Finite Group Databasebeta

← C79×#33758 #34145447

Subgroups — C79×#33758 #34145447

Order 20224.

688 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 688 conjugacy classes of subgroups — too many to draw. Only its 202 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×#466×C79C212yesmaximal, complemented
2C79×#2233C214yesmaximal, complemented
3C79×#2218C214yesmaximal, complemented
4C79×#2184C214yesmaximal, complemented
5C79×#2112C211yesmaximal, characteristic, complemented
6C22×D8×C79C2212yescomplemented
7C23×C8×C79C2211yescharacteristic
8C2×#121×C79—22no—
9C2×D16×C79C2214yescomplemented
10C2×M32×C79C2212yescomplemented
11#466×C79—22no—
12#466×C79—22no—
13#466×C79C2214yes—
14#466×C79C2214yescomplemented
15C2×#107×C79C2212yescomplemented
16C2×#102×C79—22no—
17#367×C79C2214yescomplemented
18#357×C79C2218yescomplemented
19C22⋊C16×C79C2214yescomplemented
20C22×D4×C79—22no—
21C22×D4×C79—42no—
22C23×C4×C79D411yescharacteristic
23C2×D8×C79—22no—
24C2×D8×C79—44no—
25C2×D8×C79C2314yes—
26C22×C8×C79—42no—
27C22×C8×C79D411yescharacteristic
28C22×C8×C79D412yes—
29C22×C8×C79C2312yes—
30C22×C8×C79C2311yescharacteristic
31#121×C79—24no—
32#121×C79—24no—
33#121×C79—42no—
34#121×C79—42no—
35C2×C4⋊C4×C79—22no—
36C2×C22⋊C4×C79—42no—
37D16×C79—44no—
38M32×C79—42no—
39C2×C16×C79C2314yes—
40#107×C79—22no—
41#107×C79C2314yes—
42#102×C79—24no—
43#102×C79—24no—
44C24×C79—42no—
45C24×C79D811yescharacteristic
46C2×D4×C79—24no—
47C2×D4×C79—44no—
48C2×D4×C79—44no—
49C2×D4×C79—44no—
50C2×D4×C79—44no—
51C2×D4×C79—42no—
52C2×D4×C79—88no—
53C22×C4×C79—41no—
54C22×C4×C79—41no—
55C22×C4×C79—42no—
56C22×C4×C79D812yes—
57C22×C4×C79D811yescharacteristic
58C22×C4×C79C2×D412yes—
59C22×C4×C79C2×D411yescharacteristic
60D8×C79—28no—
61D8×C79—44no—
62C2×C8×C79—22no—
63C2×C8×C79—24no—
64C2×C8×C79—41no—
65C2×C8×C79—42no—
66C2×C8×C79C2×D411yescharacteristic
67C2×C8×C79C2×D412yes—
68C2×C8×C79C2411yescharacteristic
69C4⋊C4×C79—24no—
70C4⋊C4×C79—42no—
71C22⋊C4×C79—44no—
72C22⋊C4×C79—44no—
73C16×C79—24no—
74C23×C79—24no—
75C23×C79—41no—
76C23×C79—44no—
77C23×C79—84no—
78C23×C79—84no—
79C23×C79—84no—
80C23×C79C2×D811yescharacteristic
81C23×C79C2×D812yes—
82D4×C79—44no—
83D4×C79—44no—
84D4×C79—84no—
85D4×C79—88no—
86D4×C79—88no—
87C2×C4×C79—21no—
88C2×C4×C79—22no—
89C2×C4×C79—21no—
90C2×C4×C79—22no—
91C2×C4×C79—42no—
92C2×C4×C79—41no—
93C2×C4×C79—44no—
94C2×C4×C79—84no—
95C2×C4×C79C2×D811yescharacteristic
96C2×C4×C79C2×D812yes—
97C2×C4×C79C22×D411yescharacteristic
98C8×C79—21no—
99C8×C79—22no—
100C8×C79H(5,𝔽2)12yes—
101C22×C79—22no—
102C22×C79—22no—
103C22×C79—22no—
104C22×C79—21no—
105C22×C79—44no—
106C22×C79—84no—
107C22×C79—84no—
108C22×C79—84no—
109C22×C79—168no—
110C22×C79#50914yes—
111C22×C79C22×D811yescharacteristic
112C4×C79—21no—
113C4×C79—22no—
114C4×C79—84no—
115C4×C79#53411yescharacteristic
116C4×C79#57511yescharacteristic
117#33758C7911yesmaximal, characteristic, direct product factor, Sylow
118C2×C79—24no—
119C2×C79—41no—
120C2×C79—164no—
121C2×C79#318611yescharacteristic
122C2×C79C2×#50912yes—
123C2×#466C2×C7912yescomplemented
124#2233C2×C7914yescomplemented
125#2218C2×C7914yescomplemented
126#2184C2×C7914yescomplemented
127#2112C2×C7911yescharacteristic, complemented
128C79#3375811yescharacteristic, direct product factor, Sylow
129C22×D8C22×C7912yescomplemented
