Finite Group Databasebeta

← #22620102

Subgroups — #22620102

Order 9344.

386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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
2#17988922C211yesmaximal, characteristic, complemented
3#17988905C211yesmaximal, characteristic
4#17988894C212yesmaximal, complemented
5#17988809C212yesmaximal, complemented
6#17988743C211yesmaximal, characteristic, complemented
7#17988726C211yesmaximal, characteristic
8#17988692C212yesmaximal, complemented
9#17988685C212yesmaximal, complemented
10#17988644C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2212yes—
13C2×#11924015C2212yes—
14#14556585—21no—
15#14556583C2211yescharacteristic
16#14556579C2211yescharacteristic
17#14556574—21no—
18#14556570C2211yescharacteristic
19#14556565C2211yescharacteristic
20C4×Dic146C2211yescharacteristic
21C4×D292C2211yescharacteristic
22C4×C22⋊D73—21no—
23#14556548—21no—
24#14556524C2212yes—
25#14556522C2212yes—
26C4⋊#10596831C2212yes—
27#14556515C2212yes—
28#14556515C2212yes—
29#14556514C2212yes—
30#14556511C2212yes—
31C22⋊#10596831C2211yescharacteristic
32C22⋊#10596831C2211yescharacteristic
33#14556502C2212yes—
34C22×Q8×C73C2211yescharacteristic
35C4×Q8×C73—21no—
36C4×Q8×C73—21no—
37C4×Q8×C73C2212yes—
38C4×Q8×C73C2212yes—
39C2×C4⋊C4×C73—21no—
40C2×C4⋊C4×C73C2211yescharacteristic
41C2×C42×C73—21no—
42C2×C42×C73C2211yescharacteristic
43C2×Dic146C2311yescharacteristic
44C2×D292C2311yescharacteristic
45C2×C22⋊D73—21no—
46C2×C4×D73—21no—
47#11924018—24no—
48#11924015—24no—
49C2×#10596831C2312yes—
50C2×#10596831C2312yes—
51C4⋊Dic73C2311yescharacteristic
52C4⋊Dic73C2311yescharacteristic
53#11924007—21no—
54#11924007—21no—
55#11924007—21no—
56#11924007—21no—
57C22⋊Dic73—21no—
58#11924005—21no—
59#11924005—21no—
60#11924005—21no—
61#11924005—21no—
62C4×Dic73—21no—
63C2×Q8×C73—24no—
64C2×Q8×C73—21no—
65C2×Q8×C73C2312yes—
66C22×C4×C73—21no—
67C22×C4×C73—21no—
68C22×C4×C73D411yescharacteristic
69C22×C4×C73D411yescharacteristic
70C22×C4×C73C2311yescharacteristic
71C4⋊C4×C73—22no—
72C4⋊C4×C73—22no—
73C4⋊C4×C73—21no—
74C4⋊C4×C73C2312yes—
75C42×C73—22no—
76C42×C73—22no—
77C42×C73D411yescharacteristic
78C42×C73D411yescharacteristic
79C42×C73C2311yescharacteristic
80C42×C73C2311yescharacteristic
81C23×C73C2×D411yescharacteristic
82C22×D73—21no—
83Q8×C73—24no—
84Q8×C73—22no—
85Q8×C73#4114yes—
86C2×C4×C73—24no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—41no—
92C2×C4×C73—42no—
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—42no—
100C2×Dic73—21no—
101C2×Dic73—21no—
102C2×Dic73—21no—
103D292—22no—
104C4×D73—42no—
105Dic146—22no—
106#10596831—22no—
107#10596831—22no—
108C22×C73—21no—
109C22×C73—21no—
110C22×C73#13712yes—
111C22×C73C22×D411yescharacteristic
112C2×D73—41no—
113C2×D73—41no—
114C2×D73—41no—
115C4×C73—24no—
116C4×C73—21no—
117C4×C73—21no—
118C4×C73—21no—
119C4×C73—21no—
120C4×C73—21no—
121C4×C73—42no—
122C4×C73C2×#4112yes—
123Dic73—41no—
124Dic73—41no—
125Dic73—41no—
126C2×C73—22no—
127C2×C73#52511yescharacteristic
128C2×C73C2×#13711yescharacteristic
