Finite Group Databasebeta

← #22615759

Subgroups — #22615759

Order 9344.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#14556590C211yesmaximal, characteristic, complemented
2C2×#14556549C211yesmaximal, characteristic
3#17988526C211yesmaximal, characteristic, complemented
4#17988524C211yesmaximal, characteristic
5#17988522C211yesmaximal, characteristic
6#17988508C212yesmaximal, complemented
7#17988500C212yesmaximal
8#17988484C212yesmaximal, complemented
9#17988451C211yesmaximal, characteristic, complemented
10#17988446C212yesmaximal
11#400×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2212yes—
13C22×C4×D73C2211yescharacteristic
14#14556590—24no—
15#14556549—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18C2×C4⋊Dic73C2212yes—
19C2×#11924007C2212yes—
20C2×#11924007C2212yes—
21C2×#11924007C2212yes—
22C2×#11924005C2211yescharacteristic
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2212yes—
25C2×#11924005C2212yes—
26C2×C4×Dic73C2211yescharacteristic
27C2×C4×Dic73C2211yescharacteristic
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2211yescharacteristic
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2211yescharacteristic
34#95×C73C2212yes—
35#95×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×Dic146—24no—
39C2×Dic146—42no—
40C2×Dic146—42no—
41C22×Dic73C2312yes—
42C22×Dic73C2312yes—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2311yescharacteristic
46C2×C4×D73—22no—
47C2×C4×D73—22no—
48C2×C4×D73Q814yescomplemented
49C4⋊Dic73—22no—
50C4⋊Dic73—22no—
51C4⋊Dic73—42no—
52#11924007—24no—
53#11924007—24no—
54#11924007—42no—
55#11924005—22no—
56#11924005—22no—
57#11924005—42no—
58#11924005—42no—
59C4×Dic73—22no—
60C4×Dic73D414yes—
61C22×C4×C73C2312yes—
62C22×C4×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2311yescharacteristic
66C4⋊C4×C73—22no—
67C4⋊C4×C73—22no—
68C23×C73C2411yescharacteristic
69C22×D73—21no—
70C22×D73—21no—
71C22×D73—22no—
72C22×D73—22no—
73C22×D73C2×Q812yes—
74C2×C4×C73—21no—
75C2×C4×C73—21no—
76C2×C4×C73—22no—
77C2×C4×C73—21no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73C2×D412yes—
86C2×C4×C73C2×Q812yes—
87C2×Dic73—22no—
88C2×Dic73—21no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—22no—
95C2×Dic73—22no—
96C2×Dic73C2×D412yes—
97C2×Dic73C2×D412yes—
98C2×Dic73C2×Q812yes—
99C2×Dic73#4112yes—
100C4×D73—28no—
101Dic146—48no—
102C22×C73C22×D411yescharacteristic
103C22×C73C22×Q811yescharacteristic
104C22×C73C2×#4111yescharacteristic
105C22×C73H(5,𝔽2)12yes—
106C22×C732−1+412yes—
107C2×D73—22no—
108C2×D73—24no—
109C2×D73—41no—
110C2×D73—41no—
111C2×D73—42no—
112C4×C73—22no—
113C4×C73—22no—
114C4×C73—42no—
115C4×C73—41no—
116C4×C73—42no—
117Dic73—22no—
118Dic73—42no—
119Dic73—41no—
120Dic73—42no—
121Dic73C22⋊Q814yes—
122C2×C73C2×C22⋊Q811yescharacteristic
123C2×C73#53511yescharacteristic
124C2×C73#53611yescharacteristic
125C2×C73#54212yes—
126C2×C73#54412yes—
127D73—42no—
128#2628—731nomaximal, Sylow
129C73#262811yescharacteristic, complemented, Sylow
130C2×C4⋊Q8—731no—
131C2×#117—731no—
132#400—731no—
133#400D7311yescharacteristic, complemented
134#399—731no—
135#399—731no—
136#395—732no—
137#393—732no—
138#389—732no—
139#382—731no—
140#380—732no—
141C22×Q8—732no—
142C23×C4—731no—
143C4⋊Q8—1464no—
144#117—1464no—
145C2×C4⋊C4—732no—
146C2×C4⋊C4—732no—
147C2×C4⋊C4—731no—
148C2×C4⋊C4—732no—
149C2×C4⋊C4—731no—
150C2×C4⋊C4—732no—
151C2×C4⋊C4C2×D7311yescharacteristic
152C2×C4⋊C4C2×D7311yescharacteristic
153C2×C22⋊C4—732no—
154C2×C22⋊C4—732no—
155C2×C22⋊C4—731no—
156C2×C22⋊C4—731no—
157C2×C42—731no—
158C2×C42—731no—
159#95—732no—
160#95—732no—
161#95—731no—
162#95—732no—
163#95C2×D7312yes—
164#95C2×D7311yescharacteristic
165#95C2×D7312yes—
166C24—731no—
167C2×Q8—2922no—
168C2×Q8—2922no—
169C2×Q8—1464no—
170C22×C4—731no—
171C22×C4—731no—
172C22×C4—734no—
173C22×C4—732no—
174C22×C4—732no—
175C22×C4—731no—
176C22×C4—1462no—
177C22×C4—1462no—
178C22×C4C22×D7311yescharacteristic
179C22×C4C22×D7312yes—
180C22×C4C22×D7312yes—
181C22×C4C22×D7311yescharacteristic
182C22×C4C22×D7311yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—2922no—
186C4⋊C4—2922no—
187C4⋊C4—1464no—
188C4⋊C4—1464no—
189C4⋊C4—1462no—
190C4⋊C4—1462no—
191C22⋊C4—2922no—
192C22⋊C4—2922no—
193C22⋊C4—1462no—
194C22⋊C4—1462no—
195C42—734no—
196C42—1462no—
197C23—732no—
198C23—1461no—
199C23—1461no—
200C23—1462no—
201C23—1462no—
202C23C23×D7311yescharacteristic
203Q8—2928no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—732no—
216C2×C4—732no—
217C2×C4—732no—
218C2×C4—732no—
219C2×C4—1468no—
220C2×C4—1461no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4—1462no—
224C2×C4—1462no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4—1462no—
228C2×C4—1462no—
229C2×C4D4×D7312yes—
230C2×C4Q8×D7312yes—
231C22—2921no—
232C22—2921no—
233C22—2922no—
234C22—1464no—
235C22—1462no—
236C22C2×D4×D7311yescharacteristic
237C22C2×Q8×D7311yescharacteristic
238C22#41×D7311yescharacteristic
239C22#1455663712yes—
240C22#1455663812yes—
241C4—22no—
242C4—22no—
243C4—42no—
244C4—41no—
245C4—42no—
246C4—2922no—
247C4—2921no—
248C4—2922no—
249C4—734no—
250C4—1462no—
251C2—2922no—
252C2C22⋊Q8×D7311yescharacteristic
253C2#1798915511yescharacteristic
254C2#1798915911yescharacteristic
255C2#1798920312yes—
256C2#1798921712yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#400×C73C2
hypercenter#400D73
hypocenterC73#2628
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14556590C2semidirect
3. #17988526C2semidirect
6. #17988508C2semidirect
8. #17988484C2semidirect
9. #17988451C2semidirect
11. #400×C73C2semidirect
48. C2×C4×D73Q8semidirect
129. C73#2628semidirect
133. #400D73semidirect