Finite Group Databasebeta

← C107×#33752 #41059716

Subgroups — C107×#33752 #41059716

Order 27392.

694 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 214 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×C107C212yesmaximal, complemented
2C107×#2232C214yesmaximal, complemented
3C107×#2215C214yesmaximal, complemented
4C107×#2184C214yesmaximal, complemented
5C2×C22⋊C16×C107C211yesmaximal, characteristic, complemented
6C22×D8×C107C2212yescomplemented
7C23×C8×C107C2211yescharacteristic
8C2×#121×C107—22no—
9C2×D16×C107C2214yescomplemented
10C22×C16×C107C2212yescomplemented
11#466×C107—22no—
12#466×C107—22no—
13#466×C107C2214yes—
14#466×C107C2214yescomplemented
15C2×#107×C107C2212yescomplemented
16C2×#102×C107—22no—
17#366×C107C2214yescomplemented
18#357×C107C2218yescomplemented
19C22⋊C16×C107C2214yescomplemented
20C22×D4×C107—22no—
21C22×D4×C107—42no—
22C23×C4×C107D411yescharacteristic
23C2×D8×C107—22no—
24C2×D8×C107—44no—
25C2×D8×C107C2314yes—
26C22×C8×C107—42no—
27C22×C8×C107D412yes—
28C22×C8×C107D411yescharacteristic
29C22×C8×C107C2312yes—
30C22×C8×C107C2311yescharacteristic
31#121×C107—24no—
32#121×C107—24no—
33#121×C107—42no—
34#121×C107—42no—
35C2×C4⋊C4×C107—22no—
36C2×C22⋊C4×C107—42no—
37D16×C107—44no—
38C2×C16×C107—42no—
39C2×C16×C107C2314yes—
40#107×C107—22no—
41#107×C107C2314yes—
42#102×C107—24no—
43#102×C107—24no—
44C24×C107—42no—
45C24×C107D811yescharacteristic
46C2×D4×C107—24no—
47C2×D4×C107—44no—
48C2×D4×C107—44no—
49C2×D4×C107—44no—
50C2×D4×C107—44no—
51C2×D4×C107—42no—
52C2×D4×C107—88no—
53C22×C4×C107—41no—
54C22×C4×C107—41no—
55C22×C4×C107—42no—
56C22×C4×C107D812yes—
57C22×C4×C107D811yescharacteristic
58C22×C4×C107C2×D412yes—
59C22×C4×C107C2×D411yescharacteristic
60D8×C107—28no—
61D8×C107—44no—
62C2×C8×C107—22no—
63C2×C8×C107—24no—
64C2×C8×C107—42no—
65C2×C8×C107—41no—
66C2×C8×C107C2×D411yescharacteristic
67C2×C8×C107C2×D412yes—
68C2×C8×C107C2411yescharacteristic
69C4⋊C4×C107—24no—
70C4⋊C4×C107—42no—
71C22⋊C4×C107—44no—
72C22⋊C4×C107—44no—
73C16×C107—24no—
74C23×C107—41no—
75C23×C107—41no—
76C23×C107—44no—
77C23×C107—84no—
78C23×C107—84no—
79C23×C107—84no—
80C23×C107D1614yescomplemented
81C23×C107C2×D812yes—
82C23×C107C2×D811yescharacteristic
83D4×C107—44no—
84D4×C107—44no—
85D4×C107—84no—
86D4×C107—88no—
87D4×C107—88no—
88C2×C4×C107—21no—
89C2×C4×C107—22no—
90C2×C4×C107—21no—
91C2×C4×C107—22no—
92C2×C4×C107—42no—
93C2×C4×C107—41no—
94C2×C4×C107—44no—
95C2×C4×C107—84no—
96C2×C4×C107C2×D811yescharacteristic
97C2×C4×C107C2×D812yes—
98C2×C4×C107C22×D411yescharacteristic
99C8×C107—21no—
100C8×C107—22no—
101C8×C107H(5,𝔽2)12yes—
102C22×C107—22no—
103C22×C107—21no—
104C22×C107—22no—
105C22×C107—21no—
106C22×C107—44no—
107C22×C107—84no—
108C22×C107—84no—
109C22×C107—84no—
110C22×C107—168no—
111C22×C107C2×D1614yes—
112C22×C107C2×D1612yes—
113C22×C107C22×D811yescharacteristic
114C4×C107—21no—
115C4×C107—22no—
116C4×C107—84no—
117C4×C107#53411yescharacteristic
118C4×C107#57511yescharacteristic
119#33752C10711yesmaximal, characteristic, direct product factor, Sylow
120C2×C107—24no—
121C2×C107—22no—
122C2×C107—164no—
123C2×C107#318611yescharacteristic
124C2×C107C22×D1611yescharacteristic
125C2×C107#341411yescharacteristic
126C2×#466C2×C10712yescomplemented
127#2232C2×C10714yescomplemented
128#2215C2×C10714yescomplemented
129#2184C2×C10714yescomplemented
130C2×C22⋊C16C2×C10711yescharacteristic, complemented
131C107#3375211yescharacteristic, direct product factor, Sylow
132C22×D8C22×C10712yescomplemented
