Finite Group Databasebeta

← C107×#7482 #41033446

Subgroups — C107×#7482 #41033446

Order 27392.

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

normal subgroups only

This group has 278 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×#2126C211yesmaximal, characteristic
2C107×#1884C211yesmaximal, characteristic
3C107×#1560C211yesmaximal, characteristic
4#568×C107C411yescharacteristic, complemented
5#532×C107C2211yescharacteristic
6#423×C107—21no—
7#421×C107—21no—
8#410×C107—21no—
9#410×C107C411yescharacteristic, complemented
10#354×C107C412yescomplemented
11#353×C107—21no—
12#339×C107—21no—
13#333×C107C412yescomplemented
14#331×C107—21no—
15C2×#41×C107C2×C411yescharacteristic
16C2×#41×C107D411yescharacteristic
17#131×C107—42no—
18C2×M16×C107—21no—
19C2×M16×C107—41no—
20C2×M16×C107—41no—
21C4⋊Q8×C107C2×C411yescharacteristic
22#127×C107D411yescharacteristic
23#124×C107C2×C411yescharacteristic
24#124×C107Q811yescharacteristic
25#121×C107—41no—
26C4×D4×C107—41no—
27#117×C107—21no—
28#117×C107—41no—
29C2×C42×C107D411yescharacteristic
30C4⋊C8×C107—22no—
31C4⋊C8×C107—41no—
32#104×C107—42no—
33#99×C107—22no—
34#99×C107—41no—
35#99×C107—41no—
36#41×C107—41no—
37#41×C107—41no—
38#41×C107—41no—
39#41×C107—41no—
40C2×Q8×C107C4211yescharacteristic
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×C107C22⋊C411yescharacteristic
51M16×C107—22no—
52M16×C107—42no—
53M16×C107—41no—
54M16×C107—82no—
55C2×C8×C107—41no—
56C2×C8×C107—42no—
57C2×C8×C107—42no—
58C4⋊C4×C107—41no—
59C4⋊C4×C107—41no—
60C4⋊C4×C107—81no—
61C22⋊C4×C107—41no—
62C22⋊C4×C107—41no—
63C22⋊C4×C107—42no—
64C22⋊C4×C107—41no—
65C42×C107—21no—
66C42×C107—41no—
67C42×C107—81no—
68C42×C107C22⋊C411yescharacteristic
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—42no—
78D4×C107—81no—
79D4×C107—81no—
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—41no—
90C2×C4×C107—41no—
91C2×C4×C107—41no—
92C2×C4×C107—41no—
93C2×C4×C107—81no—
94C2×C4×C107—82no—
95C2×C4×C107#9511yescharacteristic
96C2×C4×C107#9911yescharacteristic
97C8×C107—42no—
98C8×C107—82no—
99C22×C107—21no—
100C22×C107—41no—
101C22×C107—41no—
102C22×C107—41no—
103C22×C107—81no—
104C22×C107—81no—
105C22×C107#34211yescharacteristic
106C4×C107—21no—
107C4×C107—21no—
108C4×C107—21no—
109C4×C107—41no—
110C4×C107—41no—
111C4×C107—41no—
112C4×C107—161no—
113C4×C107—162no—
114C4×C107AΣL(1,𝔽16)11yescharacteristic
115C4×C107#35211yescharacteristic
116#7482C10711yesmaximal, characteristic, direct product factor, Sylow
117C2×C107—21no—
118C2×C107—41no—
119C2×C107—81no—
120C2×C107—81no—
121C2×C107#139011yescharacteristic
122#2126C2×C10711yescharacteristic
123#1884C2×C10711yescharacteristic
124#1560C2×C10711yescharacteristic
125C107#748211yescharacteristic, direct product factor, Sylow
126#568C4×C10711yescharacteristic, complemented
127#532C22×C10711yescharacteristic
128#423—21no—
129#421—21no—
130#410—21no—
131#410C4×C10711yescharacteristic, complemented
132#354C4×C10712yescomplemented
133#353—21no—
134#339—21no—
135#333C4×C10712yescomplemented
136#331—21no—
137C2×#41C2×C4×C10711yescharacteristic
138C2×#41D4×C10711yescharacteristic
139#131—42no—
140C2×M16—21no—
141C2×M16—41no—
142C2×M16—41no—
143C4⋊Q8C2×C4×C10711yescharacteristic
144#127D4×C10711yescharacteristic
145#124C2×C4×C10711yescharacteristic
146#124Q8×C10711yescharacteristic
147#121—41no—
148C4×D4—41no—
149#117—21no—
150#117—41no—
151C2×C42D4×C10711yescharacteristic
152C4⋊C8—22no—
153C4⋊C8—41no—
154#104—42no—
155#99—22no—
156#99—41no—
157#99—41no—
158#41—41no—
159#41—41no—
160#41—41no—
161#41—41no—
162C2×Q8C42×C10711yescharacteristic
163C2×Q8C4⋊C4×C10711yescharacteristic
164C2×D4—21no—
165C2×D4—21no—
166C2×D4—41no—
167C2×D4C22⋊C4×C10711yescharacteristic
168C2×D4C4⋊C4×C10711yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4C22⋊C4×C10711yescharacteristic
173M16—22no—
174M16—42no—
175M16—41no—
176M16—82no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—42no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—81no—
183C22⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—42no—
186C22⋊C4—41no—
187C42—21no—
188C42—41no—
189C42—81no—
190C42C22⋊C4×C10711yescharacteristic
191C42C4⋊C4×C10711yescharacteristic
192C23—21no—
193C23—21no—
194C23#99×C10711yescharacteristic
195Q8—41no—
196Q8—41no—
197D4—41no—
198D4—41no—
199D4—42no—
200D4—81no—
201D4—81no—
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—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—81no—
216C2×C4—82no—
217C2×C4#95×C10711yescharacteristic
218C2×C4#99×C10711yescharacteristic
219C8—42no—
220C8—82no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—81no—
226C22—81no—
227C22#342×C10711yescharacteristic
228C4—21no—
229C4—21no—
230C4—21no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—161no—
235C4—162no—
236C4AΣL(1,𝔽16)×C10711yescharacteristic
237C4#352×C10711yescharacteristic
238C2—21no—
239C2—41no—
240C2—81no—
241C2—81no—
242C2C107×#139011yescharacteristic
subgroupG/H
center, socleC2×C107#1390
commutatorC2×Q8C42×C107
Frattini, cosocle#532C22×C107
prime radical#532×C107C22
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C107 ◁ C2×C4×C107 ◁ C22×C4×C107 ◁ #532×C107 ◁ G

Complements

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

NH ≅ G/Ntype
4. #568×C107C4semidirect
9. #410×C107C4semidirect
10. #354×C107C4semidirect
13. #333×C107C4semidirect
116. #7482C107direct (N × H)
125. C107#7482direct (N × H)
126. #568C4×C107semidirect
131. #410C4×C107semidirect
132. #354C4×C107semidirect
135. #333C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#21262
C107×#18842
C107×#15602
#7482107