Finite Group Databasebeta

← #22621007

Subgroups — #22621007

Order 9344.

364 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 109 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#17989198C211yesmaximal, characteristic, complemented
2#17989162C211yesmaximal, characteristic
3#17988979C211yesmaximal, characteristic, complemented
4#17988955C211yesmaximal, characteristic, complemented
5#17988942C211yesmaximal, characteristic, complemented
6#17988811C212yesmaximal, complemented
7#17988795C212yesmaximal, complemented
8#17988748C212yesmaximal
9#17988741C212yesmaximal, complemented
10#17988646C211yesmaximal, characteristic, complemented
11#494×C73C211yesmaximal, characteristic, complemented
12C2×#11924029C2211yescharacteristic
13C2×Q8×D73C2211yescharacteristic
14C2×#11924018C2212yes—
15C2×#11924015C2212yes—
16#14556589C2211yescharacteristic
17#14556586—22no—
18#14556583C2211yescharacteristic
19#14556581—22no—
20#14556580C2211yescharacteristic
21#14556579C2211yescharacteristic
22#14556576—22no—
23#14556569—22no—
24#14556567C2212yes—
25Q8×Dic73C2212yes—
26#14556548C2211yescharacteristic
27#14556520C2212yes—
28#14556516C2212yes—
29#14556515C2212yes—
30#14556515C2212yes—
31#14556513C2212yes—
32#14556503C2212yes—
33#14556502C2211yescharacteristic
34C2×Q16×C73C2212yes—
35C2×Q16×C73C2212yes—
36C4⋊Q8×C73C2211yescharacteristic
37C4⋊Q8×C73C2211yescharacteristic
38C4×C8×C73C2211yescharacteristic
39#11924029—42no—
40C2×Dic146—21no—
41C2×Dic146C2311yescharacteristic
42Q8×D73—42no—
43C2×D292—21no—
44C2×D292C2311yescharacteristic
45C2×C4×D73—21no—
46C2×C4×D73—21no—
47C2×C4×D73C2311yescharacteristic
48#11924018—42no—
49#11924015—42no—
50C2×#10596831C2312yes—
51C4⋊Dic73—22no—
52C4⋊Dic73C2312yes—
53#11924007—22no—
54#11924007—22no—
55#11924007—22no—
56#11924007D412yes—
57#11924005—22no—
58#11924005—22no—
59#11924005—22no—
60#11924005D412yes—
61C4×Dic73—22no—
62C4×Dic73C2311yescharacteristic
63C2×Q8×C73C2311yescharacteristic
64C2×Q8×C73C2311yescharacteristic
65C2×Q8×C73C2312yes—
66Q16×C73—42no—
67Q16×C73—42no—
68C2×C8×C73C2312yes—
69C4⋊C4×C73—22no—
70C4⋊C4×C73—22no—
71C42×C73C2311yescharacteristic
72C22×D73—21no—
73C22×D73C2×D411yescharacteristic
74Q8×C73—22no—
75Q8×C73—22no—
76Q8×C73—22no—
77Q8×C73—22no—
78C2×C4×C73—22no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73C2×D412yes—
82C2×C4×C73C2411yescharacteristic
83C2×Dic73—22no—
84C2×Dic73—21no—
85C2×Dic73C2×D412yes—
86C2×Dic73C2×D411yescharacteristic
87D292—22no—
88D292—42no—
89C4×D73—22no—
90C4×D73—42no—
91C4×D73—42no—
92Dic146—22no—
93Dic146—42no—
94C8×C73—22no—
95#10596831—22no—
96C22×C73C22×D411yescharacteristic
97C2×D73—21no—
98C2×D73—22no—
99C2×D73—41no—
100C2×D73—42no—
101C4×C73—22no—
102C4×C73—41no—
103C4×C73—41no—
104C4×C73—42no—
105C4×C73H(5,𝔽2)12yes—
106Dic73—21no—
107Dic73—22no—
108Dic73—41no—
109Dic73—42no—
110C2×C73#53511yescharacteristic
111C2×C73#57812yes—
112D73—41no—
113D73—81no—
114#3223—731nomaximal, Sylow
115C73#322311yescharacteristic, complemented, Sylow
116#541—731no—
117#536—731no—
118#497—731no—
119#494D7311yescharacteristic, complemented
120#491—731no—
121#488—731no—
122#464—732no—
123#462—732no—
124#452—732no—
125#451—732no—
126#433—731no—
127C2×#41—731no—
128C22×Q8—731no—
129C2×Q16—732no—
130C2×Q16C2×D7312yes—
131C2×Q16C2×D7312yes—
132C2×SD16—732no—
133C4⋊Q8—731no—
134C4⋊Q8C2×D7311yescharacteristic
135C4⋊Q8C2×D7311yescharacteristic
136#126—1462no—
137#125—731no—
138#125—1462no—
139#124—731no—
140#124—731no—
141#123—1462no—
142C22⋊Q8—732no—
143C22⋊Q8—1462no—
144C4×Q8—732no—
145#117—731no—
146C4⋊C8—732no—
147#103—732no—
148#103—732no—
149#103—732no—
150#102—732no—
151C22⋊C8—732no—
152#97—731no—
153C4×C8C2×D7311yescharacteristic
154#41—2922no—
155C2×Q8—2922no—
156C2×Q8—731no—
157C2×Q8—1461no—
158C2×Q8C22×D7311yescharacteristic
159C2×Q8C22×D7311yescharacteristic
160C2×Q8C22×D7312yes—
161C2×D4—731no—
162C2×D4—1461no—
163C22×C4—731no—
164C22×C4—1461no—
165C22×C4—1461no—
166Q16—42no—
167Q16—42no—
168Q16—2922no—
169SD16—2922no—
170C2×C8—732no—
171C2×C8C22×D7312yes—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—732no—
175C4⋊C4—732no—
176C4⋊C4—1462no—
177C4⋊C4—1462no—
178C4⋊C4—1462no—
179C4⋊C4—1462no—
180C22⋊C4—732no—
181C22⋊C4—1462no—
182C22⋊C4—1462no—
183C22⋊C4—1462no—
184C42—731no—
185C42—1462no—
186C42C22×D7311yescharacteristic
187C23—731no—
188C23—1461no—
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—22no—
193Q8—2922no—
194Q8—1462no—
195D4—2922no—
196D4—1462no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—2922no—
201C2×C4—2922no—
202C2×C4—732no—
203C2×C4—731no—
204C2×C4—1462no—
205C2×C4—1461no—
206C2×C4—1462no—
207C2×C4D4×D7312yes—
208C2×C4C23×D7311yescharacteristic
209C8—22no—
210C8—1462no—
211C22—2922no—
212C22—2921no—
213C22—1462no—
214C22—1461no—
215C22C2×D4×D7311yescharacteristic
216C4—22no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—2922no—
221C4—2921no—
222C4—1462no—
223C4—1461no—
224C4#1455663612yes—
225C2—2921no—
226C2—5841no—
227C2#1798915011yescharacteristic
228C2#1798940012yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#494×C73C2
socleC22×C73C22×D4
hypercenter#494D73
hypocenterC73#3223
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #17989198C2semidirect
3. #17988979C2semidirect
4. #17988955C2semidirect
5. #17988942C2semidirect
6. #17988811C2semidirect
7. #17988795C2semidirect
9. #17988741C2semidirect
10. #17988646C2semidirect
11. #494×C73C2semidirect
115. C73#3223semidirect
119. #494D73semidirect