Finite Group Databasebeta

← #22616060

Subgroups — #22616060

Order 9344.

598 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14556574C211yesmaximal, characteristic, complemented
2#17988518C211yesmaximal, characteristic, complemented
3#17988513C211yesmaximal, characteristic, complemented
4#17988501C211yesmaximal, characteristic, complemented
5#17988501C212yesmaximal, complemented
6#17988495C211yesmaximal, characteristic, complemented
7#17988495C212yesmaximal, complemented
8#17988487C212yesmaximal, complemented
9#17988481C212yesmaximal, complemented
10C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
11C2×#121×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2212yes—
13C22×C22⋊D73C2211yescharacteristic
14#14556574—24no—
15C2×#11924007C2211yescharacteristic
16C2×#11924007C2211yescharacteristic
17C2×#11924007C2212yes—
18C2×C22⋊Dic73C2212yes—
19C2×C22⋊Dic73C2212yes—
20C2×C22⋊Dic73C2211yescharacteristic
21C2×C22⋊Dic73C2212yes—
22C2×C22⋊Dic73C2212yes—
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2211yescharacteristic
25C2×#11924005C2212yes—
26C2×C4×Dic73C2212yes—
27#14556498C2211yescharacteristic
28#14556498C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31C22×D4×C73C2212yes—
32C22×D4×C73C2211yescharacteristic
33C23×C4×C73C2211yescharacteristic
34#121×C73—24no—
35C2×C4⋊C4×C73C2211yescharacteristic
36C2×C22⋊C4×C73C2212yes—
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—22no—
39C2×C22⋊D73—24no—
40C2×C22⋊D73—42no—
41C2×C22⋊D73—42no—
42C2×C22⋊D73—42no—
43C22×Dic73C2312yes—
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2311yescharacteristic
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2312yes—
48#11924007—22no—
49#11924007—22no—
50#11924007—42no—
51C22⋊Dic73—22no—
52C22⋊Dic73—24no—
53C22⋊Dic73—24no—
54C22⋊Dic73—42no—
55C22⋊Dic73—42no—
56#11924005—22no—
57#11924005—22no—
58#11924005—42no—
59C4×Dic73—42no—
60C24×C73C2312yes—
61C24×C73C2311yescharacteristic
62C2×D4×C73—24no—
63C2×D4×C73—22no—
64C2×D4×C73—42no—
65C2×D4×C73—42no—
66C2×D4×C73—42no—
67C22×C4×C73—42no—
68C22×C4×C73D414yescomplemented
69C22×C4×C73C2312yes—
70C22×C4×C73C2311yescharacteristic
71C22×C4×C73C2311yescharacteristic
72C4⋊C4×C73—22no—
73C22⋊C4×C73—24no—
74C23×C73—22no—
75C23×C73—22no—
76C23×C73—21no—
77C23×C73—21no—
78C23×C73—22no—
79C23×C73—22no—
80C23×C73—22no—
81C23×C73—22no—
82C23×C73—22no—
83C23×C73—22no—
84C23×C73—22no—
85C23×C73C2×D412yes—
86C23×C73C2411yescharacteristic
87C22×D73—21no—
88C22×D73—22no—
89C22×D73—21no—
90C22×D73—22no—
91C22×D73—21no—
92D4×C73—44no—
93D4×C73—48no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—22no—
98C2×C4×C73—22no—
99C2×C4×C73—44no—
100C2×C4×C73C2×D412yes—
101C2×C4×C73C2×D412yes—
102C22⋊D73—48no—
103C22⋊D73—44no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—21no—
107C2×Dic73—21no—
108C2×Dic73—21no—
109C2×Dic73—22no—
110C2×Dic73—22no—
111C2×Dic73—22no—
112C2×Dic73—22no—
113C2×Dic73—21no—
114C2×Dic73—22no—
115C2×Dic73—21no—
116C2×Dic73#4114yes—
117C22×C73—22no—
118C22×C73—22no—
119C22×C73—22no—
120C22×C73—42no—
121C22×C73—42no—
122C22×C73—42no—
123C22×C73—42no—
124C22×C73—42no—
125C22×C73—42no—
126C22×C73—42no—
127C22×C73—42no—
128C22×C73—42no—
129C22×C73C22×D411yescharacteristic
130C22×C73C2×#4112yes—
131C22×C73H(5,𝔽2)12yes—
132C22×C73H(5,𝔽2)11yescharacteristic
133C22×C73H(5,𝔽2)11yescharacteristic
134C2×D73—41no—
135C2×D73—41no—
136C2×D73—41no—
137C2×D73—42no—
138C2×D73—42no—
139C4×C73—22no—
140C4×C73—22no—
141C4×C73—42no—
142Dic73—24no—
143Dic73—41no—
144Dic73—41no—
