Finite Group Databasebeta

← #22613334

Subgroups — #22613334

Order 9344.

610 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 161 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
2C2×#14556547C211yesmaximal, characteristic, complemented
3C22×#11924007C211yesmaximal, characteristic, complemented
4#17988518C212yesmaximal, complemented
5#17988510C212yesmaximal, complemented
6#17988483C212yesmaximal, complemented
7#17988475C212yesmaximal, complemented
8#17988467C211yesmaximal, characteristic
9#17988462C211yesmaximal, characteristic, complemented
10#17988450C211yesmaximal, characteristic, complemented
11C2×#123×C73C211yesmaximal, characteristic
12C23×Dic73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14#14556572—24no—
15#14556547—24no—
16C2×C4⋊Dic73C2212yes—
17C2×#11924007—24no—
18C2×#11924007C2212yes—
19C2×#11924007C2211yescharacteristic
20C2×#11924007C2212yes—
21C2×#11924007C2212yes—
22C2×#11924007C2211yescharacteristic
23C2×C22⋊Dic73C2211yescharacteristic
24C2×C22⋊Dic73C2211yescharacteristic
25C2×C22⋊Dic73C2212yes—
26C2×C22⋊Dic73C2211yescharacteristic
27C2×C22⋊Dic73C2211yescharacteristic
28C2×C4×Dic73C2212yes—
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2212yes—
32#14556498C2212yes—
33C22×D4×C73C2211yescharacteristic
34C23×C4×C73C2211yescharacteristic
35#123×C73—24no—
36C2×C4⋊C4×C73C2212yes—
37C2×C22⋊C4×C73C2212yes—
38C2×C22⋊C4×C73C2211yescharacteristic
39C22×Dic73—22no—
40C22×Dic73—22no—
41C22×Dic73—22no—
42C22×Dic73—24no—
43C22×Dic73D414yes—
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2312yes—
50C4⋊Dic73—24no—
51#11924007—24no—
52#11924007—24no—
53#11924007—24no—
54#11924007—22no—
55#11924007—22no—
56C22⋊Dic73—22no—
57C22⋊Dic73—22no—
58C22⋊Dic73—22no—
59C22⋊Dic73—22no—
60C22⋊Dic73—24no—
61C4×Dic73—24no—
62C24×C73C2311yescharacteristic
63C24×C73C2311yescharacteristic
64C2×D4×C73—22no—
65C2×D4×C73—22no—
66C2×D4×C73—22no—
67C22×C4×C73—22no—
68C22×C4×C73—22no—
69C22×C4×C73—22no—
70C22×C4×C73C2312yes—
71C22×C4×C73C2311yescharacteristic
72C22×C4×C73C2312yes—
73C4⋊C4×C73—24no—
74C22⋊C4×C73—24no—
75C22⋊C4×C73D414yes—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73—21no—
79C23×C73—21no—
80C23×C73—21no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73C2×D412yes—
84C23×C73C2×D412yes—
85C23×C73#4112yes—
86C23×C73C2411yescharacteristic
87D4×C73—44no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73—21no—
92C2×C4×C73—22no—
93C2×C4×C73—21no—
94C2×C4×C73—22no—
95C2×C4×C73—21no—
96C2×C4×C73—44no—
97C2×C4×C73C2×D414yes—
98C2×Dic73—28no—
99C2×Dic73—28no—
100C2×Dic73—21no—
101C2×Dic73—22no—
102C2×Dic73—21no—
103C2×Dic73—22no—
104C2×Dic73—21no—
105C2×Dic73—21no—
106C2×Dic73—22no—
107C2×Dic73—21no—
108C2×Dic73—21no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73C2×D412yes—
114C2×Dic73C2×D412yes—
115C2×Dic73#4114yes—
116C22×C73—22no—
117C22×C73—22no—
118C22×C73—24no—
119C22×C73—24no—
120C22×C73—41no—
121C22×C73—41no—
122C22×C73—41no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73#12114yes—
126C22×C73C22×D411yescharacteristic
127C22×C73C22×D411yescharacteristic
128C22×C73C2×#4112yes—
129C22×C73C2×#4111yescharacteristic
130C22×C732−1+412yes—
131C4×C73—24no—
132C4×C73—42no—
133C4×C73—41no—
134Dic73—22no—
135Dic73—22no—
136Dic73—24no—
137Dic73—41no—
