Finite Group Databasebeta

← #22620087

Subgroups — #22620087

Order 9344.

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

normal subgroups only

This group has 386 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
1C4×#11924028C211yesmaximal, characteristic
2#17988925C212yesmaximal, complemented
3#17988879C211yesmaximal, characteristic, complemented
4#17988874C211yesmaximal, characteristic, complemented
5#17988794C211yesmaximal, characteristic, complemented
6#17988789C211yesmaximal, characteristic, complemented
7#17988747C212yesmaximal
8#17988692C212yesmaximal, complemented
9#17988685C212yesmaximal, complemented
10#17988644C211yesmaximal, characteristic, complemented
11#533×C73C211yesmaximal, characteristic, complemented
12C2×#11924028C2211yescharacteristic
13C2×#11924018C2212yes—
14C2×#11924015C2212yes—
15C4×Dic146C2211yescharacteristic
16C4×Dic146C2211yescharacteristic
17C4×D292C2211yescharacteristic
18C4×D292C2211yescharacteristic
19C4×C22⋊D73—21no—
20C4×C22⋊D73—21no—
21#14556550C2211yescharacteristic
22#14556548—21no—
23C42×D73—21no—
24#14556524C2212yes—
25#14556522C2212yes—
26C4⋊#10596831C2211yescharacteristic
27C4⋊#10596831C2211yescharacteristic
28#14556515C2212yes—
29#14556515C2212yes—
30#14556514C2212yes—
31#14556511C2212yes—
32C22⋊#10596831C2212yes—
33#14556502C2212yes—
34C4⋊Q8×C73C2211yescharacteristic
35C4⋊Q8×C73C2211yescharacteristic
36#125×C73—21no—
37C22⋊Q8×C73—21no—
38C22⋊Q8×C73C2212yes—
39C4×Q8×C73—21no—
40C4×Q8×C73C2212yes—
41#117×C73—21no—
42C2×C42×C73C2211yescharacteristic
43#11924028—22no—
44#11924028—22no—
45C2×Dic146C2311yescharacteristic
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C2×C4×D73—21no—
49C2×C4×D73—21no—
50C2×C4×D73—21no—
51#11924018—24no—
52#11924015—24no—
53C2×#10596831C2312yes—
54C2×#10596831C2312yes—
55C4⋊Dic73C2311yescharacteristic
56C4⋊Dic73C2311yescharacteristic
57#11924007—21no—
58#11924007—21no—
59C22⋊Dic73—21no—
60#11924005—21no—
61#11924005—21no—
62C4×Dic73—21no—
63C4×Dic73—21no—
64C4×Dic73—21no—
65C2×Q8×C73—21no—
66C2×Q8×C73C2312yes—
67C22×C4×C73D411yescharacteristic
68C22×C4×C73D411yescharacteristic
69C22×C4×C73C2311yescharacteristic
70C4⋊C4×C73—21no—
71C4⋊C4×C73—21no—
72C4⋊C4×C73—21no—
73C4⋊C4×C73—22no—
74C4⋊C4×C73—22no—
75C4⋊C4×C73C2312yes—
76C22⋊C4×C73—22no—
77C42×C73—22no—
78C42×C73D411yescharacteristic
79C42×C73D411yescharacteristic
80C42×C73C2311yescharacteristic
81C42×C73C2311yescharacteristic
82C23×C73C2×D411yescharacteristic
83C22×D73—21no—
84Q8×C73—22no—
85Q8×C73—22no—
86Q8×C73—42no—
87C2×C4×C73—22no—
88C2×C4×C73—21no—
89C2×C4×C73—21no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—41no—
93C2×C4×C73C2×D411yescharacteristic
94C2×C4×C73C2×D411yescharacteristic
95C2×C4×C73C2×D411yescharacteristic
96C2×C4×C73C2×D411yescharacteristic
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2411yescharacteristic
99C22⋊D73—24no—
100C2×Dic73—21no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103D292—21no—
104D292#4112yes—
105C4×D73—24no—
106C4×D73—42no—
107C4×D73—42no—
108Dic146—21no—
109Dic146#4112yes—
110#10596831—22no—
111#10596831—22no—
112C22×C73—21no—
113C22×C73—21no—
114C22×C73—21no—
115C22×C73C22×D411yescharacteristic
116C2×D73—22no—
117C2×D73—41no—
118C2×D73—41no—
119C4×C73—21no—
120C4×C73—21no—
121C4×C73—21no—
122C4×C73—21no—
