Finite Group Databasebeta

← #22614238

Subgroups — #22614238

Order 9344.

624 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14556575C211yesmaximal, characteristic
2C2×#14556574C211yesmaximal, characteristic
3C2×#14556551C211yesmaximal, characteristic
4C22×#11924007C211yesmaximal, characteristic, complemented
5#17988521C212yesmaximal, complemented
6#17988516C212yesmaximal, complemented
7#17988484C212yesmaximal, complemented
8#17988448C211yesmaximal, characteristic, complemented
9#17988446C212yesmaximal, complemented
10#17988445C211yesmaximal, characteristic, complemented
11#381×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14C23×Dic73C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556575—24no—
17#14556574—24no—
18#14556551—24no—
19C2×C4⋊Dic73C2212yes—
20C2×#11924007—24no—
21C2×#11924007C2212yes—
22C2×#11924007C2212yes—
23C2×#11924007C2212yes—
24C2×#11924007C2212yes—
25C2×#11924007C2211yescharacteristic
26C2×C22⋊Dic73C2211yescharacteristic
27C2×#11924005C2212yes—
28C2×#11924005C2212yes—
29C2×#11924005C2211yescharacteristic
30C2×C4×Dic73C2211yescharacteristic
31#14556498C2212yes—
32#14556498C2212yes—
33#14556498C2212yes—
34C23×C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2211yescharacteristic
36C2×C22⋊C4×C73C2211yescharacteristic
37#95×C73C2212yes—
38#95×C73C2212yes—
39C23×D73C2311yescharacteristic
40C2×C22⋊D73—22no—
41C2×C22⋊D73—22no—
42C2×C22⋊D73D414yes—
43C22×Dic73—24no—
44C22×Dic73—22no—
45C22×Dic73—22no—
46C22×Dic73—22no—
47C22×Dic73D414yes—
48C22×Dic73C2312yes—
49C22×Dic73C2312yes—
50C22×Dic73C2311yescharacteristic
51C22×Dic73C2311yescharacteristic
52C22×Dic73C2311yescharacteristic
53C2×C4×D73—22no—
54C2×C4×D73—24no—
55C4⋊Dic73—24no—
56#11924007—24no—
57#11924007—24no—
58#11924007—22no—
59#11924007—24no—
60#11924007—24no—
61C22⋊Dic73—22no—
62#11924005—24no—
63#11924005—24no—
64#11924005—22no—
65C4×Dic73—22no—
66C24×C73C2311yescharacteristic
67C22×C4×C73—22no—
68C22×C4×C73—22no—
69C22×C4×C73—22no—
70C22×C4×C73C2311yescharacteristic
71C22×C4×C73C2311yescharacteristic
72C22×C4×C73C2312yes—
73C22×C4×C73C2312yes—
74C22⋊C4×C73—22no—
75C22⋊C4×C73—22no—
76C23×C73—22no—
77C23×C73—22no—
78C23×C73C2×D412yes—
79C23×C73C2×D412yes—
80C23×C73#4112yes—
81C23×C73C2411yescharacteristic
82C22×D73—21no—
83C22×D73—22no—
84C22×D73—21no—
85C22×D73—22no—
86C22×D73C2×D412yes—
87C2×C4×C73—21no—
88C2×C4×C73—22no—
89C2×C4×C73—21no—
90C2×C4×C73—22no—
91C2×C4×C73—22no—
92C2×C4×C73—22no—
93C2×C4×C73—22no—
94C2×C4×C73—22no—
95C2×C4×C73—22no—
96C2×C4×C73—22no—
97C2×C4×C73—44no—
98C22⋊D73—28no—
99C2×Dic73—21no—
100C2×Dic73—22no—
101C2×Dic73—21no—
102C2×Dic73—28no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73—22no—
109C2×Dic73—44no—
110C2×Dic73C2×D412yes—
111C2×Dic73C2×D412yes—
112C2×Dic73C2×D412yes—
113C2×Dic73#4114yes—
114C4×D73—44no—
115C22×C73—22no—
116C22×C73—22no—
117C22×C73—24no—
118C22×C73—24no—
119C22×C73#12114yes—
120C22×C73C22×D411yescharacteristic
121C22×C73C22×D411yescharacteristic
122C22×C73C2×#4112yes—
123C22×C73C2×#4111yescharacteristic
124C22×C732−1+412yes—
125C2×D73—22no—
126C2×D73—24no—
127C2×D73—41no—
128C2×D73—41no—
129C2×D73—42no—
130C4×C73—42no—
131C4×C73—41no—
132C4×C73—41no—
133C4×C73—42no—
134Dic73—22no—
135Dic73—22no—
136Dic73—42no—
137Dic73—42no—
