Finite Group Databasebeta

← #22614929

Subgroups — #22614929

Order 9344.

676 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14556587C211yesmaximal, characteristic
2C2×#14556577C212yesmaximal, complemented
3C2×#14556556C211yesmaximal, characteristic, complemented
4#17988505C211yesmaximal, characteristic, complemented
5#17988504C211yesmaximal, characteristic, complemented
6#17988501C211yesmaximal, characteristic, complemented
7#17988487C212yesmaximal, complemented
8#17988487C212yesmaximal, complemented
9#17988487C212yesmaximal, complemented
10#17988438C211yesmaximal, characteristic, complemented
11#394×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×D292C2211yescharacteristic
14C22×C22⋊D73C2212yes—
15C22×C22⋊D73C2212yes—
16#14556587—24no—
17#14556577—28no—
18#14556556—24no—
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×C22⋊Dic73C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28C2×C4×Dic73C2212yes—
29C2×C4×Dic73C2211yescharacteristic
30C2×C4×Dic73C2211yescharacteristic
31C2×C4×Dic73C2211yescharacteristic
32#14556498C2211yescharacteristic
33C22×D4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36C2×C22⋊C4×C73C2212yes—
37#95×C73C2211yescharacteristic
38C23×D73C2312yes—
39C2×Dic146—22no—
40C2×Dic146—22no—
41C2×Dic146D414yescomplemented
42C2×D292—22no—
43C2×D292—42no—
44C2×C22⋊D73—24no—
45C2×C22⋊D73—24no—
46C2×C22⋊D73—24no—
47C2×C22⋊D73—24no—
48C2×C22⋊D73—24no—
49C2×C22⋊D73—24no—
50C22×Dic73C2312yes—
51C22×Dic73C2311yescharacteristic
52C22×Dic73C2311yescharacteristic
53C22×Dic73C2311yescharacteristic
54C22×Dic73C2311yescharacteristic
55#11924007—22no—
56#11924007—22no—
57#11924007—24no—
58C22⋊Dic73—24no—
59C22⋊Dic73—42no—
60#11924005—24no—
61#11924005—24no—
62#11924005—42no—
63#11924005—42no—
64C4×Dic73—22no—
65C4×Dic73—22no—
66C4×Dic73—24no—
67C4×Dic73D414yes—
68C24×C73C2312yes—
69C2×D4×C73—22no—
70C2×D4×C73—42no—
71C22×C4×C73C2312yes—
72C22×C4×C73C2311yescharacteristic
73C22×C4×C73C2311yescharacteristic
74C22×C4×C73C2311yescharacteristic
75C4⋊C4×C73—22no—
76C22⋊C4×C73—24no—
77C22⋊C4×C73—42no—
78C23×C73—22no—
79C23×C73—22no—
80C23×C73—22no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73—22no—
85C23×C73C2411yescharacteristic
86C22×D73—22no—
87C22×D73—22no—
88C22×D73—22no—
89C22×D73—22no—
90C22×D73—22no—
91C22×D73—22no—
92C22×D73—22no—
93D4×C73—44no—
94C2×C4×C73—21no—
95C2×C4×C73—21no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—21no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—22no—
102C2×C4×C73C2×D412yes—
103C2×C4×C73C2×D412yes—
104C22⋊D73—48no—
105C22⋊D73—48no—
106C2×Dic73—21no—
107C2×Dic73—21no—
108C2×Dic73—22no—
109C2×Dic73—21no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73C2×D412yes—
114C2×Dic73C2×D412yes—
115C2×Dic73C2×D412yes—
116C2×Dic73C2×D412yes—
117C2×Dic73#4112yes—
118C2×Dic73#4114yes—
119D292—44no—
120Dic146—28no—
121C22×C73—42no—
122C22×C73—42no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73—42no—
128C22×C73C22×D411yescharacteristic
129C22×C73C22×D411yescharacteristic
130C22×C73C2×#4111yescharacteristic
131C22×C73C2×#4112yes—
132C22×C73H(5,𝔽2)12yes—
133C2×D73—42no—
134C2×D73—42no—
135C2×D73—42no—
136C2×D73—42no—
137C2×D73—42no—
138C2×D73—42no—
139C2×D73—42no—
140C4×C73—22no—
141C4×C73—22no—
142C4×C73—41no—
143C4×C73—42no—
144Dic73—22no—
145Dic73—41no—
146Dic73—42no—
147Dic73#12114yes—
