Finite Group Databasebeta

← #22613267

Subgroups — #22613267

Order 9344.

864 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 159 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
1C22×#11924029C211yesmaximal, characteristic
2C2×#14556576C212yesmaximal, complemented
3C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
4#17988506C211yesmaximal, characteristic, complemented
5#17988505C211yesmaximal, characteristic, complemented
6#17988504C211yesmaximal, characteristic, complemented
7#17988465C212yesmaximal, complemented
8#17988461C212yesmaximal, complemented
9#17988458C212yesmaximal, complemented
10#17988449C211yesmaximal, characteristic, complemented
11#395×C73C211yesmaximal, characteristic, complemented
12C2×#11924029—28no—
13C2×#11924029—24no—
14C22×D292C2211yescharacteristic
15C22×D292C2212yes—
16C22×C4×D73C2212yes—
17C22×C4×D73C2211yescharacteristic
18C22×C4×D73C2211yescharacteristic
19C22×C4×D73C2211yescharacteristic
20#14556576—28no—
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2211yescharacteristic
23C2×#11924007C2212yes—
24C2×#11924007C2211yescharacteristic
25C4⋊C4×D73—24no—
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×#11924005C2212yes—
29C2×#11924005C2212yes—
30C2×#11924005C2212yes—
31#14556498C2212yes—
32#14556498C2211yescharacteristic
33#14556498C2212yes—
34C22×Q8×C73C2211yescharacteristic
35C2×C4⋊C4×C73C2212yes—
36C2×C4⋊C4×C73C2211yescharacteristic
37#95×C73C2211yescharacteristic
38#95×C73C2212yes—
39C23×D73C2312yes—
40C23×D73C2311yescharacteristic
41#11924029—232no—
42C2×D292—24no—
43C2×D292—24no—
44C2×D292—24no—
45C2×D292—22no—
46C2×D292D418yes—
47C22×Dic73C2312yes—
48C22×Dic73C2311yescharacteristic
49C22×Dic73C2311yescharacteristic
50C22×Dic73C2311yescharacteristic
51C2×C4×D73—22no—
52C2×C4×D73—24no—
53C2×C4×D73—24no—
54C2×C4×D73—24no—
55C2×C4×D73—22no—
56C2×C4×D73—24no—
57C2×C4×D73—22no—
58C2×C4×D73—22no—
59C2×C4×D73—24no—
60C2×C4×D73D414yes—
61C4⋊Dic73—22no—
62#11924007—22no—
63#11924007—24no—
64#11924007—22no—
65#11924005—24no—
66#11924005—24no—
67#11924005—24no—
68#11924005—24no—
69#11924005—24no—
70C2×Q8×C73—24no—
71C2×Q8×C73—22no—
72C22×C4×C73C2312yes—
73C22×C4×C73C2311yescharacteristic
74C22×C4×C73C2312yes—
75C22×C4×C73C2311yescharacteristic
76C22×C4×C73C2311yescharacteristic
77C4⋊C4×C73—22no—
78C4⋊C4×C73—24no—
79C23×C73C2411yescharacteristic
80C22×D73—21no—
81C22×D73—21no—
82C22×D73—22no—
83C22×D73—22no—
84C22×D73—22no—
85C22×D73—22no—
86C22×D73—22no—
87C22×D73—22no—
88C22×D73—22no—
89C22×D73C2×D414yes—
90C22×D73C2×D414yes—
91C22×D73C2×D412yes—
92Q8×C73—28no—
93C2×C4×C73—21no—
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—21no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C2×C4×C73C2×D414yes—
104C2×C4×C73C2×D412yes—
105C2×C4×C73#4112yescomplemented
106C2×Dic73—21no—
107C2×Dic73—22no—
108C2×Dic73—21no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—21no—
112C2×Dic73—22no—
113C2×Dic73—22no—
114C2×Dic73C2×D412yes—
115C2×Dic73#4112yescomplemented
116D292—28no—
117D292—216no—
118C4×D73—28no—
119C4×D73—216no—
120C4×D73—28no—
121C4×D73—44no—
122C22×C73C22×D411yescharacteristic
123C22×C73C22×D412yes—
124C22×C73C2×#4111yescharacteristic
125C22×C73C2×#4111yescharacteristic
126C22×C732−1+412yes—
127C2×D73—22no—
128C2×D73—22no—
129C2×D73—24no—
130C2×D73—24no—
131C2×D73—24no—
132C2×D73—24no—
133C2×D73—24no—
134C2×D73—42no—
135C2×D73—42no—
136C2×D73—42no—
137C2×D73—42no—
138C2×D73#12014yes—
139C4×C73—24no—
140C4×C73—22no—
141C4×C73—22no—
142C4×C73—41no—
143C4×C73—42no—
144Dic73—22no—
145Dic73—22no—
146Dic73—41no—
