Finite Group Databasebeta

← #22614397

Subgroups — #22614397

Order 9344.

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

normal subgroups only

This group has 708 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×#14556576C212yesmaximal, complemented
2C2×#14556573C212yesmaximal, complemented
3C2×#14556564C211yesmaximal, characteristic
4C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
5#17988524C211yesmaximal, characteristic, complemented
6#17988523C211yesmaximal, characteristic, complemented
7#17988522C211yesmaximal, characteristic, complemented
8#17988487C212yesmaximal, complemented
9#17988456C212yesmaximal, complemented
10#17988434C211yesmaximal, characteristic, complemented
11#399×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×C22⋊D73C2211yescharacteristic
14C22×C22⋊D73C2211yescharacteristic
15C22×C4×D73C2212yes—
16C22×C4×D73C2211yescharacteristic
17#14556576—28no—
18#14556573—28no—
19#14556564—24no—
20C2×C4⋊Dic73C2212yes—
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2212yes—
24C2×#11924007C2212yes—
25C2×#11924007C2212yes—
26C4⋊C4×D73—24no—
27C2×C22⋊Dic73C2212yes—
28C2×#11924005C2212yes—
29C2×#11924005C2212yes—
30C2×#11924005C2211yescharacteristic
31C2×#11924005C2212yes—
32C2×C4×Dic73C2212yes—
33#14556498C2211yescharacteristic
34C2×C4⋊C4×C73C2212yes—
35C2×C4⋊C4×C73C2211yescharacteristic
36C2×C22⋊C4×C73C2212yes—
37C2×C22⋊C4×C73C2211yescharacteristic
38#95×C73C2211yescharacteristic
39C23×D73C2311yescharacteristic
40C23×D73C2311yescharacteristic
41C2×D292—22no—
42C2×D292—24no—
43C2×C22⋊D73—22no—
44C2×C22⋊D73—24no—
45C2×C22⋊D73—22no—
46C2×C22⋊D73—24no—
47C22×Dic73C2312yes—
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2312yes—
50C22×Dic73C2311yescharacteristic
51C2×C4×D73—24no—
52C2×C4×D73—24no—
53C2×C4×D73—24no—
54C2×C4×D73—24no—
55C2×C4×D73D414yes—
56C4⋊Dic73—22no—
57C4⋊Dic73—24no—
58#11924007—24no—
59#11924007—22no—
60#11924007—24no—
61#11924007—24no—
62C22⋊Dic73—24no—
63#11924005—22no—
64#11924005—24no—
65#11924005—24no—
66#11924005D418yescomplemented
67C4×Dic73—24no—
68C24×C73C2311yescharacteristic
69C22×C4×C73C2312yes—
70C22×C4×C73C2311yescharacteristic
71C22×C4×C73C2311yescharacteristic
72C22×C4×C73C2312yes—
73C4⋊C4×C73—22no—
74C4⋊C4×C73—24no—
75C22⋊C4×C73—22no—
76C22⋊C4×C73—24no—
77C23×C73—22no—
78C23×C73—21no—
79C23×C73—22no—
80C23×C73—21no—
81C23×C73—21no—
82C23×C73C2411yescharacteristic
83C22×D73—22no—
84C22×D73—21no—
85C22×D73—21no—
86C22×D73—22no—
87C22×D73—21no—
88C22×D73—22no—
89C22×D73—21no—
90C22×D73—21no—
91C22×D73C2×D414yes—
92C22×D73C2×D412yes—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—21no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73C2×D414yes—
102C2×C4×C73C2×D412yes—
103C22⋊D73—44no—
104C22⋊D73—44no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—21no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73C2×D414yes—
113C2×Dic73C2×D412yes—
114C2×Dic73#4114yes—
115D292—44no—
116C4×D73—28no—
117C4×D73—48no—
118C22×C73—41no—
119C22×C73—41no—
120C22×C73—41no—
121C22×C73—42no—
122C22×C73—42no—
123C22×C73C22×D411yescharacteristic
124C22×C73C22×D412yes—
125C22×C73C2×#4112yes—
126C22×C732−1+411yescharacteristic
127C22×C732−1+411yescharacteristic
128C2×D73—22no—
129C2×D73—22no—
130C2×D73—24no—
131C2×D73—24no—
132C2×D73—41no—
133C2×D73—41no—
134C2×D73—41no—
135C2×D73—42no—
136C2×D73—42no—
137C2×D73#12714yes—
138C4×C73—22no—
139C4×C73—24no—
140C4×C73—42no—
141C4×C73—41no—
142Dic73—24no—
143Dic73—42no—
144Dic73—41no—
