Finite Group Databasebeta

← #22614864

Subgroups — #22614864

Order 9344.

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

normal subgroups only

This group has 760 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×#14556577C211yesmaximal, characteristic, complemented
2C2×#14556568C212yesmaximal, complemented
3C2×#14556563C212yesmaximal, complemented
4C2×D4×Dic73C211yesmaximal, characteristic, complemented
5#17988524C211yesmaximal, characteristic, complemented
6#17988523C211yesmaximal, characteristic, complemented
7#17988495C211yesmaximal, characteristic, complemented
8#17988490C212yesmaximal, complemented
9#17988487C212yesmaximal, complemented
10#17988438C211yesmaximal, characteristic, complemented
11#392×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×C22⋊D73C2211yescharacteristic
14C22×C22⋊D73C2212yes—
15C23×Dic73C2212yes—
16#14556577—24no—
17#14556568—28no—
18#14556563—28no—
19D4×Dic73—24no—
20C2×C4⋊Dic73C2212yes—
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×#11924007C2212yes—
24C2×C22⋊Dic73C2212yes—
25C2×C22⋊Dic73C2211yescharacteristic
26C2×C22⋊Dic73C2212yes—
27C2×C22⋊Dic73C2212yes—
28C2×#11924005C2211yescharacteristic
29C2×#11924005C2212yes—
30C2×#11924005C2211yescharacteristic
31C2×C4×Dic73C2212yes—
32C2×C4×Dic73C2211yescharacteristic
33#14556498C2211yescharacteristic
34C22×D4×C73C2211yescharacteristic
35C22×D4×C73C2212yes—
36C2×C22⋊C4×C73C2212yes—
37C2×C22⋊C4×C73C2211yescharacteristic
38#95×C73C2211yescharacteristic
39C23×D73C2311yescharacteristic
40C2×Dic146—24no—
41C2×Dic146—22no—
42C2×C22⋊D73—24no—
43C2×C22⋊D73—24no—
44C2×C22⋊D73—24no—
45C2×C22⋊D73—22no—
46C2×C22⋊D73—42no—
47C22×Dic73—24no—
48C22×Dic73—24no—
49C22×Dic73—24no—
50C22×Dic73C2311yescharacteristic
51C22×Dic73C2312yes—
52C22×Dic73C2312yes—
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55C4⋊Dic73—22no—
56C4⋊Dic73—24no—
57#11924007—24no—
58#11924007D418yescomplemented
59C22⋊Dic73—24no—
60C22⋊Dic73—24no—
61C22⋊Dic73—24no—
62C22⋊Dic73—22no—
63#11924005—24no—
64#11924005—22no—
65#11924005—22no—
66C4×Dic73—42no—
67C4×Dic73D414yescomplemented
68C24×C73C2311yescharacteristic
69C24×C73C2312yes—
70C2×D4×C73—24no—
71C2×D4×C73—24no—
72C2×D4×C73—22no—
73C2×D4×C73—24no—
74C2×D4×C73—42no—
75C22×C4×C73C2311yescharacteristic
76C22×C4×C73C2311yescharacteristic
77C22×C4×C73C2312yes—
78C22⋊C4×C73—24no—
79C22⋊C4×C73—22no—
80C23×C73—22no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73—22no—
85C23×C73—22no—
86C23×C73—21no—
87C23×C73—22no—
88C23×C73—22no—
89C23×C73—21no—
90C23×C73—21no—
91C23×C73#4114yes—
92C23×C73C2411yescharacteristic
93C22×D73—21no—
94C22×D73—22no—
95C22×D73—22no—
96C22×D73—21no—
97C22×D73—21no—
98D4×C73—28no—
99D4×C73—48no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73—22no—
103C2×C4×C73—21no—
104C2×C4×C73—22no—
105C2×C4×C73C2×D412yes—
106C2×C4×C73C2×D414yes—
107C22⋊D73—48no—
108C22⋊D73—44no—
109C2×Dic73—22no—
110C2×Dic73—21no—
111C2×Dic73—22no—
112C2×Dic73—21no—
113C2×Dic73—22no—
114C2×Dic73—21no—
115C2×Dic73—22no—
116C2×Dic73—22no—
117C2×Dic73—22no—
118C2×Dic73—48no—
119C2×Dic73C2×D412yes—
120C2×Dic73C2×D414yes—
121C2×Dic73C2×D412yes—
122C2×Dic73C2×D414yes—
123Dic146—44no—
124C22×C73—24no—
125C22×C73—24no—
126C22×C73—24no—
127C22×C73—42no—
128C22×C73—42no—
129C22×C73—42no—
130C22×C73—42no—
131C22×C73—41no—
132C22×C73—41no—
133C22×C73—41no—
134C22×C73—42no—
135C22×C73—42no—
136C22×C73C22×D411yescharacteristic
137C22×C73C22×D412yes—
138C22×C73C2×#4112yes—
139C22×C73H(5,𝔽2)11yescharacteristic
140C22×C732−1+411yescharacteristic
141C2×D73—41no—
142C2×D73—41no—
143C2×D73—41no—
144C2×D73—42no—
145C2×D73—42no—
146C4×C73—22no—
147C4×C73—24no—
148C4×C73—41no—
149Dic73—22no—
150Dic73—24no—
