Finite Group Databasebeta

← C107×#7497 #41033461

Subgroups — C107×#7497 #41033461

Order 27392.

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

normal subgroups only

This group has 290 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
1C107×#2132C211yesmaximal, characteristic
2C107×#2126C211yesmaximal, characteristic
3C107×#1962C211yesmaximal, characteristic
4#532×C107C2211yescharacteristic
5#423×C107C411yescharacteristic, complemented
6C2×#104×C107—21no—
7C2×#104×C107—21no—
8#413×C107—21no—
9#410×C107—21no—
10C43×C107C411yescharacteristic, complemented
11#356×C107C412yescomplemented
12#355×C107—21no—
13#354×C107—21no—
14#353×C107C412yescomplemented
15C2×#41×C107D411yescharacteristic
16C2×#41×C107D411yescharacteristic
17C2×M16×C107—21no—
18C2×M16×C107—41no—
19C4⋊Q8×C107C2×C411yescharacteristic
20#127×C107C2×C411yescharacteristic
21#124×C107D411yescharacteristic
22#124×C107Q811yescharacteristic
23#121×C107—41no—
24C4×D4×C107—41no—
25#117×C107—41no—
26C2×C42×C107—21no—
27C2×C42×C107—41no—
28C2×C42×C107C2×C411yescharacteristic
29C4⋊C8×C107—41no—
30#104×C107—42no—
31#104×C107—42no—
32#101×C107—22no—
33#100×C107—41no—
34#99×C107—22no—
35#99×C107—41no—
36#41×C107—41no—
37#41×C107—41no—
38#41×C107—41no—
39#41×C107—41no—
40C2×Q8×C107C22⋊C411yescharacteristic
41C2×Q8×C107C4⋊C411yescharacteristic
42C2×D4×C107—21no—
43C2×D4×C107—21no—
44C2×D4×C107—41no—
45C2×D4×C107C22⋊C411yescharacteristic
46C2×D4×C107C4⋊C411yescharacteristic
47C22×C4×C107—21no—
48C22×C4×C107—21no—
49C22×C4×C107—21no—
50C22×C4×C107—41no—
51C22×C4×C107C22⋊C411yescharacteristic
52M16×C107—42no—
53M16×C107—41no—
54M16×C107—41no—
55M16×C107—81no—
56C2×C8×C107—41no—
57C2×C8×C107—81no—
58C4⋊C4×C107—41no—
59C4⋊C4×C107—81no—
60C22⋊C4×C107—41no—
61C22⋊C4×C107—41no—
62C22⋊C4×C107—42no—
63C42×C107—21no—
64C42×C107—22no—
65C42×C107—41no—
66C42×C107—44no—
67C42×C107—81no—
68C42×C107C4211yescharacteristic
69C42×C107C4⋊C411yescharacteristic
70C23×C107—21no—
71C23×C107—21no—
72C23×C107#9911yescharacteristic
73Q8×C107—41no—
74Q8×C107—41no—
75D4×C107—41no—
76D4×C107—41no—
77D4×C107—82no—
78D4×C107—81no—
79D4×C107—81no—
80C2×C4×C107—21no—
81C2×C4×C107—21no—
82C2×C4×C107—21no—
83C2×C4×C107—21no—
84C2×C4×C107—21no—
85C2×C4×C107—21no—
86C2×C4×C107—42no—
87C2×C4×C107—42no—
88C2×C4×C107—44no—
89C2×C4×C107—41no—
90C2×C4×C107—41no—
91C2×C4×C107—41no—
92C2×C4×C107—41no—
93C2×C4×C107—82no—
94C2×C4×C107#9511yescharacteristic
95C2×C4×C107#9911yescharacteristic
96C8×C107—82no—
97C8×C107—81no—
98C22×C107—21no—
99C22×C107—41no—
100C22×C107—41no—
101C22×C107—41no—
102C22×C107—81no—
103C22×C107—81no—
104C22×C107#34211yescharacteristic
105C4×C107—22no—
106C4×C107—21no—
107C4×C107—41no—
108C4×C107—44no—
109C4×C107—41no—
110C4×C107—41no—
111C4×C107—162no—
112C4×C107#35311yescharacteristic
113C4×C107#35411yescharacteristic
114#7497C10711yesmaximal, characteristic, direct product factor, Sylow
115C2×C107—21no—
116C2×C107—41no—
