Finite Group Databasebeta

← #22617960

Subgroups — #22617960

Order 9344.

528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14556571C211yesmaximal, characteristic, complemented
2C2×#14556564C211yesmaximal, characteristic
3#17988522C211yesmaximal, characteristic, complemented
4#17988520C212yesmaximal, complemented
5#17988504C212yesmaximal, complemented
6#17988503C212yesmaximal, complemented
7#17988502C212yesmaximal, complemented
8#17988500C211yesmaximal, characteristic, complemented
9#17988499C211yesmaximal, characteristic, complemented
10#17988449C211yesmaximal, characteristic, complemented
11#399×C73C211yesmaximal, characteristic, complemented
12C22×Dic146C2211yescharacteristic
13C22×D292C2211yescharacteristic
14C22×C22⋊D73C2211yescharacteristic
15C22×C22⋊D73C2211yescharacteristic
16C22×C4×D73C2211yescharacteristic
17#14556571—24no—
18#14556564—24no—
19C2×C4⋊Dic73C2212yes—
20C2×#11924007C2211yescharacteristic
21C2×#11924007C2212yes—
22C2×C22⋊Dic73C2212yes—
23C2×#11924005C2211yescharacteristic
24C2×#11924005C2212yes—
25C2×#11924005C2212yes—
26C2×#11924005C2212yes—
27C2×#11924005C2212yes—
28#14556498C2211yescharacteristic
29#14556498C2212yes—
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
38C23×D73C2311yescharacteristic
39C2×Dic146—22no—
40C2×Dic146—42no—
41C2×D292—22no—
42C2×D292—42no—
43C2×C22⋊D73—22no—
44C2×C22⋊D73—22no—
45C2×C22⋊D73—42no—
46C2×C22⋊D73—42no—
47C22×Dic73C2312yes—
48C22×Dic73C2312yes—
49C22×Dic73C2311yescharacteristic
50C22×Dic73C2311yescharacteristic
51C2×C4×D73—42no—
52C2×C4×D73D414yes—
53C4⋊Dic73—24no—
54#11924007—22no—
55#11924007—42no—
56C22⋊Dic73—42no—
57#11924005—24no—
58#11924005—22no—
59#11924005—42no—
60#11924005—42no—
61#11924005—42no—
62C24×C73C2311yescharacteristic
63C22×C4×C73C2312yes—
64C22×C4×C73C2311yescharacteristic
65C22×C4×C73C2312yes—
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—22no—
74C23×C73—21no—
75C23×C73—21no—
76C23×C73C2411yescharacteristic
77C22×D73—22no—
78C22×D73—22no—
79C22×D73—21no—
80C22×D73—21no—
81C22×D73—21no—
82C22×D73—22no—
83C22×D73—22no—
84C22×D73—21no—
85C22×D73—21no—
86C22×D73C2×D412yes—
87C2×C4×C73—22no—
88C2×C4×C73—21no—
89C2×C4×C73—22no—
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×C73C2×D412yes—
97C22⋊D73—44no—
98C22⋊D73—44no—
99C2×Dic73—22no—
100C2×Dic73—21no—
101C2×Dic73—22no—
102C2×Dic73—22no—
103C2×Dic73—22no—
104C2×Dic73—22no—
105C2×Dic73—22no—
106C2×Dic73—22no—
107C2×Dic73—22no—
108C2×Dic73C2×D412yes—
109D292—44no—
110C4×D73—44no—
111Dic146—44no—
112C22×C73—41no—
113C22×C73—41no—
114C22×C73—41no—
115C22×C73—42no—
116C22×C73—42no—
117C22×C73C22×D411yescharacteristic
118C22×C73H(5,𝔽2)12yes—
119C22×C73H(5,𝔽2)12yes—
120C22×C732−1+411yescharacteristic
121C22×C732−1+411yescharacteristic
122C2×D73—22no—
123C2×D73—22no—
124C2×D73—22no—
125C2×D73—42no—
126C2×D73—42no—
127C2×D73—41no—
128C2×D73—41no—
129C2×D73—41no—
130C2×D73—42no—
131C2×D73—42no—
132C4×C73—22no—
133C4×C73—41no—
134C4×C73—42no—
135C4×C73—42no—
136Dic73—22no—
137Dic73—42no—
138Dic73—41no—
139Dic73—42no—
140C2×C73—81no—
141C2×C73#53411yescharacteristic
142C2×C73#53511yescharacteristic
143C2×C73#53611yescharacteristic
144C2×C73#56212yes—
145C2×C73#56212yes—
