Finite Group Databasebeta

← #22621098

Subgroups — #22621098

Order 9344.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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#17989118C211yesmaximal, characteristic
2C2×#14556582C211yesmaximal, characteristic, complemented
3#17988987C212yesmaximal, complemented
4#17988940C212yesmaximal, complemented
5#17988922C211yesmaximal, characteristic, complemented
6#17988918C211yesmaximal, characteristic, complemented
7#17988898C211yesmaximal, characteristic
8#17988897C212yesmaximal, complemented
9#17988889C212yesmaximal, complemented
10#17988637C211yesmaximal, characteristic, complemented
11#481×C73C211yesmaximal, characteristic
12#14556584—21no—
13#14556582—21no—
14#14556582—21no—
15#14556582C2212yes—
16#14556582C2212yes—
17#14556582C2211yescharacteristic
18#14556578C2211yescharacteristic
19#14556572—21no—
20#14556570C2211yescharacteristic
21#14556556C2211yescharacteristic
22D4×Dic73—21no—
23D4×Dic73C2211yescharacteristic
24#14556547—21no—
25C2×C4⋊Dic73—21no—
26C2×C4⋊Dic73C2211yescharacteristic
27C2×#11924007—21no—
28C2×C4×Dic73C2211yescharacteristic
29#14556524C2212yes—
30#14556524C2212yes—
31#14556523C2212yes—
32#14556520C2212yes—
33#14556516C2212yes—
34#14556514C2212yes—
35#14556512C2212yes—
36C22⋊#10596831C2211yescharacteristic
37C8×Dic73C2212yes—
38#121×C73C2211yescharacteristic
39C2×C4⋊C4×C73C2211yescharacteristic
40#106×C73C2212yes—
41#102×C73C2212yes—
42C22⋊C8×C73C2211yescharacteristic
43C2×Dic146C2311yescharacteristic
44C22×Dic73—21no—
45C22×Dic73—21no—
46C22×Dic73D411yescharacteristic
47C22×Dic73D411yescharacteristic
48C2×#10596831C2312yes—
49C4⋊Dic73—21no—
50C4⋊Dic73—22no—
51C4⋊Dic73—22no—
52C4⋊Dic73—21no—
53C4⋊Dic73C2312yes—
54C4⋊Dic73C2311yescharacteristic
55#11924007—21no—
56#11924007—22no—
57#11924007—22no—
58#11924007—21no—
59#11924007—21no—
60C22⋊Dic73—21no—
61C22⋊Dic73—21no—
62C22⋊Dic73—21no—
63C22⋊Dic73—21no—
64C4×Dic73—21no—
65C4×Dic73D411yescharacteristic
66C4×Dic73D411yescharacteristic
67C4×Dic73C2311yescharacteristic
68C4×Dic73C2311yescharacteristic
69C2×D4×C73—21no—
70C2×D4×C73C2311yescharacteristic
71C22×C4×C73—21no—
72C22×C4×C73C2311yescharacteristic
73C2×C8×C73C2312yes—
74C4⋊C4×C73—21no—
75C4⋊C4×C73C2312yes—
76C4⋊C4×C73C2311yescharacteristic
77C22⋊C4×C73—21no—
78C23×C73—21no—
79C23×C73C2×D411yescharacteristic
80D4×C73—22no—
81D4×C73—42no—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—42no—
86C2×C4×C73C2×D411yescharacteristic
87C2×C4×C73C2411yescharacteristic
88C2×Dic73—22no—
89C2×Dic73—21no—
90C2×Dic73—21no—
91C2×Dic73—22no—
92C2×Dic73—41no—
93C2×Dic73—42no—
94C2×Dic73—42no—
95C2×Dic73C2×D411yescharacteristic
96C2×Dic73C2×D411yescharacteristic
97C2×Dic73C2×D411yescharacteristic
98C2×Dic73C2×D411yescharacteristic
99Dic146—22no—
100C8×C73—22no—
101#10596831—22no—
102C22×C73—21no—
103C22×C73—21no—
104C22×C73—41no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73#13512yes—
108C22×C73C22×D411yescharacteristic
109C4×C73—21no—
