Finite Group Databasebeta

← #22621287

Subgroups — #22621287

Order 9344.

392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 121 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#17988887C212yesmaximal, complemented
3#17988869C211yesmaximal, characteristic, complemented
4#17988864C211yesmaximal, characteristic, complemented
5#17988838C212yesmaximal, complemented
6#17988831C212yesmaximal, complemented
7#17988802C212yesmaximal, complemented
8#17988784C211yesmaximal, characteristic, complemented
9#17988779C211yesmaximal, characteristic, complemented
10#17988611C211yesmaximal, characteristic, complemented
11#532×C73C211yesmaximal, characteristic, complemented
12C2×#11924016C2212yes—
13C2×#11924013C2212yes—
14C2×#11924012C2212yes—
15#14556585—21no—
16#14556583C2211yescharacteristic
17#14556579C2211yescharacteristic
18#14556574—21no—
19#14556570C2211yescharacteristic
20#14556565C2211yescharacteristic
21C4×Dic146C2211yescharacteristic
22C4×D292C2211yescharacteristic
23C4×C22⋊D73—21no—
24#14556548—21no—
25#14556524C2212yes—
26#14556522C2212yes—
27C4⋊#10596831C2211yescharacteristic
28C4⋊#10596831C2211yescharacteristic
29C4⋊#10596831C2212yes—
30#14556514C2212yes—
31#14556512C2212yes—
32#14556512C2212yes—
33#14556511C2212yes—
34C2×#41×C73—21no—
35C4⋊Q8×C73C2211yescharacteristic
36#127×C73C2211yescharacteristic
37#124×C73—21no—
38#121×C73—21no—
39#121×C73C2212yes—
40C4×D4×C73—21no—
41C4×D4×C73C2212yes—
42C2×C42×C73C2211yescharacteristic
43C2×Dic146C2311yescharacteristic
44C2×D292C2311yescharacteristic
45C2×C22⋊D73—21no—
46C2×C4×D73—21no—
47#11924016—42no—
48#11924013—42no—
49#11924012—42no—
50C2×#10596831C2312yes—
51C2×#10596831C2312yes—
52C4⋊Dic73C2311yescharacteristic
53C4⋊Dic73C2311yescharacteristic
54#11924007—21no—
55#11924007—21no—
56#11924007—21no—
57#11924007—21no—
58C22⋊Dic73—21no—
59#11924005—21no—
60#11924005—21no—
61#11924005—21no—
62#11924005—21no—
63C4×Dic73—21no—
64#41×C73—44no—
65C2×Q8×C73—21no—
66C2×D4×C73—22no—
67C2×D4×C73—21no—
68C2×D4×C73—21no—
69C2×D4×C73C2312yes—
70C22×C4×C73—22no—
71C22×C4×C73D411yescharacteristic
72C22×C4×C73D411yescharacteristic
73C22×C4×C73C2311yescharacteristic
74C4⋊C4×C73—21no—
75C4⋊C4×C73C2312yes—
76C22⋊C4×C73—22no—
77C22⋊C4×C73—22no—
78C42×C73D411yescharacteristic
79C42×C73D411yescharacteristic
80C42×C73C2311yescharacteristic
81C42×C73C2311yescharacteristic
82C23×C73—22no—
83C23×C73C2×D411yescharacteristic
84C22×D73—21no—
85Q8×C73—42no—
86D4×C73—22no—
87D4×C73—22no—
88D4×C73—42no—
89D4×C73—44no—
90D4×C73—42no—
91C2×C4×C73—22no—
92C2×C4×C73—21no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—41no—
96C2×C4×C73—44no—
97C2×C4×C73C2×D411yescharacteristic
98C2×C4×C73C2×D411yescharacteristic
99C2×C4×C73C2×D411yescharacteristic
100C2×C4×C73C2×D411yescharacteristic
101C2×C4×C73C2×D411yescharacteristic
102C2×C4×C73C2411yescharacteristic
103C22⋊D73—42no—
104C2×Dic73—21no—
105C2×Dic73—21no—
106C2×Dic73—21no—
107D292—21no—
108D292—21no—
109C4×D73—42no—
110Dic146—21no—
111Dic146—21no—
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—42no—
129C4×C73AGL(1,ℤ/8)12yes—
130C4×C73H(5,𝔽2)11yescharacteristic
