Finite Group Databasebeta

← #22622984

Subgroups — #22622984

Order 9344.

362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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#17989316C211yesmaximal, characteristic, complemented
2#17988982C212yesmaximal, complemented
3#17988959C211yesmaximal, characteristic
4#17988806C212yesmaximal, complemented
5#17988797C211yesmaximal, characteristic, complemented
6#17988792C212yesmaximal, complemented
7#17988784C211yesmaximal, characteristic
8#17988718C211yesmaximal, characteristic, complemented
9#17988687C212yesmaximal, complemented
10C4×#11924018C211yesmaximal, characteristic, complemented
11#559×C73C211yesmaximal, characteristic
12C2×#11924018C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924016C2212yes—
15C2×#11924016C2212yes—
16C2×#11924016C2212yes—
17#14556591C2211yescharacteristic
18#14556591C2212yes—
19#14556582—21no—
20#14556582—22no—
21Q8×Dic73—21no—
22C4×Dic146C2211yescharacteristic
23C4×Dic146C2212yes—
24#14556524C2211yescharacteristic
25C4⋊#10596831C2211yescharacteristic
26C4⋊#10596831C2212yes—
27#14556515C2211yescharacteristic
28#14556514C2211yescharacteristic
29#14556514C2212yes—
30#14556512C2212yes—
31#14556502C2212yes—
32C4×#10596831C2211yescharacteristic
33#127×C73C2211yescharacteristic
34#124×C73—21no—
35#124×C73C2212yes—
36#123×C73—22no—
37C4×Q8×C73C2211yescharacteristic
38C4×Q8×C73C2211yescharacteristic
39C4×D4×C73—21no—
40C4×D4×C73C2212yes—
41C2×Dic146C2312yes—
42C2×Dic146C2311yescharacteristic
43#11924018—22no—
44#11924018—42no—
45#11924016—24no—
46#11924016—42no—
47#11924016—42no—
48C2×#10596831C2311yescharacteristic
49C2×#10596831C2312yes—
50C2×#10596831C2311yescharacteristic
51C4⋊Dic73—22no—
52C4⋊Dic73—21no—
53C4⋊Dic73—22no—
54C4⋊Dic73—21no—
55C4⋊Dic73C2311yescharacteristic
56#11924007—22no—
57#11924007—21no—
58C4×Dic73—22no—
59C4×Dic73—21no—
60C2×Q8×C73D411yescharacteristic
61C2×Q8×C73C2311yescharacteristic
62C2×D4×C73—21no—
63C2×D4×C73—21no—
64C2×D4×C73C2312yes—
65C22×C4×C73—22no—
66C4⋊C4×C73—21no—
67C4⋊C4×C73D411yescharacteristic
68C4⋊C4×C73D412yes—
69C4⋊C4×C73C2311yescharacteristic
70C22⋊C4×C73—22no—
71C22⋊C4×C73—22no—
72C22⋊C4×C73—22no—
73C42×C73—21no—
74C42×C73C2312yes—
75C42×C73C2311yescharacteristic
76C23×C73—22no—
77Q8×C73—22no—
78Q8×C73—21no—
79Q8×C73—21no—
80D4×C73—22no—
81D4×C73—22no—
82D4×C73—42no—
83D4×C73—81no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—82no—
87C2×C4×C73C2×D412yes—
88C2×C4×C73C2×D412yes—
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2411yescharacteristic
92C2×Dic73—21no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95Dic146—22no—
96Dic146—21no—
97Dic146—21no—
98Dic146—22no—
99#10596831—21no—
100#10596831—22no—
101#10596831#4112yes—
102C22×C73—42no—
103C22×C73—42no—
104C22×C73—42no—
105C22×C73C22×D411yescharacteristic
106C4×C73—22no—
107C4×C73—22no—
108C4×C73—21no—
109C4×C73—41no—
110C4×C73—41no—
111C4×C73#13712yes—
