Finite Group Databasebeta

← C2×#455×C179 #37506237

Subgroups — C2×#455×C179 #37506237

Order 22912.

760 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 216 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
1C2×H(5,𝔽2)×C179C211yesmaximal, characteristic
2C2×#137×C179C212yesmaximal, complemented
3C2×#124×C179C211yesmaximal, characteristic, complemented
4#455×C179C218yesmaximal, direct product factor
5C2×#104×C179C212yesmaximal, complemented
6C2×#100×C179C211yesmaximal, characteristic, complemented
7H(5,𝔽2)×C179—24no—
8H(5,𝔽2)×C179—22no—
9H(5,𝔽2)×C179C2214yes—
10C2×#41×C179—22no—
11C2×#41×C179C2212yes—
12C22×Q8×C179C2211yescharacteristic, complemented
13C22×D4×C179—22no—
14C22×D4×C179—22no—
15C22×D4×C179C2211yescharacteristic
16#137×C179—24no—
17#137×C179C2218yescomplemented
18C2×Q16×C179—22no—
19C2×SD16×C179—22no—
20C2×M16×C179C2212yescomplemented
21#124×C179—22no—
22#124×C179C2214yescomplemented
23C2×C22⋊C4×C179—22no—
24C2×C42×C179C2211yescharacteristic, complemented
25#104×C179C2218yescomplemented
26#100×C179C2214yescomplemented
27C24×C179—22no—
28C24×C179D412yes—
29#41×C179—28no—
30#41×C179—28no—
31#41×C179—22no—
32#41×C179—22no—
33#41×C179D414yes—
34#41×C179C2314yes—
35C2×Q8×C179—21no—
36C2×Q8×C179—22no—
37C2×Q8×C179—22no—
38C2×Q8×C179D412yes—
39C2×Q8×C179C2312yescomplemented
40C2×D4×C179—24no—
41C2×D4×C179—28no—
42C2×D4×C179—28no—
43C2×D4×C179—22no—
44C2×D4×C179—28no—
45C2×D4×C179—28no—
46C2×D4×C179—22no—
47C2×D4×C179—22no—
48C2×D4×C179D412yes—
49C2×D4×C179D412yes—
50C2×D4×C179C2312yes—
51C22×C4×C179—22no—
52C22×C4×C179—22no—
53C22×C4×C179—21no—
54C22×C4×C179—21no—
55C22×C4×C179C2311yescharacteristic
56Q16×C179—28no—
57SD16×C179—28no—
58M16×C179—22no—
59M16×C179C2314yescomplemented
60C2×C8×C179—22no—
61C22⋊C4×C179—28no—
62C42×C179—21no—
63C42×C179C2312yescomplemented
64C23×C179—28no—
65C23×C179—22no—
66C23×C179—22no—
67C23×C179—22no—
68C23×C179—44no—
69C23×C179—84no—
70C23×C179C2×D411yescharacteristic
71C23×C179C2×D414yes—
72Q8×C179—22no—
73Q8×C179—24no—
74Q8×C179—42no—
75Q8×C179C2×D414yes—
76D4×C179—216no—
77D4×C179—24no—
78D4×C179—24no—
79D4×C179—24no—
80D4×C179—22no—
81D4×C179—24no—
82D4×C179C2×D414yes—
83C2×C4×C179—28no—
84C2×C4×C179—22no—
85C2×C4×C179—24no—
86C2×C4×C179—24no—
87C2×C4×C179—22no—
88C2×C4×C179—22no—
89C2×C4×C179—42no—
90C2×C4×C179—41no—
91C2×C4×C179—41no—
92C2×C4×C179C2×D411yescharacteristic
93C2×C4×C179C2×D412yes—
94C2×C4×C179C2×D412yes—
95C2×C4×C179C2411yescharacteristic
96C8×C179—24no—
97C22×C179—22no—
98C22×C179—24no—
99C22×C179—24no—
100C22×C179—44no—
101C22×C179—44no—
102C22×C179—44no—
103C22×C179—82no—
104C22×C179—88no—
105C22×C179#12011yescharacteristic
106C22×C179#12011yescharacteristic
107C22×C179C22×D411yescharacteristic
108C4×C179—24no—
109C4×C179—42no—
110C4×C179—42no—
111C4×C179#12012yes—
112C4×C179C22×D412yes—
113C2×C179—21no—
114C2×C179—21no—
115C2×C179—44no—
116C2×C179—44no—
117C2×C179#45512yesdirect product factor
118C2×C179C2×#12011yescharacteristic
119C179C2×#45511yescharacteristic, direct product factor, Sylow
120C2×#455C17911yesmaximal, characteristic, direct product factor, Sylow
121C2×H(5,𝔽2)C2×C17911yescharacteristic
122C2×#137C2×C17912yescomplemented
123C2×#124C2×C17911yescharacteristic, complemented
124#455C2×C17918yesdirect product factor
125C2×#104C2×C17912yescomplemented
126C2×#100C2×C17911yescharacteristic, complemented
127H(5,𝔽2)—24no—
128H(5,𝔽2)—22no—
129H(5,𝔽2)C22×C17914yes—
