Finite Group Databasebeta

← C107×#7282 #41033246

Subgroups — C107×#7282 #41033246

Order 27392.

388 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C107×#1870C211yesmaximal, characteristic
2C4×#100×C107C211yesmaximal, characteristic
3C4×#99×C107C211yesmaximal, characteristic
4C22×M16×C107C411yescharacteristic, complemented
5C2×C4×D4×C107C2211yescharacteristic
6C2×#100×C107—21no—
7C2×#99×C107—21no—
8C2×C22⋊C8×C107—21no—
9C2×C22⋊C8×C107C411yescharacteristic, complemented
10C4×M16×C107—21no—
11C4×C22⋊C4×C107—21no—
12#343×C107C412yescomplemented
13#342×C107C412yes—
14#336×C107—21no—
15C22×D4×C107D411yescharacteristic
16C23×C4×C107C2×C411yescharacteristic
17C23×C4×C107D411yescharacteristic
18C2×M16×C107—22no—
19C2×M16×C107—42no—
20C2×M16×C107—41no—
21C22×C8×C107—21no—
22C22×C8×C107—21no—
23C4×D4×C107—41no—
24C4×D4×C107—41no—
25C2×C4⋊C4×C107C2×C411yescharacteristic
26C2×C22⋊C4×C107—22no—
27C2×C22⋊C4×C107C2×C411yescharacteristic
28C2×C22⋊C4×C107Q811yescharacteristic
29C2×C42×C107—41no—
30C2×C42×C107D411yescharacteristic
31#100×C107—24no—
32#99×C107—24no—
33C22⋊C8×C107—42no—
34C22⋊C8×C107—41no—
35#97×C107—41no—
36C4×C8×C107—41no—
37#95×C107—41no—
38C24×C107C22⋊C411yescharacteristic
39C24×C107C4⋊C411yescharacteristic
40C2×D4×C107—22no—
41C2×D4×C107—22no—
42C2×D4×C107—41no—
43C22×C4×C107—21no—
44C22×C4×C107—21no—
45C22×C4×C107—21no—
46C22×C4×C107—21no—
47C22×C4×C107—41no—
48C22×C4×C107—41no—
49C22×C4×C107—41no—
50C22×C4×C107—41no—
51C22×C4×C107—42no—
52C22×C4×C107C4211yescharacteristic
53C22×C4×C107C22⋊C411yescharacteristic
54C22×C4×C107C22⋊C411yescharacteristic
55C22×C4×C107C4⋊C411yescharacteristic
56C22×C4×C107C4⋊C411yescharacteristic
57M16×C107—24no—
58M16×C107—42no—
59M16×C107—42no—
60M16×C107—42no—
61C2×C8×C107—22no—
62C2×C8×C107—42no—
63C2×C8×C107—41no—
64C2×C8×C107—41no—
65C2×C8×C107—41no—
66C2×C8×C107—41no—
67C2×C8×C107—41no—
68C4⋊C4×C107—41no—
69C22⋊C4×C107—24no—
70C22⋊C4×C107—41no—
71C22⋊C4×C107—41no—
72C22⋊C4×C107—42no—
73C42×C107—21no—
74C42×C107—21no—
75C42×C107—81no—
76C42×C107—81no—
77C23×C107—21no—
78C23×C107—21no—
79C23×C107—21no—
80C23×C107—21no—
81C23×C107—21no—
82C23×C107—41no—
83C23×C107—41no—
84C23×C107—41no—
85C23×C107—41no—
86C23×C107#9511yescharacteristic
87C23×C107#10412yes—
88D4×C107—44no—
89C2×C4×C107—21no—
90C2×C4×C107—21no—
91C2×C4×C107—21no—
92C2×C4×C107—21no—
93C2×C4×C107—21no—
94C2×C4×C107—21no—
95C2×C4×C107—21no—
96C2×C4×C107—42no—
97C2×C4×C107—41no—
98C2×C4×C107—41no—
99C2×C4×C107—41no—
100C2×C4×C107—41no—
101C2×C4×C107—41no—
102C2×C4×C107—41no—
103C2×C4×C107—41no—
104C2×C4×C107—44no—
105C2×C4×C107—81no—
106C2×C4×C107—82no—
107C2×C4×C107—82no—
108C2×C4×C107#9911yescharacteristic
109C2×C4×C107#9911yescharacteristic
110C2×C4×C107#10412yes—
111C8×C107—44no—
112C8×C107—42no—
113C8×C107—81no—
114C22×C107—21no—
115C22×C107—21no—
116C22×C107—22no—
117C22×C107—42no—
118C22×C107—41no—
119C22×C107—41no—
120C22×C107—41no—
121C22×C107—41no—
122C22×C107—41no—
123C22×C107—81no—
124C22×C107—81no—
125C22×C107—81no—
126C22×C107#33911yescharacteristic
127C22×C107#33911yescharacteristic
128C22×C107#34211yescharacteristic
129C4×C107—22no—
130C4×C107—21no—
131C4×C107—41no—
132C4×C107—41no—
133C4×C107—41no—
134C4×C107—84no—
135C4×C107AΣL(1,𝔽16)11yescharacteristic
136C4×C107#35211yescharacteristic
137#7282C10711yesmaximal, characteristic, direct product factor, Sylow
138C2×C107—21no—
