Finite Group Databasebeta

← C107×#7493 #41033457

Subgroups — C107×#7493 #41033457

Order 27392.

334 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 66 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×#353×C107C211yesmaximal, characteristic
2C107×#1887C211yesmaximal, characteristic
3C107×#1555C211yesmaximal, characteristic
4C2×#127×C107C2211yescharacteristic
5#518×C107C411yescharacteristic, complemented
6#432×C107—21no—
7#418×C107—21no—
8C2×#100×C107C411yescharacteristic, complemented
9C2×#99×C107—21no—
10#353×C107—21no—
11#353×C107C412yescomplemented
12#339×C107—21no—
13#331×C107—21no—
14#331×C107C412yescomplemented
15C22×D4×C107—41no—
16C22×D4×C107C2×C411yescharacteristic
17C22×D4×C107D411yescharacteristic
18C2×M16×C107—21no—
19#127×C107—41no—
20#127×C107C2×C411yescharacteristic
21#127×C107C2×C411yescharacteristic
22#127×C107D411yescharacteristic
23#127×C107Q811yescharacteristic
24C4×D4×C107—42no—
25#117×C107—21no—
26C2×C22⋊C4×C107—41no—
27C2×C22⋊C4×C107—41no—
28C2×C42×C107D411yescharacteristic
29C4⋊C8×C107—22no—
30#102×C107—42no—
31#100×C107—41no—
32#99×C107—22no—
33#99×C107—41no—
34C22⋊C8×C107—41no—
35#97×C107—41no—
36C24×C107—21no—
37C24×C107—21no—
38C2×D4×C107—21no—
39C2×D4×C107—21no—
40C2×D4×C107—41no—
41C2×D4×C107—41no—
42C2×D4×C107—41no—
43C2×D4×C107—41no—
44C2×D4×C107—41no—
45C2×D4×C107—41no—
46C2×D4×C107—41no—
47C2×D4×C107—41no—
48C2×D4×C107—84no—
49C2×D4×C107C4211yescharacteristic
50C2×D4×C107C22⋊C411yescharacteristic
51C2×D4×C107C4⋊C411yescharacteristic
52C2×D4×C107C4⋊C411yescharacteristic
53C22×C4×C107—21no—
54C22×C4×C107—42no—
55C22×C4×C107—81no—
56C22×C4×C107C22⋊C411yescharacteristic
57M16×C107—41no—
58M16×C107—41no—
59C2×C8×C107—42no—
60C2×C8×C107—41no—
61C4⋊C4×C107—22no—
62C22⋊C4×C107—41no—
63C22⋊C4×C107—42no—
64C22⋊C4×C107—42no—
65C22⋊C4×C107—81no—
66C42×C107—21no—
67C42×C107—41no—
68C42×C107C22⋊C411yescharacteristic
69C42×C107C4⋊C411yescharacteristic
70C23×C107—21no—
71C23×C107—21no—
72C23×C107—21no—
73C23×C107—21no—
74C23×C107—41no—
75C23×C107—41no—
76C23×C107—41no—
77C23×C107—41no—
78C23×C107—82no—
79C23×C107—82no—
80C23×C107#9911yescharacteristic
81D4×C107—41no—
82D4×C107—41no—
83D4×C107—41no—
84D4×C107—41no—
85D4×C107—42no—
86D4×C107—81no—
87D4×C107—82no—
88D4×C107—82no—
89D4×C107—82no—
90D4×C107—82no—
91C2×C4×C107—21no—
92C2×C4×C107—21no—
93C2×C4×C107—21no—
94C2×C4×C107—21no—
95C2×C4×C107—42no—
96C2×C4×C107—42no—
97C2×C4×C107—82no—
98C2×C4×C107—162no—
99C2×C4×C107—162no—
100C2×C4×C107#9511yescharacteristic
101C2×C4×C107#9911yescharacteristic
102C8×C107—82no—
103C8×C107—81no—
104C22×C107—41no—
105C22×C107—41no—
106C22×C107—41no—
107C22×C107—41no—
108C22×C107—41no—
109C22×C107—81no—
110C22×C107—81no—
111C22×C107—81no—
112C22×C107—81no—
113C22×C107—82no—
114C22×C107—82no—
115C22×C107—161no—
116C22×C107—161no—
117C22×C107#34211yescharacteristic
118C22×C107AΣL(1,𝔽16)11yescharacteristic
119C22×C107#35211yescharacteristic
120C4×C107—22no—
121C4×C107—21no—
122C4×C107—21no—
123C4×C107—41no—
124C4×C107—82no—
125C4×C107—162no—
126#7493C10711yesmaximal, characteristic, direct product factor, Sylow
127C2×C107—21no—
128C2×C107—21no—
129C2×C107—21no—
130C2×C107—81no—
131C2×C107—81no—
132C2×C107—81no—
133C2×C107—81no—
