Finite Group Databasebeta

← C107×#13795 #41039759

Subgroups — C107×#13795 #41039759

Order 27392.

2782 conjugacy classes of subgroups.

The subgroup lattice has 292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#117×C107C212yesmaximal
2C23×C4⋊C4×C107C211yesmaximal, characteristic
3C107×C4⋊#95C218yesmaximal, complemented
4C107×C22⋊#95C214yesmaximal
5C24×C4×C107C2212yes—
6C24×C4×C107C2211yescharacteristic
7C2×#117×C107—28no—
8C2×#117×C107—28no—
9C2×#117×C107C4116yescomplemented
10C22×C4⋊C4×C107—28no—
11C22×C4⋊C4×C107C418yescomplemented
12C22×C4⋊C4×C107C2214yes—
13C22×C4⋊C4×C107C2214yes—
14C22×C22⋊C4×C107C2214yes—
15C22×C42×C107C2214yes—
16C2×#95×C107C22116yes—
17C25×C107C2311yescharacteristic
18C23×C4×C107—28no—
19C23×C4×C107—48no—
20C23×C4×C107C2×C418yes—
21C23×C4×C107C2×C414yes—
22C23×C4×C107C2×C418yes—
23C23×C4×C107D418yes—
24C23×C4×C107D414yes—
25C23×C4×C107Q814yes—
26C23×C4×C107C2318yes—
27C23×C4×C107C2314yes—
28C23×C4×C107C2312yes—
29#117×C107—264no—
30C2×C4⋊C4×C107—232no—
31C2×C4⋊C4×C107—28no—
32C2×C4⋊C4×C107—28no—
33C2×C4⋊C4×C107—28no—
34C2×C4⋊C4×C107—28no—
35C2×C4⋊C4×C107C2×C4116yes—
36C2×C4⋊C4×C107C2×C4116yescomplemented
37C2×C22⋊C4×C107—28no—
38C2×C22⋊C4×C107—28no—
39C2×C22⋊C4×C107C2×C4116yes—
40C2×C42×C107—28no—
41C2×C42×C107—28no—
42C2×C42×C107C2×C4116yescomplemented
43#95×C107—416no—
44C24×C107—24no—
45C24×C107—24no—
46C24×C107C22×C414yes—
47C24×C107C22×C412yes—
48C24×C107C2×D412yes—
49C24×C107C2×D414yes—
50C24×C107C2×Q812yes—
51C24×C107C2411yescharacteristic
52C22×C4×C107—216no—
53C22×C4×C107—28no—
54C22×C4×C107—28no—
55C22×C4×C107—28no—
56C22×C4×C107—216no—
57C22×C4×C107—216no—
58C22×C4×C107—216no—
59C22×C4×C107—416no—
60C22×C4×C107—432no—
61C22×C4×C107C42116yes—
62C22×C4×C107C22⋊C4116yes—
63C22×C4×C107C22⋊C4132yes—
64C22×C4×C107C4⋊C4116yes—
65C22×C4×C107C4⋊C4132yes—
66C22×C4×C107C22×C4116yes—
67C22×C4×C107C22×C418yes—
68C22×C4×C107C22×C414yes—
69C22×C4×C107C22×C414yes—
70C22×C4×C107C22×C414yes—
71C22×C4×C107C2×D414yes—
72C22×C4×C107C2×D414yes—
73C22×C4×C107C2×D414yes—
74C22×C4×C107C2×Q814yes—
75C4⋊C4×C107—232no—
76C4⋊C4×C107—232no—
77C22⋊C4×C107—232no—
78C42×C107—232no—
79C23×C107—24no—
80C23×C107—24no—
81C23×C107—216no—
82C23×C107—28no—
83C23×C107—28no—
84C23×C107—28no—
85C23×C107—28no—
86C23×C107C2×C4214yes—
87C23×C107C2×C22⋊C418yes—
88C23×C107C2×C22⋊C414yes—
89C23×C107C2×C4⋊C414yes—
90C23×C107C2×C4⋊C418yes—
91C23×C107C23×C411yescharacteristic
92C23×C107C23×C412yes—
93C23×C107C22×D412yes—
94C23×C107C22×D411yescharacteristic
95C23×C107C22×Q811yescharacteristic
96C23×C107H(5,𝔽2)14yes—
97C23×C1072−1+414yes—
98C2×C4×C107—216no—
99C2×C4×C107—28no—
100C2×C4×C107—216no—
