Finite Group Databasebeta

← #22621305

Subgroups — #22621305

Order 9344.

348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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
1#17989144C211yesmaximal, characteristic, complemented
2#17989121C211yesmaximal, characteristic
3#17988895C212yesmaximal, complemented
4#17988883C211yesmaximal, characteristic, complemented
5#17988878C211yesmaximal, characteristic, complemented
6#17988845C212yesmaximal, complemented
7#17988833C212yesmaximal
8#17988810C212yesmaximal, complemented
9#17988798C211yesmaximal, characteristic, complemented
10#17988793C211yesmaximal, characteristic, complemented
11#423×C73C211yesmaximal, characteristic, complemented
12C2×Dic292C2212yes—
13C2×#11924017C2212yes—
14#14556591C2211yescharacteristic
15#14556591C2211yescharacteristic
16#14556585—21no—
17#14556583—21no—
18#14556583C2211yescharacteristic
19#14556579C2211yescharacteristic
20#14556574—21no—
21#14556570—21no—
22#14556570C2211yescharacteristic
23#14556570C2212yes—
24#14556565C2211yescharacteristic
25C4×Dic146—21no—
26C4×Dic146C2211yescharacteristic
27C4×Dic146C2212yes—
28C4×D292C2211yescharacteristic
29C4×C22⋊D73—21no—
30#14556550—21no—
31#14556548—21no—
32#14556525C2212yes—
33#14556523C2212yes—
34#14556516C2212yes—
35#14556516C2212yes—
36#14556516C2212yes—
37#14556513C2212yes—
38C2×M16×C73C2212yes—
39C2×C42×C73C2211yescharacteristic
40C4⋊C8×C73C2211yescharacteristic
41C4⋊C8×C73C2211yescharacteristic
42C4⋊C8×C73C2212yes—
43C2×Dic146—21no—
44C2×Dic146C2311yescharacteristic
45C2×Dic146C2312yes—
46C2×D292C2311yescharacteristic
47C2×C22⋊D73—21no—
48C2×C4×D73—21no—
49Dic292—42no—
50#11924017—42no—
51C4⋊Dic73—21no—
52C4⋊Dic73—21no—
53C4⋊Dic73—21no—
54C4⋊Dic73C2312yes—
55C4⋊Dic73C2311yescharacteristic
56C4⋊Dic73C2311yescharacteristic
57#11924007—21no—
58#11924007—21no—
59#11924007—21no—
60#11924007—22no—
61#11924007—22no—
62#11924007—21no—
63C22⋊Dic73—22no—
64C22⋊Dic73—21no—
65#11924005—21no—
66#11924005—21no—
67#11924005—21no—
68#11924005—21no—
69C4×Dic73—21no—
70C4×Dic73—22no—
71C22×C4×C73D411yescharacteristic
72C22×C4×C73D411yescharacteristic
73C22×C4×C73C2311yescharacteristic
74M16×C73—42no—
75C2×C8×C73C2312yes—
76C2×C8×C73C2312yes—
77C42×C73D411yescharacteristic
78C42×C73D411yescharacteristic
79C42×C73C2311yescharacteristic
80C42×C73C2311yescharacteristic
81C23×C73C2×D411yescharacteristic
82C22×D73—21no—
83C2×C4×C73—22no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—41no—
87C2×C4×C73C2×D411yescharacteristic
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2×D411yescharacteristic
92C2×C4×C73C2411yescharacteristic
93C22⋊D73—42no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—22no—
97C2×Dic73—22no—
98C2×Dic73—21no—
99D292—21no—
100D292—21no—
101C4×D73—42no—
102Dic146—22no—
103Dic146—21no—
104Dic146—21no—
105Dic146—22no—
106Dic146—42no—
107C8×C73—22no—
108C8×C73—22no—
109C22×C73—21no—
110C22×C73—21no—
111C22×C73—21no—
112C22×C73C22×D411yescharacteristic
113C2×D73—41no—
114C2×D73—41no—
115C2×D73—41no—
116C4×C73—21no—
117C4×C73—21no—
118C4×C73—21no—
119C4×C73—21no—
120C4×C73#13712yes—
121C4×C73H(5,𝔽2)11yescharacteristic
122C4×C732−1+411yescharacteristic
123Dic73—42no—
124Dic73—41no—
125Dic73—41no—
126Dic73—42no—