145Dic73#12314yescomplemented
146C2×C73—81no—
147C2×C73C2×#12311yescharacteristic
148C2×C73C2×#12711yescharacteristic
149C2×C73#53611yescharacteristic
150C2×C73#54712yes—
151C2×C73#54712yes—
152D73—24no—
153D73—81no—
154#2501—731nomaximal, Sylow
155C73#250111yescharacteristic, complemented, Sylow
156C2×#123—732no—
157C2×#123—732no—
158C2×#121—731no—
159C22×C4⋊C4—731no—
160#399—731no—
161#399—731no—
162#399—731no—
163#399D7311yescharacteristic, complemented
164#390—732no—
165#384—732no—
166C4×C22⋊C4—731no—
167C22×D4—731no—
168C22×D4—731no—
169C22×D4—731no—
170C23×C4—731no—
171C23×C4—732no—
172#123—1468no—
173#123—1468no—
174#121—1464no—
175C2×C4⋊C4—732no—
176C2×C4⋊C4—731no—
177C2×C4⋊C4—731no—
178C2×C4⋊C4—732no—
179C2×C4⋊C4—732no—
180C2×C4⋊C4—732no—
181C2×C4⋊C4—1464no—
182C2×C4⋊C4C2×D7311yescharacteristic
183C2×C4⋊C4C2×D7312yes—
184C2×C22⋊C4—732no—
185C2×C22⋊C4—732no—
186C2×C22⋊C4—731no—
187C2×C22⋊C4—732no—
188C2×C22⋊C4—732no—
189C2×C22⋊C4C2×D7311yescharacteristic
190C2×C22⋊C4C2×D7312yes—
191C2×C42—732no—
192#95—731no—
193#95C2×D7311yescharacteristic
194C24—731no—
195C24—731no—
196C24C22×D7311yescharacteristic
197C2×D4—1462no—
198C2×D4—1464no—
199C2×D4—1462no—
200C2×D4—1464no—
201C2×D4—1462no—
202C2×D4—1464no—
203C22×C4—731no—
204C22×C4—732no—
205C22×C4—734no—
206C22×C4—732no—
207C22×C4—731no—
208C22×C4—1464no—
209C22×C4—1464no—
210C22×C4—1464no—
211C22×C4—1464no—
212C22×C4C22×D7312yes—
213C22×C4C22×D7311yescharacteristic
214C22×C4C22×D7311yescharacteristic
215C22×C4C22×D7312yes—
216C4⋊C4—22no—
217C4⋊C4—24no—
218C4⋊C4—1464no—
219C4⋊C4—1462no—
220C4⋊C4—1464no—
221C4⋊C4—1464no—
222C4⋊C4—1462no—
223C4⋊C4—1464no—
224C22⋊C4—22no—
225C22⋊C4—24no—
226C22⋊C4—738no—
227C22⋊C4—1464no—
228C22⋊C4—1464no—
229C22⋊C4—1462no—
230C22⋊C4—1464no—
231C42—1464no—
232C23—22no—
233C23—21no—
234C23—22no—
235C23—21no—
236C23—21no—
237C23—734no—
238C23—732no—
239C23—1462no—
240C23—1461no—
241C23—1462no—
242C23—1461no—
243C23—1461no—
244C23—1462no—
245C23—1461no—
246C23—1461no—
247C23C23×D7311yescharacteristic
248D4—2924no—
249D4—2924no—
250D4—2924no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—2928no—
260C2×C4—732no—
261C2×C4—734no—
262C2×C4—734no—
263C2×C4—1468no—
264C2×C4—1462no—
265C2×C4—1462no—
266C2×C4—1461no—
267C2×C4—1462no—
268C2×C4—1462no—
269C2×C4—1462no—
270C2×C4—1462no—
271C2×C4D4×D7314yes—
272C2×C4D4×D7312yes—
273C22—41no—
274C22—41no—
275C22—42no—
276C22—42no—
277C22—41no—
278C22—2921no—
279C22—2921no—
280C22—2922no—
281C22—2922no—
282C22—2921no—
283C22—734no—
284C22—1462no—
285C22—1464no—
286C22—1464no—
287C22—1462no—
288C22C2×D4×D7311yescharacteristic
289C22C2×D4×D7312yes—
290C22#41×D7312yes—
291C22#1455663811yescharacteristic
292C22#1455663911yescharacteristic
293C4—24no—
294C4—22no—
295C4—42no—
296C4—41no—
297C4—2922no—
298C4—2921no—
299C4—734no—
300C4—1464no—
301C2—81no—
302C2—5841no—
303C2—1464no—
304C2#123×D7311yescharacteristic
305C2#127×D7311yescharacteristic
306C2#1798916011yescharacteristic
307C2#1798923512yes—
308C2#1798923912yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2501
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14556576C2semidirect
2. C2×#14556573C2semidirect
4. C2×C4⋊C4×D73C2semidirect
5. #17988524C2semidirect
6. #17988523C2semidirect
7. #17988522C2semidirect
8. #17988487C2semidirect
9. #17988456C2semidirect
10. #17988434C2semidirect
11. #399×C73C2semidirect
66. #11924005D4semidirect
145. Dic73#123semidirect
155. C73#2501semidirect
163. #399D73semidirect