101C2×C4×C107—232no—
102C2×C4×C107—432no—
103C2×C4×C107—48no—
104C2×C4×C107—416no—
105C2×C4×C107—48no—
106C2×C4×C107—416no—
107C2×C4×C107#95164yescomplemented
108C2×C4×C107C2×C4218yes—
109C2×C4×C107C2×C22⋊C418yes—
110C2×C4×C107C2×C22⋊C418yes—
111C2×C4×C107C2×C22⋊C418yes—
112C2×C4×C107C2×C4⋊C418yes—
113C2×C4×C107C2×C4⋊C418yes—
114C2×C4×C107C2×C4⋊C418yes—
115C22×C107—24no—
116C22×C107—24no—
117C22×C107—216no—
118C22×C107—28no—
119C22×C107—216no—
120C22×C107—28no—
121C22×C107C2×#9518yes—
122C22×C107C22×C4211yescharacteristic
123C22×C107C22×C22⋊C411yescharacteristic
124C22×C107C22×C22⋊C412yes—
125C22×C107C22×C4⋊C411yescharacteristic
126C22×C107C22×C4⋊C412yes—
127C22×C107#51812yes—
128C22×C107#51912yes—
129C22×C107#52018yes—
130C22×C107#53514yes—
131C22×C107#53614yes—
132C22×C107#53714yes—
133C22×C107#54414yes—
134C4×C107—48no—
135C4×C107—416no—
136C4×C107C2×#95116yes—
137#13795C10711yesmaximal, characteristic, direct product factor, Sylow
138C2×C107—28no—
139C2×C107C22×#9511yescharacteristic
140C2×C107#227412yes—
141C2×C107#230911yescharacteristic
142C2×C107#231011yescharacteristic
143C2×C107#231114yes—
144C2×C107#231612yes—
145C2×C107#231714yes—
146C22×#117C2×C10712yes—
147C23×C4⋊C4C2×C10711yescharacteristic
148C4⋊#95C2×C10718yescomplemented
149C22⋊#95C2×C10714yes—
150C107#1379511yescharacteristic, direct product factor, Sylow
151C24×C4C22×C10712yes—
152C24×C4C22×C10711yescharacteristic
153C2×#117—28no—
154C2×#117—28no—
155C2×#117C4×C107116yescomplemented
156C22×C4⋊C4—28no—
157C22×C4⋊C4C4×C10718yescomplemented
158C22×C4⋊C4C22×C10714yes—
159C22×C4⋊C4C22×C10714yes—
160C22×C22⋊C4C22×C10714yes—
161C22×C42C22×C10714yes—
162C2×#95C22×C107116yes—
163C25C23×C10711yescharacteristic
164C23×C4—28no—
165C23×C4—48no—
166C23×C4C2×C4×C10718yes—
167C23×C4C2×C4×C10714yes—
168C23×C4C2×C4×C10718yes—
169C23×C4D4×C10718yes—
170C23×C4D4×C10714yes—
171C23×C4Q8×C10714yes—
172C23×C4C23×C10718yes—
173C23×C4C23×C10714yes—
174C23×C4C23×C10712yes—
175#117—264no—
176C2×C4⋊C4—232no—
177C2×C4⋊C4—28no—
178C2×C4⋊C4—28no—
179C2×C4⋊C4—28no—
180C2×C4⋊C4—28no—
181C2×C4⋊C4C2×C4×C107116yes—
182C2×C4⋊C4C2×C4×C107116yescomplemented
183C2×C22⋊C4—28no—
184C2×C22⋊C4—28no—
185C2×C22⋊C4C2×C4×C107116yes—
186C2×C42—28no—
187C2×C42—28no—
188C2×C42C2×C4×C107116yescomplemented
189#95—416no—
190C24—24no—
191C24—24no—
192C24C22×C4×C10714yes—
193C24C22×C4×C10712yes—
194C24C2×D4×C10712yes—
195C24C2×D4×C10714yes—
196C24C2×Q8×C10712yes—
197C24C24×C10711yescharacteristic
198C22×C4—216no—
199C22×C4—28no—
200C22×C4—28no—
201C22×C4—28no—
202C22×C4—216no—
203C22×C4—216no—
204C22×C4—216no—
205C22×C4—416no—
206C22×C4—432no—
207C22×C4C42×C107116yes—
