Finite Group Databasebeta

← #22622861

Subgroups — #22622861

Order 9344.

326 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 133 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
1Q8×Dic146C211yesmaximal, characteristic
2#17989316C211yesmaximal, characteristic
3#17988995C212yesmaximal
4#17988985C211yesmaximal, characteristic
5#17988892C212yesmaximal
6#17988882C211yesmaximal, characteristic
7#17988872C211yesmaximal, characteristic
8#17988870C212yesmaximal
9#17988717C211yesmaximal, characteristic
10#17988694C212yesmaximal
11C4×Q16×C73C211yesmaximal, characteristic
12#14556591—21no—
13#14556591—21no—
14#14556591C2211yescharacteristic
15#14556591C2211yescharacteristic
16#14556590—22no—
17#14556590C2212yes—
18#14556582—22no—
19#14556582C2212yes—
20Q8×Dic73C2212yes—
21Q8×Dic73C2212yes—
22C4×Dic146—21no—
23C4×Dic146—21no—
24C4×Dic146C2211yescharacteristic
25#14556524C2212yes—
26#14556523C2212yes—
27#14556523C2212yes—
28#14556522C2212yes—
29C4⋊#10596831C2211yescharacteristic
30#14556520C2212yes—
31#14556515C2212yes—
32#14556515C2212yes—
33#14556501C2212yes—
34C2×Q16×C73C2211yescharacteristic
35C4×Q8×C73C2211yescharacteristic
36C4×Q8×C73C2211yescharacteristic
37#107×C73C2211yescharacteristic
38#103×C73C2211yescharacteristic
39#103×C73C2211yescharacteristic
40C4×C8×C73C2211yescharacteristic
41C2×Dic146—21no—
42C2×Dic146—21no—
43C2×Dic146—22no—
44C2×Dic146D411yescharacteristic
45C2×#10596831C2312yes—
46C4⋊Dic73—21no—
47C4⋊Dic73—21no—
48C4⋊Dic73—22no—
49C4⋊Dic73—22no—
50C4⋊Dic73—22no—
51C4⋊Dic73D411yescharacteristic
52C4⋊Dic73C2312yes—
53C4⋊Dic73C2312yes—
54#11924007—22no—
55#11924007—22no—
56#11924007D412yes—
57C4×Dic73—22no—
58C4×Dic73—22no—
59C4×Dic73C2312yes—
60C2×Q8×C73C2311yescharacteristic
61C2×Q8×C73C2311yescharacteristic
62Q16×C73Q814yescomplemented
63C2×C8×C73C2311yescharacteristic
64C2×C8×C73C2311yescharacteristic
65C4⋊C4×C73—21no—
66C4⋊C4×C73—21no—
67C4⋊C4×C73C2311yescharacteristic
68C4⋊C4×C73C2311yescharacteristic
69C42×C73—21no—
70C42×C73—21no—
71C42×C73C2311yescharacteristic
72Q8×C73—21no—
73Q8×C73—21no—
74Q8×C73C2×Q812yes—
75Q8×C73C2×Q812yes—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73C2×D411yescharacteristic
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2411yescharacteristic
83C2×Dic73—22no—
84C2×Dic73—22no—
85C2×Dic73C2×D412yes—
86C2×Dic73C2×D412yes—
87Dic146—22no—
88Dic146—42no—
89Dic146—82no—
90Dic146—81no—
91C8×C73—21no—
92C8×C73C2×Q812yes—
93#10596831—22no—
94C22×C73C22×D411yescharacteristic
95C4×C73—22no—
96C4×C73—22no—
97C4×C73—21no—
98C4×C73—41no—
99C4×C73—41no—
100C4×C73#13712yes—
101C4×C73C22×Q811yescharacteristic
102C4×C732−1+411yescharacteristic
103Dic73—22no—
104Dic73—22no—
105Dic73—42no—
106Dic73—42no—
107C2×C73D4×Q811yescharacteristic
108C2×C73C2×#13711yescharacteristic
109C2×C73#57711yescharacteristic
110#3387—731nomaximal, Sylow
111C73#338711yescharacteristic, complemented, Sylow
112Q82—731no—
113#557—731no—
114#501—732no—
115#498—731no—
116#479—732no—
117#477—731no—
118#475—731no—
119#475—732no—
120#446—731no—
121#441—732no—
122C4×Q16D7311yescharacteristic
123C2×Q16C2×D7311yescharacteristic
124C4⋊Q8—732no—
125C4⋊Q8—731no—
126C4⋊Q8—731no—
127C4⋊Q8—1461no—
128C4⋊Q8—1461no—
129C4⋊Q8—1462no—
130#125—732no—
131#125—1462no—
132C4×Q8—731no—
133C4×Q8—732no—
134C4×Q8—732no—
135C4×Q8—1461no—
136C4×Q8—1461no—
137C4×Q8C2×D7311yescharacteristic
138C4×Q8C2×D7311yescharacteristic
139#107—732no—
140#107C2×D7311yescharacteristic
141#106—732no—
142#106—732no—
143#106—732no—
144C4⋊C8—732no—
145C4⋊C8—731no—
146#103—732no—
147#103—732no—
148#103C2×D7311yescharacteristic
149#103C2×D7311yescharacteristic
150#97—732no—
151C4×C8C2×D7311yescharacteristic
152C2×Q8—731no—
153C2×Q8—1462no—
154C2×Q8—1461no—
155C2×Q8—1461no—
156C2×Q8C22×D7311yescharacteristic
157C2×Q8C22×D7311yescharacteristic
158Q16Dic14614yescomplemented
159C2×C8—732no—
160C2×C8C22×D7311yescharacteristic
161C2×C8C22×D7311yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—732no—
165C4⋊C4—731no—
166C4⋊C4—732no—
167C4⋊C4—732no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C4⋊C4—1462no—
171C4⋊C4—1462no—
172C4⋊C4—1462no—
173C4⋊C4—1461no—
174C4⋊C4—1461no—
175C4⋊C4C22×D7311yescharacteristic
176C4⋊C4C22×D7311yescharacteristic
177C42—21no—
178C42—21no—
179C42—732no—
180C42—1462no—
181C42—1462no—
182C42C22×D7311yescharacteristic
183Q8—21no—
184Q8—21no—
185Q8—2922no—
186Q8—5841no—
187Q8—5842no—
188Q8—1462no—
189Q8C2×Dic14612yes—
190Q8C2×Dic14612yes—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—732no—
196C2×C4—732no—
197C2×C4—1462no—
198C2×C4—1462no—
199C2×C4D4×D7311yescharacteristic
200C2×C4D4×D7311yescharacteristic
201C2×C4C23×D7311yescharacteristic
202C8—21no—
203C8—1462no—
204C8C2×Dic14612yes—
205C22C2×D4×D7311yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—41no—
210C4—41no—
211C4—2922no—
212C4—2922no—
213C4—1462no—
214C4—1462no—
215C4#1455662312yes—
216C4C22×Dic14611yescharacteristic
217C4#1455663811yescharacteristic
218C2D4×Dic14611yescharacteristic
219C2C2×#1455662311yescharacteristic
220C2#1798939411yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×Q16×C73C2
socleC22×C73C22×D4
hypercenterC4×Q16D73
hypocenterC73#3387
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
62. Q16×C73Q8semidirect
111. C73#3387semidirect
158. Q16Dic146semidirect