Finite Group Databasebeta

← #22620821

Subgroups — #22620821

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#17988930C212yesmaximal, complemented
3#17988927C212yesmaximal, complemented
4#17988843C212yesmaximal, complemented
5#17988828C211yesmaximal, characteristic, complemented
6#17988744C212yesmaximal, complemented
7#17988741C212yesmaximal, complemented
8#17988553C211yesmaximal, characteristic
9#467×C73C211yesmaximal, characteristic, complemented
10C2×#11924028C2211yescharacteristic
11C2×Q8×D73C2212yes—
12C2×Dic292C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924012C2211yescharacteristic
15#14556590—22no—
16#14556577—22no—
17#14556576—22no—
18#14556573—22no—
19#14556571C2212yes—
20#14556570C2212yes—
21#14556567C2212yes—
22#14556549C2212yes—
23#14556525C2211yescharacteristic
24#14556522C2212yes—
25#14556516C2212yes—
26#14556515C2212yes—
27#14556514C2212yes—
28#14556503C2212yes—
29#14556503C2212yes—
30C2×Q16×C73C2211yescharacteristic
31C22×C8×C73C2211yescharacteristic
32C22⋊Q8×C73C2212yes—
33#107×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—
48#11924012—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—
62C2×C8×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—21no—
95C22×C73—21no—
96C22×C73C22×D411yescharacteristic
97C2×D73—22no—
98C2×D73—22no—
99C2×D73—22no—
100C4×C73—21no—
101C4×C73—42no—
102C4×C73—42no—
103C4×C73H(5,𝔽2)11yescharacteristic
104C4×C73H(5,𝔽2)11yescharacteristic
105Dic73—22no—
106Dic73—42no—
107Dic73—42no—
108C2×C73—41no—
109C2×C73#53411yescharacteristic
110C2×C73#57811yescharacteristic
111C2×C73#57811yescharacteristic
112D73—42no—
113#3202—731nomaximal, Sylow
114C73#320211yescharacteristic, complemented, Sylow
115#536—732no—
116#485—732no—
117#485—732no—
118#470—732no—
119#467—731no—
120#467D7311yescharacteristic, complemented
121#451—732no—
122#451—732no—
123#408—731no—
124C2×#41—731no—
125C22×Q8—732no—
126C2×Q16—732no—
127C2×Q16—731no—
128C2×Q16C2×D7311yescharacteristic
129C2×M16—731no—
130C22×C8C2×D7311yescharacteristic
131C4⋊Q8—1462no—
132#124—1462no—
133#123—1462no—
134#123—1462no—
135C22⋊Q8—732no—
136C22⋊Q8—732no—
137C22⋊Q8—732no—
138C22⋊Q8C2×D7312yes—
139#117—732no—
140#107—731no—
141#107C2×D7311yescharacteristic
142#106—732no—
143#103—732no—
144#103—732no—
145#103—732no—
146#103C2×D7312yes—
147C22⋊C8—732no—
148C22⋊C8—732no—
149#41—2921no—
150#41—2921no—
151C2×Q8—2922no—
152C2×Q8—2922no—
153C2×Q8—731no—
154C2×Q8—732no—
155C2×Q8—1462no—
156C2×Q8C22×D7312yes—
157C2×D4—732no—
158C2×D4—731no—
159C22×C4—732no—
160C22×C4—1462no—
161C22×C4C22×D7311yescharacteristic
162Q16—41no—
163Q16—2921no—
164Q16—2922no—
165M16—2921no—
166C2×C8—41no—
167C2×C8—732no—
168C2×C8C22×D7311yescharacteristic
169C2×C8C22×D7311yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—732no—
172C4⋊C4—1462no—
173C4⋊C4—1462no—
174C4⋊C4—1462no—
175C4⋊C4C22×D7312yes—
176C22⋊C4—22no—
177C22⋊C4—1462no—
178C22⋊C4—1462no—
179C22⋊C4—1462no—
180C22⋊C4—1462no—
181C42—1462no—
182C23—732no—
183C23D4×D7311yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—2921no—
187Q8—2924no—
188Q8—1462no—
189Q8—1462no—
190D4—2921no—
191D4—2922no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—2924no—
197C2×C4—732no—
198C2×C4—1462no—
199C2×C4—1462no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4D4×D7311yescharacteristic
203C2×C4C23×D7311yescharacteristic
204C8—21no—
205C8—21no—
206C8—1462no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—1462no—
211C22—1462no—
212C22—1462no—
213C22C2×D4×D7311yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—2922no—
218C4—2922no—
219C4—1462no—
220C4#1455663611yescharacteristic
221C4#1455663711yescharacteristic
222C2—41no—
223C2—2922no—
224C2#1798914511yescharacteristic
225C2#1798940011yescharacteristic
226C2#1798940111yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#467×C73C2
socleC22×C73C22×D4
hypercenter#467D73
hypocenterC73#3202
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #17988930C2semidirect
3. #17988927C2semidirect
4. #17988843C2semidirect
5. #17988828C2semidirect
6. #17988744C2semidirect
7. #17988741C2semidirect
9. #467×C73C2semidirect
114. C73#3202semidirect
120. #467D73semidirect