Finite Group Databasebeta

← #22620968

Subgroups — #22620968

Order 9344.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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#17989121C211yesmaximal, characteristic, complemented
2#17988979C211yesmaximal, characteristic, complemented
3#17988974C211yesmaximal, characteristic, complemented
4#17988955C211yesmaximal, characteristic, complemented
5#17988951C211yesmaximal, characteristic, complemented
6#17988806C212yesmaximal, complemented
7#17988799C212yesmaximal, complemented
8#17988749C212yesmaximal, complemented
9#17988732C212yesmaximal, complemented
10#17988644C211yesmaximal, characteristic, complemented
11#532×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2212yes—
13C2×#11924016C2212yes—
14C2×#11924015C2212yes—
15C2×#11924013C2212yes—
16#14556585—21no—
17#14556583C2211yescharacteristic
18#14556579C2211yescharacteristic
19#14556574—21no—
20#14556570C2211yescharacteristic
21#14556565C2211yescharacteristic
22C4×Dic146C2211yescharacteristic
23C4×D292C2211yescharacteristic
24C4×C22⋊D73—21no—
25#14556548—21no—
26C4⋊#10596831C2212yes—
27#14556515C2212yes—
28#14556515C2212yes—
29#14556512C2212yes—
30#14556512C2212yes—
31C22⋊#10596831C2212yes—
32#14556502C2211yescharacteristic
33#14556502C2211yescharacteristic
34C2×#41×C73C2212yes—
35C4⋊Q8×C73C2211yescharacteristic
36#127×C73C2211yescharacteristic
37#124×C73C2212yes—
38#121×C73—21no—
39#121×C73—21no—
40C4×D4×C73—21no—
41C4×D4×C73—21no—
42C2×C42×C73C2211yescharacteristic
43C2×Dic146C2311yescharacteristic
44C2×D292C2311yescharacteristic
45C2×C22⋊D73—21no—
46C2×C4×D73—21no—
47#11924018—42no—
48#11924016—42no—
49#11924015—42no—
50#11924013—42no—
51C2×#10596831C2312yes—
52C2×#10596831C2312yes—
53C4⋊Dic73C2311yescharacteristic
54C4⋊Dic73C2311yescharacteristic
55#11924007—21no—
56#11924007—21no—
57#11924007—21no—
58#11924007—21no—
59C22⋊Dic73—21no—
60#11924005—21no—
61#11924005—21no—
62#11924005—21no—
63#11924005—21no—
64C4×Dic73—21no—
65#41×C73—42no—
66#41×C73—42no—
67C2×Q8×C73C2312yes—
68C2×D4×C73—22no—
69C2×D4×C73—21no—
70C2×D4×C73—21no—
71C2×D4×C73C2312yes—
72C22×C4×C73—22no—
73C22×C4×C73D411yescharacteristic
74C22×C4×C73D411yescharacteristic
75C22×C4×C73C2311yescharacteristic
76C4⋊C4×C73—21no—
77C4⋊C4×C73—21no—
78C22⋊C4×C73—22no—
79C22⋊C4×C73—22no—
80C42×C73D411yescharacteristic
81C42×C73D411yescharacteristic
82C42×C73C2311yescharacteristic
83C42×C73C2311yescharacteristic
84C23×C73—22no—
85C23×C73C2×D411yescharacteristic
86C22×D73—21no—
87Q8×C73—22no—
88Q8×C73—22no—
89D4×C73—22no—
90D4×C73—22no—
91D4×C73—42no—
92D4×C73—42no—
93D4×C73—44no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—41no—
97C2×C4×C73—41no—
98C2×C4×C73—44no—
99C2×C4×C73C2×D411yescharacteristic
100C2×C4×C73C2×D411yescharacteristic
101C2×C4×C73C2×D411yescharacteristic
102C2×C4×C73C2×D411yescharacteristic
103C2×C4×C73C2×D411yescharacteristic
104C2×C4×C73C2411yescharacteristic
105C22⋊D73—42no—
106C2×Dic73—21no—
107C2×Dic73—21no—
108C2×Dic73—21no—
109D292—22no—
110C4×D73—42no—
111Dic146—22no—
112#10596831—22no—
113#10596831—22no—
114C22×C73—21no—
115C22×C73—21no—
116C22×C73—21no—
117C22×C73—42no—
118C22×C73—42no—
119C22×C73—42no—
120C22×C73C22×D411yescharacteristic
121C2×D73—41no—
122C2×D73—41no—
123C2×D73—41no—
124C4×C73—21no—
125C4×C73—21no—
126C4×C73—21no—
