Finite Group Databasebeta

← #22614241

Subgroups — #22614241

Order 9344.

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

normal subgroups only

This group has 584 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×#14556551C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
3#17988527C211yesmaximal, characteristic, complemented
4#17988525C211yesmaximal, characteristic, complemented
5#17988523C211yesmaximal, characteristic, complemented
6#17988482C212yesmaximal, complemented
7#17988463C212yesmaximal
8#17988458C212yesmaximal, complemented
9#17988446C211yesmaximal, characteristic, complemented
10#17988445C212yesmaximal, complemented
11#399×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14C22×C4×D73C2211yescharacteristic
15C22×C4×D73C2212yes—
16#14556551—24no—
17C2×C4⋊Dic73C2211yescharacteristic
18C2×#11924007C2212yes—
19C2×#11924007C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2212yes—
22C4⋊C4×D73—24no—
23C2×C22⋊Dic73C2212yes—
24C2×#11924005C2212yes—
25C2×#11924005C2211yescharacteristic
26C2×C4×Dic73C2211yescharacteristic
27#14556498C2212yes—
28#14556498C2212yes—
29#14556498C2211yescharacteristic
30#14556498C2212yes—
31#14556498C2212yes—
32C2×C4⋊C4×C73C2211yescharacteristic
33C2×C4⋊C4×C73C2212yes—
34C2×C22⋊C4×C73C2211yescharacteristic
35C2×C22⋊C4×C73C2212yes—
36#95×C73C2211yescharacteristic
37C23×D73C2311yescharacteristic
38C2×C22⋊D73—22no—
39C2×C22⋊D73—22no—
40C2×C22⋊D73Q814yes—
41C22×Dic73—22no—
42C22×Dic73—24no—
43C22×Dic73C2311yescharacteristic
44C22×Dic73C2312yes—
45C22×Dic73C2312yes—
46C22×Dic73C2311yescharacteristic
47C22×Dic73C2311yescharacteristic
48C2×C4×D73—24no—
49C2×C4×D73—24no—
50C2×C4×D73—42no—
51C2×C4×D73—42no—
52C2×C4×D73D414yes—
53C4⋊Dic73—22no—
54#11924007—22no—
55#11924007—24no—
56#11924007—24no—
57#11924007—42no—
58C22⋊Dic73—42no—
59#11924005—22no—
60#11924005—24no—
61C4×Dic73—22no—
62C24×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C22×C4×C73C2312yes—
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2311yescharacteristic
67C4⋊C4×C73—22no—
68C4⋊C4×C73—42no—
69C22⋊C4×C73—22no—
70C22⋊C4×C73—42no—
71C23×C73—21no—
72C23×C73—22no—
73C23×C73—21no—
74C23×C73—22no—
75C23×C73C2×Q812yes—
76C23×C73C2411yescharacteristic
77C22×D73—22no—
78C22×D73—22no—
79C22×D73C2×D412yes—
80C22×D73C2×Q812yes—
81C22×D73#4112yes—
82C2×C4×C73—22no—
83C2×C4×C73—21no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—22no—
91C2×C4×C73C2×D412yes—
92C22⋊D73—28no—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—44no—
104C2×Dic73C2×D412yes—
105C2×Dic73C2×Q812yes—
106C2×Dic73#4114yes—
107C4×D73—28no—
108C4×D73—48no—
109C22×C73—22no—
110C22×C73—24no—
111C22×C73—41no—
112C22×C73—41no—
113C22×C73—42no—
114C22×C73C22×D411yescharacteristic
115C22×C73C22×Q811yescharacteristic
116C22×C73C2×#4111yescharacteristic
117C22×C73C2×#4112yes—
118C22×C73H(5,𝔽2)12yes—
119C2×D73—22no—
120C2×D73—22no—
121C2×D73—24no—
122C2×D73—24no—
123C2×D73C22⋊Q814yes—
124C4×C73—22no—
125C4×C73—42no—
126C4×C73—41no—
127C4×C73—42no—
128Dic73—22no—
129Dic73—41no—
130Dic73—42no—
131Dic73—42no—
132Dic73#12314yes—
133C2×C73—42no—