112C4×C73C2×#4111yescharacteristic
113C4×C73H(5,𝔽2)11yescharacteristic
114Dic73—42no—
115Dic73—41no—
116Dic73—41no—
117C2×C73—82no—
118C2×C73#55011yescharacteristic
119C2×C73C2×#13711yescharacteristic
120C2×C73#57711yescharacteristic
121#3400—731nomaximal, Sylow
122C73#340011yescharacteristic, complemented, Sylow
123#559D7311yescharacteristic
124#557—731no—
125#497—732no—
126#492—731no—
127#464—732no—
128#462—731no—
129#461—732no—
130#460—731no—
131#446—731no—
132#440—732no—
133C4×Q16—731no—
134C2×Q16—732no—
135C2×Q16—731no—
136C2×SD16—732no—
137C2×SD16—732no—
138C2×SD16—732no—
139C4⋊Q8—732no—
140C4⋊Q8—731no—
141#127C2×D7311yescharacteristic
142#125—1461no—
143#125—1462no—
144#124—21no—
145#124C2×D7312yes—
146#123—22no—
147C4×Q8—731no—
148C4×Q8—732no—
149C4×Q8—1461no—
150C4×Q8C2×D7311yescharacteristic
151C4×Q8C2×D7311yescharacteristic
152C4×D4—21no—
153C4×D4C2×D7312yes—
154#107—731no—
155C4⋊C8—731no—
156C4⋊C8—732no—
157#103—731no—
158#103—731no—
159#103—732no—
160#102—732no—
161#97—732no—
162C4×C8—731no—
163C2×Q8—732no—
164C2×Q8—731no—
165C2×Q8C22⋊D7311yescharacteristic
166C2×Q8C22×D7311yescharacteristic
167C2×D4—21no—
168C2×D4—21no—
169C2×D4C22×D7312yes—
170C22×C4—22no—
171Q16—2922no—
172Q16—1462no—
173SD16—2922no—
174SD16—2922no—
175SD16—1464no—
176C2×C8—731no—
177C2×C8—731no—
178C2×C8—732no—
179C4⋊C4—21no—
180C4⋊C4—731no—
181C4⋊C4—1462no—
182C4⋊C4—1461no—
183C4⋊C4—1462no—
184C4⋊C4—1461no—
185C4⋊C4—1462no—
186C4⋊C4—1461no—
187C4⋊C4C22⋊D7311yescharacteristic
188C4⋊C4C22⋊D7312yes—
189C4⋊C4C22×D7311yescharacteristic
190C22⋊C4—22no—
191C22⋊C4—22no—
192C22⋊C4—22no—
193C42—21no—
194C42—1462no—
195C42—1461no—
196C42C22×D7311yescharacteristic
197C42C22×D7312yes—
198C23—22no—
199Q8—22no—
200Q8—21no—
201Q8—21no—
202Q8—1462no—
203Q8—1461no—
204Q8—1461no—
205Q8—1462no—
206D4—22no—
207D4—22no—
208D4—42no—
209D4—81no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—82no—
213C2×C4—1461no—
214C2×C4—1462no—
215C2×C4—1461no—
216C2×C4C2×C22⋊D7312yes—
217C2×C4C2×C22⋊D7312yes—
218C2×C4C2×C22⋊D7311yescharacteristic
219C2×C4C2×C22⋊D7311yescharacteristic
220C2×C4C23×D7311yescharacteristic
221C8—732no—
222C8—1461no—
223C8—1462no—
224C22—42no—
225C22—42no—
226C22—42no—
227C22C22×C22⋊D7311yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—41no—
232C4—41no—
233C4—2921no—
234C4—2922no—
235C4—2921no—
236C4#1455662112yes—
237C4#41×D7311yescharacteristic
238C4#1455663711yescharacteristic
239C2—82no—
240C2#1798925611yescharacteristic
241C2C2×#1455662111yescharacteristic
242C2#1798939811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#559×C73C2
socleC22×C73C22×D4
hypercenter#559D73
hypocenterC73#3400
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #17989316C2semidirect
2. #17988982C2semidirect
4. #17988806C2semidirect
5. #17988797C2semidirect
6. #17988792C2semidirect
8. #17988718C2semidirect
9. #17988687C2semidirect
10. C4×#11924018C2semidirect
122. C73#3400semidirect