Finite Group Databasebeta

← #22621016

Subgroups — #22621016

Order 9344.

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

normal subgroups only

This group has 364 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#17989199C211yesmaximal, characteristic, complemented
2#17989163C211yesmaximal, characteristic
3#17988981C211yesmaximal, characteristic, complemented
4#17988967C211yesmaximal, characteristic, complemented
5#17988956C211yesmaximal, characteristic, complemented
6#17988942C211yesmaximal, characteristic, complemented
7#17988810C212yesmaximal, complemented
8#17988798C212yesmaximal, complemented
9#17988751C212yesmaximal
10#17988745C212yesmaximal, complemented
11#433×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C22×Dic146C2211yescharacteristic
14C2×Dic292C2212yes—
15C2×Dic292C2212yes—
16C2×Dic292C2212yes—
17C2×#11924017C2212yes—
18#14556591C2211yescharacteristic
19#14556591C2211yescharacteristic
20#14556591C2211yescharacteristic
21#14556584—22no—
22#14556583C2211yescharacteristic
23#14556581—22no—
24#14556579C2211yescharacteristic
25#14556579C2211yescharacteristic
26#14556575—22no—
27#14556571—22no—
28#14556570C2212yes—
29C4×Dic146C2212yes—
30#14556516C2212yes—
31#14556516C2212yes—
32#14556516C2212yes—
33#14556513C2212yes—
34#117×C73C2211yescharacteristic
35C4⋊C8×C73C2212yes—
36C22⋊C8×C73C2212yes—
37#97×C73C2211yescharacteristic
38C4×C8×C73C2211yescharacteristic
39#11924028—42no—
40C2×Dic146—21no—
41C2×Dic146—42no—
42C2×Dic146C2311yescharacteristic
43C2×Dic146C2311yescharacteristic
44C2×Dic146C2311yescharacteristic
45C2×Dic146C2312yes—
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C22×Dic73—21no—
49C2×C4×D73—21no—
50Dic292—42no—
51Dic292—42no—
52Dic292—42no—
53#11924017—42no—
54C4⋊Dic73—22no—
55C4⋊Dic73—22no—
56C4⋊Dic73—22no—
57C4⋊Dic73C2312yes—
58#11924007—22no—
59#11924007—22no—
60#11924007—22no—
61C22⋊Dic73—22no—
62#11924005—22no—
63#11924005—22no—
64C4×Dic73—22no—
65C22×C4×C73C2311yescharacteristic
66C2×C8×C73C2312yes—
67C2×C8×C73C2312yes—
68C4⋊C4×C73D412yes—
69C22⋊C4×C73D412yes—
70C42×C73C2311yescharacteristic
71C42×C73C2311yescharacteristic
72C23×C73C2×D411yescharacteristic
73C22×D73—21no—
74C2×C4×C73—22no—
75C2×C4×C73C2×D412yes—
76C2×C4×C73C2×D412yes—
77C2×C4×C73C2×D411yescharacteristic
78C2×C4×C73C2411yescharacteristic
79C22⋊D73—42no—
80C2×Dic73—22no—
81C2×Dic73—22no—
82C2×Dic73—21no—
83C2×Dic73—21no—
84C2×Dic73—21no—
85C2×Dic73—42no—
86D292—22no—
87C4×D73—42no—
88Dic146—22no—
89Dic146—22no—
90Dic146—22no—
91Dic146—22no—
92Dic146—22no—
93Dic146—42no—
94C8×C73—22no—
95C8×C73—22no—
96C22×C73—21no—
97C22×C73—22no—
98C22×C73C22×D411yescharacteristic
99C2×D73—41no—
100C2×D73—42no—
101C4×C73—21no—
102C4×C73—22no—
103C4×C73—22no—
104C4×C73H(5,𝔽2)12yes—
105Dic73—41no—
106Dic73—41no—
107Dic73—41no—
108Dic73—42no—
109Dic73—42no—
110C2×C73—41no—
111C2×C73#53511yescharacteristic
112C2×C73#57812yes—
113D73—81no—
114#3223—731nomaximal, Sylow
115C73#322311yescharacteristic, complemented, Sylow
116#541—731no—
117#536—731no—
118#497—731no—
119#494—731no—
120#491—731no—
121#488—731no—
122#464—732no—
123#462—732no—
124#452—732no—
125#451—732no—
126#433D7311yescharacteristic, complemented
127C2×#41—731no—
128C22×Q8—731no—
129C2×Q16—732no—
130C2×Q16—732no—
131C2×Q16—732no—
132C2×SD16—732no—
133C4⋊Q8—731no—
134C4⋊Q8—731no—
135C4⋊Q8—731no—
136#126—1462no—
137#125—731no—
138#125—1462no—
139#124—731no—
140#124—731no—
141#123—1462no—
142C22⋊Q8—732no—
143C22⋊Q8—1462no—
144C4×Q8—732no—
145#117C2×D7311yescharacteristic
146C4⋊C8C2×D7312yes—
147#103—732no—
148#103—732no—
149#103—732no—
150#102—732no—
151C22⋊C8C2×D7312yes—
152#97C2×D7311yescharacteristic
153C4×C8C2×D7311yescharacteristic
154#41—2922no—
155C2×Q8—2922no—
156C2×Q8—731no—
157C2×Q8—731no—
158C2×Q8—731no—
159C2×Q8—732no—
160C2×Q8—1461no—
161C2×D4—731no—
162C2×D4—1461no—
163C22×C4—1461no—
164C22×C4—1461no—
165C22×C4C22×D7311yescharacteristic
166Q16—2922no—
167Q16—2922no—
168Q16—2922no—
169SD16—2922no—
170C2×C8C22×D7312yes—
171C2×C8C22×D7312yes—
172C4⋊C4—732no—
173C4⋊C4—1462no—
174C4⋊C4—1462no—
175C4⋊C4—1462no—
176C4⋊C4—1462no—
177C4⋊C4—1462no—
178C4⋊C4—1462no—
179C4⋊C4D29212yes—
180C22⋊C4—1462no—
181C22⋊C4—1462no—
182C22⋊C4—1462no—
183C22⋊C4D29212yes—
184C42—1462no—
185C42C22×D7311yescharacteristic
186C42C22×D7311yescharacteristic
187C23—1461no—
188C23C2×D29211yescharacteristic
189Q8—2922no—
190Q8—1462no—
191Q8—1462no—
192Q8—1462no—
193Q8—1462no—
194Q8—1462no—
195D4—2922no—
196D4—1462no—
197C2×C4—22no—
198C2×C4—2922no—
199C2×C4—2922no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4C2×D29212yes—
206C2×C4C2×D29212yes—
207C2×C4C2×D29211yescharacteristic
208C2×C4C23×D7311yescharacteristic
209C8—22no—
210C8—22no—
211C22—22no—
212C22—21no—
213C22—2922no—
214C22—2921no—
215C22C22×D29211yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—2922no—
220C4—2921no—
221C4—2921no—
222C4—2921no—
223C4—2922no—
224C4#1455663712yes—
225C2—41no—
226C2—5841no—
227C2#1798915611yescharacteristic
228C2#1798940412yes—
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#433×C73C2
socleC22×C73C22×D4
hypercenter#433D73
hypocenterC73#3223
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #17989199C2semidirect
3. #17988981C2semidirect
4. #17988967C2semidirect
5. #17988956C2semidirect
6. #17988942C2semidirect
7. #17988810C2semidirect
8. #17988798C2semidirect
10. #17988745C2semidirect
11. #433×C73C2semidirect
115. C73#3223semidirect
126. #433D73semidirect