Finite Group Databasebeta

← #22620643

Subgroups — #22620643

Order 9344.

366 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 115 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#17989142C211yesmaximal, characteristic, complemented
2#17989116C211yesmaximal, characteristic
3#17988993C211yesmaximal, characteristic, complemented
4#17988982C211yesmaximal, characteristic, complemented
5#17988956C211yesmaximal, characteristic, complemented
6#17988827C212yesmaximal, complemented
7#17988815C212yesmaximal
8#17988691C212yesmaximal, complemented
9#17988684C212yesmaximal, complemented
10#97×D73C211yesmaximal, characteristic, complemented
11#489×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2212yes—
13C2×#11924016C2212yes—
14C2×C8×D73C2212yes—
15#14556591C2211yescharacteristic
16#14556584—21no—
17#14556583C2211yescharacteristic
18#14556582—21no—
19#14556573—21no—
20#14556571C2212yes—
21#14556567—21no—
22#14556567C2211yescharacteristic
23#14556562C2211yescharacteristic
24Q8×Dic73—21no—
25Q8×Dic73C2211yescharacteristic
26#14556556C2212yes—
27D4×Dic73C2211yescharacteristic
28#14556551—21no—
29#14556549—21no—
30#14556547—21no—
31C42×D73C2211yescharacteristic
32#14556524C2212yes—
33#14556522C2212yes—
34#14556516C2212yes—
35#14556516C2212yes—
36#14556502C2211yescharacteristic
37#14556501C2212yes—
38C4⋊Q8×C73C2211yescharacteristic
39#124×C73C2211yescharacteristic
40#103×C73C2212yes—
41#102×C73C2212yes—
42#97×C73C2211yescharacteristic
43C2×Dic146C2312yes—
44C2×C22⋊D73—21no—
45C22×Dic73—21no—
46C2×C4×D73D411yescharacteristic
47C2×C4×D73D411yescharacteristic
48C2×C4×D73C2311yescharacteristic
49#11924018—24no—
50#11924016—24no—
51C2×#10596831C2312yes—
52C8×D73—24no—
53C4⋊Dic73—21no—
54C4⋊Dic73—21no—
55C4⋊Dic73—22no—
56C4⋊Dic73—21no—
57C4⋊Dic73C2311yescharacteristic
58C4⋊Dic73C2311yescharacteristic
59#11924007—21no—
60#11924007—21no—
61#11924007—21no—
62#11924007—22no—
63C22⋊Dic73—21no—
64C22⋊Dic73—21no—
65#11924005—22no—
66#11924005—21no—
67C4×Dic73—21no—
68C4×Dic73—22no—
69C4×Dic73D411yescharacteristic
70C4×Dic73D411yescharacteristic
71C4×Dic73C2311yescharacteristic
72C2×Q8×C73—21no—
73C2×Q8×C73C2311yescharacteristic
74C2×D4×C73C2311yescharacteristic
75C2×C8×C73C2312yes—
76C4⋊C4×C73—21no—
77C4⋊C4×C73C2312yes—
78C22⋊C4×C73—21no—
79C22⋊C4×C73—21no—
80C42×C73C2311yescharacteristic
81C23×C73—21no—
82C22×D73C2×D411yescharacteristic
83Q8×C73—22no—
84Q8×C73—42no—
85D4×C73—22no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2411yescharacteristic
91C22⋊D73—42no—
92C2×Dic73—22no—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—42no—
96C2×Dic73C2×D411yescharacteristic
97C2×Dic73C2×D411yescharacteristic
98C2×Dic73C2×D411yescharacteristic
99C4×D73—22no—
100C4×D73—22no—
101C4×D73—41no—
102Dic146—22no—
103Dic146—22no—
104C8×C73—22no—
105#10596831#4114yes—
106C22×C73—41no—
107C22×C73—41no—
108C22×C73—41no—
109C22×C73C22×D411yescharacteristic
110C2×D73—21no—
111C2×D73—21no—
112C2×D73#13712yes—
113C4×C73—21no—
114C4×C73—21no—
115C4×C73—41no—
116C4×C73—42no—
117C4×C73C2×#4112yes—
