Finite Group Databasebeta

← #22619775

Subgroups — #22619775

Order 9344.

362 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 141 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#17989215C211yesmaximal, characteristic
2#17989065C211yesmaximal, characteristic
3#17988896C212yesmaximal, complemented
4#17988892C212yesmaximal, complemented
5#17988880C212yesmaximal, complemented
6#17988870C212yesmaximal, complemented
7#17988629C211yesmaximal, characteristic
8#17988623C211yesmaximal, characteristic
9#17988615C211yesmaximal, characteristic
10C2×#14556515C211yesmaximal, characteristic
11#419×C73C211yesmaximal, characteristic
12C22×#10596831C2211yescharacteristic
13#14556591—21no—
14#14556590C2212yes—
15#14556583—21no—
16#14556582C2212yes—
17#14556568—22no—
18Q8×Dic73—21no—
19Q8×Dic73—21no—
20Q8×Dic73C2212yes—
21Q8×Dic73C2212yes—
22#14556550—22no—
23#14556550C2211yescharacteristic
24#14556550C2211yescharacteristic
25C2×C4⋊Dic73C2211yescharacteristic
26#14556525C2212yes—
27#14556524C2211yescharacteristic
28#14556524C2211yescharacteristic
29#14556523C2212yes—
30#14556522C2211yescharacteristic
31#14556522C2211yescharacteristic
32#14556520C2212yes—
33#14556520C2212yes—
34#14556515C2212yes—
35#14556515C2212yes—
36C22×Q8×C73C2211yescharacteristic
37C2×M16×C73C2211yescharacteristic
38#117×C73C2211yescharacteristic
39#103×C73C2212yes—
40#103×C73C2212yes—
41C2×Dic146—22no—
42C22×Dic73—21no—
43C2×#10596831—22no—
44C2×#10596831C2311yescharacteristic
45C2×#10596831C2311yescharacteristic
46C4⋊Dic73—21no—
47C4⋊Dic73—22no—
48C4⋊Dic73—22no—
49C4⋊Dic73—22no—
50C4⋊Dic73D411yescharacteristic
51C4⋊Dic73D411yescharacteristic
52C4⋊Dic73C2312yes—
53C4⋊Dic73C2311yescharacteristic
54C4⋊Dic73C2311yescharacteristic
55#11924007—22no—
56#11924007—22no—
57C22⋊Dic73—21no—
58C22⋊Dic73D412yes—
59C4×Dic73—21no—
60C4×Dic73—22no—
61C4×Dic73—22no—
62C4×Dic73C2312yes—
63C2×Q8×C73—21no—
64C2×Q8×C73—22no—
65C2×Q8×C73Q814yescomplemented
66C2×Q8×C73C2312yes—
67C22×C4×C73—21no—
68C22×C4×C73C2311yescharacteristic
69M16×C73—22no—
70C2×C8×C73C2312yes—
71C4⋊C4×C73C2311yescharacteristic
72C4⋊C4×C73C2311yescharacteristic
73C22⋊C4×C73—21no—
74C42×C73—21no—
75C23×C73C2×D411yescharacteristic
76Q8×C73—24no—
77Q8×C73—22no—
78Q8×C73C2×Q814yes—
79C2×C4×C73—24no—
80C2×C4×C73—22no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×Q812yes—
85C2×C4×C73#4112yes—
86C2×C4×C73C2411yescharacteristic
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—22no—
90C2×Dic73—81no—
91C2×Dic73C2×D412yes—
92C2×Dic73C2×D412yes—
93Dic146—82no—
94C8×C73—22no—
95#10596831—21no—
96#10596831—21no—
97C22×C73—21no—
98C22×C73—21no—
99C22×C73C22⋊Q812yes—
100C22×C73C22×D411yescharacteristic
101C4×C73—24no—
102C4×C73—41no—
103C4×C73—41no—
104C4×C73C22⋊Q812yes—
105C4×C73C22×Q811yescharacteristic
