Finite Group Databasebeta

← #22614894

Subgroups — #22614894

Order 9344.

724 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14556564C212yesmaximal, complemented
2C2×#14556562C211yesmaximal, characteristic, complemented
3C2×#14556553C211yesmaximal, characteristic, complemented
4#17988517C211yesmaximal, characteristic, complemented
5#17988514C211yesmaximal, characteristic, complemented
6#17988495C211yesmaximal, characteristic, complemented
7#17988481C212yesmaximal, complemented
8#17988463C212yesmaximal, complemented
9#17988463C212yesmaximal, complemented
10#95×D73C211yesmaximal, characteristic, complemented
11#394×C73C211yesmaximal, characteristic, complemented
12C22×D292C2211yescharacteristic
13C22×C22⋊D73C2212yes—
14C22×C22⋊D73C2212yes—
15C22×C4×D73C2212yes—
16C22×C4×D73C2211yescharacteristic
17C22×C4×D73C2211yescharacteristic
18#14556564—28no—
19#14556562—24no—
20#14556553—24no—
21C2×C4⋊Dic73C2211yescharacteristic
22C2×#11924007C2212yes—
23C2×C22⋊Dic73C2212yes—
24C2×C22⋊Dic73C2212yes—
25C2×#11924005C2211yescharacteristic
26C2×#11924005C2212yes—
27C2×#11924005C2211yescharacteristic
28C2×C4×Dic73C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2211yescharacteristic
31#14556498C2212yes—
32#14556498C2212yes—
33C22×D4×C73C2211yescharacteristic
34C2×C4⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36C2×C22⋊C4×C73C2212yes—
37#95×C73C2211yescharacteristic
38C23×D73C2311yescharacteristic
39C23×D73C2311yescharacteristic
40C2×D292—22no—
41C2×D292—22no—
42C2×D292D414yescomplemented
43C2×C22⋊D73—24no—
44C2×C22⋊D73—24no—
45C2×C22⋊D73—24no—
46C2×C22⋊D73—24no—
47C2×C22⋊D73—24no—
48C2×C22⋊D73—42no—
49C22×Dic73C2311yescharacteristic
50C22×Dic73C2312yes—
51C22×Dic73C2311yescharacteristic
52C22×Dic73C2312yes—
53C2×C4×D73—24no—
54C2×C4×D73—22no—
55C2×C4×D73—24no—
56C2×C4×D73—42no—
57C2×C4×D73—42no—
58C2×C4×D73—42no—
59C2×C4×D73D414yescomplemented
60C4⋊Dic73—22no—
61#11924007—24no—
62C22⋊Dic73—24no—
63C22⋊Dic73—24no—
64#11924005—22no—
65#11924005—24no—
66#11924005—22no—
67C4×Dic73—22no—
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—21no—
89C22×D73—22no—
90C22×D73—21no—
91C22×D73—22no—
92C22×D73C2×D412yes—
93C22×D73C2×D412yes—
94C22×D73C2×D412yes—
95C22×D73#4112yes—
96D4×C73—44no—
97C2×C4×C73—21no—
98C2×C4×C73—21no—
99C2×C4×C73—22no—
100C2×C4×C73—22no—
101C2×C4×C73—21no—
102C2×C4×C73—22no—
103C2×C4×C73—22no—
104C2×C4×C73—22no—
105C2×C4×C73C2×D412yes—
106C2×C4×C73C2×D412yes—
107C22⋊D73—48no—
108C22⋊D73—48no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—21no—
113C2×Dic73—22no—
114C2×Dic73—22no—
115C2×Dic73—22no—
116C2×Dic73—22no—
117C2×Dic73C2×D412yes—
118C2×Dic73#4114yes—
119D292—28no—
120C4×D73—44no—
121C4×D73—48no—
122C4×D73—44no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73—42no—
128C22×C73—42no—
129C22×C73—42no—
130C22×C73C22×D411yescharacteristic
131C22×C73C22×D411yescharacteristic
132C22×C73C2×#4111yescharacteristic
133C22×C73C2×#4112yes—
134C22×C73H(5,𝔽2)12yes—
135C2×D73—22no—
136C2×D73—22no—
137C2×D73—24no—
138C2×D73—24no—
139C2×D73—22no—
140C2×D73—24no—
141C2×D73—41no—
142C2×D73—41no—
143C2×D73—42no—
144C2×D73#12114yes—
145C4×C73—22no—
146C4×C73—22no—
147C4×C73—41no—
148C4×C73—42no—
149Dic73—22no—
150Dic73—24no—
151Dic73—42no—
152Dic73—41no—
153C2×C73—82no—
154C2×C73C2×#12111yescharacteristic
155C2×C73#53211yescharacteristic
156C2×C73#53411yescharacteristic
157C2×C73#54612yes—