130C23×C8C22×C7911yescharacteristic
131C2×#121—22no—
132C2×D16C22×C7914yescomplemented
133C2×M32C22×C7912yescomplemented
134#466—22no—
135#466—22no—
136#466C22×C7914yes—
137#466C22×C7914yescomplemented
138C2×#107C22×C7912yescomplemented
139C2×#102—22no—
140#367C22×C7914yescomplemented
141#357C22×C7918yescomplemented
142C22⋊C16C22×C7914yescomplemented
143C22×D4—22no—
144C22×D4—42no—
145C23×C4D4×C7911yescharacteristic
146C2×D8—22no—
147C2×D8—44no—
148C2×D8C23×C7914yes—
149C22×C8—42no—
150C22×C8D4×C7912yes—
151C22×C8D4×C7911yescharacteristic
152C22×C8C23×C7912yes—
153C22×C8C23×C7911yescharacteristic
154#121—24no—
155#121—24no—
156#121—42no—
157#121—42no—
158C2×C4⋊C4—22no—
159C2×C22⋊C4—42no—
160D16—44no—
161M32—42no—
162C2×C16C23×C7914yes—
163#107—22no—
164#107C23×C7914yes—
165#102—24no—
166#102—24no—
167C24—42no—
168C24D8×C7911yescharacteristic
169C2×D4—24no—
170C2×D4—44no—
171C2×D4—44no—
172C2×D4—44no—
173C2×D4—44no—
174C2×D4—42no—
175C2×D4—88no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—42no—
179C22×C4D8×C7912yes—
180C22×C4D8×C7911yescharacteristic
181C22×C4C2×D4×C7912yes—
182C22×C4C2×D4×C7911yescharacteristic
183D8—28no—
184D8—44no—
185C2×C8—22no—
186C2×C8—24no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8C2×D4×C7911yescharacteristic
190C2×C8C2×D4×C7912yes—
191C2×C8C24×C7911yescharacteristic
192C4⋊C4—24no—
193C4⋊C4—42no—
194C22⋊C4—44no—
195C22⋊C4—44no—
196C16—24no—
197C23—24no—
198C23—41no—
199C23—44no—
200C23—84no—
201C23—84no—
202C23—84no—
203C23C2×D8×C7911yescharacteristic
204C23C2×D8×C7912yes—
205D4—44no—
206D4—44no—
207D4—84no—
208D4—88no—
209D4—88no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—44no—
217C2×C4—84no—
218C2×C4C2×D8×C7911yescharacteristic
219C2×C4C2×D8×C7912yes—
220C2×C4C22×D4×C7911yescharacteristic
221C8—22no—
222C8—21no—
223C8H(5,𝔽2)×C7912yes—
224C22—22no—
225C22—22no—
226C22—22no—
227C22—21no—
228C22—44no—
229C22—84no—
230C22—84no—
231C22—84no—
232C22—168no—
233C22#509×C7914yes—
234C22C22×D8×C7911yescharacteristic
235C4—22no—
236C4—21no—
237C4—84no—
238C4#534×C7911yescharacteristic
239C4#575×C7911yescharacteristic
240C2—24no—
241C2—41no—
242C2—164no—
243C2C79×#318611yescharacteristic
244C2C2×#509×C7912yes—
subgroupG/H
center, socleC22×C79C22×D8
commutator, Frattini, cosocleC2×C8C24×C79
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C79 ◁ C23×C4×C79 ◁ C23×C8×C79 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#466×C79C2semidirect
2. C79×#2233C2semidirect
3. C79×#2218C2semidirect
4. C79×#2184C2semidirect
5. C79×#2112C2semidirect
6. C22×D8×C79C22semidirect
9. C2×D16×C79C22semidirect
10. C2×M32×C79C22semidirect
14. #466×C79C22semidirect
15. C2×#107×C79C22semidirect
17. #367×C79C22semidirect
18. #357×C79C22semidirect
19. C22⋊C16×C79C22semidirect
117. #33758C79direct (N × H)
123. C2×#466C2×C79semidirect
124. #2233C2×C79semidirect
125. #2218C2×C79semidirect
126. #2184C2×C79semidirect
127. #2112C2×C79semidirect
128. C79#33758direct (N × H)
129. C22×D8C22×C79semidirect
132. C2×D16C22×C79semidirect
133. C2×M32C22×C79semidirect
137. #466C22×C79semidirect
138. C2×#107C22×C79semidirect
140. #367C22×C79semidirect
141. #357C22×C79semidirect
142. C22⋊C16C22×C79semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C792
C79×#22332
C79×#22182
C79×#21842
C79×#21122
#3375879