Finite Group Databasebeta

← #22622660

Subgroups — #22622660

Order 9344.

382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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#17989259C211yesmaximal, characteristic
2#17988953C212yesmaximal, complemented
3#17988935C211yesmaximal, characteristic, complemented
4#17988884C212yesmaximal, complemented
5#17988864C211yesmaximal, characteristic, complemented
6#17988787C211yesmaximal, characteristic, complemented
7#17988787C212yesmaximal, complemented
8#17988718C211yesmaximal, characteristic, complemented
9#17988685C212yesmaximal, complemented
10C4×#11924015C211yesmaximal, characteristic, complemented
11#557×C73C211yesmaximal, characteristic, complemented
12C2×#11924029—21no—
13C2×#11924015C2211yescharacteristic
14C2×#11924015C2212yes—
15#14556588C2211yescharacteristic
16#14556588C2212yes—
17#14556566—21no—
18#14556566—22no—
19C4×D292C2211yescharacteristic
20C4×D292C2212yes—
21#14556524C2212yes—
22#14556522C2211yescharacteristic
23C4⋊#10596831C2211yescharacteristic
24C4⋊#10596831C2212yes—
25#14556515C2211yescharacteristic
26#14556511C2212yes—
27#14556511C2212yes—
28#14556511C2212yes—
29#14556511C2211yescharacteristic
30#14556511C2212yes—
31#14556502C2212yes—
32C4×#10596831C2211yescharacteristic
33C4⋊Q8×C73—21no—
34C4⋊Q8×C73C2211yescharacteristic
35#125×C73—22no—
36#125×C73C2212yes—
37C4×Q8×C73—21no—
38C4×Q8×C73C2211yescharacteristic
39C4×Q8×C73C2212yes—
40C4×Q8×C73C2211yescharacteristic
41#11924029—44no—
42C2×D292—22no—
43C2×D292—21no—
44C2×D292—22no—
45C2×D292—21no—
46C2×D292C2311yescharacteristic
47C2×D292C2312yes—
48C2×C4×D73—22no—
49C2×C4×D73—21no—
50#11924015—22no—
51#11924015—24no—
52C2×#10596831C2311yescharacteristic
53C2×#10596831C2311yescharacteristic
54C2×#10596831C2312yes—
55C4⋊Dic73C2311yescharacteristic
56#11924005—22no—
57#11924005—21no—
58C2×Q8×C73—21no—
59C2×Q8×C73D411yescharacteristic
60C2×Q8×C73C2311yescharacteristic
61C4⋊C4×C73—22no—
62C4⋊C4×C73—21no—
63C4⋊C4×C73—22no—
64C4⋊C4×C73—21no—
65C4⋊C4×C73—22no—
66C4⋊C4×C73D411yescharacteristic
67C4⋊C4×C73D412yes—
68C4⋊C4×C73C2311yescharacteristic
69C4⋊C4×C73C2312yes—
70C42×C73—22no—
71C42×C73—21no—
72C42×C73C2312yes—
73C42×C73C2311yescharacteristic
74C22×D73—22no—
75C22×D73—21no—
76Q8×C73—22no—
77Q8×C73—21no—
78Q8×C73—42no—
79Q8×C73#4112yescomplemented
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—22no—
83C2×C4×C73C2×D412yes—
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D412yes—
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2411yescharacteristic
88C2×Dic73—21no—
89D292—21no—
90D292—22no—
91D292—21no—
92D292—22no—
93D292—44no—
94D292—42no—
95D292—82no—
96D292—81no—
97C4×D73—44no—
98C4×D73—42no—
99#10596831—21no—
100#10596831—22no—
101#10596831—21no—
102C22×C73C22×D411yescharacteristic
103C2×D73—42no—
104C2×D73—41no—
105C2×D73—42no—
106C2×D73—41no—
107C2×D73—42no—
108C2×D73—41no—
109C4×C73—22no—
110C4×C73—22no—
111C4×C73—22no—
112C4×C73—21no—
113C4×C73—42no—
114C4×C73—41no—
115C4×C73AGL(1,ℤ/8)12yes—
116C4×C73C2×#4111yescharacteristic
117C4×C732−1+411yescharacteristic