134C2×C107#139011yescharacteristic
135C2×#353C2×C10711yescharacteristic
136#1887C2×C10711yescharacteristic
137#1555C2×C10711yescharacteristic
138C107#749311yescharacteristic, direct product factor, Sylow
139C2×#127C22×C10711yescharacteristic
140#518C4×C10711yescharacteristic, complemented
141#432—21no—
142#418—21no—
143C2×#100C4×C10711yescharacteristic, complemented
144C2×#99—21no—
145#353—21no—
146#353C4×C10712yescomplemented
147#339—21no—
148#331—21no—
149#331C4×C10712yescomplemented
150C22×D4—41no—
151C22×D4C2×C4×C10711yescharacteristic
152C22×D4D4×C10711yescharacteristic
153C2×M16—21no—
154#127—41no—
155#127C2×C4×C10711yescharacteristic
156#127C2×C4×C10711yescharacteristic
157#127D4×C10711yescharacteristic
158#127Q8×C10711yescharacteristic
159C4×D4—42no—
160#117—21no—
161C2×C22⋊C4—41no—
162C2×C22⋊C4—41no—
163C2×C42D4×C10711yescharacteristic
164C4⋊C8—22no—
165#102—42no—
166#100—41no—
167#99—22no—
168#99—41no—
169C22⋊C8—41no—
170#97—41no—
171C24—21no—
172C24—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—41no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4—41no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4—41no—
183C2×D4—84no—
184C2×D4C42×C10711yescharacteristic
185C2×D4C22⋊C4×C10711yescharacteristic
186C2×D4C4⋊C4×C10711yescharacteristic
187C2×D4C4⋊C4×C10711yescharacteristic
188C22×C4—21no—
189C22×C4—42no—
190C22×C4—81no—
191C22×C4C22⋊C4×C10711yescharacteristic
192M16—41no—
193M16—41no—
194C2×C8—42no—
195C2×C8—41no—
196C4⋊C4—22no—
197C22⋊C4—41no—
198C22⋊C4—42no—
199C22⋊C4—42no—
200C22⋊C4—81no—
201C42—21no—
202C42—41no—
203C42C22⋊C4×C10711yescharacteristic
204C42C4⋊C4×C10711yescharacteristic
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—41no—
210C23—41no—
211C23—41no—
212C23—41no—
213C23—82no—
214C23—82no—
215C23#99×C10711yescharacteristic
216D4—41no—
217D4—41no—
218D4—41no—
219D4—41no—
220D4—42no—
221D4—81no—
222D4—82no—
223D4—82no—
224D4—82no—
225D4—82no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—82no—
233C2×C4—162no—
234C2×C4—162no—
235C2×C4#95×C10711yescharacteristic
236C2×C4#99×C10711yescharacteristic
237C8—81no—
238C8—82no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—81no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22—82no—
249C22—82no—
250C22—161no—
251C22—161no—
252C22#342×C10711yescharacteristic
253C22AΣL(1,𝔽16)×C10711yescharacteristic
254C22#352×C10711yescharacteristic
255C4—22no—
256C4—21no—
257C4—21no—
258C4—41no—
259C4—82no—
260C4—162no—
261C2—21no—
262C2—21no—
263C2—21no—
264C2—81no—
265C2—81no—
266C2—81no—
267C2—81no—
268C2C107×#139011yescharacteristic
subgroupG/H
center, socleC2×C107#1390
commutatorC2×D4C42×C107
Frattini, cosocleC2×#127C22×C107
prime radicalC2×#127×C107C22
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C23×C107 ◁ C22×C4×C107 ◁ C2×#127×C107 ◁ G

Complements

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

NH ≅ G/Ntype
5. #518×C107C4semidirect
8. C2×#100×C107C4semidirect
11. #353×C107C4semidirect
14. #331×C107C4semidirect
126. #7493C107direct (N × H)
138. C107#7493direct (N × H)
140. #518C4×C107semidirect
143. C2×#100C4×C107semidirect
146. #353C4×C107semidirect
149. #331C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#353×C1072
C107×#18872
C107×#15552
#7493107