Finite Group Databasebeta

← C107×#7285 #41033249

Subgroups — C107×#7285 #41033249

Order 27392.

324 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 82 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×#1870C211yesmaximal, characteristic
2C107×#1460C211yesmaximal, characteristic
3C107×#1459C211yesmaximal, characteristic
4C22×M16×C107C411yescharacteristic
5C2×C4×D4×C107C2211yescharacteristic
6#431×C107—21no—
7C2×C22⋊C8×C107—21no—
8C2×C22⋊C8×C107—21no—
9C2×C22⋊C8×C107C411yescharacteristic
10#336×C107—21no—
11#324×C107C412yes—
12#323×C107—21no—
13#323×C107—21no—
14#323×C107C412yes—
15C22×D4×C107Q811yescharacteristic
16C23×C4×C107C2×C411yescharacteristic
17C23×C4×C107D411yescharacteristic
18C2×M16×C107—42no—
19C2×M16×C107—41no—
20C22×C8×C107—21no—
21C22×C8×C107—21no—
22C22×C8×C107—41no—
23C4×D4×C107—41no—
24C4×D4×C107—41no—
25C2×C4⋊C4×C107C2×C411yescharacteristic
26C2×C22⋊C4×C107C2×C411yescharacteristic
27C2×C22⋊C4×C107D411yescharacteristic
28C2×C42×C107D411yescharacteristic
29C4⋊C8×C107—41no—
30C22⋊C8×C107—22no—
31C22⋊C8×C107—22no—
32C22⋊C8×C107—42no—
33C22⋊C8×C107—41no—
34C22⋊C8×C107—41no—
35C4×C8×C107—41no—
36C24×C107C4⋊C411yescharacteristic
37C24×C107C4⋊C411yescharacteristic
38C2×D4×C107—22no—
39C2×D4×C107—22no—
40C2×D4×C107—41no—
41C22×C4×C107—21no—
42C22×C4×C107—21no—
43C22×C4×C107—21no—
44C22×C4×C107—21no—
45C22×C4×C107—41no—
46C22×C4×C107—41no—
47C22×C4×C107—41no—
48C22×C4×C107—41no—
49C22×C4×C107C4211yescharacteristic
50C22×C4×C107C22⋊C411yescharacteristic
51C22×C4×C107C22⋊C411yescharacteristic
52C22×C4×C107C22⋊C411yescharacteristic
53C22×C4×C107C4⋊C411yescharacteristic
54M16×C107—42no—
55M16×C107—42no—
56C2×C8×C107—22no—
57C2×C8×C107—41no—
58C2×C8×C107—41no—
59C2×C8×C107—42no—
60C2×C8×C107—42no—
61C2×C8×C107—41no—
62C2×C8×C107—41no—
63C2×C8×C107—41no—
64C2×C8×C107—81no—
65C2×C8×C107—81no—
66C4⋊C4×C107—41no—
67C22⋊C4×C107—41no—
68C22⋊C4×C107—41no—
69C42×C107—21no—
70C42×C107—21no—
71C23×C107—21no—
72C23×C107—21no—
73C23×C107—21no—
74C23×C107—21no—
75C23×C107—21no—
76C23×C107—41no—
77C23×C107—41no—
78C23×C107—41no—
79C23×C107—41no—
80C23×C107#9511yescharacteristic
81C23×C107#10812yes—
82D4×C107—44no—
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—21no—
90C2×C4×C107—42no—
91C2×C4×C107—41no—
92C2×C4×C107—41no—
93C2×C4×C107—41no—
94C2×C4×C107—41no—
95C2×C4×C107—41no—
96C2×C4×C107—41no—
97C2×C4×C107—41no—
98C2×C4×C107—81no—
99C2×C4×C107#9911yescharacteristic
100C2×C4×C107#9911yescharacteristic
101C2×C4×C107#10812yes—
102C8×C107—42no—
103C8×C107—81no—
104C8×C107—82no—
105C8×C107—82no—
106C22×C107—21no—
107C22×C107—21no—
108C22×C107—22no—
109C22×C107—42no—
110C22×C107—41no—
111C22×C107—41no—
112C22×C107—41no—
113C22×C107—41no—
114C22×C107—41no—
115C22×C107—81no—
116C22×C107—81no—
117C22×C107—81no—
118C22×C107#34111yescharacteristic
119C22×C107#34111yescharacteristic
120C22×C107#34211yescharacteristic
121C4×C107—22no—
122C4×C107—21no—
123C4×C107—41no—
124C4×C107—41no—
125C4×C107—41no—
126C4×C107AΣL(1,𝔽16)11yescharacteristic