148Dic73#12414yescomplemented
149C2×C73—82no—
150C2×C73C2×#12111yescharacteristic
151C2×C73C2×#12411yescharacteristic
152C2×C73#53511yescharacteristic
153C2×C73#55012yes—
154C2×C73#55912yes—
155D73—82no—
156#2548—731nomaximal, Sylow
157C73#254811yescharacteristic, complemented, Sylow
158C2×#127—731no—
159C2×#124—732no—
160C2×C4×Q8—731no—
161#394—731no—
162#394—731no—
163#394—731no—
164#394D7311yescharacteristic, complemented
165#390—732no—
166#390—732no—
167#390—732no—
168C4×C4⋊C4—731no—
169C22×Q8—731no—
170C22×D4—732no—
171C22×D4—732no—
172C22×D4—731no—
173C22×D4C2×D7311yescharacteristic
174#127—1464no—
175#124—1468no—
176C4×Q8—1464no—
177C2×C4⋊C4—731no—
178C2×C4⋊C4—731no—
179C2×C4⋊C4—732no—
180C2×C4⋊C4C2×D7311yescharacteristic
181C2×C22⋊C4—732no—
182C2×C22⋊C4—732no—
183C2×C22⋊C4—732no—
184C2×C22⋊C4—732no—
185C2×C22⋊C4—732no—
186C2×C22⋊C4—732no—
187C2×C22⋊C4C2×D7312yes—
188C2×C22⋊C4C2×D7312yes—
189C2×C42—731no—
190C2×C42—731no—
191C2×C42—731no—
192C2×C42—732no—
193#95—731no—
194#95C2×D7311yescharacteristic
195C24—732no—
196C24C22×D7312yes—
197C2×Q8—734no—
198C2×Q8—1462no—
199C2×Q8—1462no—
200C2×D4—22no—
201C2×D4—42no—
202C2×D4—2922no—
203C2×D4—1464no—
204C2×D4—1464no—
205C2×D4—1464no—
206C2×D4—1464no—
207C2×D4—1464no—
208C2×D4—1464no—
209C2×D4—1462no—
210C22×C4—731no—
211C22×C4—731no—
212C22×C4—731no—
213C22×C4—732no—
214C22×C4—731no—
215C22×C4C22×D7312yes—
216C22×C4C22×D7311yescharacteristic
217C22×C4C22×D7311yescharacteristic
218C22×C4C22×D7311yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—1464no—
221C4⋊C4—1462no—
222C4⋊C4—1462no—
223C22⋊C4—24no—
224C22⋊C4—42no—
225C22⋊C4—2922no—
226C22⋊C4—2922no—
227C22⋊C4—2922no—
228C22⋊C4—1464no—
229C22⋊C4—1464no—
230C22⋊C4—1464no—
231C42—734no—
232C42—1462no—
233C42—1462no—
234C42—1464no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—1462no—
243C23—1462no—
244C23—1462no—
245C23—1462no—
246C23—1462no—
247C23—1462no—
248C23—1462no—
249C23C23×D7311yescharacteristic
250Q8—1468no—
251D4—44no—
252D4—2924no—
253D4—2928no—
254D4—2928no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—732no—
264C2×C4—732no—
265C2×C4—732no—
266C2×C4—734no—
267C2×C4—732no—
268C2×C4—732no—
269C2×C4—1462no—
270C2×C4—1461no—
271C2×C4—1462no—
272C2×C4—1462no—
273C2×C4—1462no—
274C2×C4—1461no—
275C2×C4—1461no—
276C2×C4D4×D7312yes—
277C2×C4D4×D7312yes—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—2922no—
286C22—2922no—
287C22—2922no—
288C22—2922no—
289C22—2922no—
290C22—2922no—
291C22—2922no—
292C22C2×D4×D7311yescharacteristic
293C22C2×D4×D7311yescharacteristic
294C22#41×D7312yes—
295C22#41×D7311yescharacteristic
296C22#1455663612yes—
297C4—22no—
298C4—22no—
299C4—41no—
300C4—42no—
301C4—2921no—
302C4—2922no—
303C4—734no—
304C4—734no—
305C4—1462no—
306C2—82no—
307C2—5842no—
308C2#121×D7311yescharacteristic
309C2#124×D7311yescharacteristic
310C2#1798915211yescharacteristic
311C2#1798925512yes—
312C2#1798932112yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2548
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14556577C2semidirect
3. C2×#14556556C2semidirect
4. #17988505C2semidirect
5. #17988504C2semidirect
6. #17988501C2semidirect
7. #17988487C2semidirect
8. #17988487C2semidirect
9. #17988487C2semidirect
10. #17988438C2semidirect
11. #394×C73C2semidirect
41. C2×Dic146D4semidirect
148. Dic73#124semidirect
157. C73#2548semidirect
164. #394D73semidirect