Finite Group Databasebeta

← C107×#7508 #41033472

Subgroups — C107×#7508 #41033472

Order 27392.

290 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 70 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×#355×C107C211yesmaximal, characteristic
2C2×#354×C107C211yesmaximal, characteristic
3C107×#1959C211yesmaximal, characteristic
4C2×#124×C107C2211yescharacteristic
5C2×#103×C107—21no—
6C2×#102×C107—21no—
7C2×#101×C107—21no—
8C2×#99×C107—21no—
9C2×#97×C107C411yescharacteristic, complemented
10#384×C107C411yescharacteristic, complemented
11#355×C107—21no—
12#355×C107C412yescomplemented
13#354×C107—21no—
14#354×C107C412yescomplemented
15C22×Q8×C107D411yescharacteristic
16C22×D4×C107D411yescharacteristic
17C2×M16×C107—41no—
18C22×C8×C107—21no—
19#124×C107—41no—
20#124×C107C2×C411yescharacteristic
21#124×C107C2×C411yescharacteristic
22#124×C107D411yescharacteristic
23#124×C107Q811yescharacteristic
24C2×C4⋊C4×C107—21no—
25C2×C4⋊C4×C107—41no—
26C2×C22⋊C4×C107—41no—
27C2×C22⋊C4×C107—41no—
28C2×C42×C107C2×C411yescharacteristic
29#103×C107—42no—
30#102×C107—42no—
31#101×C107—22no—
32#101×C107—41no—
33#99×C107—22no—
34#99×C107—41no—
35#97×C107—41no—
36C24×C107—21no—
37C2×Q8×C107—21no—
38C2×Q8×C107—41no—
39C2×Q8×C107—41no—
40C2×Q8×C107C22⋊C411yescharacteristic
41C2×Q8×C107C4⋊C411yescharacteristic
42C2×D4×C107—21no—
43C2×D4×C107—41no—
44C2×D4×C107—41no—
45C2×D4×C107C22⋊C411yescharacteristic
46C2×D4×C107C4⋊C411yescharacteristic
47C22×C4×C107—21no—
48C22×C4×C107—21no—
49C22×C4×C107—41no—
50C22×C4×C107—81no—
51C22×C4×C107C22⋊C411yescharacteristic
52M16×C107—42no—
53M16×C107—81no—
54C2×C8×C107—22no—
55C2×C8×C107—41no—
56C2×C8×C107—41no—
57C2×C8×C107—81no—
58C4⋊C4×C107—41no—
59C4⋊C4×C107—41no—
60C4⋊C4×C107—82no—
61C22⋊C4×C107—41no—
62C22⋊C4×C107—41no—
63C22⋊C4×C107—41no—
64C22⋊C4×C107—41no—
65C22⋊C4×C107—42no—
66C22⋊C4×C107—81no—
67C42×C107—21no—
68C42×C107C4211yescharacteristic
69C42×C107C4⋊C411yescharacteristic
70C23×C107—21no—
71C23×C107—21no—
72C23×C107—41no—
73C23×C107—41no—
74C23×C107—81no—
75C23×C107—81no—
76C23×C107#9911yescharacteristic
77Q8×C107—41no—
78Q8×C107—41no—
79Q8×C107—81no—
80D4×C107—41no—
81D4×C107—41no—
82D4×C107—81no—
83C2×C4×C107—21no—
84C2×C4×C107—21no—
85C2×C4×C107—21no—
86C2×C4×C107—21no—
87C2×C4×C107—21no—
88C2×C4×C107—21no—
89C2×C4×C107—41no—
90C2×C4×C107—41no—
91C2×C4×C107—41no—
92C2×C4×C107—41no—
93C2×C4×C107—82no—
94C2×C4×C107—82no—
95C2×C4×C107—81no—
96C2×C4×C107—161no—
97C2×C4×C107—161no—
98C2×C4×C107#9511yescharacteristic
99C2×C4×C107#9911yescharacteristic
100C8×C107—42no—
101C8×C107—82no—
102C22×C107—21no—
103C22×C107—21no—
104C22×C107—41no—
105C22×C107—41no—
106C22×C107—81no—
107C22×C107—81no—
108C22×C107—81no—
109C22×C107—81no—
110C22×C107—161no—
111C22×C107#34211yescharacteristic
112C22×C107#35311yescharacteristic
113C22×C107#35411yescharacteristic
114C4×C107—21no—
115C4×C107—21no—
116C4×C107—41no—
117C4×C107—41no—
118C4×C107—41no—
119C4×C107—41no—
120C4×C107—162no—
121C4×C107—161no—
122#7508C10711yesmaximal, characteristic, direct product factor, Sylow
123C2×C107—21no—
124C2×C107—21no—
125C2×C107—81no—
126C2×C107—81no—
127C2×C107#139311yescharacteristic
128C2×C107#140611yescharacteristic