127C4×C107#35211yescharacteristic
128#7285C10711yesmaximal, characteristic, direct product factor, Sylow
129C2×C107—21no—
130C2×C107—21no—
131C2×C107—42no—
132C2×C107—81no—
133C2×C107#129811yescharacteristic
134C2×C107#139011yescharacteristic
135C2×C107#139511yescharacteristic
136#1870C2×C10711yescharacteristic
137#1460C2×C10711yescharacteristic
138#1459C2×C10711yescharacteristic
139C107#728511yescharacteristic, direct product factor, Sylow
140C22×M16C4×C10711yescharacteristic
141C2×C4×D4C22×C10711yescharacteristic
142#431—21no—
143C2×C22⋊C8—21no—
144C2×C22⋊C8—21no—
145C2×C22⋊C8C4×C10711yescharacteristic
146#336—21no—
147#324C4×C10712yes—
148#323—21no—
149#323—21no—
150#323C4×C10712yes—
151C22×D4Q8×C10711yescharacteristic
152C23×C4C2×C4×C10711yescharacteristic
153C23×C4D4×C10711yescharacteristic
154C2×M16—42no—
155C2×M16—41no—
156C22×C8—21no—
157C22×C8—21no—
158C22×C8—41no—
159C4×D4—41no—
160C4×D4—41no—
161C2×C4⋊C4C2×C4×C10711yescharacteristic
162C2×C22⋊C4C2×C4×C10711yescharacteristic
163C2×C22⋊C4D4×C10711yescharacteristic
164C2×C42D4×C10711yescharacteristic
165C4⋊C8—41no—
166C22⋊C8—22no—
167C22⋊C8—22no—
168C22⋊C8—42no—
169C22⋊C8—41no—
170C22⋊C8—41no—
171C4×C8—41no—
172C24C4⋊C4×C10711yescharacteristic
173C24C4⋊C4×C10711yescharacteristic
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—41no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4C42×C10711yescharacteristic
186C22×C4C22⋊C4×C10711yescharacteristic
187C22×C4C22⋊C4×C10711yescharacteristic
188C22×C4C22⋊C4×C10711yescharacteristic
189C22×C4C4⋊C4×C10711yescharacteristic
190M16—42no—
191M16—42no—
192C2×C8—22no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—81no—
201C2×C8—81no—
202C4⋊C4—41no—
203C22⋊C4—41no—
204C22⋊C4—41no—
205C42—21no—
206C42—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—21no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23#95×C10711yescharacteristic
217C23#108×C10712yes—
218D4—44no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—81no—
235C2×C4#99×C10711yescharacteristic
236C2×C4#99×C10711yescharacteristic
237C2×C4#108×C10712yes—
238C8—42no—
239C8—81no—
240C8—82no—
241C8—82no—
242C22—21no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—41no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22#341×C10711yescharacteristic
255C22#341×C10711yescharacteristic
256C22#342×C10711yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—41no—
261C4—41no—
262C4AΣL(1,𝔽16)×C10711yescharacteristic
263C4#352×C10711yescharacteristic
264C2—21no—
265C2—21no—
266C2—42no—
267C2—81no—
268C2C107×#129811yescharacteristic
269C2C107×#139011yescharacteristic
270C2C107×#139511yescharacteristic
subgroupG/H
centerC2×C4×C107#99
commutatorC22×C4C42×C107
Frattini, cosocleC2×C4×D4C22×C107
socleC22×C107#342
prime radicalC22×D4×C107Q8
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C22×C4×C107 ◁ C2×C4×D4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
128. #7285C107direct (N × H)
139. C107#7285direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#18702
C107×#14602
C107×#14592
#7285107