139C2×C107—21no—
140C2×C107—42no—
141C2×C107—81no—
142C2×C107#129711yescharacteristic
143C2×C107#139011yescharacteristic
144C2×C107#139511yescharacteristic
145#1870C2×C10711yescharacteristic
146C4×#100C2×C10711yescharacteristic
147C4×#99C2×C10711yescharacteristic
148C107#728211yescharacteristic, direct product factor, Sylow
149C22×M16C4×C10711yescharacteristic, complemented
150C2×C4×D4C22×C10711yescharacteristic
151C2×#100—21no—
152C2×#99—21no—
153C2×C22⋊C8—21no—
154C2×C22⋊C8C4×C10711yescharacteristic, complemented
155C4×M16—21no—
156C4×C22⋊C4—21no—
157#343C4×C10712yescomplemented
158#342C4×C10712yes—
159#336—21no—
160C22×D4D4×C10711yescharacteristic
161C23×C4C2×C4×C10711yescharacteristic
162C23×C4D4×C10711yescharacteristic
163C2×M16—22no—
164C2×M16—42no—
165C2×M16—41no—
166C22×C8—21no—
167C22×C8—21no—
168C4×D4—41no—
169C4×D4—41no—
170C2×C4⋊C4C2×C4×C10711yescharacteristic
171C2×C22⋊C4—22no—
172C2×C22⋊C4C2×C4×C10711yescharacteristic
173C2×C22⋊C4Q8×C10711yescharacteristic
174C2×C42—41no—
175C2×C42D4×C10711yescharacteristic
176#100—24no—
177#99—24no—
178C22⋊C8—42no—
179C22⋊C8—41no—
180#97—41no—
181C4×C8—41no—
182#95—41no—
183C24C22⋊C4×C10711yescharacteristic
184C24C4⋊C4×C10711yescharacteristic
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—41no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—42no—
197C22×C4C42×C10711yescharacteristic
198C22×C4C22⋊C4×C10711yescharacteristic
199C22×C4C22⋊C4×C10711yescharacteristic
200C22×C4C4⋊C4×C10711yescharacteristic
201C22×C4C4⋊C4×C10711yescharacteristic
202M16—24no—
203M16—42no—
204M16—42no—
205M16—42no—
206C2×C8—22no—
207C2×C8—42no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—41no—
213C4⋊C4—41no—
214C22⋊C4—24no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—42no—
218C42—21no—
219C42—21no—
220C42—81no—
221C42—81no—
222C23—21no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—21no—
227C23—41no—
228C23—41no—
229C23—41no—
230C23—41no—
231C23#95×C10711yescharacteristic
232C23#104×C10712yes—
233D4—44no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—44no—
250C2×C4—81no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4#99×C10711yescharacteristic
254C2×C4#99×C10711yescharacteristic
255C2×C4#104×C10712yes—
256C8—44no—
257C8—42no—
258C8—81no—
259C22—21no—
260C22—21no—
261C22—22no—
262C22—42no—
263C22—41no—
264C22—41no—
265C22—41no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22—81no—
270C22—81no—
271C22#339×C10711yescharacteristic
272C22#339×C10711yescharacteristic
273C22#342×C10711yescharacteristic
274C4—21no—
275C4—22no—
276C4—41no—
277C4—41no—
278C4—41no—
279C4—84no—
280C4AΣL(1,𝔽16)×C10711yescharacteristic
281C4#352×C10711yescharacteristic
282C2—21no—
283C2—21no—
284C2—42no—
285C2—81no—
286C2C107×#129711yescharacteristic
287C2C107×#139011yescharacteristic
288C2C107×#139511yescharacteristic
subgroupG/H
centerC2×C4×C107#99
commutatorC22×C4C42×C107
Frattini, cosocleC2×C4×D4C22×C107
socleC22×C107#342
prime radicalC22×D4×C107D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C22×C4×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
4. C22×M16×C107C4semidirect
9. C2×C22⋊C8×C107C4semidirect
12. #343×C107C4semidirect
137. #7282C107direct (N × H)
148. C107#7282direct (N × H)
149. C22×M16C4×C107semidirect
154. C2×C22⋊C8C4×C107semidirect
157. #343C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#18702
C4×#100×C1072
C4×#99×C1072
#7282107