Finite Group Databasebeta

← C107×#7481 #41033445

Subgroups — C107×#7481 #41033445

Order 27392.

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

normal subgroups only

This group has 284 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×#354×C107C211yesmaximal, characteristic
2C107×#1888C211yesmaximal, characteristic
3C107×#1533C211yesmaximal, characteristic
4C2×#124×C107C2211yescharacteristic
5#519×C107C411yescharacteristic, complemented
6#432×C107—21no—
7#418×C107—21no—
8C2×#101×C107C411yescharacteristic, complemented
9C2×#99×C107—21no—
10#354×C107—21no—
11#354×C107C412yescomplemented
12#339×C107—21no—
13#329×C107—21no—
14#329×C107C412yescomplemented
15C22×Q8×C107C2×C411yescharacteristic
16C22×D4×C107D411yescharacteristic
17C2×M16×C107—21no—
18#124×C107—41no—
19#124×C107C2×C411yescharacteristic
20#124×C107C2×C411yescharacteristic
21#124×C107D411yescharacteristic
22#124×C107Q811yescharacteristic
23C4×Q8×C107—42no—
24#117×C107—21no—
25#117×C107—41no—
26C2×C22⋊C4×C107—41no—
27C2×C22⋊C4×C107—41no—
28C2×C42×C107D411yescharacteristic
29C4⋊C8×C107—41no—
30#102×C107—42no—
31#101×C107—41no—
32#99×C107—22no—
33#99×C107—41no—
34C22⋊C8×C107—41no—
35#97×C107—22no—
36C24×C107—21no—
37C2×Q8×C107—21no—
38C2×Q8×C107—41no—
39C2×Q8×C107—41no—
40C2×Q8×C107C4211yescharacteristic
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—81no—
50C22×C4×C107C22⋊C411yescharacteristic
51M16×C107—41no—
52M16×C107—41no—
53C2×C8×C107—42no—
54C2×C8×C107—41no—
55C4⋊C4×C107—22no—
56C4⋊C4×C107—42no—
57C22⋊C4×C107—41no—
58C22⋊C4×C107—41no—
59C22⋊C4×C107—41no—
60C22⋊C4×C107—41no—
61C22⋊C4×C107—41no—
62C22⋊C4×C107—42no—
63C22⋊C4×C107—81no—
64C42×C107—21no—
65C42×C107—41no—
66C42×C107—42no—
67C42×C107C22⋊C411yescharacteristic
68C42×C107C4⋊C411yescharacteristic
69C23×C107—21no—
70C23×C107—21no—
71C23×C107—41no—
72C23×C107—41no—
73C23×C107—82no—
74C23×C107#9911yescharacteristic
75Q8×C107—41no—
76Q8×C107—41no—
77Q8×C107—42no—
78D4×C107—41no—
79D4×C107—41no—
80D4×C107—81no—
81C2×C4×C107—21no—
82C2×C4×C107—21no—
83C2×C4×C107—21no—
84C2×C4×C107—21no—
85C2×C4×C107—21no—
86C2×C4×C107—21no—
87C2×C4×C107—41no—
88C2×C4×C107—41no—
89C2×C4×C107—42no—
90C2×C4×C107—81no—
91C2×C4×C107—82no—
92C2×C4×C107—162no—
93C2×C4×C107#9511yescharacteristic
94C2×C4×C107#9911yescharacteristic
95C8×C107—81no—
96C8×C107—82no—
97C22×C107—41no—
98C22×C107—41no—
99C22×C107—41no—
100C22×C107—81no—
101C22×C107—81no—
102C22×C107—82no—
103C22×C107—161no—
104C22×C107#34211yescharacteristic
105C22×C107AΣL(1,𝔽16)11yescharacteristic
106C22×C107#35211yescharacteristic
107C4×C107—21no—
108C4×C107—21no—
109C4×C107—41no—
110C4×C107—41no—
111C4×C107—41no—
112C4×C107—41no—
113C4×C107—82no—
114C4×C107—162no—
115#7481C10711yesmaximal, characteristic, direct product factor, Sylow
116C2×C107—21no—
117C2×C107—21no—
118C2×C107—21no—
119C2×C107—81no—
120C2×C107—81no—
121C2×C107#139011yescharacteristic
122C2×#354C2×C10711yescharacteristic
123#1888C2×C10711yescharacteristic
124#1533C2×C10711yescharacteristic
