Finite Group Databasebeta

← #22621173

Subgroups — #22621173

Order 9344.

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

normal subgroups only

This group has 328 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#17989144C211yesmaximal, characteristic, complemented
2#17989121C211yesmaximal, characteristic
3#17988996C211yesmaximal, characteristic, complemented
4#17988996C211yesmaximal, characteristic, complemented
5#17988947C211yesmaximal, characteristic, complemented
6#17988947C211yesmaximal, characteristic, complemented
7#17988929C212yesmaximal, complemented
8#17988912C212yesmaximal
9#17988895C212yesmaximal, complemented
10#17988888C212yesmaximal, complemented
11#432×C73C211yesmaximal, characteristic, complemented
12#14556591C2211yescharacteristic
13#14556591C2211yescharacteristic
14#14556585—21no—
15#14556583C2211yescharacteristic
16#14556583C2212yes—
17#14556579C2211yescharacteristic
18#14556574—21no—
19#14556570—21no—
20#14556570—21no—
21#14556570C2211yescharacteristic
22#14556565C2211yescharacteristic
23C4×Dic146—21no—
24C4×Dic146—21no—
25C4×Dic146C2211yescharacteristic
26C4×D292C2211yescharacteristic
27C4×C22⋊D73—21no—
28#14556550C2212yes—
29#14556548—21no—
30#14556525C2212yes—
31#14556525C2212yes—
32#14556523C2212yes—
33#14556523C2212yes—
34#14556516C2212yes—
35#14556516C2212yes—
36#14556513C2212yes—
37#14556513C2212yes—
38C2×C42×C73C2211yescharacteristic
39C4⋊C8×C73C2212yes—
40C22⋊C8×C73C2212yes—
41#97×C73C2211yescharacteristic
42#97×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146—21no—
45C2×Dic146C2311yescharacteristic
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C2×C4×D73—21no—
49C4⋊Dic73—21no—
50C4⋊Dic73—21no—
51C4⋊Dic73C2312yes—
52C4⋊Dic73C2312yes—
53C4⋊Dic73C2311yescharacteristic
54C4⋊Dic73C2311yescharacteristic
55#11924007—21no—
56#11924007—21no—
57#11924007—21no—
58#11924007—22no—
59#11924007—22no—
60#11924007—21no—
61C22⋊Dic73—22no—
62C22⋊Dic73—21no—
63#11924005—21no—
64#11924005—21no—
65#11924005—21no—
66#11924005—21no—
67C4×Dic73—21no—
68C4×Dic73—22no—
69C22×C4×C73D411yescharacteristic
70C22×C4×C73D411yescharacteristic
71C22×C4×C73C2311yescharacteristic
72C2×C8×C73C2312yes—
73C2×C8×C73C2312yes—
74C42×C73D411yescharacteristic
75C42×C73D411yescharacteristic
76C42×C73C2311yescharacteristic
77C42×C73C2311yescharacteristic
78C23×C73C2×D411yescharacteristic
79C22×D73—21no—
80C2×C4×C73—22no—
81C2×C4×C73—41no—
82C2×C4×C73—41no—
83C2×C4×C73C2×D411yescharacteristic
84C2×C4×C73C2×D411yescharacteristic
85C2×C4×C73C2×D411yescharacteristic
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2411yescharacteristic
89C22⋊D73—42no—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—21no—
95D292—22no—
96C4×D73—42no—
97Dic146—22no—
98Dic146—42no—
99Dic146—42no—
100C8×C73—22no—
101C8×C73—22no—
102C22×C73—21no—
103C22×C73—21no—
104C22×C73—21no—
105C22×C73C22×D411yescharacteristic
106C2×D73—41no—
107C2×D73—41no—
108C2×D73—41no—
109C4×C73—21no—
110C4×C73—21no—
111C4×C73—21no—
112C4×C73—21no—
113C4×C73—21no—
114C4×C732−1+412yes—
115Dic73—41no—