106C4×C73C2×#4111yescharacteristic
107Dic73—22no—
108Dic73—22no—
109Dic73—42no—
110Dic73—41no—
111Dic73—41no—
112C2×C73—22no—
113C2×C73C2×C22⋊Q811yescharacteristic
114C2×C73#57711yescharacteristic
115C2×C73#57811yescharacteristic
116#3082—731nomaximal, Sylow
117C73#308211yescharacteristic, complemented, Sylow
118#544—731no—
119#519—731no—
120#479—732no—
121#479—732no—
122#477—732no—
123#475—732no—
124#428—731no—
125#427—731no—
126#424—731no—
127#419D7311yescharacteristic
128C2×#103—731no—
129C22×Q8C2×D7311yescharacteristic
130C2×M16C2×D7311yescharacteristic
131C22×C8—731no—
132C4⋊Q8—732no—
133C4⋊Q8—1461no—
134#125—732no—
135#125—1461no—
136C22⋊Q8—1462no—
137C4×Q8—732no—
138C4×Q8—732no—
139C4×Q8—1461no—
140C4×Q8—1461no—
141#117—731no—
142#117—731no—
143#117—1462no—
144#117C2×D7311yescharacteristic
145C2×C4⋊C4—731no—
146#107—732no—
147#107—731no—
148#107—731no—
149#106—732no—
150#106—731no—
151#106—731no—
152C4⋊C8—732no—
153C4⋊C8—732no—
154#103—732no—
155#103—732no—
156#103C2×D7312yes—
157#103C2×D7312yes—
158C2×Q8—21no—
159C2×Q8—22no—
160C2×Q8—1462no—
161C2×Q8Dic14614yescomplemented
162C2×Q8C22×D7312yes—
163C22×C4—21no—
164C22×C4—1461no—
165C22×C4C22×D7311yescharacteristic
166M16—22no—
167C2×C8—731no—
168C2×C8—731no—
169C2×C8—1462no—
170C2×C8C22×D7312yes—
171C4⋊C4—731no—
172C4⋊C4—731no—
173C4⋊C4—732no—
174C4⋊C4—731no—
175C4⋊C4—731no—
176C4⋊C4—1462no—
177C4⋊C4—1462no—
178C4⋊C4—1462no—
179C4⋊C4—1462no—
180C4⋊C4—1462no—
181C4⋊C4—1461no—
182C4⋊C4C22×D7311yescharacteristic
183C4⋊C4C22×D7311yescharacteristic
184C22⋊C4—21no—
185C22⋊C4—732no—
186C22⋊C4—1461no—
187C42—21no—
188C42—732no—
189C42—1462no—
190C42—1462no—
191C42—1461no—
192C23D4×D7311yescharacteristic
193Q8—24no—
194Q8—22no—
195Q8—5842no—
196Q8C2×Dic14614yes—
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—5841no—
202C2×C4—732no—
203C2×C4—732no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1462no—
207C2×C4D4×D7311yescharacteristic
208C2×C4C2×Dic14612yes—
209C2×C4#1192402712yes—
210C2×C4C23×D7311yescharacteristic
211C8—22no—
212C8—1461no—
213C8—1461no—
214C22—21no—
215C22—21no—
216C22#1455656812yes—
217C22C2×D4×D7311yescharacteristic
218C4—24no—
219C4—41no—
220C4—41no—
221C4—2922no—
222C4—2921no—
223C4—2921no—
224C4—1462no—
225C4—1462no—
226C4#1455656812yes—
227C4C22×Dic14611yescharacteristic
228C4C2×#1192402711yescharacteristic
229C2—22no—
230C2C2×#1455656811yescharacteristic
231C2#1798939611yescharacteristic
232C2#1798940311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#419×C73C2
socleC22×C73C22×D4
hypercenter#419D73
hypocenterC73#3082
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #17988896C2semidirect
4. #17988892C2semidirect
5. #17988880C2semidirect
6. #17988870C2semidirect
65. C2×Q8×C73Q8semidirect
117. C73#3082semidirect
161. C2×Q8Dic146semidirect