147Dic73—42no—
148C2×C73C2×#12011yescharacteristic
149C2×C73#52511yescharacteristic
150C2×C73#53611yescharacteristic
151C2×C73#54712yes—
152C2×C73#54712yes—
153D73—24no—
154D73—44no—
155#2406—731nomaximal, Sylow
156C73#240611yescharacteristic, complemented, Sylow
157C22×#41—731no—
158C2×#123—732no—
159C22×C4⋊C4—731no—
160#395—731no—
161#395D7311yescharacteristic, complemented
162#394—731no—
163#394—731no—
164#386—732no—
165#385—732no—
166#385—732no—
167#381—731no—
168C2×#41—1464no—
169C2×#41—1468no—
170C22×Q8C2×D7311yescharacteristic
171C22×D4—732no—
172C22×D4—731no—
173C23×C4—731no—
174C23×C4—731no—
175C23×C4—731no—
176C23×C4—732no—
177#123—1468no—
178C2×C4⋊C4—731no—
179C2×C4⋊C4—731no—
180C2×C4⋊C4—731no—
181C2×C4⋊C4—732no—
182C2×C4⋊C4—1464no—
183C2×C4⋊C4C2×D7311yescharacteristic
184C2×C4⋊C4C2×D7312yes—
185C2×C22⋊C4—732no—
186C2×C22⋊C4—732no—
187C2×C22⋊C4—732no—
188C2×C22⋊C4—732no—
189C2×C22⋊C4—732no—
190#95—732no—
191#95—731no—
192#95—732no—
193#95C2×D7311yescharacteristic
194#95C2×D7312yes—
195C24—731no—
196C24—732no—
197#41—14632no—
198C2×Q8—22no—
199C2×Q8—24no—
200C2×D4—738no—
201C2×D4—1464no—
202C2×D4—1464no—
203C2×D4—1464no—
204C2×D4—1462no—
205C22×C4—731no—
206C22×C4—731no—
207C22×C4—734no—
208C22×C4—732no—
209C22×C4—731no—
210C22×C4—1462no—
211C22×C4—1464no—
212C22×C4—1462no—
213C22×C4—1464no—
214C22×C4—1462no—
215C22×C4—1464no—
216C22×C4—1464no—
217C22×C4—1464no—
218C22×C4—1462no—
219C22×C4C22×D7312yes—
220C22×C4C22×D7311yescharacteristic
221C22×C4C22×D7311yescharacteristic
222C22×C4C22×D7312yes—
223C22×C4C22×D7311yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—24no—
226C4⋊C4—1462no—
227C4⋊C4—1462no—
228C4⋊C4—1462no—
229C4⋊C4—1464no—
230C22⋊C4—1464no—
231C22⋊C4—1464no—
232C22⋊C4—1464no—
233C22⋊C4—1464no—
234C22⋊C4—1464no—
235C23—734no—
236C23—732no—
237C23—734no—
238C23—1462no—
239C23—1462no—
240C23—1462no—
241C23—1462no—
242C23—1462no—
243C23—1462no—
244C23—1461no—
245C23—1461no—
246C23—1462no—
247C23C23×D7311yescharacteristic
248Q8—28no—
249D4—14616no—
250D4—1468no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—2924no—
262C2×C4—732no—
263C2×C4—732no—
264C2×C4—1468no—
265C2×C4—14616no—
266C2×C4—1468no—
267C2×C4—1462no—
268C2×C4—1462no—
269C2×C4—1461no—
270C2×C4—1462no—
271C2×C4—1462no—
272C2×C4—1461no—
273C2×C4—1462no—
274C2×C4—1461no—
275C2×C4D4×D7312yes—
276C2×C4D4×D7314yes—
277C2×C4#1192402912yescomplemented
278C22—2922no—
279C22—2922no—
280C22—2922no—
281C22—2922no—
282C22—734no—
283C22—1464no—
284C22—1464no—
285C22—1464no—
286C22—1462no—
287C22—1464no—
288C22—1464no—
289C22—1462no—
290C22C2×D4×D7311yescharacteristic
291C22C2×D4×D7312yes—
292C22#41×D7311yescharacteristic
293C22C2×#1192402911yescharacteristic
294C22#1455663912yes—
295C4—22no—
296C4—24no—
297C4—22no—
298C4—42no—
299C4—41no—
300C4—2922no—
301C4—2921no—
302C4—1462no—
303C4—1462no—
304C2—2924no—
305C2—1464no—
306C2#120×D7311yescharacteristic
307C2#1798910011yescharacteristic
308C2#1798916211yescharacteristic
309C2#1798923912yes—
310C2#1798924012yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#395×C73C2
hypercenter#395D73
hypocenterC73#2406
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#14556576C2semidirect
3. C2×C4⋊C4×D73C2semidirect
4. #17988506C2semidirect
5. #17988505C2semidirect
6. #17988504C2semidirect
7. #17988465C2semidirect
8. #17988461C2semidirect
9. #17988458C2semidirect
10. #17988449C2semidirect
11. #395×C73C2semidirect
105. C2×C4×C73#41semidirect
115. C2×Dic73#41semidirect
156. C73#2406semidirect
161. #395D73semidirect
277. C2×C4#11924029semidirect