Finite Group Databasebeta

← #22622980

Subgroups — #22622980

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#17989322C211yesmaximal, characteristic
2#17988979C212yesmaximal, complemented
3#17988961C211yesmaximal, characteristic
4#17988809C212yesmaximal, complemented
5#17988794C211yesmaximal, characteristic, complemented
6#17988789C212yesmaximal, complemented
7#17988787C211yesmaximal, characteristic
8#17988718C211yesmaximal, characteristic, complemented
9#17988685C212yesmaximal, complemented
10C4×#11924018C211yesmaximal, characteristic, complemented
11#557×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924015C2212yes—
15C2×#11924015C2212yes—
16C2×#11924015C2212yes—
17#14556588C2211yescharacteristic
18#14556580—21no—
19#14556579C2212yes—
20#14556576—22no—
21C4×Dic146C2211yescharacteristic
22C4×D292C2212yes—
23#14556553—21no—
24#14556524C2211yescharacteristic
25C4⋊#10596831C2211yescharacteristic
26C4⋊#10596831C2212yes—
27#14556515C2211yescharacteristic
28#14556515C2212yes—
29#14556514C2211yescharacteristic
30#14556511C2212yes—
31#14556502C2212yes—
32C4×#10596831C2211yescharacteristic
33C4⋊Q8×C73C2211yescharacteristic
34C4⋊Q8×C73C2212yes—
35#125×C73—21no—
36#125×C73—22no—
37C4×Q8×C73—21no—
38C4×Q8×C73C2211yescharacteristic
39C4×Q8×C73C2212yes—
40C4×Q8×C73C2211yescharacteristic
41C2×Dic146C2311yescharacteristic
42C2×D292—21no—
43C2×D292—21no—
44C2×D292C2312yes—
45C2×C4×D73—22no—
46#11924018—22no—
47#11924018—42no—
48#11924015—24no—
49#11924015—42no—
50#11924015—42no—
51C2×#10596831C2311yescharacteristic
52C2×#10596831C2312yes—
53C2×#10596831C2311yescharacteristic
54C4⋊Dic73C2311yescharacteristic
55#11924007—21no—
56#11924005—22no—
57#11924005—22no—
58#11924005—22no—
59C4×Dic73—21no—
60C2×Q8×C73D411yescharacteristic
61C2×Q8×C73C2312yes—
62C2×Q8×C73C2311yescharacteristic
63C4⋊C4×C73—22no—
64C4⋊C4×C73—21no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73—21no—
67C4⋊C4×C73—22no—
68C4⋊C4×C73—21no—
69C4⋊C4×C73D411yescharacteristic
70C4⋊C4×C73D412yes—
71C4⋊C4×C73C2311yescharacteristic
72C42×C73—22no—
73C42×C73—21no—
74C42×C73C2311yescharacteristic
75C42×C73C2312yes—
76C22×D73—22no—
77Q8×C73—22no—
78Q8×C73—22no—
79Q8×C73—21no—
80Q8×C73—21no—
81Q8×C73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
85C2×C4×C73C2×D412yes—
86C2×C4×C73C2×D412yes—
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2411yescharacteristic
90C2×Dic73—21no—
91C2×Dic73—21no—
92D292—22no—
93D292—22no—
94D292—42no—
95D292—81no—
96C4×D73—82no—
97Dic146—21no—
98Dic146—21no—
99#10596831—21no—
100#10596831—22no—
101#10596831#4112yes—
102C22×C73C22×D411yescharacteristic
103C2×D73—42no—
104C2×D73—42no—
105C2×D73—42no—
106C4×C73—22no—
107C4×C73—22no—
108C4×C73—21no—
109C4×C73—42no—
110C4×C73—41no—
111C4×C73—41no—
112C4×C73#13712yes—
113C4×C73C2×#4111yescharacteristic
114C4×C73H(5,𝔽2)11yescharacteristic
115Dic73—41no—
116Dic73—41no—
117C2×C73#55011yescharacteristic
118C2×C73C2×#13711yescharacteristic
119C2×C73#57711yescharacteristic
120D73—82no—
121#3400—731nomaximal, Sylow
122C73#340011yescharacteristic, complemented, Sylow
123#559—731no—
124#557D7311yescharacteristic, complemented
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⋊Q8C2×D7312yes—
140C4⋊Q8C2×D7311yescharacteristic
141#127—731no—
142#125—21no—
143#125—22no—
144#124—732no—
145#124—1461no—
146#123—1462no—
147C4×Q8—21no—
148C4×Q8—731no—
149C4×Q8C2×D7311yescharacteristic
150C4×Q8C2×D7312yes—
151C4×Q8C2×D7311yescharacteristic
152C4×D4—732no—
153C4×D4—1461no—
154#107—731no—
155C4⋊C8—731no—
156C4⋊C8—732no—
157#103—731no—
158#103—732no—
159#103—731no—
160#102—732no—
161#97—732no—
162C4×C8—731no—
163C2×Q8—731no—
164C2×Q8C22⋊D7311yescharacteristic
165C2×Q8C22×D7312yes—
166C2×Q8C22×D7311yescharacteristic
167C2×D4—732no—
168C2×D4—1461no—
169C2×D4—1461no—
170C22×C4—1462no—
171Q16—2922no—
172Q16—1462no—
173SD16—2922no—
174SD16—2922no—
175SD16—1464no—
176C2×C8—731no—
177C2×C8—731no—
178C2×C8—732no—
179C4⋊C4—22no—
180C4⋊C4—21no—
181C4⋊C4—22no—
182C4⋊C4—21no—
183C4⋊C4—22no—
184C4⋊C4—21no—
185C4⋊C4—731no—
186C4⋊C4—1461no—
187C4⋊C4C22⋊D7311yescharacteristic
188C4⋊C4C22⋊D7312yes—
189C4⋊C4C22×D7311yescharacteristic
190C22⋊C4—1462no—
191C22⋊C4—1462no—
192C22⋊C4—1462no—
193C42—22no—
194C42—21no—
195C42—1461no—
196C42C22×D7311yescharacteristic
197C42C22×D7312yes—
198C23—1462no—
199Q8—22no—
200Q8—22no—
201Q8—21no—
202Q8—21no—
203Q8—22no—
204Q8—1461no—
205Q8—1461no—
206D4—2922no—
207D4—5841no—
208D4—1462no—
209D4—1462no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—5842no—
214C2×C4—1461no—
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—2922no—
225C22—2922no—
226C22—2922no—
227C22C22×C22⋊D7311yescharacteristic
228C4—22no—
229C4—22no—
230C4—21no—
231C4—41no—
232C4—42no—
233C4—41no—
234C4—2921no—
235C4—2921no—
236C4#1455662212yes—
237C4#41×D7311yescharacteristic
238C4#1455663711yescharacteristic
239C2—5842no—
240C2#1798925611yescharacteristic
241C2C2×#1455662211yescharacteristic
242C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#557×C73C2
socleC22×C73C22×D4
hypercenter#557D73
hypocenterC73#3400
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
2. #17988979C2semidirect
4. #17988809C2semidirect
5. #17988794C2semidirect
6. #17988789C2semidirect
8. #17988718C2semidirect
9. #17988685C2semidirect
10. C4×#11924018C2semidirect
11. #557×C73C2semidirect
122. C73#3400semidirect
124. #557D73semidirect