Finite Group Databasebeta

← C107×#7487 #41033451

Subgroups — C107×#7487 #41033451

Order 27392.

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

normal subgroups only

This group has 298 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
2C107×#1885C211yesmaximal, characteristic
3C2×#329×C107C211yesmaximal, characteristic
4C2×#124×C107C2211yescharacteristic
5#518×C107C411yescharacteristic
6#419×C107—21no—
7C2×#101×C107—21no—
8C2×#100×C107C411yescharacteristic
9C2×#97×C107—21no—
10#355×C107—21no—
11#355×C107C412yescomplemented
12#339×C107—21no—
13#329×C107—21no—
14#329×C107C412yescomplemented
15C22×Q8×C107D411yescharacteristic
16C22×D4×C107C2×C411yescharacteristic
17C2×M16×C107—21no—
18C2×M16×C107—41no—
19C22×C8×C107—41no—
20#124×C107—41no—
21#124×C107C2×C411yescharacteristic
22#124×C107C2×C411yescharacteristic
23#124×C107D411yescharacteristic
24#124×C107Q811yescharacteristic
25C4×D4×C107—42no—
26#117×C107—21no—
27C2×C22⋊C4×C107—41no—
28C2×C22⋊C4×C107—41no—
29C2×C42×C107D411yescharacteristic
30#103×C107—42no—
31#101×C107—22no—
32#101×C107—41no—
33#100×C107—41no—
34#97×C107—22no—
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×C107C4211yescharacteristic
46C2×D4×C107C4⋊C411yescharacteristic
47C22×C4×C107—21no—
48C22×C4×C107—21no—
49C22×C4×C107—42no—
50C22×C4×C107C22⋊C411yescharacteristic
51M16×C107—42no—
52M16×C107—41no—
53M16×C107—41no—
54M16×C107—81no—
55C2×C8×C107—42no—
56C2×C8×C107—44no—
57C2×C8×C107—41no—
58C2×C8×C107—81no—
59C4⋊C4×C107—22no—
60C22⋊C4×C107—41no—
61C22⋊C4×C107—41no—
62C22⋊C4×C107—41no—
63C22⋊C4×C107—41no—
64C22⋊C4×C107—42no—
65C22⋊C4×C107—41no—
66C42×C107—21no—
67C42×C107—41no—
68C42×C107C22⋊C411yescharacteristic
69C42×C107C4⋊C411yescharacteristic
70C23×C107—21no—
71C23×C107—21no—
72C23×C107—41no—
73C23×C107—41no—
74C23×C107—82no—
75C23×C107#9911yescharacteristic
76Q8×C107—41no—
77Q8×C107—41no—
78Q8×C107—81no—
79D4×C107—41no—
80D4×C107—41no—
81D4×C107—42no—
82C2×C4×C107—21no—
83C2×C4×C107—21no—
84C2×C4×C107—21no—
85C2×C4×C107—21no—
86C2×C4×C107—21no—
87C2×C4×C107—21no—
88C2×C4×C107—42no—
89C2×C4×C107—41no—
90C2×C4×C107—41no—
91C2×C4×C107—42no—
92C2×C4×C107—162no—
93C2×C4×C107#9511yescharacteristic
94C2×C4×C107#9911yescharacteristic
95C8×C107—44no—
96C8×C107—81no—
97C8×C107—82no—
98C22×C107—22no—
99C22×C107—41no—
100C22×C107—41no—
101C22×C107—81no—
102C22×C107—81no—
103C22×C107—82no—
104C22×C107—161no—
105C22×C107#34211yescharacteristic
106C22×C107AΣL(1,𝔽16)11yescharacteristic
107C22×C107#35211yescharacteristic
108C4×C107—21no—
109C4×C107—21no—
110C4×C107—41no—
111C4×C107—41no—
112C4×C107—41no—
113C4×C107—41no—
114C4×C107—82no—
115#7487C10711yesmaximal, characteristic, direct product factor, Sylow
116C2×C107—21no—
117C2×C107—21no—
118C2×C107—81no—
119C2×C107—81no—
