Finite Group Databasebeta

← #22619336

Subgroups — #22619336

Order 9344.

716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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#17989423C211yesmaximal, characteristic
2#17989161C212yesmaximal, complemented
3#17988776C218yesmaximal, complemented
4#17988561C211yesmaximal, characteristic, complemented
5#17988560C212yesmaximal, complemented
6#536×C73C211yesmaximal, characteristic, complemented
7#14556639—21no—
8#14556638—22no—
9#14556637—22no—
10#14556636—21no—
11#14556636C2214yes—
12C2×#11924028—22no—
13C2×#11924028C2212yes—
14#41×D73—24no—
15#14556589—22no—
16#14556580—22no—
17#14556574C2218yescomplemented
18#14556567—24no—
19#14556550C2212yescomplemented
20#14556506C2214yescomplemented
21#14556505C2218yescomplemented
22C2×#41×C73C2211yescharacteristic
23C22×Q8×C73C2211yescharacteristic, complemented
24C4⋊Q8×C73—21no—
25#124×C73—21no—
26#123×C73C2214yescomplemented
27C22⋊Q8×C73—22no—
28#117×C73C2211yescharacteristic, complemented
29#11924029—24no—
30#11924028—24no—
31#11924028—24no—
32#11924028—22no—
33#11924028—22no—
34#11924028—24no—
35#11924028—22no—
36#11924028—22no—
37#11924027—24no—
38#11924027—28no—
39C2×Dic146—22no—
40C2×Dic146D412yes—
41Q8×D73—24no—
42C2×D292—22no—
43C2×D292D412yes—
44C2×C22⋊D73—24no—
45C2×C22⋊D73C2314yes—
46D4×D73—24no—
47D4×D73—28no—
48C2×C4×D73—24no—
49C2×C4×D73D414yes—
50C4⋊Dic73—22no—
51#11924007—28no—
52C22⋊Dic73C2314yes—
53#11924005—28no—
54C4×Dic73—22no—
55#41×C73—22no—
56#41×C73—22no—
57C2×Q8×C73—21no—
58C2×Q8×C73—21no—
59C2×Q8×C73—22no—
60C2×Q8×C73—22no—
61C2×Q8×C73D411yescharacteristic
62C2×D4×C73D411yescharacteristic
63C2×D4×C73C2312yes—
64C22×C4×C73D412yes—
65C22×C4×C73C2312yes—
66C22×C4×C73C2311yescharacteristic
67C4⋊C4×C73—21no—
68C4⋊C4×C73—24no—
69C22⋊C4×C73—24no—
70C22⋊C4×C73C2312yes—
71C42×C73—21no—
72C23×C73C2×D412yes—
73C23×C73C2411yescharacteristic
74C22×D73—24no—
75C22×D73C2×D414yes—
76Q8×C73—22no—
77Q8×C73—41no—
78Q8×C73—42no—
79Q8×C73—41no—
80D4×C73—24no—
81D4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—22no—
84C2×C4×C73—22no—
85C2×C4×C73—22no—
86C2×C4×C73—24no—
87C2×C4×C73C2×D412yes—
88C2×C4×C73C2×D412yes—
89C2×C4×C73C2×D412yes—
90C2×C4×C73C2×D411yescharacteristic
91C2×C4×C73C2×D411yescharacteristic
92C22⋊D73—28no—
93C22⋊D73—24no—
94C22⋊D73—24no—
95C2×Dic73—24no—
96C2×Dic73—24no—
97C2×Dic73C2×D414yes—
98D292—24no—
99D292—22no—
100D292—22no—
101C4×D73—28no—
102C4×D73—24no—
103C4×D73—24no—
104Dic146—24no—
105Dic146—22no—
106Dic146—22no—
107C22×C73—22no—
108C22×C73—41no—
109C22×C73—42no—
110C22×C73C22×D412yes—
111C22×C73C22×D411yescharacteristic
112C2×D73—24no—
113C2×D73—44no—
114C2×D73—84no—
115C4×C73—22no—
116C4×C73—42no—
117C4×C73—42no—
118C4×C73#12011yescharacteristic
119C4×C73#12012yes—
120C4×C73#12011yescharacteristic
121Dic73—24no—
122Dic73—44no—
123C2×C73—22no—
124C2×C73—21no—
125C2×C73—42no—
126C2×C73C2×#12011yescharacteristic
127D73—44no—
128#3028—731nomaximal, Sylow
129C73#302811yescharacteristic, complemented, Sylow