133C23×C8C22×C10711yescharacteristic
134C2×#121—22no—
135C2×D16C22×C10714yescomplemented
136C22×C16C22×C10712yescomplemented
137#466—22no—
138#466—22no—
139#466C22×C10714yes—
140#466C22×C10714yescomplemented
141C2×#107C22×C10712yescomplemented
142C2×#102—22no—
143#366C22×C10714yescomplemented
144#357C22×C10718yescomplemented
145C22⋊C16C22×C10714yescomplemented
146C22×D4—22no—
147C22×D4—42no—
148C23×C4D4×C10711yescharacteristic
149C2×D8—22no—
150C2×D8—44no—
151C2×D8C23×C10714yes—
152C22×C8—42no—
153C22×C8D4×C10712yes—
154C22×C8D4×C10711yescharacteristic
155C22×C8C23×C10712yes—
156C22×C8C23×C10711yescharacteristic
157#121—24no—
158#121—24no—
159#121—42no—
160#121—42no—
161C2×C4⋊C4—22no—
162C2×C22⋊C4—42no—
163D16—44no—
164C2×C16—42no—
165C2×C16C23×C10714yes—
166#107—22no—
167#107C23×C10714yes—
168#102—24no—
169#102—24no—
170C24—42no—
171C24D8×C10711yescharacteristic
172C2×D4—24no—
173C2×D4—44no—
174C2×D4—44no—
175C2×D4—44no—
176C2×D4—44no—
177C2×D4—42no—
178C2×D4—88no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—42no—
182C22×C4D8×C10712yes—
183C22×C4D8×C10711yescharacteristic
184C22×C4C2×D4×C10712yes—
185C22×C4C2×D4×C10711yescharacteristic
186D8—28no—
187D8—44no—
188C2×C8—22no—
189C2×C8—24no—
190C2×C8—41no—
191C2×C8—42no—
192C2×C8C2×D4×C10711yescharacteristic
193C2×C8C2×D4×C10712yes—
194C2×C8C24×C10711yescharacteristic
195C4⋊C4—24no—
196C4⋊C4—42no—
197C22⋊C4—44no—
198C22⋊C4—44no—
199C16—24no—
200C23—41no—
201C23—41no—
202C23—44no—
203C23—84no—
204C23—84no—
205C23—84no—
206C23D16×C10714yescomplemented
207C23C2×D8×C10712yes—
208C23C2×D8×C10711yescharacteristic
209D4—44no—
210D4—44no—
211D4—84no—
212D4—88no—
213D4—88no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4—84no—
222C2×C4C2×D8×C10711yescharacteristic
223C2×C4C2×D8×C10712yes—
224C2×C4C22×D4×C10711yescharacteristic
225C8—22no—
226C8—21no—
227C8H(5,𝔽2)×C10712yes—
228C22—22no—
229C22—21no—
230C22—22no—
231C22—21no—
232C22—44no—
233C22—84no—
234C22—84no—
235C22—84no—
236C22—168no—
237C22C2×D16×C10714yes—
238C22C2×D16×C10712yes—
239C22C22×D8×C10711yescharacteristic
240C4—22no—
241C4—21no—
242C4—84no—
243C4#534×C10711yescharacteristic
244C4#575×C10711yescharacteristic
245C2—24no—
246C2—22no—
247C2—164no—
248C2C107×#318611yescharacteristic
249C2C22×D16×C10711yescharacteristic
250C2C107×#341411yescharacteristic
subgroupG/H
center, socleC22×C107C22×D8
commutator, Frattini, cosocleC2×C8C24×C107
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ C23×C8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#466×C107C2semidirect
2. C107×#2232C2semidirect
3. C107×#2215C2semidirect
4. C107×#2184C2semidirect
5. C2×C22⋊C16×C107C2semidirect
6. C22×D8×C107C22semidirect
9. C2×D16×C107C22semidirect
10. C22×C16×C107C22semidirect
14. #466×C107C22semidirect
15. C2×#107×C107C22semidirect
17. #366×C107C22semidirect
18. #357×C107C22semidirect
19. C22⋊C16×C107C22semidirect
80. C23×C107D16semidirect
119. #33752C107direct (N × H)
126. C2×#466C2×C107semidirect
127. #2232C2×C107semidirect
128. #2215C2×C107semidirect
129. #2184C2×C107semidirect
130. C2×C22⋊C16C2×C107semidirect
131. C107#33752direct (N × H)
132. C22×D8C22×C107semidirect
135. C2×D16C22×C107semidirect
136. C22×C16C22×C107semidirect
140. #466C22×C107semidirect
141. C2×#107C22×C107semidirect
143. #366C22×C107semidirect
144. #357C22×C107semidirect
145. C22⋊C16C22×C107semidirect
206. C23D16×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1072
C107×#22322
C107×#22152
C107×#21842
C2×C22⋊C16×C1072
#33752107