120C2×C107#139011yescharacteristic
121C2×C107#140312yes—
122C2×#355C2×C10711yescharacteristic
123#1885C2×C10711yescharacteristic
124C2×#329C2×C10711yescharacteristic
125C107#748711yescharacteristic, direct product factor, Sylow
126C2×#124C22×C10711yescharacteristic
127#518C4×C10711yescharacteristic
128#419—21no—
129C2×#101—21no—
130C2×#100C4×C10711yescharacteristic
131C2×#97—21no—
132#355—21no—
133#355C4×C10712yescomplemented
134#339—21no—
135#329—21no—
136#329C4×C10712yescomplemented
137C22×Q8D4×C10711yescharacteristic
138C22×D4C2×C4×C10711yescharacteristic
139C2×M16—21no—
140C2×M16—41no—
141C22×C8—41no—
142#124—41no—
143#124C2×C4×C10711yescharacteristic
144#124C2×C4×C10711yescharacteristic
145#124D4×C10711yescharacteristic
146#124Q8×C10711yescharacteristic
147C4×D4—42no—
148#117—21no—
149C2×C22⋊C4—41no—
150C2×C22⋊C4—41no—
151C2×C42D4×C10711yescharacteristic
152#103—42no—
153#101—22no—
154#101—41no—
155#100—41no—
156#97—22no—
157#97—41no—
158C24—21no—
159C2×Q8—21no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8C22⋊C4×C10711yescharacteristic
163C2×Q8C4⋊C4×C10711yescharacteristic
164C2×D4—21no—
165C2×D4—41no—
166C2×D4—41no—
167C2×D4C42×C10711yescharacteristic
168C2×D4C4⋊C4×C10711yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—42no—
172C22×C4C22⋊C4×C10711yescharacteristic
173M16—42no—
174M16—41no—
175M16—41no—
176M16—81no—
177C2×C8—42no—
178C2×C8—44no—
179C2×C8—41no—
180C2×C8—81no—
181C4⋊C4—22no—
182C22⋊C4—41no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—42no—
187C22⋊C4—41no—
188C42—21no—
189C42—41no—
190C42C22⋊C4×C10711yescharacteristic
191C42C4⋊C4×C10711yescharacteristic
192C23—21no—
193C23—21no—
194C23—41no—
195C23—41no—
196C23—82no—
197C23#99×C10711yescharacteristic
198Q8—41no—
199Q8—41no—
200Q8—81no—
201D4—41no—
202D4—41no—
203D4—42no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—162no—
215C2×C4#95×C10711yescharacteristic
216C2×C4#99×C10711yescharacteristic
217C8—44no—
218C8—81no—
219C8—82no—
220C22—22no—
221C22—41no—
222C22—41no—
223C22—81no—
224C22—81no—
225C22—82no—
226C22—161no—
227C22#342×C10711yescharacteristic
228C22AΣL(1,𝔽16)×C10711yescharacteristic
229C22#352×C10711yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—41no—
234C4—41no—
235C4—41no—
236C4—82no—
237C2—21no—
238C2—21no—
239C2—81no—
240C2—81no—
241C2C107×#139011yescharacteristic
242C2C107×#140312yes—
subgroupG/H
center, socleC22×C107AΣL(1,𝔽16)
commutatorC2×D4C42×C107
Frattini, cosocleC2×#124C22×C107
prime radicalC22×D4×C107C2×C4
LCSG ▷ C2×D4 ▷ 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
11. #355×C107C4semidirect
14. #329×C107C4semidirect
115. #7487C107direct (N × H)
125. C107#7487direct (N × H)
133. #355C4×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×#355×C1072
C107×#18852
C2×#329×C1072
#7487107