118Dic73—41no—
119C2×C73#54811yescharacteristic
120C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C73#57711yescharacteristic
122D73—82no—
123D73—81no—
124#3368—731nomaximal, Sylow
125C73#336811yescharacteristic, complemented, Sylow
126#557D7311yescharacteristic, complemented
127#550—731no—
128#490—732no—
129#486—731no—
130#478—732no—
131#474—731no—
132#460—732no—
133#460—731no—
134#446—731no—
135#440—732no—
136C4×SD16—731no—
137C2×#41—1461no—
138C2×SD16—731no—
139C2×SD16—732no—
140C4⋊Q8—21no—
141C4⋊Q8C2×D7311yescharacteristic
142#127—731no—
143#127—732no—
144#125—22no—
145#125C2×D7312yes—
146#121—1461no—
147#121—1462no—
148C4×Q8—21no—
149C4×Q8C2×D7311yescharacteristic
150C4×Q8C2×D7312yes—
151C4×Q8C2×D7311yescharacteristic
152C4×D4—731no—
153C4×D4—732no—
154#107—732no—
155#106—731no—
156C4⋊C8—731no—
157C4⋊C8—732no—
158#103—731no—
159#102—731no—
160#102—732no—
161#102—732no—
162#102—732no—
163#102—732no—
164#97—732no—
165C4×C8—731no—
166#41—2924no—
167C2×Q8—21no—
168C2×Q8C22⋊D7311yescharacteristic
169C2×Q8C22×D7311yescharacteristic
170C2×D4—731no—
171C2×D4—732no—
172C2×D4—1462no—
173C2×D4—1461no—
174C2×D4—1462no—
175C2×D4—1461no—
176C22×C4—1462no—
177C22×C4—1461no—
178SD16—1462no—
179SD16—1464no—
180C2×C8—731no—
181C2×C8—731no—
182C2×C8—732no—
183C4⋊C4—22no—
184C4⋊C4—21no—
185C4⋊C4—22no—
186C4⋊C4—21no—
187C4⋊C4—22no—
188C4⋊C4—731no—
189C4⋊C4C22⋊D7311yescharacteristic
190C4⋊C4C22⋊D7312yes—
191C4⋊C4C22×D7311yescharacteristic
192C4⋊C4C22×D7312yes—
193C22⋊C4—1462no—
194C22⋊C4—1461no—
195C42—22no—
196C42—21no—
197C42C22×D7311yescharacteristic
198C42C22×D7312yes—
199C23—1462no—
200C23—1461no—
201Q8—22no—
202Q8—21no—
203Q8—42no—
204Q8#1192402912yescomplemented
205D4—2924no—
206D4—2922no—
207D4—5842no—
208D4—5841no—
209D4—1461no—
210D4—1462no—
211D4—1461no—
212D4—1462no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—2924no—
217C2×C4—2922no—
218C2×C4—1461no—
219C2×C4C2×C22⋊D7312yes—
220C2×C4C2×C22⋊D7311yescharacteristic
221C2×C4C2×C22⋊D7312yes—
222C2×C4C2×C22⋊D7311yescharacteristic
223C2×C4C23×D7311yescharacteristic
224C8—1461no—
225C8—1462no—
226C8—1461no—
227C22—2922no—
228C22—2921no—
229C22—2922no—
230C22—2921no—
231C22—2922no—
232C22—2921no—
233C22C22×C22⋊D7311yescharacteristic
234C4—22no—
235C4—21no—
236C4—22no—
237C4—22no—
238C4—41no—
239C4—42no—
240C4—2921no—
241C4#1455661612yes—
242C4C2×#1192402911yescharacteristic
243C4#1455663911yescharacteristic
244C2—5842no—
245C2—5841no—
246C2#1798924811yescharacteristic
247C2C2×#1455661611yescharacteristic
248C2#1798939511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#557×C73C2
socleC22×C73C22×D4
hypercenter#557D73
hypocenterC73#3368
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. #17988953C2semidirect
3. #17988935C2semidirect
4. #17988884C2semidirect
5. #17988864C2semidirect
6. #17988787C2semidirect
7. #17988787C2semidirect
8. #17988718C2semidirect
9. #17988685C2semidirect
10. C4×#11924015C2semidirect
11. #557×C73C2semidirect
79. Q8×C73#41semidirect
125. C73#3368semidirect
126. #557D73semidirect
204. Q8#11924029semidirect