130C2×#41—22no—
131C2×#41C22×C17912yes—
132C22×Q8C22×C17911yescharacteristic, complemented
133C22×D4—22no—
134C22×D4—22no—
135C22×D4C22×C17911yescharacteristic
136#137—24no—
137#137C22×C17918yescomplemented
138C2×Q16—22no—
139C2×SD16—22no—
140C2×M16C22×C17912yescomplemented
141#124—22no—
142#124C22×C17914yescomplemented
143C2×C22⋊C4—22no—
144C2×C42C22×C17911yescharacteristic, complemented
145#104C22×C17918yescomplemented
146#100C22×C17914yescomplemented
147C24—22no—
148C24D4×C17912yes—
149#41—28no—
150#41—28no—
151#41—22no—
152#41—22no—
153#41D4×C17914yes—
154#41C23×C17914yes—
155C2×Q8—21no—
156C2×Q8—22no—
157C2×Q8—22no—
158C2×Q8D4×C17912yes—
159C2×Q8C23×C17912yescomplemented
160C2×D4—24no—
161C2×D4—28no—
162C2×D4—28no—
163C2×D4—22no—
164C2×D4—28no—
165C2×D4—28no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4D4×C17912yes—
169C2×D4D4×C17912yes—
170C2×D4C23×C17912yes—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4C23×C17911yescharacteristic
176Q16—28no—
177SD16—28no—
178M16—22no—
179M16C23×C17914yescomplemented
180C2×C8—22no—
181C22⋊C4—28no—
182C42—21no—
183C42C23×C17912yescomplemented
184C23—28no—
185C23—22no—
186C23—22no—
187C23—22no—
188C23—44no—
189C23—84no—
190C23C2×D4×C17911yescharacteristic
191C23C2×D4×C17914yes—
192Q8—22no—
193Q8—24no—
194Q8—42no—
195Q8C2×D4×C17914yes—
196D4—216no—
197D4—24no—
198D4—24no—
199D4—24no—
200D4—22no—
201D4—24no—
202D4C2×D4×C17914yes—
203C2×C4—28no—
204C2×C4—22no—
205C2×C4—24no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4C2×D4×C17911yescharacteristic
213C2×C4C2×D4×C17912yes—
214C2×C4C2×D4×C17912yes—
215C2×C4C24×C17911yescharacteristic
216C8—24no—
217C22—22no—
218C22—24no—
219C22—24no—
220C22—44no—
221C22—44no—
222C22—44no—
223C22—82no—
224C22—88no—
225C22#120×C17911yescharacteristic
226C22#120×C17911yescharacteristic
227C22C22×D4×C17911yescharacteristic
228C4—24no—
229C4—42no—
230C4—42no—
231C4#120×C17912yes—
232C4C22×D4×C17912yes—
233C2—21no—
234C2—21no—
235C2—44no—
236C2—44no—
237C2#455×C17912yesdirect product factor
238C2C2×#120×C17911yescharacteristic
subgroupG/H
center, socleC22×C179#120
commutator, Frattini, cosocleC2×C4C24×C179
prime radicalC2×H(5,𝔽2)×C179C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C179 ◁ C22×C4×C179 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#137×C179C2semidirect
3. C2×#124×C179C2semidirect
4. #455×C179C2direct (N × H)
5. C2×#104×C179C2semidirect
6. C2×#100×C179C2semidirect
12. C22×Q8×C179C22semidirect
17. #137×C179C22semidirect
20. C2×M16×C179C22semidirect
22. #124×C179C22semidirect
24. C2×C42×C179C22semidirect
25. #104×C179C22semidirect
26. #100×C179C22semidirect
39. C2×Q8×C179C23semidirect
59. M16×C179C23semidirect
63. C42×C179C23semidirect
117. C2×C179#455direct (N × H)
119. C179C2×#455direct (N × H)
120. C2×#455C179direct (N × H)
122. C2×#137C2×C179semidirect
123. C2×#124C2×C179semidirect
124. #455C2×C179direct (N × H)
125. C2×#104C2×C179semidirect
126. C2×#100C2×C179semidirect
132. C22×Q8C22×C179semidirect
137. #137C22×C179semidirect
140. C2×M16C22×C179semidirect
142. #124C22×C179semidirect
144. C2×C42C22×C179semidirect
145. #104C22×C179semidirect
146. #100C22×C179semidirect
159. C2×Q8C23×C179semidirect
179. M16C23×C179semidirect
183. C42C23×C179semidirect
237. C2#455×C179direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×H(5,𝔽2)×C1792
C2×#137×C1792
C2×#124×C1792
#455×C1792
C2×#104×C1792
C2×#100×C1792
C2×#455179