118Dic73—21no—
119Dic73—21no—
120Dic73—21no—
121Dic73—42no—
122Dic73—41no—
123Dic73—41no—
124C2×C73—81no—
125C2×C73#53211yescharacteristic
126C2×C73C2×#13711yescharacteristic
127C2×C73#57511yescharacteristic
128D73—22no—
129#3181—731nomaximal, Sylow
130C73#318111yescharacteristic, complemented, Sylow
131#533—731no—
132#529—731no—
133#501—731no—
134#497—731no—
135#491—731no—
136#489D7311yescharacteristic, complemented
137#467—732no—
138#465—732no—
139#441—732no—
140#440—732no—
141C2×#97—731no—
142C2×Q16—732no—
143C2×SD16—732no—
144C22×C8—732no—
145C4⋊Q8—731no—
146C4⋊Q8C2×D7311yescharacteristic
147#126—1461no—
148#125—731no—
149#125—1461no—
150#124C2×D7311yescharacteristic
151#123—1461no—
152C22⋊Q8—731no—
153C22⋊Q8—732no—
154C22⋊Q8—1461no—
155#121—731no—
156C4×Q8—731no—
157C4×Q8—732no—
158C4×Q8—1461no—
159C4×D4—731no—
160C4×D4—1461no—
161#117—1461no—
162#117—1461no—
163C2×C42—731no—
164#107—732no—
165#106—732no—
166#103—732no—
167#103—732no—
168#103C2×D7312yes—
169#102C2×D7312yes—
170#97—732no—
171#97—731no—
172#97C2×D7311yescharacteristic
173C2×Q8—21no—
174C2×Q8—732no—
175C2×Q8C22×D7311yescharacteristic
176C2×D4—1461no—
177C2×D4C22×D7311yescharacteristic
178C22×C4—731no—
179C22×C4—731no—
180C22×C4—731no—
181C22×C4—1461no—
182Q16—1464no—
183SD16—1464no—
184C2×C8—732no—
185C2×C8—1464no—
186C2×C8C22×D7312yes—
187C4⋊C4—21no—
188C4⋊C4—731no—
189C4⋊C4—731no—
190C4⋊C4—1461no—
191C4⋊C4—1462no—
192C4⋊C4—1461no—
193C4⋊C4—1462no—
194C4⋊C4—1461no—
195C4⋊C4—1461no—
196C4⋊C4—1461no—
197C4⋊C4—1461no—
198C4⋊C4C22×D7312yes—
199C22⋊C4—21no—
200C22⋊C4—21no—
201C22⋊C4—1462no—
202C22⋊C4—1461no—
203C22⋊C4—1461no—
204C22⋊C4—1461no—
205C42—731no—
206C42—731no—
207C42—731no—
208C42—1461no—
209C42—1462no—
210C42C22×D7311yescharacteristic
211C23—21no—
212C23—731no—
213Q8—22no—
214Q8—42no—
215Q8—1462no—
216Q8—1462no—
217D4—22no—
218D4—2922no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—2921no—
222C2×C4—2922no—
223C2×C4—731no—
224C2×C4—731no—
225C2×C4—731no—
226C2×C4—1462no—
227C2×C4—1461no—
228C2×C4—1462no—
229C2×C4—1461no—
230C2×C4—1462no—
231C2×C4D4×D7311yescharacteristic
232C2×C4D4×D7311yescharacteristic
233C2×C4C23×D7311yescharacteristic
234C8—22no—
235C8—734no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22—732no—
240C22—1461no—
241C22—1461no—
242C22C2×D4×D7311yescharacteristic
243C4—21no—
244C4—21no—
245C4—42no—
246C4—41no—
247C4—2921no—
248C4—2921no—
249C4—2922no—
250C4—1461no—
251C4—1461no—
252C4—1461no—
253C4#41×D7312yes—
254C2—81no—
255C2—1462no—
256C2#1798913611yescharacteristic
257C2#137×D7311yescharacteristic
258C2#1798938311yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#489×C73C2
socleC22×C73C22×D4
hypercenter#489D73
hypocenterC73#3181
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #17989142C2semidirect
3. #17988993C2semidirect
4. #17988982C2semidirect
5. #17988956C2semidirect
6. #17988827C2semidirect
8. #17988691C2semidirect
9. #17988684C2semidirect
10. #97×D73C2semidirect
11. #489×C73C2semidirect
130. C73#3181semidirect
136. #489D73semidirect