130#585—731no—
131#536—732no—
132#536D7311yescharacteristic, complemented
133#458—738no—
134#410—731no—
135#410—732no—
1362−1+4—1462no—
1372−1+4—1461no—
138H(5,𝔽2)—734no—
139H(5,𝔽2)—1462no—
140H(5,𝔽2)—1461no—
141C2×#41—732no—
142C2×#41—1464no—
143C2×#41—1462no—
144C2×#41C2×D7311yescharacteristic
145C22×Q8C2×D7311yescharacteristic, complemented
146C4⋊Q8—21no—
147C4⋊Q8—1462no—
148#124—21no—
149#124—1462no—
150#123—738no—
151#123C2×D7314yescomplemented
152C22⋊Q8—22no—
153C22⋊Q8—1464no—
154#117—732no—
155#117C2×D7311yescharacteristic, complemented
156#99—734no—
157#99—738no—
158#41—22no—
159#41—22no—
160#41—1464no—
161#41—1464no—
162#41—1468no—
163#41—1464no—
164#41—1464no—
165#41—1462no—
166#41—1462no—
167#41—1462no—
168#41—1462no—
169#41—1464no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—21no—
173C2×Q8—21no—
174C2×Q8—732no—
175C2×Q8—1462no—
176C2×Q8—1464no—
177C2×Q8C22⋊D7311yescharacteristic
178C2×D4—734no—
179C2×D4—732no—
180C2×D4—1462no—
181C2×D4—1468no—
182C2×D4—1464no—
183C2×D4—1464no—
184C2×D4C22⋊D7311yescharacteristic
185C2×D4C22×D7312yes—
186C22×C4—734no—
187C22×C4—1464no—
188C22×C4C22⋊D7312yes—
189C22×C4C22×D7312yes—
190C22×C4C22×D7311yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—24no—
193C4⋊C4—1468no—
194C4⋊C4—1462no—
195C22⋊C4—24no—
196C22⋊C4—734no—
197C22⋊C4—1468no—
198C22⋊C4C22×D7312yes—
199C42—21no—
200C42—1462no—
201C23—734no—
202C23—1464no—
203C23C2×C22⋊D7312yes—
204C23C23×D7311yescharacteristic
205Q8—22no—
206Q8—41no—
207Q8—41no—
208Q8—42no—
209Q8—1464no—
210Q8—1462no—
211Q8—1462no—
212D4—24no—
213D4—22no—
214D4—1464no—
215D4—1468no—
216D4—1464no—
217D4—1464no—
218D4—1462no—
219D4—1462no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—734no—
226C2×C4—1468no—
227C2×C4—1464no—
228C2×C4—1464no—
229C2×C4—1464no—
230C2×C4—1464no—
231C2×C4D4×D7312yes—
232C2×C4D4×D7312yes—
233C2×C4C2×C22⋊D7312yes—
234C2×C4C2×C22⋊D7311yescharacteristic
235C2×C4C2×C22⋊D7311yescharacteristic
236C22—22no—
237C22—41no—
238C22—42no—
239C22—2924no—
240C22—5844no—
241C22—1464no—
242C22C2×D4×D7312yes—
243C22C22×C22⋊D7311yescharacteristic
244C4—22no—
245C4—42no—
246C4—42no—
247C4—2924no—
248C4—1464no—
249C4#1455655911yescharacteristic
250C4#1455655911yescharacteristic
251C4#1455655912yes—
252C2—21no—
253C2—22no—
254C2—42no—
255C2—2924no—
256C2C2×#1455655911yescharacteristic
subgroupG/H
centerC2C2×#14556559
commutatorC23×C73C24
FrattiniC23C23×D73
Fitting#536×C73C2
socleC2×C73C2×#120
hypercenter#536D73
hypocenterC73#3028
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #17989161C2semidirect
3. #17988776C2semidirect
4. #17988561C2semidirect
5. #17988560C2semidirect
6. #536×C73C2semidirect
17. #14556574C22semidirect
19. #14556550C22semidirect
20. #14556506C22semidirect
21. #14556505C22semidirect
23. C22×Q8×C73C22semidirect
26. #123×C73C22semidirect
28. #117×C73C22semidirect
129. C73#3028semidirect
132. #536D73semidirect
145. C22×Q8C2×D73semidirect
151. #123C2×D73semidirect
155. #117C2×D73semidirect