151Dic73—41no—
152Dic73—42no—
153Dic73#12714yes—
154C2×C73—44no—
155C2×C73—81no—
156C2×C73#52511yescharacteristic
157C2×C73C2×#12711yescharacteristic
158C2×C73#53711yescharacteristic
159C2×C73#54612yes—
160C2×C73#54812yes—
161D73—81no—
162#2540—731nomaximal, Sylow
163C73#254011yescharacteristic, complemented, Sylow
164C2×#124—731no—
165C2×C22⋊Q8—732no—
166C2×#121—732no—
167C2×C4×D4—731no—
168#399—731no—
169#399—731no—
170#392—731no—
171#392D7311yescharacteristic, complemented
172#390—732no—
173#390—732no—
174C4×C4⋊C4—731no—
175C22×Q8—731no—
176C22×D4—732no—
177C22×D4—731no—
178C22×D4C2×D7311yescharacteristic
179C22×D4C2×D7312yes—
180C23×C4—732no—
181#124—1464no—
182C22⋊Q8—1468no—
183#121—1468no—
184C4×D4—1464no—
185C2×C4⋊C4—732no—
186C2×C4⋊C4—731no—
187C2×C4⋊C4—732no—
188C2×C4⋊C4—732no—
189C2×C22⋊C4—732no—
190C2×C22⋊C4—732no—
191C2×C22⋊C4—732no—
192C2×C22⋊C4—731no—
193C2×C22⋊C4—732no—
194C2×C22⋊C4—731no—
195C2×C22⋊C4—731no—
196C2×C22⋊C4C2×D7312yes—
197C2×C22⋊C4C2×D7311yescharacteristic
198C2×C42—732no—
199C2×C42—731no—
200#95—731no—
201#95C2×D7311yescharacteristic
202C24—731no—
203C24C22×D7311yescharacteristic
204C24C22×D7312yes—
205C2×Q8—1464no—
206C2×Q8—1462no—
207C2×D4—24no—
208C2×D4—24no—
209C2×D4—22no—
210C2×D4—24no—
211C2×D4—42no—
212C2×D4—2922no—
213C2×D4—1464no—
214C2×D4—1464no—
215C2×D4—1462no—
216C2×D4—1464no—
217C22×C4—731no—
218C22×C4—732no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—732no—
222C22×C4—1464no—
223C22×C4—1464no—
224C22×C4—1464no—
225C22×C4C22×D7311yescharacteristic
226C22×C4C22×D7311yescharacteristic
227C22×C4C22×D7312yes—
228C4⋊C4—738no—
229C4⋊C4—1464no—
230C4⋊C4—1462no—
231C4⋊C4—1464no—
232C22⋊C4—24no—
233C22⋊C4—22no—
234C22⋊C4—1462no—
235C22⋊C4—1464no—
236C22⋊C4—1464no—
237C22⋊C4—1464no—
238C22⋊C4—1462no—
239C22⋊C4—1464no—
240C22⋊C4—1462no—
241C42—2922no—
242C42—734no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—22no—
248C23—22no—
249C23—21no—
250C23—22no—
251C23—22no—
252C23—21no—
253C23—21no—
254C23—1461no—
255C23—1462no—
256C23—1462no—
257C23—1461no—
258C23—1461no—
259C23#1192402714yes—
260C23C23×D7311yescharacteristic
261Q8—2924no—
262D4—28no—
263D4—48no—
264D4—2924no—
265D4—2928no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—2928no—
272C2×C4—732no—
273C2×C4—734no—
274C2×C4—732no—
275C2×C4—734no—
276C2×C4—1462no—
277C2×C4—1461no—
278C2×C4—1462no—
279C2×C4—1462no—
280C2×C4—1462no—
281C2×C4—1462no—
282C2×C4—1461no—
283C2×C4—1462no—
284C2×C4—1461no—
285C2×C4D4×D7312yes—
286C2×C4D4×D7314yes—
287C22—24no—
288C22—24no—
289C22—24no—
290C22—42no—
291C22—42no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—42no—
297C22—42no—
298C22—41no—
299C22—2921no—
300C22—2921no—
301C22—2922no—
302C22—2922no—
303C22—2921no—
304C22C2×D4×D7311yescharacteristic
305C22C2×D4×D7312yes—
306C22C2×#1192402712yes—
307C22#1455663611yescharacteristic
308C22#1455663811yescharacteristic
309C4—24no—
310C4—22no—
311C4—41no—
312C4—2922no—
313C4—2921no—
314C4—734no—
315C4—1462no—
316C4—1464no—
317C2—44no—
318C2—81no—
319C2—5841no—
320C2#1798909311yescharacteristic
321C2#127×D7311yescharacteristic
322C2#1798916611yescharacteristic
323C2#1798922412yes—
324C2#1798924312yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#392×C73C2
hypercenter#392D73
hypocenterC73#2540
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14556577C2semidirect
2. C2×#14556568C2semidirect
3. C2×#14556563C2semidirect
4. C2×D4×Dic73C2semidirect
5. #17988524C2semidirect
6. #17988523C2semidirect
7. #17988495C2semidirect
8. #17988490C2semidirect
9. #17988487C2semidirect
10. #17988438C2semidirect
11. #392×C73C2semidirect
58. #11924007D4semidirect
67. C4×Dic73D4semidirect
163. C73#2540semidirect
171. #392D73semidirect