117C2×C107—81no—
118C2×C107—81no—
119C2×C107#139311yescharacteristic
120#2132C2×C10711yescharacteristic
121#2126C2×C10711yescharacteristic
122#1962C2×C10711yescharacteristic
123C107#749711yescharacteristic, direct product factor, Sylow
124#532C22×C10711yescharacteristic
125#423C4×C10711yescharacteristic, complemented
126C2×#104—21no—
127C2×#104—21no—
128#413—21no—
129#410—21no—
130C43C4×C10711yescharacteristic, complemented
131#356C4×C10712yescomplemented
132#355—21no—
133#354—21no—
134#353C4×C10712yescomplemented
135C2×#41D4×C10711yescharacteristic
136C2×#41D4×C10711yescharacteristic
137C2×M16—21no—
138C2×M16—41no—
139C4⋊Q8C2×C4×C10711yescharacteristic
140#127C2×C4×C10711yescharacteristic
141#124D4×C10711yescharacteristic
142#124Q8×C10711yescharacteristic
143#121—41no—
144C4×D4—41no—
145#117—41no—
146C2×C42—21no—
147C2×C42—41no—
148C2×C42C2×C4×C10711yescharacteristic
149C4⋊C8—41no—
150#104—42no—
151#104—42no—
152#101—22no—
153#100—41no—
154#99—22no—
155#99—41no—
156#41—41no—
157#41—41no—
158#41—41no—
159#41—41no—
160C2×Q8C22⋊C4×C10711yescharacteristic
161C2×Q8C4⋊C4×C10711yescharacteristic
162C2×D4—21no—
163C2×D4—21no—
164C2×D4—41no—
165C2×D4C22⋊C4×C10711yescharacteristic
166C2×D4C4⋊C4×C10711yescharacteristic
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—41no—
171C22×C4C22⋊C4×C10711yescharacteristic
172M16—42no—
173M16—41no—
174M16—41no—
175M16—81no—
176C2×C8—41no—
177C2×C8—81no—
178C4⋊C4—41no—
179C4⋊C4—81no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—42no—
183C42—21no—
184C42—22no—
185C42—41no—
186C42—44no—
187C42—81no—
188C42C42×C10711yescharacteristic
189C42C4⋊C4×C10711yescharacteristic
190C23—21no—
191C23—21no—
192C23#99×C10711yescharacteristic
193Q8—41no—
194Q8—41no—
195D4—41no—
196D4—41no—
197D4—82no—
198D4—81no—
199D4—81no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—82no—
214C2×C4#95×C10711yescharacteristic
215C2×C4#99×C10711yescharacteristic
216C8—82no—
217C8—81no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—81no—
223C22—81no—
224C22#342×C10711yescharacteristic
225C4—22no—
226C4—21no—
227C4—41no—
228C4—44no—
229C4—41no—
230C4—41no—
231C4—162no—
232C4#353×C10711yescharacteristic
233C4#354×C10711yescharacteristic
234C2—21no—
235C2—41no—
236C2—81no—
237C2—81no—
238C2C107×#139311yescharacteristic
subgroupG/H
centerC4×C107#353
commutatorC42C42×C107
Frattini, cosocle#532C22×C107
socleC2×C107#1393
prime radical#532×C107C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C107 ◁ C2×C4×C107 ◁ C22×C4×C107 ◁ #532×C107 ◁ G

Complements

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

NH ≅ G/Ntype
5. #423×C107C4semidirect
10. C43×C107C4semidirect
11. #356×C107C4semidirect
14. #353×C107C4semidirect
114. #7497C107direct (N × H)
123. C107#7497direct (N × H)
125. #423C4×C107semidirect
130. C43C4×C107semidirect
131. #356C4×C107semidirect
134. #353C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#21322
C107×#21262
C107×#19622
#7497107