110C4×C73—41no—
111C4×C73—42no—
112C4×C732−1+412yes—
113Dic73—21no—
114Dic73—21no—
115Dic73—21no—
116Dic73—21no—
117Dic73—41no—
118Dic73—42no—
119Dic73—41no—
120C2×C73—22no—
121C2×C73—81no—
122C2×C73#53611yescharacteristic
123C2×C73C2×#13511yescharacteristic
124C2×C73#57511yescharacteristic
125#3232—731nomaximal, Sylow
126C73#323211yescharacteristic, complemented, Sylow
127#529—731no—
128C2×#125—731no—
129#499—732no—
130#488—732no—
131#484—731no—
132#483—731no—
133#481D7311yescharacteristic
134#480—731no—
135#479—732no—
136#478—732no—
137#431—731no—
138#126—1461no—
139#125—732no—
140#125—732no—
141#125—731no—
142#125—1461no—
143#125—1461no—
144#124—731no—
145#123—1461no—
146C22⋊Q8—731no—
147#121C2×D7311yescharacteristic
148C4×Q8—731no—
149C4×D4—731no—
150C4×D4—1461no—
151#117—1461no—
152C2×C4⋊C4—731no—
153C2×C4⋊C4—1461no—
154C2×C4⋊C4—1461no—
155C2×C4⋊C4C2×D7311yescharacteristic
156C2×C42—731no—
157#107—732no—
158#107—732no—
159#106—732no—
160#106C2×D7312yes—
161C4⋊C8—732no—
162#103—732no—
163#103—732no—
164#102—732no—
165#102C2×D7312yes—
166C22⋊C8—731no—
167C22⋊C8C2×D7311yescharacteristic
168C4×C8—732no—
169C2×Q8—731no—
170C2×D4—21no—
171C2×D4C22×D7311yescharacteristic
172C22×C4—21no—
173C22×C4—731no—
174C22×C4—731no—
175C22×C4—1461no—
176C22×C4—1461no—
177C22×C4C22×D7311yescharacteristic
178C2×C8—732no—
179C2×C8C22×D7312yes—
180C4⋊C4—21no—
181C4⋊C4—732no—
182C4⋊C4—731no—
183C4⋊C4—1462no—
184C4⋊C4—1462no—
185C4⋊C4—1461no—
186C4⋊C4—1461no—
187C4⋊C4—1462no—
188C4⋊C4—1462no—
189C4⋊C4—1461no—
190C4⋊C4—1461no—
191C4⋊C4—1461no—
192C4⋊C4C22×D7312yes—
193C4⋊C4C22×D7311yescharacteristic
194C22⋊C4—21no—
195C22⋊C4—1461no—
196C22⋊C4—1461no—
197C22⋊C4—1461no—
198C22⋊C4—1461no—
199C42—731no—
200C42—731no—
201C42—731no—
202C42—731no—
203C42—1461no—
204C23—21no—
205C23D4×D7311yescharacteristic
206Q8—1462no—
207D4—22no—
208D4—42no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—42no—
213C2×C4—2922no—
214C2×C4—2922no—
215C2×C4—2921no—
216C2×C4—731no—
217C2×C4—731no—
218C2×C4—731no—
219C2×C4—731no—
220C2×C4—1461no—
221C2×C4—1461no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4D4×D7311yescharacteristic
225C2×C4C23×D7311yescharacteristic
226C8—22no—
227C8—1462no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22#1455661212yes—
234C22C2×D4×D7311yescharacteristic
235C4—21no—
236C4—42no—
237C4—41no—
238C4—2921no—
239C4—2921no—
240C4—2922no—
241C4—1461no—
242C4—1461no—
243C4—1461no—
244C4—1461no—
245C4#1455663812yes—
246C2—22no—
247C2—81no—
248C2#1798915911yescharacteristic
249C2C2×#1455661211yescharacteristic
250C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#481×C73C2
socleC22×C73C22×D4
hypercenter#481D73
hypocenterC73#3232
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#14556582C2semidirect
3. #17988987C2semidirect
4. #17988940C2semidirect
5. #17988922C2semidirect
6. #17988918C2semidirect
8. #17988897C2semidirect
9. #17988889C2semidirect
10. #17988637C2semidirect
126. C73#3232semidirect