Finite Group Databasebeta

← #22614232

Subgroups — #22614232

Order 9344.

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

normal subgroups only

This group has 624 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×#14556573C212yesmaximal
2C2×#14556551C211yesmaximal, characteristic
3C2×C4⋊C4×D73C211yesmaximal, characteristic, complemented
4#17988519C211yesmaximal, characteristic, complemented
5#17988518C211yesmaximal, characteristic, complemented
6#17988512C211yesmaximal, characteristic, complemented
7#17988484C212yesmaximal, complemented
8#17988449C212yesmaximal, complemented
9#17988446C211yesmaximal, characteristic, complemented
10#17988445C212yesmaximal, complemented
11#397×C73C211yesmaximal, characteristic, complemented
12C22×C22⋊D73C2211yescharacteristic
13C23×Dic73C2211yescharacteristic
14C22×C4×D73C2212yes—
15C22×C4×D73C2211yescharacteristic
16#14556573—28no—
17#14556551—24no—
18C2×C4⋊Dic73C2212yes—
19C2×C4⋊Dic73C2211yescharacteristic
20C2×#11924007C2212yes—
21C2×#11924007C2212yes—
22C2×#11924007C2212yes—
23C2×#11924007C2211yescharacteristic
24C4⋊C4×D73—24no—
25C2×C22⋊Dic73C2212yes—
26C2×#11924005C2212yes—
27C2×#11924005C2211yescharacteristic
28C2×C4×Dic73C2211yescharacteristic
29#14556498C2212yes—
30#14556498C2212yes—
31#14556498C2211yescharacteristic
32#14556498C2212yes—
33C2×C4⋊C4×C73C2211yescharacteristic
34C2×C22⋊C4×C73C2212yes—
35C2×C22⋊C4×C73C2211yescharacteristic
36#95×C73C2211yescharacteristic
37#95×C73C2212yes—
38C23×D73C2311yescharacteristic
39C2×C22⋊D73—22no—
40C2×C22⋊D73—22no—
41C2×C22⋊D73D414yes—
42C22×Dic73—22no—
43C22×Dic73—24no—
44C22×Dic73C2311yescharacteristic
45C22×Dic73C2312yes—
46C22×Dic73C2312yes—
47C22×Dic73C2311yescharacteristic
48C22×Dic73C2311yescharacteristic
49C2×C4×D73—24no—
50C2×C4×D73—24no—
51C2×C4×D73—24no—
52C2×C4×D73—24no—
53C2×C4×D73D414yes—
54C4⋊Dic73—22no—
55C4⋊Dic73—24no—
56#11924007—22no—
57#11924007—24no—
58#11924007—24no—
59#11924007—24no—
60C22⋊Dic73—24no—
61#11924005—22no—
62#11924005—24no—
63C4×Dic73—22no—
64C24×C73C2311yescharacteristic
65C22×C4×C73C2311yescharacteristic
66C22×C4×C73C2312yes—
67C22×C4×C73C2312yes—
68C22×C4×C73C2311yescharacteristic
69C4⋊C4×C73—22no—
70C22⋊C4×C73—24no—
71C22⋊C4×C73—22no—
72C23×C73—21no—
73C23×C73—22no—
74C23×C73—21no—
75C23×C73—22no—
76C23×C73C2×D412yes—
77C23×C73C2411yescharacteristic
78C22×D73—22no—
79C22×D73—22no—
80C22×D73C2×D412yes—
81C22×D73C2×D412yes—
82C22×D73#4112yes—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
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×C73—22no—
92C2×C4×C73C2×D412yes—
93C22⋊D73—28no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—22no—
97C2×Dic73—21no—
98C2×Dic73—22no—
99C2×Dic73—22no—
100C2×Dic73—22no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—44no—
105C2×Dic73C2×D412yes—
106C2×Dic73C2×D412yes—
107C2×Dic73#4114yes—
108C4×D73—28no—
109C4×D73—48no—
110C22×C73—22no—
111C22×C73—24no—
112C22×C73—41no—
113C22×C73—41no—
114C22×C73—42no—
115C22×C73C22×D411yescharacteristic
116C22×C73C22×D411yescharacteristic
117C22×C73C2×#4111yescharacteristic
118C22×C73C2×#4112yes—
119C22×C732−1+412yes—
120C2×D73—22no—
121C2×D73—22no—
122C2×D73—24no—
123C2×D73—24no—
124C2×D73#12114yes—
125C4×C73—22no—
