Finite Group Databasebeta

← #22615717

Subgroups — #22615717

Order 9344.

526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14556575C211yesmaximal, characteristic
2C22×#11924007C211yesmaximal, characteristic, complemented
3#17988529C212yesmaximal, complemented
4#17988522C212yesmaximal, complemented
5#17988520C212yesmaximal, complemented
6#17988516C212yesmaximal, complemented
7#17988466C211yesmaximal, characteristic
8#17988464C211yesmaximal, characteristic
9#17988459C211yesmaximal, characteristic, complemented
10#17988448C211yesmaximal, characteristic, complemented
11#385×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14C23×Dic73C2211yescharacteristic
15#14556575—24no—
16C2×C4⋊Dic73C2211yescharacteristic
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007—24no—
19C2×#11924007C2212yes—
20C2×#11924007C2212yes—
21C2×#11924007C2212yes—
22C2×C22⋊Dic73C2211yescharacteristic
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C23×C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2211yescharacteristic
36#95×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—22no—
39C2×C22⋊D73—22no—
40C2×C22⋊D73—22no—
41C22×Dic73—22no—
42C22×Dic73—22no—
43C22×Dic73—22no—
44C22×Dic73—42no—
45C22×Dic73D414yes—
46C22×Dic73C2312yes—
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2312yes—
49C22×Dic73C2311yescharacteristic
50C22×Dic73C2311yescharacteristic
51C4⋊Dic73—22no—
52C4⋊Dic73—22no—
53#11924007—24no—
54#11924007—24no—
55#11924007—42no—
56C22⋊Dic73—22no—
57#11924005—22no—
58#11924005—22no—
59#11924005—42no—
60#11924005—42no—
61C24×C73C2311yescharacteristic
62C22×C4×C73—22no—
63C22×C4×C73—42no—
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2312yes—
66C22×C4×C73C2312yes—
67C22×C4×C73C2311yescharacteristic
68C4⋊C4×C73—42no—
69C22⋊C4×C73—22no—
70C22⋊C4×C73—22no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73C2×D412yes—
74C23×C73#4112yes—
75C23×C73#4112yes—
76C23×C73C2411yescharacteristic
77C22×D73—21no—
78C22×D73—21no—
79C22×D73—21no—
80C22×D73—22no—
81C22×D73—22no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—44no—
93C22⋊D73—44no—
94C2×Dic73—28no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—22no—
100C2×Dic73—21no—
101C2×Dic73—22no—
102C2×Dic73—21no—
103C2×Dic73—21no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—44no—
109C2×Dic73C2×D412yes—
110C2×Dic73C2×D412yes—
111C22×C73—22no—
112C22×C73—22no—
113C22×C73—24no—
114C22×C73—24no—
115C22×C73#12314yes—
116C22×C73C22×D411yescharacteristic
117C22×C73C2×#4111yescharacteristic
118C22×C73C2×#4111yescharacteristic
119C22×C73H(5,𝔽2)12yes—
120C22×C732−1+412yes—
121C2×D73—41no—
122C2×D73—41no—
123C2×D73—41no—
124C2×D73—42no—
125C2×D73—42no—
126C4×C73—41no—
127C4×C73—42no—
128C4×C73—41no—
129C4×C73—42no—
130Dic73—22no—
131Dic73—22no—
132Dic73—41no—
133Dic73—42no—
134Dic73—42no—
135C2×C73—24no—
136C2×C73C2×#12311yescharacteristic
137C2×C73#53511yescharacteristic
138C2×C73#53611yescharacteristic
139C2×C73#53912yes—
140C2×C73#53912yes—
141D73—81no—
