—
188D4—2922no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—2924no—
194C2×C4—732no—
195C2×C4—1462no—
196C2×C4—1462no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4D4×D7311yescharacteristic
200C2×C4C23×D7311yescharacteristic
201C8—21no—
202C8—21no—
203C8—1462no—
204C22—21no—
205C22—22no—
206C22—1462no—
207C22—1464no—
208C22C2×D4×D7311yescharacteristic
209C4—21no—
210C4—42no—
211C4—42no—
212C4—2922no—
213C4—2922no—
214C4—1462no—
215C4#1455663611yescharacteristic
216C4#1455663711yescharacteristic
217C2—41no—
218C2—2922no—
219C2#1798914511yescharacteristic
220C2#1798940312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#470×C73C2
socleC22×C73C22×D4
hypercenter#470D73
hypocenterC73#3202
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #17988931C2semidirect
3. #17988926C2semidirect
4. #17988845C2semidirect
5. #17988826C2semidirect
6. #17988744C2semidirect
7. #17988741C2semidirect
9. #470×C73C2semidirect
111. C73#3202semidirect
116. #470D73semidirect