208C22×C4C22⋊C4×C107116yes—
209C22×C4C22⋊C4×C107132yes—
210C22×C4C4⋊C4×C107116yes—
211C22×C4C4⋊C4×C107132yes—
212C22×C4C22×C4×C107116yes—
213C22×C4C22×C4×C10718yes—
214C22×C4C22×C4×C10714yes—
215C22×C4C22×C4×C10714yes—
216C22×C4C22×C4×C10714yes—
217C22×C4C2×D4×C10714yes—
218C22×C4C2×D4×C10714yes—
219C22×C4C2×D4×C10714yes—
220C22×C4C2×Q8×C10714yes—
221C4⋊C4—232no—
222C4⋊C4—232no—
223C22⋊C4—232no—
224C42—232no—
225C23—24no—
226C23—24no—
227C23—216no—
228C23—28no—
229C23—28no—
230C23—28no—
231C23—28no—
232C23C2×C42×C10714yes—
233C23C2×C22⋊C4×C10718yes—
234C23C2×C22⋊C4×C10714yes—
235C23C2×C4⋊C4×C10714yes—
236C23C2×C4⋊C4×C10718yes—
237C23C23×C4×C10711yescharacteristic
238C23C23×C4×C10712yes—
239C23C22×D4×C10712yes—
240C23C22×D4×C10711yescharacteristic
241C23C22×Q8×C10711yescharacteristic
242C23H(5,𝔽2)×C10714yes—
243C232−1+4×C10714yes—
244C2×C4—216no—
245C2×C4—28no—
246C2×C4—216no—
247C2×C4—232no—
248C2×C4—432no—
249C2×C4—416no—
250C2×C4—48no—
251C2×C4—48no—
252C2×C4—416no—
253C2×C4#95×C107164yescomplemented
254C2×C4C2×C42×C10718yes—
255C2×C4C2×C22⋊C4×C10718yes—
256C2×C4C2×C22⋊C4×C10718yes—
257C2×C4C2×C22⋊C4×C10718yes—
258C2×C4C2×C4⋊C4×C10718yes—
259C2×C4C2×C4⋊C4×C10718yes—
260C2×C4C2×C4⋊C4×C10718yes—
261C22—28no—
262C22—24no—
263C22—24no—
264C22—216no—
265C22—28no—
266C22—216no—
267C22C2×#95×C10718yes—
268C22C22×C42×C10711yescharacteristic
269C22C22×C22⋊C4×C10711yescharacteristic
270C22C22×C22⋊C4×C10712yes—
271C22C22×C4⋊C4×C10711yescharacteristic
272C22C22×C4⋊C4×C10712yes—
273C22#518×C10712yes—
274C22#519×C10712yes—
275C22#520×C10718yes—
276C22#535×C10714yes—
277C22#536×C10714yes—
278C22#537×C10714yes—
279C22#544×C10714yes—
280C4—48no—
281C4—416no—
282C4C2×#95×C107116yes—
283C2—28no—
284C2C22×#95×C10711yescharacteristic
285C2C107×#227412yes—
286C2C107×#230911yescharacteristic
287C2C107×#231011yescharacteristic
288C2C107×#231114yes—
289C2C107×#231612yes—
290C2C107×#231714yes—
subgroupG/H
center, socleC24×C107C24
commutatorC22C22×C42×C107
Frattini, cosocleC24C24×C107
prime radicalC25×C107C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×C4⋊#95C2semidirect
9. C2×#117×C107C4semidirect
11. C22×C4⋊C4×C107C4semidirect
36. C2×C4⋊C4×C107C2×C4semidirect
42. C2×C42×C107C2×C4semidirect
107. C2×C4×C107#95semidirect
137. #13795C107direct (N × H)
148. C4⋊#95C2×C107semidirect
150. C107#13795direct (N × H)
155. C2×#117C4×C107semidirect
157. C22×C4⋊C4C4×C107semidirect
182. C2×C4⋊C4C2×C4×C107semidirect
188. C2×C42C2×C4×C107semidirect
253. C2×C4#95×C107semidirect

Maximal subgroups

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

subgroupindex
C22×#117×C1072
C23×C4⋊C4×C1072
C107×C4⋊#952
C107×C22⋊#952
#13795107