138Dic73—41no—
139Dic73—42no—
140C2×C73—24no—
141C2×C73—81no—
142C2×C73C2×#12111yescharacteristic
143C2×C73#52511yescharacteristic
144C2×C73#53611yescharacteristic
145C2×C73#54712yes—
146C2×C73#55212yes—
147#2413—731nomaximal, Sylow
148C73#241311yescharacteristic, complemented, Sylow
149C2×#123—731no—
150C2×#123D7311yescharacteristic
151C2×#117—731no—
152C22×C4⋊C4—731no—
153#398—732no—
154#396—732no—
155#389—732no—
156#388—732no—
157#386—731no—
158#385—731no—
159#381—731no—
160C22×D4C2×D7311yescharacteristic
161C23×C4—731no—
162C23×C4—731no—
163C23×C4C2×D7311yescharacteristic
164#123—24no—
165#123—1464no—
166#117—1464no—
167C2×C4⋊C4—732no—
168C2×C4⋊C4—732no—
169C2×C4⋊C4—732no—
170C2×C4⋊C4—731no—
171C2×C4⋊C4—731no—
172C2×C4⋊C4—732no—
173C2×C4⋊C4—1464no—
174C2×C4⋊C4C2×D7312yes—
175C2×C22⋊C4—731no—
176C2×C22⋊C4—731no—
177C2×C22⋊C4—731no—
178C2×C22⋊C4—731no—
179C2×C22⋊C4—732no—
180C2×C22⋊C4C2×D7312yes—
181C2×C22⋊C4C2×D7311yescharacteristic
182C2×C42—732no—
183#95—732no—
184#95—732no—
185#95—732no—
186#95—732no—
187C24C22×D7311yescharacteristic
188C24C22×D7311yescharacteristic
189C2×D4—22no—
190C2×D4—22no—
191C2×D4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—734no—
196C22×C4—732no—
197C22×C4—731no—
198C22×C4—731no—
199C22×C4—731no—
200C22×C4—732no—
201C22×C4—731no—
202C22×C4—1464no—
203C22×C4—1462no—
204C22×C4—1462no—
205C22×C4—1462no—
206C22×C4C22×D7312yes—
207C22×C4C22×D7311yescharacteristic
208C22×C4C22×D7312yes—
209C4⋊C4—24no—
210C4⋊C4—1464no—
211C4⋊C4—1464no—
212C4⋊C4—1462no—
213C4⋊C4—1462no—
214C4⋊C4—1464no—
215C4⋊C4—1464no—
216C22⋊C4—24no—
217C22⋊C4—1464no—
218C22⋊C4—1462no—
219C22⋊C4—1462no—
220C22⋊C4—1462no—
221C22⋊C4—1462no—
222C22⋊C4C22⋊D7314yes—
223C42—1464no—
224C23—22no—
225C23—22no—
226C23—21no—
227C23—21no—
228C23—22no—
229C23—21no—
230C23—22no—
231C23D4×D7312yes—
232C23C2×C22⋊D7312yes—
233C23#1192402712yes—
234C23C23×D7311yescharacteristic
235D4—44no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—44no—
245C2×C4—732no—
246C2×C4—732no—
247C2×C4—734no—
248C2×C4—1461no—
249C2×C4—1461no—
250C2×C4—1462no—
251C2×C4—1462no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1468no—
256C2×C4—1468no—
257C2×C4—1462no—
258C2×C4—1461no—
259C2×C4—1461no—
260C2×C4—1462no—
261C2×C4—1461no—
262C2×C4—1461no—
263C2×C4C2×C22⋊D7314yes—
264C22—22no—
265C22—24no—
266C22—24no—
267C22—22no—
268C22—41no—
269C22—42no—
270C22—42no—
271C22—41no—
272C22—41no—
273C22#1455656214yes—
274C22C2×D4×D7311yescharacteristic
275C22C22×C22⋊D7311yescharacteristic
276C22#41×D7312yes—
277C22C2×#1192402711yescharacteristic
278C22#1455663812yes—
279C4—24no—
280C4—42no—
281C4—41no—
282C4—2921no—
283C4—2922no—
284C4—2921no—
285C4—1462no—
286C4—1462no—
287C4—1464no—
288C2—24no—
289C2—81no—
290C2C2×#1455656211yescharacteristic
291C2#1798909511yescharacteristic
292C2#1798915911yescharacteristic
293C2#1798923612yes—
294C2#1798927412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#123×C73C2
hypercenterC2×#123D73
hypocenterC73#2413
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#14556547C2semidirect
3. C22×#11924007C2semidirect
4. #17988518C2semidirect
5. #17988510C2semidirect
6. #17988483C2semidirect
7. #17988475C2semidirect
9. #17988462C2semidirect
10. #17988450C2semidirect
148. C73#2413semidirect