Finite Group Databasebeta

← #22621014

Subgroups — #22621014

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#17988982C211yesmaximal, characteristic, complemented
3#17988966C211yesmaximal, characteristic, complemented
4#17988955C211yesmaximal, characteristic, complemented
5#17988941C211yesmaximal, characteristic, complemented
6#17988806C212yesmaximal, complemented
7#17988794C212yesmaximal, complemented
8#17988749C212yesmaximal
9#17988743C212yesmaximal, complemented
10#17988648C211yesmaximal, characteristic, complemented
11#536×C73C211yesmaximal, characteristic
12C2×#11924018C2212yes—
13C2×#11924018C2212yes—
14C2×#11924018C2212yes—
15C2×#11924016C2212yes—
16#14556591C2211yescharacteristic
17#14556584—22no—
18#14556583C2211yescharacteristic
19#14556581—22no—
20#14556570C2212yes—
21C4×Dic146C2212yes—
22C4⋊#10596831C2212yes—
23#14556515C2212yes—
24#14556515C2212yes—
25#14556515C2212yes—
26#14556512C2212yes—
27C22⋊#10596831C2212yes—
28#14556502C2211yescharacteristic
29C4×#10596831C2211yescharacteristic
30C2×#41×C73C2211yescharacteristic
31C22×Q8×C73C2211yescharacteristic
32C4⋊Q8×C73C2211yescharacteristic
33C4⋊Q8×C73C2211yescharacteristic
34#124×C73C2211yescharacteristic
35#124×C73C2211yescharacteristic
36#123×C73—22no—
37C22⋊Q8×C73—22no—
38#117×C73C2211yescharacteristic
39C2×Dic146C2312yes—
40#11924018—42no—
41#11924018—42no—
42#11924018—42no—
43#11924016—42no—
44C2×#10596831C2312yes—
45C2×#10596831C2312yes—
46C4⋊Dic73—22no—
47C4⋊Dic73C2312yes—
48#11924007—22no—
49#11924007—22no—
50#11924007—22no—
51C22⋊Dic73—22no—
52C4×Dic73—22no—
53#41×C73—42no—
54C2×Q8×C73—21no—
55C2×Q8×C73—42no—
56C2×Q8×C73C2311yescharacteristic
57C2×Q8×C73C2311yescharacteristic
58C2×Q8×C73C2311yescharacteristic
59C2×D4×C73—21no—
60C2×D4×C73C2311yescharacteristic
61C22×C4×C73—21no—
62C22×C4×C73—21no—
63C22×C4×C73C2311yescharacteristic
64C4⋊C4×C73—22no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73D412yes—
67C22⋊C4×C73—22no—
68C22⋊C4×C73—22no—
69C22⋊C4×C73D412yes—
70C42×C73C2311yescharacteristic
71C42×C73C2311yescharacteristic
72C23×C73—21no—
73C23×C73C2×D411yescharacteristic
74Q8×C73—22no—
75Q8×C73—22no—
76Q8×C73—22no—
77Q8×C73—42no—
78D4×C73—22no—
79D4×C73—42no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—42no—
85C2×C4×C73—42no—
86C2×C4×C73C2×D412yes—
87C2×C4×C73C2×D412yes—
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2411yescharacteristic
90C2×Dic73—22no—
91C2×Dic73—22no—
92Dic146—22no—
93Dic146—22no—
94#10596831—22no—
95#10596831—22no—
96C22×C73—21no—
97C22×C73—22no—
98C22×C73—41no—
99C22×C73—42no—
100C22×C73C22×D411yescharacteristic
101C4×C73—21no—
102C4×C73—22no—
103C4×C73—22no—
104C4×C73—41no—
105C4×C73—41no—
106C4×C73—41no—
107C4×C73H(5,𝔽2)12yes—
108Dic73—42no—
109Dic73—42no—
110C2×C73—41no—
111C2×C73—81no—
112C2×C73#53511yescharacteristic
113C2×C73#57812yes—
114#3223—731nomaximal, Sylow
115C73#322311yescharacteristic, complemented, Sylow
116#541—731no—
117#536D7311yescharacteristic
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#433—731no—
127C2×#41C2×D7311yescharacteristic
128C22×Q8C2×D7311yescharacteristic
129C2×Q16—732no—
130C2×Q16—732no—
131C2×Q16—732no—
132C2×SD16—732no—
133C4⋊Q8—731no—
134C4⋊Q8C2×D7311yescharacteristic
135C4⋊Q8C2×D7311yescharacteristic
136#126—1462no—
137#125—731no—
138#125—1462no—
139#124C2×D7311yescharacteristic
140#124C2×D7311yescharacteristic
141#123—22no—
142C22⋊Q8—22no—
143C22⋊Q8—732no—
144C4×Q8—732no—
145#117C2×D7311yescharacteristic
146C4⋊C8—732no—
147#103—732no—
148#103—732no—
149#103—732no—
150#102—732no—
151C22⋊C8—732no—
152#97—731no—
153C4×C8—731no—
154#41—42no—
155C2×Q8—21no—
156C2×Q8—42no—
157C2×Q8—732no—
158C2×Q8C22×D7311yescharacteristic
159C2×Q8C22×D7311yescharacteristic
160C2×Q8C22×D7311yescharacteristic
161C2×D4—21no—
162C2×D4C22×D7311yescharacteristic
163C22×C4—21no—
164C22×C4—21no—
165C22×C4C22×D7311yescharacteristic
166Q16—2922no—
167Q16—2922no—
168Q16—2922no—
169SD16—2922no—
170C2×C8—732no—
171C2×C8—732no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—732no—
175C4⋊C4—1462no—
176C4⋊C4—1462no—
177C4⋊C4—1462no—
178C4⋊C4—1462no—
179C4⋊C4C22⋊D7312yes—
180C22⋊C4—22no—
181C22⋊C4—22no—
182C22⋊C4—1462no—
183C22⋊C4C22⋊D7312yes—
184C42—1462no—
185C42C22×D7311yescharacteristic
186C42C22×D7311yescharacteristic
187C23—21no—
188C23C2×C22⋊D7311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—1462no—
194Q8—1462no—
195D4—22no—
196D4—42no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—1462no—
204C2×C4—1462no—
205C2×C4C2×C22⋊D7312yes—
206C2×C4C2×C22⋊D7312yes—
207C2×C4C2×C22⋊D7311yescharacteristic
208C2×C4C23×D7311yescharacteristic
209C8—1462no—
210C8—1462no—
211C22—22no—
212C22—21no—
213C22—42no—
214C22—41no—
215C22C22×C22⋊D7311yescharacteristic
216C4—22no—
217C4—22no—
218C4—21no—
219C4—41no—
220C4—41no—
221C4—41no—
222C4—2922no—
223C4—2922no—
224C4#1455663612yes—
225C2—41no—
226C2—81no—
227C2#1798915411yescharacteristic
228C2#1798940212yes—
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#536×C73C2
socleC22×C73C22×D4
hypercenter#536D73
hypocenterC73#3223
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
1. #17989199C2semidirect
2. #17988982C2semidirect
3. #17988966C2semidirect
4. #17988955C2semidirect
5. #17988941C2semidirect
6. #17988806C2semidirect
7. #17988794C2semidirect
9. #17988743C2semidirect
10. #17988648C2semidirect
115. C73#3223semidirect