146D73—42no—
147D73—81no—
148#2816—731nomaximal, Sylow
149C73#281611yescharacteristic, complemented, Sylow
150C2×C22⋊Q8—731no—
151C2×#121—731no—
152#399—731no—
153#399D7311yescharacteristic, complemented
154#398—732no—
155#394—732no—
156#394—732no—
157#394—732no—
158#393—731no—
159#393—731no—
160#381—731no—
161C22×Q8—731no—
162C22×D4—731no—
163C22×D4—731no—
164C22×D4—731no—
165C23×C4—731no—
166C22⋊Q8—1464no—
167#121—1464no—
168C2×C4⋊C4—732no—
169C2×C4⋊C4—731no—
170C2×C4⋊C4—732no—
171C2×C4⋊C4C2×D7311yescharacteristic
172C2×C4⋊C4C2×D7312yes—
173C2×C22⋊C4—732no—
174C2×C22⋊C4—732no—
175C2×C22⋊C4—732no—
176C2×C22⋊C4—732no—
177C2×C22⋊C4—731no—
178C2×C22⋊C4—732no—
179C2×C22⋊C4C2×D7311yescharacteristic
180C2×C22⋊C4C2×D7312yes—
181#95—731no—
182#95—732no—
183#95—732no—
184#95—732no—
185#95C2×D7311yescharacteristic
186C24—731no—
187C24—731no—
188C24C22×D7311yescharacteristic
189C2×Q8—2922no—
190C2×Q8—1462no—
191C2×D4—2922no—
192C2×D4—2922no—
193C2×D4—2922no—
194C2×D4—1462no—
195C2×D4—1462no—
196C2×D4—1462no—
197C22×C4—2922no—
198C22×C4—734no—
199C22×C4—731no—
200C22×C4—732no—
201C22×C4—732no—
202C22×C4—731no—
203C22×C4C22×D7312yes—
204C22×C4C22×D7311yescharacteristic
205C22×C4C22×D7312yes—
206C22×C4C22×D7311yescharacteristic
207C4⋊C4—22no—
208C4⋊C4—42no—
209C4⋊C4—2922no—
210C4⋊C4—1462no—
211C4⋊C4—1464no—
212C22⋊C4—22no—
213C22⋊C4—42no—
214C22⋊C4—2922no—
215C22⋊C4—2922no—
216C22⋊C4—2922no—
217C22⋊C4—2922no—
218C22⋊C4—1464no—
219C22⋊C4—1462no—
220C23—21no—
221C23—22no—
222C23—22no—
223C23—21no—
224C23—21no—
225C23—732no—
226C23—1461no—
227C23—1462no—
228C23—1462no—
229C23—1461no—
230C23—1461no—
231C23—1462no—
232C23—1462no—
233C23—1461no—
234C23—1461no—
235C23C23×D7311yescharacteristic
236Q8—2924no—
237D4—2924no—
238D4—2924no—
239D4—2924no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—22no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—2924no—
250C2×C4—732no—
251C2×C4—1461no—
252C2×C4—1462no—
253C2×C4—1462no—
254C2×C4—1462no—
255C2×C4—1462no—
256C2×C4—1462no—
257C2×C4—1462no—
258C2×C4—1462no—
259C2×C4—1462no—
260C2×C4D4×D7312yes—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—42no—
266C22—2922no—
267C22—2922no—
268C22—2921no—
269C22—2921no—
270C22—2921no—
271C22—2922no—
272C22—2922no—
273C22—1462no—
274C22—1462no—
275C22—1462no—
276C22C2×D4×D7311yescharacteristic
277C22#1455663612yes—
278C22#1455663712yes—
279C22#1455663811yescharacteristic
280C22#1455663911yescharacteristic
281C4—22no—
282C4—41no—
283C4—42no—
284C4—42no—
285C4—2922no—
286C4—2921no—
287C4—2922no—
288C4—1462no—
289C2—81no—
290C2—2922no—
291C2—5841no—
292C2#1798914811yescharacteristic
293C2#1798915011yescharacteristic
294C2#1798916011yescharacteristic
295C2#1798933312yes—
296C2#1798933412yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#399×C73C2
hypercenter#399D73
hypocenterC73#2816
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14556571C2semidirect
3. #17988522C2semidirect
4. #17988520C2semidirect
5. #17988504C2semidirect
6. #17988503C2semidirect
7. #17988502C2semidirect
8. #17988500C2semidirect
9. #17988499C2semidirect
10. #17988449C2semidirect
11. #399×C73C2semidirect
149. C73#2816semidirect
153. #399D73semidirect