158C2×C73#55312yes—
159D73—24no—
160D73—42no—
161#2543—731nomaximal, Sylow
162C73#254311yescharacteristic, complemented, Sylow
163C2×#121—731no—
164C2×#121—732no—
165C2×C4×D4—731no—
166#398—731no—
167#397—731no—
168#394D7311yescharacteristic, complemented
169#392—731no—
170#388—732no—
171#386—732no—
172#386—732no—
173C2×#95—731no—
174C22×D4—732no—
175C22×D4—732no—
176C22×D4—731no—
177C22×D4C2×D7311yescharacteristic
178C23×C4—731no—
179C23×C4—731no—
180C23×C4—732no—
181#121—1468no—
182#121—1464no—
183C4×D4—1464no—
184C2×C4⋊C4—732no—
185C2×C4⋊C4—731no—
186C2×C4⋊C4C2×D7311yescharacteristic
187C2×C22⋊C4—732no—
188C2×C22⋊C4—732no—
189C2×C22⋊C4—731no—
190C2×C22⋊C4—731no—
191C2×C22⋊C4—732no—
192C2×C22⋊C4C2×D7312yes—
193C2×C22⋊C4C2×D7312yes—
194C2×C42—731no—
195#95—732no—
196#95—731no—
197#95—732no—
198#95—732no—
199#95C2×D7311yescharacteristic
200C24—731no—
201C24—731no—
202C24C22×D7312yes—
203C2×D4—22no—
204C2×D4—42no—
205C2×D4—2922no—
206C2×D4—734no—
207C2×D4—1462no—
208C2×D4—1462no—
209C2×D4—1464no—
210C2×D4—1464no—
211C2×D4—1464no—
212C2×D4—1464no—
213C2×D4—1464no—
214C22×C4—2922no—
215C22×C4—2922no—
216C22×C4—2922no—
217C22×C4—734no—
218C22×C4—732no—
219C22×C4—731no—
220C22×C4—731no—
221C22×C4—732no—
222C22×C4—1462no—
223C22×C4—1464no—
224C22×C4—1464no—
225C22×C4C22×D7312yes—
226C22×C4C22×D7311yescharacteristic
227C22×C4C22×D7311yescharacteristic
228C22×C4C22×D7311yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—1464no—
231C4⋊C4—1462no—
232C22⋊C4—24no—
233C22⋊C4—42no—
234C22⋊C4—1462no—
235C22⋊C4—1464no—
236C22⋊C4—1464no—
237C22⋊C4—1464no—
238C22⋊C4—1462no—
239C42—1462no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—22no—
246C23—22no—
247C23—732no—
248C23—732no—
249C23—732no—
250C23—732no—
251C23—1461no—
252C23—1462no—
253C23—1461no—
254C23—1462no—
255C23—1462no—
256C23—1462no—
257C23C23×D7311yescharacteristic
258D4—44no—
259D4—2928no—
260D4—2928no—
261D4—1468no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—2924no—
271C2×C4—2924no—
272C2×C4—2928no—
273C2×C4—732no—
274C2×C4—734no—
275C2×C4—1461no—
276C2×C4—1462no—
277C2×C4—1462no—
278C2×C4—1462no—
279C2×C4—1462no—
280C2×C4—1462no—
281C2×C4—1462no—
282C2×C4—1462no—
283C2×C4D4×D7312yes—
284C2×C4D4×D7312yes—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—2921no—
293C22—2921no—
294C22—2922no—
295C22—734no—
296C22—1464no—
297C22—1462no—
298C22—1462no—
299C22—1462no—
300C22—1464no—
301C22—1464no—
302C22C2×D4×D7311yescharacteristic
303C22C2×D4×D7311yescharacteristic
304C22#41×D7312yes—
305C22#41×D7311yescharacteristic
306C22#1455663612yes—
307C4—22no—
308C4—22no—
309C4—41no—
310C4—42no—
311C4—2921no—
312C4—2922no—
313C4—1462no—
314C4—1464no—
315C2—82no—
316C2—2922no—
317C2—1464no—
318C2#121×D7311yescharacteristic
319C2#1798913611yescharacteristic
320C2#1798914711yescharacteristic
321C2#1798923412yes—
322C2#1798928212yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#394×C73C2
hypercenter#394D73
hypocenterC73#2543
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14556564C2semidirect
2. C2×#14556562C2semidirect
3. C2×#14556553C2semidirect
4. #17988517C2semidirect
5. #17988514C2semidirect
6. #17988495C2semidirect
7. #17988481C2semidirect
8. #17988463C2semidirect
9. #17988463C2semidirect
10. #95×D73C2semidirect
11. #394×C73C2semidirect
42. C2×D292D4semidirect
59. C2×C4×D73D4semidirect
162. C73#2543semidirect
168. #394D73semidirect