145Dic73—41no—
146Dic73—42no—
147C2×C73—42no—
148C2×C73—82no—
149C2×C73#53211yescharacteristic
150C2×C73#53411yescharacteristic
151C2×C73#53511yescharacteristic
152C2×C73#53812yes—
153C2×C73#54012yes—
154D73—81no—
155#2661—731nomaximal, Sylow
156C73#266111yescharacteristic, complemented, Sylow
157C2×#123—731no—
158C2×#121D7311yescharacteristic, complemented
159#398—731no—
160#397—731no—
161#394—731no—
162#394—732no—
163#392—731no—
164#392—732no—
165#390—732no—
166#388—732no—
167C4×C22⋊C4—731no—
168C22×D4—731no—
169C22×D4—732no—
170C22×D4C2×D7312yes—
171C22×D4C2×D7311yescharacteristic
172C23×C4C2×D7311yescharacteristic
173#123—1464no—
174#121—24no—
175C2×C4⋊C4—732no—
176C2×C4⋊C4—731no—
177C2×C4⋊C4—731no—
178C2×C4⋊C4C2×D7311yescharacteristic
179C2×C22⋊C4—732no—
180C2×C22⋊C4—732no—
181C2×C22⋊C4—732no—
182C2×C22⋊C4—731no—
183C2×C22⋊C4—732no—
184C2×C22⋊C4—732no—
185C2×C22⋊C4—731no—
186C2×C22⋊C4—731no—
187C2×C22⋊C4C2×D7312yes—
188C2×C42—732no—
189#95—731no—
190#95—731no—
191#95—732no—
192#95—732no—
193C24—731no—
194C24C22×D7312yes—
195C24C22×D7311yescharacteristic
196C2×D4—24no—
197C2×D4—22no—
198C2×D4—42no—
199C2×D4—42no—
200C2×D4—42no—
201C2×D4—2922no—
202C2×D4—2922no—
203C2×D4—2922no—
204C2×D4—1464no—
205C2×D4—1462no—
206C22×C4—42no—
207C22×C4—732no—
208C22×C4—732no—
209C22×C4—731no—
210C22×C4—731no—
211C22×C4—731no—
212C22×C4C22⋊D7314yescomplemented
213C22×C4C22×D7312yes—
214C22×C4C22×D7311yescharacteristic
215C22×C4C22×D7311yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—2922no—
218C4⋊C4—1462no—
219C4⋊C4—1462no—
220C22⋊C4—24no—
221C22⋊C4—2922no—
222C22⋊C4—2922no—
223C22⋊C4—2922no—
224C22⋊C4—1464no—
225C22⋊C4—1464no—
226C22⋊C4—1462no—
227C22⋊C4—1462no—
228C22⋊C4—1462no—
229C42—2922no—
230C23—22no—
231C23—22no—
232C23—21no—
233C23—21no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—1461no—
242C23—1462no—
243C23—1461no—
244C23—1462no—
245C23—1461no—
246C23C2×C22⋊D7312yes—
247C23C23×D7311yescharacteristic
248D4—44no—
249D4—48no—
250D4—2924no—
251D4—2928no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—44no—
258C2×C4—734no—
259C2×C4—1461no—
260C2×C4—1461no—
261C2×C4—1461no—
262C2×C4—1462no—
263C2×C4—1462no—
264C2×C4—1462no—
265C2×C4—1461no—
266C2×C4—1462no—
267C2×C4—1462no—
268C2×C4—1461no—
269C2×C4—1462no—
270C2×C4—1462no—
271C2×C4C2×C22⋊D7312yes—
272C2×C4C2×C22⋊D7312yes—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—42no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—2921no—
286C22—2921no—
287C22—2921no—
288C22—2922no—
289C22—2922no—
290C22C22×C22⋊D7311yescharacteristic
291C22#41×D7312yes—
292C22#1455663612yes—
293C22#1455663611yescharacteristic
294C22#1455663611yescharacteristic
295C4—22no—
296C4—22no—
297C4—42no—
298C4—2921no—
299C4—2921no—
300C4—2921no—
301C4—2922no—
302C4—1464no—
303C2—42no—
304C2—82no—
305C2—5841no—
306C2#1798913311yescharacteristic
307C2#1798914611yescharacteristic
308C2#1798915411yescharacteristic
309C2#1798916912yes—
310C2#1798918712yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
FittingC2×#121×C73C2
hypercenterC2×#121D73
hypocenterC73#2661
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#14556574C2semidirect
2. #17988518C2semidirect
3. #17988513C2semidirect
4. #17988501C2semidirect
5. #17988501C2semidirect
6. #17988495C2semidirect
7. #17988495C2semidirect
8. #17988487C2semidirect
9. #17988481C2semidirect
10. C4×C22⋊Dic73C2semidirect
11. C2×#121×C73C2semidirect
68. C22×C4×C73D4semidirect
156. C73#2661semidirect
158. C2×#121D73semidirect
212. C22×C4C22⋊D73semidirect