129C2×C107#140711yescharacteristic
130C2×#355C2×C10711yescharacteristic
131C2×#354C2×C10711yescharacteristic
132#1959C2×C10711yescharacteristic
133C107#750811yescharacteristic, direct product factor, Sylow
134C2×#124C22×C10711yescharacteristic
135C2×#103—21no—
136C2×#102—21no—
137C2×#101—21no—
138C2×#99—21no—
139C2×#97C4×C10711yescharacteristic, complemented
140#384C4×C10711yescharacteristic, complemented
141#355—21no—
142#355C4×C10712yescomplemented
143#354—21no—
144#354C4×C10712yescomplemented
145C22×Q8D4×C10711yescharacteristic
146C22×D4D4×C10711yescharacteristic
147C2×M16—41no—
148C22×C8—21no—
149#124—41no—
150#124C2×C4×C10711yescharacteristic
151#124C2×C4×C10711yescharacteristic
152#124D4×C10711yescharacteristic
153#124Q8×C10711yescharacteristic
154C2×C4⋊C4—21no—
155C2×C4⋊C4—41no—
156C2×C22⋊C4—41no—
157C2×C22⋊C4—41no—
158C2×C42C2×C4×C10711yescharacteristic
159#103—42no—
160#102—42no—
161#101—22no—
162#101—41no—
163#99—22no—
164#99—41no—
165#97—41no—
166C24—21no—
167C2×Q8—21no—
168C2×Q8—41no—
169C2×Q8—41no—
170C2×Q8C22⋊C4×C10711yescharacteristic
171C2×Q8C4⋊C4×C10711yescharacteristic
172C2×D4—21no—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4C22⋊C4×C10711yescharacteristic
176C2×D4C4⋊C4×C10711yescharacteristic
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—41no—
180C22×C4—81no—
181C22×C4C22⋊C4×C10711yescharacteristic
182M16—42no—
183M16—81no—
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—81no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—82no—
191C22⋊C4—41no—
192C22⋊C4—41no—
193C22⋊C4—41no—
194C22⋊C4—41no—
195C22⋊C4—42no—
196C22⋊C4—81no—
197C42—21no—
198C42C42×C10711yescharacteristic
199C42C4⋊C4×C10711yescharacteristic
200C23—21no—
201C23—21no—
202C23—41no—
203C23—41no—
204C23—81no—
205C23—81no—
206C23#99×C10711yescharacteristic
207Q8—41no—
208Q8—41no—
209Q8—81no—
210D4—41no—
211D4—41no—
212D4—81no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—82no—
224C2×C4—82no—
225C2×C4—81no—
226C2×C4—161no—
227C2×C4—161no—
228C2×C4#95×C10711yescharacteristic
229C2×C4#99×C10711yescharacteristic
230C8—42no—
231C8—82no—
232C22—21no—
233C22—21no—
234C22—41no—
235C22—41no—
236C22—81no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—161no—
241C22#342×C10711yescharacteristic
242C22#353×C10711yescharacteristic
243C22#354×C10711yescharacteristic
244C4—21no—
245C4—21no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—162no—
251C4—161no—
252C2—21no—
253C2—21no—
254C2—81no—
255C2—81no—
256C2C107×#139311yescharacteristic
257C2C107×#140611yescharacteristic
258C2C107×#140711yescharacteristic
subgroupG/H
center, socleC22×C107#353
commutatorC42C42×C107
Frattini, cosocleC2×#124C22×C107
prime radicalC22×D4×C107D4
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C107 ◁ C22×C4×C107 ◁ C2×#124×C107 ◁ G

Complements

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

NH ≅ G/Ntype
9. C2×#97×C107C4semidirect
10. #384×C107C4semidirect
12. #355×C107C4semidirect
14. #354×C107C4semidirect
122. #7508C107direct (N × H)
133. C107#7508direct (N × H)
139. C2×#97C4×C107semidirect
140. #384C4×C107semidirect
142. #355C4×C107semidirect
144. #354C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#355×C1072
C2×#354×C1072
C107×#19592
#7508107