127Dic73—41no—
128C2×C73—41no—
129C2×C73#53711yescharacteristic
130C2×C73C2×#13711yescharacteristic
131C2×C73#57511yescharacteristic
132D73—81no—
133#3252—731nomaximal, Sylow
134C73#325211yescharacteristic, complemented, Sylow
135#533—731no—
136#529—731no—
137#479—732no—
138#477—731no—
139#476—731no—
140#470—732no—
141#468—732no—
142#464—732no—
143#462—731no—
144#461—731no—
145#423D7311yescharacteristic, complemented
146C2×Q16—732no—
147C2×SD16—732no—
148C2×M16C2×D7312yes—
149C4⋊Q8—731no—
150C4⋊Q8—731no—
151#126—1461no—
152#125—731no—
153#125—1461no—
154#124—731no—
155#123—1461no—
156C22⋊Q8—731no—
157C22⋊Q8—732no—
158C22⋊Q8—1461no—
159#121—731no—
160C4×Q8—731no—
161C4×Q8—732no—
162C4×Q8—1461no—
163C4×D4—731no—
164C4×D4—1461no—
165#117—1461no—
166#117—1461no—
167C2×C42C2×D7311yescharacteristic
168#107—732no—
169#106—732no—
170C4⋊C8C2×D7311yescharacteristic
171C4⋊C8C2×D7311yescharacteristic
172C4⋊C8C2×D7312yes—
173#103—732no—
174#103—732no—
175#103—732no—
176#102—732no—
177C2×Q8—731no—
178C2×Q8—732no—
179C2×Q8—1461no—
180C2×D4—731no—
181C2×D4—1461no—
182C22×C4—1461no—
183C22×C4D29211yescharacteristic
184C22×C4D29211yescharacteristic
185C22×C4C22×D7311yescharacteristic
186Q16—2922no—
187SD16—2922no—
188M16—42no—
189C2×C8C22×D7312yes—
190C2×C8C22×D7312yes—
191C4⋊C4—732no—
192C4⋊C4—731no—
193C4⋊C4—731no—
194C4⋊C4—1461no—
195C4⋊C4—1461no—
196C4⋊C4—1461no—
197C4⋊C4—1462no—
198C4⋊C4—1461no—
199C4⋊C4—1462no—
200C4⋊C4—1461no—
201C4⋊C4—1461no—
202C4⋊C4—1461no—
203C22⋊C4—1462no—
204C22⋊C4—1461no—
205C22⋊C4—1461no—
206C22⋊C4—1461no—
207C22⋊C4—1461no—
208C22⋊C4—1461no—
209C42—1461no—
210C42—1462no—
211C42D29211yescharacteristic
212C42D29211yescharacteristic
213C42C22×D7311yescharacteristic
214C42C22×D7311yescharacteristic
215C23—1461no—
216C23C2×D29211yescharacteristic
217Q8—2922no—
218Q8—1462no—
219Q8—1461no—
220Q8—1461no—
221Q8—1462no—
222D4—2922no—
223D4—1461no—
224D4—1461no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—2922no—
230C2×C4—1461no—
231C2×C4—1461no—
232C2×C4—1462no—
233C2×C4—1462no—
234C2×C4—1461no—
235C2×C4C2×D29211yescharacteristic
236C2×C4C2×D29211yescharacteristic
237C2×C4C2×D29211yescharacteristic
238C2×C4C2×D29211yescharacteristic
239C2×C4C2×D29211yescharacteristic
240C2×C4C23×D7311yescharacteristic
241C8—22no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—2921no—
247C22—2921no—
248C22—2921no—
249C22C22×D29211yescharacteristic
250C4—21no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—2921no—
255C4—2921no—
256C4—2922no—
257C4—2921no—
258C4—2922no—
259C4#1455662412yes—
260C4#1455663611yescharacteristic
261C4#1455663911yescharacteristic
262C2—41no—
263C2—5841no—
264C2#1798916811yescharacteristic
265C2C2×#1455662411yescharacteristic
266C2#1798938711yescharacteristic
subgroupG/H
centerC22C22×D292
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#423×C73C2
socleC22×C73C22×D4
hypercenter#423D73
hypocenterC73#3252
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
1. #17989144C2semidirect
3. #17988895C2semidirect
4. #17988883C2semidirect
5. #17988878C2semidirect
6. #17988845C2semidirect
8. #17988810C2semidirect
9. #17988798C2semidirect
10. #17988793C2semidirect
11. #423×C73C2semidirect
134. C73#3252semidirect
145. #423D73semidirect