126C4×C73—42no—
127C4×C73—41no—
128C4×C73—42no—
129Dic73—22no—
130Dic73—42no—
131Dic73—41no—
132Dic73—42no—
133Dic73#12314yescomplemented
134C2×C73—42no—
135C2×C73C2×#12111yescharacteristic
136C2×C73C2×#12311yescharacteristic
137C2×C73#53611yescharacteristic
138C2×C73#54712yes—
139C2×C73#55212yes—
140D73—24no—
141#2486—731nomaximal, Sylow
142C73#248611yescharacteristic, complemented, Sylow
143C2×#123—732no—
144C2×C4×D4—731no—
145C22×C4⋊C4—731no—
146#398—731no—
147#398—731no—
148#397—731no—
149#397D7311yescharacteristic, complemented
150#389—732no—
151#381—732no—
152#380—732no—
153#380—731no—
154C22×D4—731no—
155C23×C4—731no—
156C23×C4—731no—
157C23×C4—732no—
158#123—1468no—
159C4×D4—1464no—
160C2×C4⋊C4—732no—
161C2×C4⋊C4—731no—
162C2×C4⋊C4—731no—
163C2×C4⋊C4—732no—
164C2×C4⋊C4—732no—
165C2×C4⋊C4—732no—
166C2×C4⋊C4—1464no—
167C2×C4⋊C4C2×D7311yescharacteristic
168C2×C22⋊C4—732no—
169C2×C22⋊C4—731no—
170C2×C22⋊C4—732no—
171C2×C22⋊C4C2×D7311yescharacteristic
172C2×C22⋊C4C2×D7312yes—
173C2×C42—731no—
174#95—732no—
175#95—732no—
176#95—731no—
177#95—732no—
178#95C2×D7311yescharacteristic
179#95C2×D7312yes—
180C24—731no—
181C24C22×D7311yescharacteristic
182C2×D4—734no—
183C2×D4—1462no—
184C2×D4—1462no—
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—1464no—
194C22×C4—1464no—
195C22×C4—1462no—
196C22×C4—1464no—
197C22×C4C22×D7311yescharacteristic
198C22×C4C22×D7312yes—
199C22×C4C22×D7312yes—
200C22×C4C22×D7311yescharacteristic
201C4⋊C4—22no—
202C4⋊C4—1464no—
203C4⋊C4—1464no—
204C4⋊C4—1464no—
205C4⋊C4—1464no—
206C4⋊C4—1462no—
207C4⋊C4—1462no—
208C22⋊C4—24no—
209C22⋊C4—22no—
210C22⋊C4—1462no—
211C22⋊C4—1464no—
212C22⋊C4—1464no—
213C42—1462no—
214C23—21no—
215C23—22no—
216C23—21no—
217C23—22no—
218C23—732no—
219C23—732no—
220C23—732no—
221C23—1462no—
222C23—1462no—
223C23D4×D7312yes—
224C23C23×D7311yescharacteristic
225D4—1468no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—2928no—
236C2×C4—2924no—
237C2×C4—732no—
238C2×C4—734no—
239C2×C4—732no—
240C2×C4—1468no—
241C2×C4—1462no—
242C2×C4—1462no—
243C2×C4—1461no—
244C2×C4—1462no—
245C2×C4—1462no—
246C2×C4—1462no—
247C2×C4—1462no—
248C2×C4—1462no—
249C2×C4—1461no—
250C2×C4—1461no—
251C2×C4D4×D7312yes—
252C22—24no—
253C22—22no—
254C22—41no—
255C22—42no—
256C22—41no—
257C22—734no—
258C22—1462no—
259C22—1464no—
260C22—1464no—
261C22—1462no—
262C22C2×D4×D7311yescharacteristic
263C22C2×D4×D7311yescharacteristic
264C22#41×D7312yes—
265C22#41×D7311yescharacteristic
266C22#1455663812yes—
267C4—22no—
268C4—41no—
269C4—42no—
270C4—42no—
271C4—2922no—
272C4—2922no—
273C4—2921no—
274C4—734no—
275C4—1462no—
276C2—42no—
277C2—1464no—
278C2#121×D7311yescharacteristic
279C2#123×D7311yescharacteristic
280C2#1798915711yescharacteristic
281C2#1798923512yes—
282C2#1798927312yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#397×C73C2
hypercenter#397D73
hypocenterC73#2486
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×D73C2semidirect
4. #17988519C2semidirect
5. #17988518C2semidirect
6. #17988512C2semidirect
7. #17988484C2semidirect
8. #17988449C2semidirect
9. #17988446C2semidirect
10. #17988445C2semidirect
11. #397×C73C2semidirect
133. Dic73#123semidirect
142. C73#2486semidirect
149. #397D73semidirect