125C107#748111yescharacteristic, direct product factor, Sylow
126C2×#124C22×C10711yescharacteristic
127#519C4×C10711yescharacteristic, complemented
128#432—21no—
129#418—21no—
130C2×#101C4×C10711yescharacteristic, complemented
131C2×#99—21no—
132#354—21no—
133#354C4×C10712yescomplemented
134#339—21no—
135#329—21no—
136#329C4×C10712yescomplemented
137C22×Q8C2×C4×C10711yescharacteristic
138C22×D4D4×C10711yescharacteristic
139C2×M16—21no—
140#124—41no—
141#124C2×C4×C10711yescharacteristic
142#124C2×C4×C10711yescharacteristic
143#124D4×C10711yescharacteristic
144#124Q8×C10711yescharacteristic
145C4×Q8—42no—
146#117—21no—
147#117—41no—
148C2×C22⋊C4—41no—
149C2×C22⋊C4—41no—
150C2×C42D4×C10711yescharacteristic
151C4⋊C8—41no—
152#102—42no—
153#101—41no—
154#99—22no—
155#99—41no—
156C22⋊C8—41no—
157#97—22no—
158C24—21no—
159C2×Q8—21no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8C42×C10711yescharacteristic
163C2×Q8C4⋊C4×C10711yescharacteristic
164C2×D4—21no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4C22⋊C4×C10711yescharacteristic
168C2×D4C4⋊C4×C10711yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—81no—
172C22×C4C22⋊C4×C10711yescharacteristic
173M16—41no—
174M16—41no—
175C2×C8—42no—
176C2×C8—41no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C22⋊C4—41no—
180C22⋊C4—41no—
181C22⋊C4—41no—
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—42no—
185C22⋊C4—81no—
186C42—21no—
187C42—41no—
188C42—42no—
189C42C22⋊C4×C10711yescharacteristic
190C42C4⋊C4×C10711yescharacteristic
191C23—21no—
192C23—21no—
193C23—41no—
194C23—41no—
195C23—82no—
196C23#99×C10711yescharacteristic
197Q8—41no—
198Q8—41no—
199Q8—42no—
200D4—41no—
201D4—41no—
202D4—81no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—81no—
213C2×C4—82no—
214C2×C4—162no—
215C2×C4#95×C10711yescharacteristic
216C2×C4#99×C10711yescharacteristic
217C8—81no—
218C8—82no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—81no—
223C22—81no—
224C22—82no—
225C22—161no—
226C22#342×C10711yescharacteristic
227C22AΣL(1,𝔽16)×C10711yescharacteristic
228C22#352×C10711yescharacteristic
229C4—21no—
230C4—21no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—41no—
235C4—82no—
236C4—162no—
237C2—21no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—81no—
242C2C107×#139011yescharacteristic
subgroupG/H
center, socleC2×C107#1390
commutatorC2×Q8C42×C107
Frattini, cosocleC2×#124C22×C107
prime radicalC22×D4×C107D4
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C23×C107 ◁ C22×C4×C107 ◁ C2×#124×C107 ◁ G

Complements

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

NH ≅ G/Ntype
5. #519×C107C4semidirect
8. C2×#101×C107C4semidirect
11. #354×C107C4semidirect
14. #329×C107C4semidirect
115. #7481C107direct (N × H)
125. C107#7481direct (N × H)
127. #519C4×C107semidirect
130. C2×#101C4×C107semidirect
133. #354C4×C107semidirect
136. #329C4×C107semidirect

Maximal subgroups

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

subgroupindex
C2×#354×C1072
C107×#18882
C107×#15332
#7481107