Finite Group Databasebeta

← #22620639

Subgroups — #22620639

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#17989122C211yesmaximal, characteristic
3#17988997C211yesmaximal, characteristic, complemented
4#17988979C211yesmaximal, characteristic, complemented
5#17988947C211yesmaximal, characteristic, complemented
6#17988827C212yesmaximal, complemented
7#17988819C212yesmaximal
8#17988691C212yesmaximal, complemented
9#17988690C212yesmaximal, complemented
10#97×D73C211yesmaximal, characteristic, complemented
11#491×C73C211yesmaximal, characteristic, complemented
12C2×#11924018C2212yes—
13C2×#11924015C2212yes—
14C2×C8×D73C2212yes—
15#14556591C2211yescharacteristic
16#14556586—21no—
17#14556582—21no—
18#14556579C2211yescharacteristic
19#14556576—21no—
20#14556571—21no—
21#14556571C2211yescharacteristic
22#14556567C2212yes—
23#14556566C2211yescharacteristic
24Q8×Dic73C2212yes—
25#14556556—21no—
26#14556556C2211yescharacteristic
27#14556553—21no—
28#14556553C2211yescharacteristic
29#14556549—21no—
30#14556549—21no—
31C42×D73C2211yescharacteristic
32#14556524C2212yes—
33#14556522C2212yes—
34#14556516C2212yes—
35#14556513C2212yes—
36#14556502C2211yescharacteristic
37#14556501C2212yes—
38C4⋊Q8×C73C2211yescharacteristic
39#125×C73C2211yescharacteristic
40#103×C73C2212yes—
41#103×C73C2212yes—
42#97×C73C2211yescharacteristic
43C2×Dic146—21no—
44C2×Dic146C2311yescharacteristic
45C2×D292—21no—
46C2×D292C2311yescharacteristic
47C2×C4×D73—21no—
48C2×C4×D73D411yescharacteristic
49C2×C4×D73D411yescharacteristic
50C2×C4×D73C2311yescharacteristic
51#11924018—24no—
52#11924015—24no—
53C2×#10596831C2312yes—
54C8×D73—24no—
55C4⋊Dic73—21no—
56C4⋊Dic73—21no—
57C4⋊Dic73—22no—
58C4⋊Dic73C2312yes—
59#11924007—22no—
60#11924007—21no—
61#11924005—22no—
62#11924005—21no—
63#11924005—21no—
64#11924005—21no—
65#11924005—21no—
66#11924005—21no—
67C4×Dic73—21no—
68C4×Dic73—22no—
69C4×Dic73D411yescharacteristic
70C4×Dic73D411yescharacteristic
71C4×Dic73C2311yescharacteristic
72C2×Q8×C73C2312yes—
73C2×C8×C73C2312yes—
74C4⋊C4×C73—21no—
75C4⋊C4×C73—21no—
76C4⋊C4×C73—21no—
77C4⋊C4×C73—21no—
78C4⋊C4×C73C2311yescharacteristic
79C4⋊C4×C73C2311yescharacteristic
80C42×C73C2311yescharacteristic
81C22×D73—21no—
82C22×D73C2×D411yescharacteristic
83Q8×C73—22no—
84Q8×C73—22no—
85C2×C4×C73—21no—
86C2×C4×C73—21no—
87C2×C4×C73—22no—
88C2×C4×C73C2×D411yescharacteristic
89C2×C4×C73C2×D411yescharacteristic
90C2×C4×C73C2411yescharacteristic
91C2×Dic73—21no—
92C2×Dic73—22no—
93C2×Dic73C2×D411yescharacteristic
94C2×Dic73C2×D411yescharacteristic
95C2×Dic73C2×D411yescharacteristic
96D292—22no—
97D292—42no—
98C4×D73—22no—
99C4×D73—22no—
100C4×D73—41no—
101C4×D73—42no—
102Dic146—22no—
103Dic146—42no—
104C8×C73—22no—
105#10596831#4114yes—
106C22×C73C22×D411yescharacteristic
107C2×D73—21no—
108C2×D73—21no—
109C2×D73—41no—
110C2×D73—41no—
111C2×D73—41no—
112C2×D73#13712yes—
113C4×C73—21no—
114C4×C73—21no—
115C4×C73—42no—
116C4×C73—41no—
117C4×C73—41no—
118C4×C73C2×#4112yes—
119Dic73—21no—
120Dic73—21no—
121Dic73—21no—
122Dic73—41no—
123Dic73—42no—
124C2×C73#53211yescharacteristic
125C2×C73C2×#13711yescharacteristic
126C2×C73#57511yescharacteristic
127D73—22no—
128D73—81no—
129#3181—731nomaximal, Sylow
130C73#318111yescharacteristic, complemented, Sylow
131#533—731no—
132#529—731no—
133#501—731no—
134#497—731no—
135#491D7311yescharacteristic, complemented
136#489—731no—
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—1461no—
149#125C2×D7311yescharacteristic
150#124—731no—
151#123—1461no—
152C22⋊Q8—732no—
153C22⋊Q8—731no—
154C22⋊Q8—1461no—
155#121—731no—
156C4×Q8—732no—
157C4×Q8—731no—
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#103C2×D7312yes—
168#103C2×D7312yes—
169#102—732no—
170#97—732no—
171#97—731no—
172#97C2×D7311yescharacteristic
173C2×Q8—731no—
174C2×Q8—1461no—
175C2×Q8C22×D7312yes—
176C2×D4—731no—
177C2×D4—1461no—
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—21no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—732no—
192C4⋊C4—1461no—
193C4⋊C4—1462no—
194C4⋊C4—1461no—
195C4⋊C4—1462no—
196C4⋊C4—1461no—
197C4⋊C4C22×D7311yescharacteristic
198C4⋊C4C22×D7311yescharacteristic
199C22⋊C4—1461no—
200C22⋊C4—1461no—
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—731no—
212C23—1461no—
213Q8—22no—
214Q8—22no—
215Q8—2922no—
216Q8—1462no—
217D4—2922no—
218D4—1462no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—2921no—
223C2×C4—2922no—
224C2×C4—731no—
225C2×C4—731no—
226C2×C4—731no—
227C2×C4—1462no—
228C2×C4—1461no—
229C2×C4—1462no—
230C2×C4—1462no—
231C2×C4D4×D7311yescharacteristic
232C2×C4D4×D7311yescharacteristic
233C2×C4C23×D7311yescharacteristic
234C8—22no—
235C8—734no—
236C22—2921no—
237C22—2921no—
238C22—2921no—
239C22—732no—
240C22—1461no—
241C22—1461no—
242C22C2×D4×D7311yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—42no—
248C4—2922no—
249C4—2921no—
250C4—1461no—
251C4—1461no—
252C4—1461no—
253C4#41×D7312yes—
254C2—5841no—
255C2—1462no—
256C2#1798913611yescharacteristic
257C2#137×D7311yescharacteristic
258C2#1798938611yescharacteristic
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#491×C73C2
socleC22×C73C22×D4
hypercenter#491D73
hypocenterC73#3181
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
1. #17989142C2semidirect
3. #17988997C2semidirect
4. #17988979C2semidirect
5. #17988947C2semidirect
6. #17988827C2semidirect
8. #17988691C2semidirect
9. #17988690C2semidirect
10. #97×D73C2semidirect
11. #491×C73C2semidirect
130. C73#3181semidirect
135. #491D73semidirect