142#2623—731nomaximal, Sylow
143C73#262311yescharacteristic, complemented, Sylow
144C2×#123—731no—
145C22×C4⋊C4—731no—
146#400—732no—
147#399—732no—
148#398—732no—
149#397—732no—
150#386—731no—
151#386—731no—
152#385—731no—
153#385D7311yescharacteristic, complemented
154#381—731no—
155C22×D4—731no—
156C23×C4—731no—
157C23×C4—731no—
158C23×C4C2×D7311yescharacteristic
159#123—1464no—
160C2×C4⋊C4—732no—
161C2×C4⋊C4—732no—
162C2×C4⋊C4—732no—
163C2×C4⋊C4—731no—
164C2×C4⋊C4—731no—
165C2×C4⋊C4—1464no—
166C2×C4⋊C4C2×D7312yes—
167C2×C22⋊C4—732no—
168C2×C22⋊C4—732no—
169C2×C22⋊C4—731no—
170C2×C22⋊C4—731no—
171C2×C22⋊C4—731no—
172C2×C22⋊C4C2×D7311yescharacteristic
173C2×C22⋊C4C2×D7311yescharacteristic
174#95—732no—
175#95—732no—
176#95—732no—
177#95—732no—
178#95—732no—
179#95C2×D7312yes—
180C24—731no—
181C24C22×D7311yescharacteristic
182C2×D4—1462no—
183C2×D4—1462no—
184C2×D4—1462no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—2922no—
188C22×C4—734no—
189C22×C4—731no—
190C22×C4—731no—
191C22×C4—732no—
192C22×C4—731no—
193C22×C4—732no—
194C22×C4—1462no—
195C22×C4—1462no—
196C22×C4—1462no—
197C22×C4C22×D7312yes—
198C22×C4C22×D7311yescharacteristic
199C22×C4C22×D7312yes—
200C22×C4C22×D7311yescharacteristic
201C4⋊C4—42no—
202C4⋊C4—2922no—
203C4⋊C4—1464no—
204C4⋊C4—1464no—
205C4⋊C4—1462no—
206C4⋊C4—1462no—
207C22⋊C4—22no—
208C22⋊C4—22no—
209C22⋊C4—2922no—
210C22⋊C4—2922no—
211C22⋊C4—1462no—
212C22⋊C4—1462no—
213C22⋊C4—1462no—
214C23—22no—
215C23—22no—
216C23—1461no—
217C23—1461no—
218C23—1461no—
219C23—1462no—
220C23—1462no—
221C23D4×D7312yes—
222C23#1192402812yes—
223C23#1192402912yes—
224C23C23×D7311yescharacteristic
225D4—2924no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—44no—
237C2×C4—2924no—
238C2×C4—732no—
239C2×C4—732no—
240C2×C4—1462no—
241C2×C4—1461no—
242C2×C4—1461no—
243C2×C4—1462no—
244C2×C4—1461no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4—1462no—
248C2×C4—1462no—
249C2×C4—1468no—
250C2×C4—1461no—
251C2×C4—1461no—
252C2×C4—1461no—
253C2×C4—1461no—
254C22—22no—
255C22—22no—
256C22—24no—
257C22—24no—
258C22—2921no—
259C22—2921no—
260C22—2922no—
261C22—2922no—
262C22—2921no—
263C22#1455657614yes—
264C22C2×D4×D7311yescharacteristic
265C22C2×#1192402811yescharacteristic
266C22C2×#1192402911yescharacteristic
267C22#1455663612yes—
268C22#1455663812yes—
269C4—42no—
270C4—41no—
271C4—41no—
272C4—42no—
273C4—2922no—
274C4—2922no—
275C4—2921no—
276C4—1462no—
277C4—1462no—
278C2—24no—
279C2—5841no—
280C2C2×#1455657611yescharacteristic
281C2#1798915211yescharacteristic
282C2#1798915911yescharacteristic
283C2#1798917912yes—
284C2#1798918612yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#385×C73C2
hypercenter#385D73
hypocenterC73#2623
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C22×#11924007C2semidirect
3. #17988529C2semidirect
4. #17988522C2semidirect
5. #17988520C2semidirect
6. #17988516C2semidirect
9. #17988459C2semidirect
10. #17988448C2semidirect
11. #385×C73C2semidirect
143. C73#2623semidirect
153. #385D73semidirect