127C4×C73—21no—
128C4×C73—21no—
129C4×C73—42no—
130C4×C73H(5,𝔽2)12yes—
131Dic73—41no—
132Dic73—41no—
133Dic73—41no—
134C2×C73—41no—
135C2×C73—82no—
136C2×C73#53511yescharacteristic
137C2×C73#57511yescharacteristic
138C2×C73#57511yescharacteristic
139D73—81no—
140#3219—731nomaximal, Sylow
141C73#321911yescharacteristic, complemented, Sylow
142#532D7311yescharacteristic, complemented
143#529—731no—
144#497—731no—
145#496—731no—
146#491—731no—
147#490—731no—
148#464—732no—
149#463—732no—
150#452—732no—
151#449—732no—
152#432—731no—
153C2×#41C2×D7312yes—
154C2×Q16—732no—
155C2×SD16—732no—
156C2×SD16—732no—
157C2×D8—732no—
158C4⋊Q8C2×D7311yescharacteristic
159#127C2×D7311yescharacteristic
160#126—1461no—
161#125—731no—
162#124—731no—
163#124C2×D7312yes—
164#123—1461no—
165C22⋊Q8—731no—
166#121—21no—
167#121—21no—
168#121—731no—
169C4×Q8—731no—
170C4×D4—21no—
171C4×D4—21no—
172C4×D4—731no—
173C4×D4—1461no—
174#117—1461no—
175C2×C42C2×D7311yescharacteristic
176C4⋊C8—732no—
177#103—732no—
178#103—732no—
179#102—732no—
180#102—732no—
181C22⋊C8—732no—
182#97—731no—
183#97—731no—
184#41—42no—
185#41—42no—
186C2×Q8—731no—
187C2×Q8C22×D7312yes—
188C2×D4—22no—
189C2×D4—21no—
190C2×D4—21no—
191C2×D4—731no—
192C2×D4—1461no—
193C2×D4C22×D7312yes—
194C22×C4—22no—
195C22×C4—1461no—
196C22×C4C22⋊D7311yescharacteristic
197C22×C4C22⋊D7311yescharacteristic
198C22×C4C22×D7311yescharacteristic
199Q16—2922no—
200SD16—2922no—
201SD16—2922no—
202D8—2922no—
203C2×C8—732no—
204C2×C8—732no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—731no—
208C4⋊C4—731no—
209C4⋊C4—1461no—
210C4⋊C4—1461no—
211C4⋊C4—1461no—
212C4⋊C4—1461no—
213C22⋊C4—22no—
214C22⋊C4—22no—
215C22⋊C4—1461no—
216C22⋊C4—1461no—
217C22⋊C4—1461no—
218C22⋊C4—1461no—
219C22⋊C4—1461no—
220C42—1461no—
221C42C22⋊D7311yescharacteristic
222C42C22⋊D7311yescharacteristic
223C42C22×D7311yescharacteristic
224C42C22×D7311yescharacteristic
225C23—22no—
226C23—1461no—
227C23C2×C22⋊D7311yescharacteristic
228Q8—22no—
229Q8—22no—
230Q8—1462no—
231D4—22no—
232D4—22no—
233D4—42no—
234D4—42no—
235D4—44no—
236D4—2922no—
237D4—1462no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—44no—
243C2×C4—2922no—
244C2×C4—1461no—
245C2×C4—1461no—
246C2×C4—1461no—
247C2×C4C2×C22⋊D7311yescharacteristic
248C2×C4C2×C22⋊D7311yescharacteristic
249C2×C4C2×C22⋊D7311yescharacteristic
250C2×C4C2×C22⋊D7311yescharacteristic
251C2×C4C2×C22⋊D7311yescharacteristic
252C2×C4C23×D7311yescharacteristic
253C8—1462no—
254C8—1462no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—2921no—
262C22—2921no—
263C22—2921no—
264C22C22×C22⋊D7311yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—2921no—
272C4—2921no—
273C4—2921no—
274C4#1455663612yes—
275C2—41no—
276C2—82no—
277C2—5841no—
278C2#1798915411yescharacteristic
279C2#1798938511yescharacteristic
280C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#532×C73C2
socleC22×C73C22×D4
hypercenter#532D73
hypocenterC73#3219
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #17989121C2semidirect
2. #17988979C2semidirect
3. #17988974C2semidirect
4. #17988955C2semidirect
5. #17988951C2semidirect
6. #17988806C2semidirect
7. #17988799C2semidirect
8. #17988749C2semidirect
9. #17988732C2semidirect
10. #17988644C2semidirect
11. #532×C73C2semidirect
141. C73#3219semidirect
142. #532D73semidirect