116Dic73—42no—
117Dic73—42no—
118Dic73—41no—
119Dic73—41no—
120C2×C73—41no—
121C2×C73#53611yescharacteristic
122C2×C73#57511yescharacteristic
123C2×C73#57511yescharacteristic
124D73—81no—
125#3240—731nomaximal, Sylow
126C73#324011yescharacteristic, complemented, Sylow
127#533—731no—
128#529—731no—
129#501—731no—
130#501—731no—
131#489—731no—
132#489—731no—
133#485—732no—
134#482—732no—
135#479—732no—
136#478—732no—
137#432D7311yescharacteristic, complemented
138C4⋊Q8—731no—
139C4⋊Q8—731no—
140#126—1461no—
141#125—731no—
142#125—732no—
143#124—731no—
144#123—1461no—
145C22⋊Q8—731no—
146C22⋊Q8—1461no—
147C22⋊Q8—1461no—
148#121—731no—
149C4×Q8—731no—
150C4×Q8—1461no—
151C4×Q8—1461no—
152C4×D4—731no—
153C4×D4—1461no—
154#117—732no—
155#117—1461no—
156C2×C42C2×D7311yescharacteristic
157#107—732no—
158#107—732no—
159#106—732no—
160#106—732no—
161C4⋊C8C2×D7312yes—
162#103—732no—
163#103—732no—
164#102—732no—
165#102—732no—
166C22⋊C8C2×D7312yes—
167#97C2×D7311yescharacteristic
168#97C2×D7311yescharacteristic
169C2×Q8—731no—
170C2×Q8—1461no—
171C2×Q8—1461no—
172C2×D4—731no—
173C2×D4—1461no—
174C22×C4—1461no—
175C22×C4D29211yescharacteristic
176C22×C4D29211yescharacteristic
177C22×C4C22×D7311yescharacteristic
178C2×C8C22×D7312yes—
179C2×C8C22×D7312yes—
180C4⋊C4—732no—
181C4⋊C4—732no—
182C4⋊C4—731no—
183C4⋊C4—731no—
184C4⋊C4—1461no—
185C4⋊C4—1461no—
186C4⋊C4—1461no—
187C4⋊C4—1461no—
188C4⋊C4—1462no—
189C4⋊C4—1462no—
190C4⋊C4—1461no—
191C4⋊C4—1461no—
192C22⋊C4—1462no—
193C22⋊C4—1461no—
194C22⋊C4—1461no—
195C22⋊C4—1461no—
196C22⋊C4—1461no—
197C22⋊C4—1461no—
198C42—1462no—
199C42—1461no—
200C42D29211yescharacteristic
201C42D29211yescharacteristic
202C42C22×D7311yescharacteristic
203C42C22×D7311yescharacteristic
204C23—1461no—
205C23C2×D29211yescharacteristic
206Q8—2922no—
207Q8—2922no—
208Q8—1462no—
209D4—2922no—
210D4—1462no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—2922no—
215C2×C4—1461no—
216C2×C4—1461no—
217C2×C4—1462no—
218C2×C4—1462no—
219C2×C4—1461no—
220C2×C4C2×D29211yescharacteristic
221C2×C4C2×D29211yescharacteristic
222C2×C4C2×D29211yescharacteristic
223C2×C4C2×D29211yescharacteristic
224C2×C4C2×D29211yescharacteristic
225C2×C4C23×D7311yescharacteristic
226C8—22no—
227C8—22no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—2921no—
232C22—2921no—
233C22—2921no—
234C22C22×D29211yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—21no—
240C4—2921no—
241C4—2921no—
242C4—2922no—
243C4—2922no—
244C4—2921no—
245C4#1455663812yes—
246C2—41no—
247C2—5841no—
248C2#1798916311yescharacteristic
249C2#1798938711yescharacteristic
250C2#1798938711yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#432×C73C2
socleC22×C73C22×D4
hypercenter#432D73
hypocenterC73#3240
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #17989144C2semidirect
3. #17988996C2semidirect
4. #17988996C2semidirect
5. #17988947C2semidirect
6. #17988947C2semidirect
7. #17988929C2semidirect
9. #17988895C2semidirect
10. #17988888C2semidirect
11. #432×C73C2semidirect
126. C73#3240semidirect
137. #432D73semidirect