138Dic73#12314yescomplemented
139C2×C73—24no—
140C2×C73C2×#12111yescharacteristic
141C2×C73C2×#12311yescharacteristic
142C2×C73#53611yescharacteristic
143C2×C73#54712yes—
144C2×C73#55212yes—
145D73—42no—
146#2486—731nomaximal, Sylow
147C73#248611yescharacteristic, complemented, Sylow
148C2×#123—731no—
149C2×#123—731no—
150C2×C4×D4—731no—
151C22×C4⋊C4—731no—
152#398—732no—
153#397—732no—
154#389—732no—
155#381—731no—
156#381D7311yescharacteristic, complemented
157#380—731no—
158#380—732no—
159C22×D4—731no—
160C23×C4—731no—
161C23×C4—731no—
162C23×C4—731no—
163C23×C4C2×D7311yescharacteristic
164#123—1464no—
165#123—1464no—
166C4×D4—1464no—
167C2×C4⋊C4—732no—
168C2×C4⋊C4—732no—
169C2×C4⋊C4—731no—
170C2×C4⋊C4—732no—
171C2×C4⋊C4—732no—
172C2×C4⋊C4—732no—
173C2×C4⋊C4—1464no—
174C2×C22⋊C4—731no—
175C2×C22⋊C4—731no—
176C2×C22⋊C4—732no—
177C2×C22⋊C4—732no—
178C2×C22⋊C4C2×D7311yescharacteristic
179C2×C22⋊C4C2×D7311yescharacteristic
180C2×C42—731no—
181#95—732no—
182#95—732no—
183#95—732no—
184#95C2×D7312yes—
185#95C2×D7312yes—
186C24—731no—
187C24C22×D7311yescharacteristic
188C2×D4—734no—
189C2×D4—1462no—
190C2×D4—1462no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—731no—
195C22×C4—734no—
196C22×C4—731no—
197C22×C4—731no—
198C22×C4—732no—
199C22×C4—732no—
200C22×C4—1462no—
201C22×C4—1464no—
202C22×C4—1462no—
203C22×C4—1462no—
204C22×C4—1462no—
205C22×C4—1464no—
206C22×C4C22×D7311yescharacteristic
207C22×C4C22×D7311yescharacteristic
208C22×C4C22×D7312yes—
209C22×C4C22×D7312yes—
210C4⋊C4—1464no—
211C4⋊C4—1464no—
212C4⋊C4—1464no—
213C4⋊C4—1462no—
214C4⋊C4—1464no—
215C4⋊C4—1464no—
216C22⋊C4—22no—
217C22⋊C4—22no—
218C22⋊C4—1462no—
219C22⋊C4—1464no—
220C22⋊C4—1464no—
221C22⋊C4—1462no—
222C42—1462no—
223C23—22no—
224C23—22no—
225C23—732no—
226C23—1461no—
227C23—1462no—
228C23—1461no—
229C23—1462no—
230C23D4×D7312yes—
231C23D4×D7312yes—
232C23#1192402812yes—
233C23C23×D7311yescharacteristic
234D4—1468no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—44no—
246C2×C4—2924no—
247C2×C4—2924no—
248C2×C4—732no—
249C2×C4—734no—
250C2×C4—732no—
251C2×C4—732no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4—1462no—
257C2×C4—1462no—
258C2×C4—1468no—
259C2×C4—1461no—
260C2×C4—1462no—
261C2×C4—1461no—
262C22—22no—
263C22—24no—
264C22—24no—
265C22—22no—
266C22—2921no—
267C22—2922no—
268C22—2921no—
269C22—1464no—
270C22—1462no—
271C22#1455656414yes—
272C22C2×D4×D7311yescharacteristic
273C22C2×D4×D7311yescharacteristic
274C22#41×D7312yes—
275C22C2×#1192402811yescharacteristic
276C22#1455663812yes—
277C4—41no—
278C4—42no—
279C4—42no—
280C4—41no—
281C4—2922no—
282C4—2922no—
283C4—734no—
284C4—1462no—
285C4—1462no—
286C2—24no—
287C2—2922no—
288C2C2×#1455656411yescharacteristic
289C2#123×D7311yescharacteristic
290C2#1798915911yescharacteristic
291C2#1798923512yes—
292C2#1798927012yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#381×C73C2
hypercenter#381D73
hypocenterC73#2486
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
4. C22×#11924007C2semidirect
5. #17988521C2semidirect
6. #17988516C2semidirect
7. #17988484C2semidirect
8. #17988448C2semidirect
9. #17988446C2semidirect
10. #17988445C2semidirect
11. #381×C73C2semidirect
138. Dic73#123semidirect
147. C73#2486semidirect
156. #381D73semidirect