129C2×C73#57511yescharacteristic
130D73—81no—
131#3117—731nomaximal, Sylow
132C73#311711yescharacteristic, complemented, Sylow
133#529—731no—
134C2×C4×Q8D7311yescharacteristic, complemented
135#484—731no—
136#481—731no—
137#479—732no—
138#464—732no—
139#451—731no—
140#448—731no—
141#441—732no—
142#440—732no—
143#432—731no—
144C22×Q8C2×D7311yescharacteristic
145C2×Q16—732no—
146C2×SD16—732no—
147#126—1461no—
148#125—731no—
149#124—731no—
150#123—1461no—
151C22⋊Q8—731no—
152#121—731no—
153C4×Q8—21no—
154C4×Q8—21no—
155C4×Q8—731no—
156C4×Q8C2×D7312yes—
157C4×Q8C2×D7312yes—
158C4×D4—731no—
159C4×D4—1461no—
160#117—1461no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4C2×D7311yescharacteristic
163C2×C42—21no—
164C2×C42C2×D7311yescharacteristic
165#107—732no—
166#106—732no—
167C4⋊C8—732no—
168#103—732no—
169#103—732no—
170#103—732no—
171#102—732no—
172C22⋊C8—731no—
173C22⋊C8—731no—
174#97—732no—
175C2×Q8—24no—
176C2×Q8—21no—
177C2×Q8—731no—
178C2×Q8C22×D7312yes—
179C2×D4—731no—
180C2×D4—1461no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—1461no—
184C22×C4C22⋊D7311yescharacteristic
185C22×C4C22⋊D7311yescharacteristic
186C22×C4C22×D7311yescharacteristic
187Q16—1464no—
188SD16—1464no—
189C2×C8—732no—
190C2×C8—732no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—21no—
194C4⋊C4—731no—
195C4⋊C4—731no—
196C4⋊C4—1461no—
197C4⋊C4—1461no—
198C4⋊C4—1461no—
199C4⋊C4—1461no—
200C4⋊C4C22×D7312yes—
201C22⋊C4—1461no—
202C22⋊C4—1461no—
203C22⋊C4—1461no—
204C22⋊C4—1461no—
205C22⋊C4—1461no—
206C42—22no—
207C42—22no—
208C42—1461no—
209C42C22⋊D7311yescharacteristic
210C42C22⋊D7311yescharacteristic
211C42C22×D7311yescharacteristic
212C42C22×D7311yescharacteristic
213C23—1461no—
214C23C2×C22⋊D7311yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—1462no—
218Q8#1192402814yes—
219D4—2922no—
220D4—1462no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—2922no—
229C2×C4—1461no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4C2×C22⋊D7311yescharacteristic
233C2×C4C2×C22⋊D7311yescharacteristic
234C2×C4C2×C22⋊D7311yescharacteristic
235C2×C4C2×C22⋊D7311yescharacteristic
236C2×C4C2×C22⋊D7311yescharacteristic
237C2×C4C23×D7311yescharacteristic
238C8—1462no—
239C8—1462no—
240C22—21no—
241C22—21no—
242C22—2921no—
243C22—2921no—
244C22—2921no—
245C22#1455662212yes—
246C22C22×C22⋊D7311yescharacteristic
247C4—21no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—24no—
252C4—21no—
253C4—42no—
254C4—2921no—
255C4—2921no—
256C4—2921no—
257C4C2×#1192402812yes—
258C2—22no—
259C2—5841no—
260C2#1798909811yescharacteristic
261C2C2×#1455662211yescharacteristic
262C2#1798938511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
FittingC2×C4×Q8×C73C2
socleC22×C73C22×D4
hypercenterC2×C4×Q8D73
hypocenterC73#3117
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #17988922C2semidirect
4. #17988894C2semidirect
5. #17988809C2semidirect
6. #17988743C2semidirect
8. #17988692C2semidirect
9. #17988685C2semidirect
10. #17988644C2semidirect
11. C2×C4×Q8×C73C2semidirect
132. C73#3117semidirect
134. C2×C4×Q8D73semidirect