Finite Group Databasebeta

← #22615715

Subgroups — #22615715

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×#14556572C211yesmaximal, characteristic
2C22×#11924007C211yesmaximal, characteristic, complemented
3#17988528C212yesmaximal, complemented
4#17988523C212yesmaximal, complemented
5#17988521C212yesmaximal, complemented
6#17988515C212yesmaximal, complemented
7#17988467C211yesmaximal, characteristic
8#17988462C211yesmaximal, characteristic, complemented
9#17988460C211yesmaximal, characteristic, complemented
10#17988448C211yesmaximal, characteristic, complemented
11#386×C73C211yesmaximal, characteristic
12C23×Dic73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14#14556572—24no—
15C2×C4⋊Dic73C2212yes—
16C2×#11924007—24no—
17C2×#11924007C2212yes—
18C2×#11924007C2211yescharacteristic
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2212yes—
22C2×C22⋊Dic73C2211yescharacteristic
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2211yescharacteristic
26C2×C22⋊Dic73C2212yes—
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32C22×D4×C73C2211yescharacteristic
33C23×C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2212yes—
37C22×Dic73—22no—
38C22×Dic73—22no—
39C22×Dic73—22no—
40C22×Dic73—42no—
41C22×Dic73D414yes—
42C22×Dic73C2311yescharacteristic
43C22×Dic73C2312yes—
44C22×Dic73C2312yes—
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C4⋊Dic73—42no—
49#11924007—24no—
50#11924007—24no—
51#11924007—22no—
52#11924007—22no—
53#11924007—42no—
54C22⋊Dic73—22no—
55C22⋊Dic73—22no—
56C22⋊Dic73—22no—
57C22⋊Dic73—22no—
58C22⋊Dic73—42no—
59C24×C73C2311yescharacteristic
60C24×C73C2311yescharacteristic
61C2×D4×C73—22no—
62C2×D4×C73—22no—
63C2×D4×C73—22no—
64C22×C4×C73—22no—
65C22×C4×C73—42no—
66C22×C4×C73C2311yescharacteristic
67C22×C4×C73C2312yes—
68C22×C4×C73C2312yes—
69C22⋊C4×C73—22no—
70C22⋊C4×C73—42no—
71C23×C73—22no—
72C23×C73—22no—
73C23×C73—21no—
74C23×C73—21no—
75C23×C73—21no—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73C2×D412yes—
79C23×C73#4112yes—
80C23×C73#4112yes—
81C23×C73C2411yescharacteristic
82D4×C73—44no—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
85C2×C4×C73—22no—
86C2×C4×C73—21no—
87C2×C4×C73—21no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—44no—
93C2×Dic73—28no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—21no—
97C2×Dic73—21no—
98C2×Dic73—21no—
99C2×Dic73—21no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
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—41no—
116C22×C73—41no—
117C22×C73—41no—
118C22×C73—42no—
119C22×C73—42no—
120C22×C73#12314yes—
121C22×C73C22×D411yescharacteristic
122C22×C73C2×#4111yescharacteristic
123C22×C73C2×#4111yescharacteristic
124C22×C73H(5,𝔽2)12yes—
125C22×C732−1+412yes—
126C4×C73—41no—
127C4×C73—42no—
128C4×C73—42no—
129Dic73—22no—
130Dic73—22no—
131Dic73—41no—
132Dic73—42no—
133Dic73—41no—
134Dic73—42no—
135C2×C73—24no—
136C2×C73—81no—
137C2×C73C2×#12311yescharacteristic
138C2×C73#53511yescharacteristic
139C2×C73#53611yescharacteristic
140C2×C73#53912yes—
141C2×C73#53912yes—
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#386D7311yescharacteristic
152#385—731no—
153#385—731no—
154#381—731no—
155C22×D4C2×D7311yescharacteristic
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—732no—
164C2×C4⋊C4—731no—
165C2×C4⋊C4—731no—
166C2×C4⋊C4—1464no—
167C2×C22⋊C4—732no—
168C2×C22⋊C4—731no—
169C2×C22⋊C4—731no—
170C2×C22⋊C4—731no—
171C2×C22⋊C4—731no—
172C2×C22⋊C4C2×D7311yescharacteristic
173C2×C22⋊C4C2×D7312yes—
174#95—732no—
175#95—732no—
176#95—732no—
177#95—732no—
178#95—732no—
179#95C2×D7312yes—
180C24C22×D7311yescharacteristic
181C24C22×D7311yescharacteristic
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—22no—
185C22×C4—22no—
186C22×C4—42no—
187C22×C4—2922no—
188C22×C4—734no—
189C22×C4—731no—
190C22×C4—731no—
191C22×C4—731no—
192C22×C4—732no—
193C22×C4—732no—
194C22×C4—731no—
195C22×C4—1462no—
196C22×C4—1462no—
197C22×C4—1462no—
198C22×C4C22×D7312yes—
199C22×C4C22×D7311yescharacteristic
200C22×C4C22×D7312yes—
201C4⋊C4—2922no—
202C4⋊C4—2922no—
203C4⋊C4—1464no—
204C4⋊C4—1464no—
205C4⋊C4—1462no—
206C4⋊C4—1462no—
207C22⋊C4—22no—
208C22⋊C4—42no—
209C22⋊C4—2922no—
210C22⋊C4—1462no—
211C22⋊C4—1462no—
212C22⋊C4—1462no—
213C22⋊C4—1462no—
214C23—22no—
215C23—22no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—22no—
220C23—22no—
221C23D4×D7312yes—
222C23#1192402712yes—
223C23#1192402812yes—
224C23C23×D7311yescharacteristic
225D4—44no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—44no—
236C2×C4—2924no—
237C2×C4—732no—
238C2×C4—732no—
239C2×C4—1461no—
240C2×C4—1461no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4—1462no—
244C2×C4—1462no—
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—41no—
259C22—41no—
260C22—42no—
261C22—42no—
262C22—41no—
263C22#1455657314yes—
264C22C2×D4×D7311yescharacteristic
265C22C2×#1192402711yescharacteristic
266C22C2×#1192402811yescharacteristic
267C22#1455663612yes—
268C22#1455663812yes—
269C4—42no—
270C4—42no—
271C4—41no—
272C4—2922no—
273C4—2921no—
274C4—2921no—
275C4—2922no—
276C4—1462no—
277C4—1462no—
278C2—24no—
279C2—81no—
280C2C2×#1455657311yescharacteristic
281C2#1798915211yescharacteristic
282C2#1798915911yescharacteristic
283C2#1798917912yes—
284C2#1798918212yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#386×C73C2
hypercenter#386D73
hypocenterC73#2623
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C22×#11924007C2semidirect
3. #17988528C2semidirect
4. #17988523C2semidirect
5. #17988521C2semidirect
6. #17988515C2semidirect
8. #17988462C2semidirect
9. #17988460C2semidirect
10. #17988448C2semidirect
143. C73#2623semidirect