131C4×C732−1+411yescharacteristic
132Dic73—41no—
133Dic73—41no—
134Dic73—41no—
135C2×C73—41no—
136C2×C73—82no—
137C2×C73#53711yescharacteristic
138C2×C73C2×AGL(1,ℤ/8)11yescharacteristic
139C2×C73#57511yescharacteristic
140D73—81no—
141#3251—731nomaximal, Sylow
142C73#325111yescharacteristic, complemented, Sylow
143#532D7311yescharacteristic, complemented
144#529—731no—
145#478—732no—
146#475—731no—
147#474—731no—
148#469—732no—
149#468—732no—
150#463—732no—
151#460—731no—
152#459—731no—
153#423—731no—
154C2×#41—21no—
155C2×SD16—732no—
156C2×D8—732no—
157C2×M16—732no—
158C4⋊Q8C2×D7311yescharacteristic
159#127C2×D7311yescharacteristic
160#126—1461no—
161#125—731no—
162#124—21no—
163#124—731no—
164#123—1461no—
165C22⋊Q8—731no—
166#121—21no—
167#121—731no—
168#121C2×D7312yes—
169C4×Q8—731no—
170C4×D4—21no—
171C4×D4—731no—
172C4×D4—1461no—
173C4×D4C2×D7312yes—
174#117—1461no—
175C2×C42C2×D7311yescharacteristic
176#107—732no—
177#106—732no—
178C4⋊C8—731no—
179C4⋊C8—731no—
180C4⋊C8—732no—
181#103—732no—
182#102—732no—
183#102—732no—
184#102—732no—
185#41—44no—
186C2×Q8—21no—
187C2×Q8—731no—
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
199SD16—2922no—
200D8—2922no—
201M16—2922no—
202C2×C8—732no—
203C2×C8—732no—
204C4⋊C4—21no—
205C4⋊C4—731no—
206C4⋊C4—731no—
207C4⋊C4—1461no—
208C4⋊C4—1461no—
209C4⋊C4—1461no—
210C4⋊C4—1461no—
211C4⋊C4C22×D7312yes—
212C22⋊C4—22no—
213C22⋊C4—22no—
214C22⋊C4—1461no—
215C22⋊C4—1461no—
216C22⋊C4—1461no—
217C22⋊C4—1461no—
218C22⋊C4—1461no—
219C42—1461no—
220C42C22⋊D7311yescharacteristic
221C42C22⋊D7311yescharacteristic
222C42C22×D7311yescharacteristic
223C42C22×D7311yescharacteristic
224C23—22no—
225C23—1461no—
226C23C2×C22⋊D7311yescharacteristic
227Q8—42no—
228Q8—1461no—
229Q8—1461no—
230D4—22no—
231D4—22no—
232D4—42no—
233D4—44no—
234D4—42no—
235D4—2922no—
236D4—1461no—
237D4—1461no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—44no—
244C2×C4—2922no—
245C2×C4—1461no—
246C2×C4—1461no—
247C2×C4—1461no—
248C2×C4C2×C22⋊D7311yescharacteristic
249C2×C4C2×C22⋊D7311yescharacteristic
250C2×C4C2×C22⋊D7311yescharacteristic
251C2×C4C2×C22⋊D7311yescharacteristic
252C2×C4C2×C22⋊D7311yescharacteristic
253C2×C4C23×D7311yescharacteristic
254C8—1462no—
255C8—1462no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—2921no—
263C22—2921no—
264C22—2921no—
265C22C22×C22⋊D7311yescharacteristic
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—42no—
271C4—2921no—
272C4—2921no—
273C4—2921no—
274C4#1455661712yes—
275C4#1455663711yescharacteristic
276C4#1455663811yescharacteristic
277C2—41no—
278C2—82no—
279C2—5841no—
280C2#1798916511yescharacteristic
281C2C2×#1455661711yescharacteristic
282C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#532×C73C2
socleC22×C73C22×D4
hypercenter#532D73
hypocenterC73#3251
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. #17988887C2semidirect
3. #17988869C2semidirect
4. #17988864C2semidirect
5. #17988838C2semidirect
6. #17988831C2semidirect
7. #17988802C2semidirect
8. #17988784C2semidirect
9. #17988779C2semidirect
10. #17988611C2semidirect
11. #532×C73C2semidirect
142. C73#3251semidirect
143. #532D73semidirect