Finite Group Databasebeta

← #22622839

Subgroups — #22622839

Order 9344.

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

normal subgroups only

This group has 340 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, complemented
2#17989294C211yesmaximal, characteristic
3#17988994C212yesmaximal, complemented
4#17988992C211yesmaximal, characteristic, complemented
5#17988896C212yesmaximal, complemented
6#17988882C211yesmaximal, characteristic, complemented
7#17988877C211yesmaximal, characteristic
8#17988865C212yesmaximal
9#17988717C211yesmaximal, characteristic, complemented
10#17988688C212yesmaximal
11C4×SD16×C73C211yesmaximal, characteristic
12#14556591—21no—
13#14556591C2211yescharacteristic
14#14556591C2211yescharacteristic
15#14556590—22no—
16#14556590C2212yes—
17#14556582C2212yes—
18#14556570—21no—
19#14556568—22no—
20Q8×Dic73C2212yes—
21C4×Dic146—21no—
22C4×Dic146C2211yescharacteristic
23D4×Dic73C2212yes—
24C2×C4⋊Dic73—21no—
25#14556525C2212yes—
26#14556525C2212yes—
27#14556524C2212yes—
28#14556522C2212yes—
29C4⋊#10596831C2211yescharacteristic
30#14556520C2212yes—
31#14556515C2212yes—
32#14556512C2212yes—
33#14556501C2212yes—
34C2×SD16×C73C2211yescharacteristic
35C4×Q8×C73C2211yescharacteristic
36C4×D4×C73C2211yescharacteristic
37#106×C73C2211yescharacteristic
38#103×C73C2211yescharacteristic
39#102×C73C2211yescharacteristic
40C4×C8×C73C2211yescharacteristic
41C2×Dic146—21no—
42C2×Dic146—21no—
43C2×Dic146—22no—
44C2×Dic146D411yescharacteristic
45C22×Dic73—22no—
46C2×#10596831C2312yes—
47C4⋊Dic73—21no—
48C4⋊Dic73—21no—
49C4⋊Dic73—22no—
50C4⋊Dic73—22no—
51C4⋊Dic73D411yescharacteristic
52C4⋊Dic73C2312yes—
53C4⋊Dic73C2312yes—
54#11924007—22no—
55#11924007—22no—
56#11924007D412yes—
57C22⋊Dic73—22no—
58C4×Dic73—22no—
59C4×Dic73C2312yes—
60C2×Q8×C73C2311yescharacteristic
61C2×D4×C73C2311yescharacteristic
62C22×C4×C73—21no—
63SD16×C73Q814yescomplemented
64C2×C8×C73C2311yescharacteristic
65C2×C8×C73C2311yescharacteristic
66C4⋊C4×C73—21no—
67C4⋊C4×C73C2311yescharacteristic
68C4⋊C4×C73C2311yescharacteristic
69C22⋊C4×C73—21no—
70C42×C73—21no—
71C42×C73C2311yescharacteristic
72C23×C73—21no—
73Q8×C73—21no—
74Q8×C73C2×Q812yes—
75D4×C73—21no—
76D4×C73C2×Q812yes—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—42no—
81C2×C4×C73C2×D411yescharacteristic
82C2×C4×C73C2×D411yescharacteristic
83C2×C4×C73C2411yescharacteristic
84C2×Dic73—22no—
85C2×Dic73—22no—
86C2×Dic73—82no—
87C2×Dic73C2×D412yes—
88C2×Dic73C2×D412yes—
89Dic146—22no—
90Dic146—82no—
91Dic146—81no—
92Dic146—81no—
93C8×C73—21no—
94C8×C73C2×Q812yes—
95#10596831—22no—
96C22×C73—22no—
97C22×C73—41no—
98C22×C73—41no—
99C22×C73C22×D411yescharacteristic
100C4×C73—22no—
101C4×C73—21no—
102C4×C73—41no—
103C4×C73—41no—
104C4×C73#13712yes—
105C4×C73C22×Q811yescharacteristic
106C4×C732−1+411yescharacteristic
107Dic73—22no—
108Dic73—22no—
109Dic73—42no—