134C2×C73C2×C22⋊Q811yescharacteristic
135C2×C73C2×#12311yescharacteristic
136C2×C73#53511yescharacteristic
137C2×C73#55312yes—
138C2×C73#55412yes—
139D73—24no—
140#2487—731nomaximal, Sylow
141C73#248711yescharacteristic, complemented, Sylow
142C2×C4×D4—731no—
143C22×C4⋊C4—731no—
144#400—731no—
145#400—731no—
146#399—731no—
147#399D7311yescharacteristic, complemented
148#389—732no—
149#386—732no—
150#385—732no—
151#380—732no—
152#380—731no—
153C22×D4—731no—
154C23×C4—732no—
155C23×C4—731no—
156C23×C4—731no—
157C4×D4—1464no—
158C2×C4⋊C4—732no—
159C2×C4⋊C4—732no—
160C2×C4⋊C4—731no—
161C2×C4⋊C4—731no—
162C2×C4⋊C4—732no—
163C2×C4⋊C4—1464no—
164C2×C4⋊C4C2×D7311yescharacteristic
165C2×C4⋊C4C2×D7312yes—
166C2×C22⋊C4—732no—
167C2×C22⋊C4—731no—
168C2×C22⋊C4—732no—
169C2×C22⋊C4C2×D7311yescharacteristic
170C2×C22⋊C4C2×D7312yes—
171C2×C42—731no—
172#95—732no—
173#95—732no—
174#95—731no—
175#95—732no—
176#95—732no—
177#95C2×D7311yescharacteristic
178C24—731no—
179C24C22×D7311yescharacteristic
180C2×D4—734no—
181C2×D4—1462no—
182C2×D4—1462no—
183C22×C4—2922no—
184C22×C4—2922no—
185C22×C4—731no—
186C22×C4—731no—
187C22×C4—734no—
188C22×C4—731no—
189C22×C4—732no—
190C22×C4—732no—
191C22×C4—1464no—
192C22×C4—1464no—
193C22×C4—1462no—
194C22×C4—1464no—
195C22×C4C22×D7312yes—
196C22×C4C22×D7312yes—
197C22×C4C22×D7311yescharacteristic
198C22×C4C22×D7311yescharacteristic
199C4⋊C4—22no—
200C4⋊C4—42no—
201C4⋊C4—2922no—
202C4⋊C4—1464no—
203C4⋊C4—1464no—
204C4⋊C4—1462no—
205C4⋊C4—1462no—
206C22⋊C4—22no—
207C22⋊C4—42no—
208C22⋊C4—2922no—
209C22⋊C4—1464no—
210C22⋊C4—1462no—
211C42—1462no—
212C23—21no—
213C23—22no—
214C23—21no—
215C23—22no—
216C23—732no—
217C23—732no—
218C23—732no—
219C23—1462no—
220C23—1462no—
221C23Q8×D7312yes—
222C23C23×D7311yescharacteristic
223D4—1468no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—2928no—
234C2×C4—2924no—
235C2×C4—732no—
236C2×C4—734no—
237C2×C4—732no—
238C2×C4—1468no—
239C2×C4—1461no—
240C2×C4—1462no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4—1462no—
244C2×C4—1462no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4—1461no—
248C2×C4—1461no—
249C2×C4D4×D7312yes—
250C22—24no—
251C22—22no—
252C22—41no—
253C22—42no—
254C22—41no—
255C22—734no—
256C22—1462no—
257C22—1464no—
258C22—1464no—
259C22—1462no—
260C22C2×D4×D7311yescharacteristic
261C22C2×Q8×D7311yescharacteristic
262C22#41×D7311yescharacteristic
263C22#41×D7312yes—
264C22#1455663612yes—
265C4—22no—
266C4—42no—
267C4—41no—
268C4—42no—
269C4—2922no—
270C4—2922no—
271C4—2921no—
272C4—734no—
273C4—1462no—
274C2—42no—
275C2—1464no—
276C2C22⋊Q8×D7311yescharacteristic
277C2#123×D7311yescharacteristic
278C2#1798915011yescharacteristic
279C2#1798928212yes—
280C2#1798929112yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2487
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D73C2semidirect
3. #17988527C2semidirect
4. #17988525C2semidirect
5. #17988523C2semidirect
6. #17988482C2semidirect
8. #17988458C2semidirect
9. #17988446C2semidirect
10. #17988445C2semidirect
11. #399×C73C2semidirect
141. C73#2487semidirect
147. #399D73semidirect