123C4×C73—42no—
124C4×C73—42no—
125C4×C73#13712yes—
126C4×C73C2×#4111yescharacteristic
127C4×C73C2×#4111yescharacteristic
128Dic73—22no—
129Dic73—41no—
130Dic73—41no—
131C2×C73—41no—
132C2×C73#52511yescharacteristic
133C2×C73C2×#13711yescharacteristic
134C2×C73#57511yescharacteristic
135D73—42no—
136#3116—731nomaximal, Sylow
137C73#311611yescharacteristic, complemented, Sylow
138#533D7311yescharacteristic, complemented
139C4×#41—731no—
140#485—732no—
141#477—731no—
142#476—731no—
143#462—731no—
144#461—731no—
145#452—732no—
146#441—732no—
147#440—732no—
148#432—731no—
149C2×#41—731no—
150C2×Q16—732no—
151C2×SD16—732no—
152C4⋊Q8C2×D7311yescharacteristic
153C4⋊Q8C2×D7311yescharacteristic
154#125—21no—
155C22⋊Q8—21no—
156C22⋊Q8C2×D7312yes—
157C4×Q8—21no—
158C4×Q8—731no—
159C4×Q8—731no—
160C4×Q8C2×D7312yes—
161C4×D4—731no—
162C4×D4—731no—
163C4×D4—1461no—
164C4×D4—1461no—
165#117—21no—
166#117—731no—
167#117—1461no—
168C2×C42—1461no—
169C2×C42C2×D7311yescharacteristic
170#107—732no—
171#106—732no—
172C4⋊C8—731no—
173C4⋊C8—731no—
174#103—732no—
175#103—732no—
176#103—732no—
177#102—732no—
178C22⋊C8—732no—
179#97—732no—
180#41—1462no—
181#41—1462no—
182C2×Q8—21no—
183C2×Q8—731no—
184C2×Q8C22×D7312yes—
185C2×D4—731no—
186C2×D4—1461no—
187C22×C4—1461no—
188C22×C4—1461no—
189C22×C4—1461no—
190C22×C4C22⋊D7311yescharacteristic
191C22×C4C22⋊D7311yescharacteristic
192C22×C4C22×D7311yescharacteristic
193Q16—1464no—
194SD16—1464no—
195C2×C8—732no—
196C2×C8—732no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—731no—
203C4⋊C4—731no—
204C4⋊C4—1461no—
205C4⋊C4—1461no—
206C4⋊C4C22×D7312yes—
207C22⋊C4—22no—
208C22⋊C4—1461no—
209C22⋊C4—1461no—
210C22⋊C4—1461no—
211C42—22no—
212C42—1461no—
213C42—1461no—
214C42—1461no—
215C42C22⋊D7311yescharacteristic
216C42C22⋊D7311yescharacteristic
217C42C22×D7311yescharacteristic
218C42C22×D7311yescharacteristic
219C23—1461no—
220C23C2×C22⋊D7311yescharacteristic
221Q8—22no—
222Q8—22no—
223Q8—42no—
224Q8—732no—
225Q8—1461no—
226D4—732no—
227D4—1464no—
228D4—1461no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—2922no—
236C2×C4—2922no—
237C2×C4—1464no—
238C2×C4—1461no—
239C2×C4—1461no—
240C2×C4—1461no—
241C2×C4C2×C22⋊D7311yescharacteristic
242C2×C4C2×C22⋊D7311yescharacteristic
243C2×C4C2×C22⋊D7311yescharacteristic
244C2×C4C2×C22⋊D7311yescharacteristic
245C2×C4C2×C22⋊D7311yescharacteristic
246C2×C4C23×D7311yescharacteristic
247C8—1462no—
248C8—1462no—
249C22—21no—
250C22—21no—
251C22—21no—
252C22—2921no—
253C22—2921no—
254C22—1462no—
255C22C22×C22⋊D7311yescharacteristic
256C4—21no—
257C4—21no—
258C4—21no—
259C4—21no—
260C4—42no—
261C4—42no—
262C4—2921no—
263C4—2921no—
264C4—1462no—
265C4#1455662212yes—
266C4#41×D7311yescharacteristic
267C4#41×D7311yescharacteristic
268C2—41no—
269C2—2922no—
270C2#1798909411yescharacteristic
271C2C2×#1455662211yescharacteristic
272C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#533×C73C2
socleC22×C73C22×D4
hypercenter#533D73
hypocenterC73#3116
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #17988925C2semidirect
3. #17988879C2semidirect
4. #17988874C2semidirect
5. #17988794C2semidirect
6. #17988789C2semidirect
8. #17988692C2semidirect
9. #17988685C2semidirect
10. #17988644C2semidirect
11. #533×C73C2semidirect
137. C73#3116semidirect
138. #533D73semidirect