110Dic73—42no—
111C2×C73—42no—
112C2×C73D4×Q811yescharacteristic
113C2×C73C2×#13711yescharacteristic
114C2×C73#57611yescharacteristic
115#3385—731nomaximal, Sylow
116C73#338511yescharacteristic, complemented, Sylow
117Q82—731no—
118#554—731no—
119#501—732no—
120#500—731no—
121#479—732no—
122#477—731no—
123#476—731no—
124#474—732no—
125#446—731no—
126#440—732no—
127C4×SD16D7311yescharacteristic
128C2×SD16C2×D7311yescharacteristic
129C4⋊Q8—732no—
130C4⋊Q8—731no—
131C4⋊Q8—731no—
132C4⋊Q8—1461no—
133C4⋊Q8—1462no—
134#125—732no—
135C22⋊Q8—1462no—
136C22⋊Q8—1461no—
137C4×Q8—731no—
138C4×Q8—732no—
139C4×Q8—1461no—
140C4×Q8C2×D7311yescharacteristic
141C4×D4—732no—
142C4×D4C2×D7311yescharacteristic
143C2×C4⋊C4—1461no—
144#107—732no—
145#107—732no—
146#107—732no—
147#106—732no—
148#106C2×D7311yescharacteristic
149C4⋊C8—732no—
150C4⋊C8—731no—
151#103—732no—
152#103C2×D7311yescharacteristic
153#102—732no—
154#102C2×D7311yescharacteristic
155#97—732no—
156C4×C8C2×D7311yescharacteristic
157C2×Q8—731no—
158C2×Q8—1462no—
159C2×Q8—1461no—
160C2×Q8—1461no—
161C2×Q8C22×D7311yescharacteristic
162C2×D4C22×D7311yescharacteristic
163C22×C4—21no—
164C22×C4—1462no—
165SD16Dic14614yescomplemented
166C2×C8—732no—
167C2×C8C22×D7311yescharacteristic
168C2×C8C22×D7311yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—732no—
171C4⋊C4—731no—
172C4⋊C4—732no—
173C4⋊C4—732no—
174C4⋊C4—1462no—
175C4⋊C4—1462no—
176C4⋊C4—1462no—
177C4⋊C4—1462no—
178C4⋊C4—1461no—
179C4⋊C4—1461no—
180C4⋊C4C22×D7311yescharacteristic
181C4⋊C4C22×D7311yescharacteristic
182C22⋊C4—21no—
183C22⋊C4—1462no—
184C42—21no—
185C42—732no—
186C42—1462no—
187C42C22×D7311yescharacteristic
188C23—21no—
189Q8—21no—
190Q8—5841no—
191Q8—5841no—
192Q8—5842no—
193Q8—1462no—
194Q8C2×Dic14612yes—
195D4—21no—
196D4C2×Dic14612yes—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—42no—
201C2×C4—5842no—
202C2×C4—732no—
203C2×C4—732no—
204C2×C4—1462no—
205C2×C4—1462no—
206C2×C4D4×D7311yescharacteristic
207C2×C4D4×D7311yescharacteristic
208C2×C4C23×D7311yescharacteristic
209C8—21no—
210C8—1462no—
211C8C2×Dic14612yes—
212C22—22no—
213C22—41no—
214C22—41no—
215C22C2×D4×D7311yescharacteristic
216C4—21no—
217C4—22no—
218C4—41no—
219C4—41no—
220C4—2922no—
221C4—2922no—
222C4—1462no—
223C4—1462no—
224C4#1455662012yes—
225C4C22×Dic14611yescharacteristic
226C4#1455663811yescharacteristic
227C2—42no—
228C2D4×Dic14611yescharacteristic
229C2C2×#1455662011yescharacteristic
230C2#1798938911yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC4×SD16×C73C2
socleC22×C73C22×D4
hypercenterC4×SD16D73
hypocenterC73#3385
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. Q8×Dic146C2semidirect
3. #17988994C2semidirect
4. #17988992C2semidirect
5. #17988896C2semidirect
6. #17988882C2semidirect
9. #17988717C2semidirect
63. SD16×C73Q8semidirect
116. C73#3385semidirect
165. SD16Dic146semidirect