Finite Group Databasebeta

← C107×#10432 #41036396

Subgroups — C107×#10432 #41036396

Order 27392.

630 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 146 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×#2537C211yesmaximal, characteristic
2C107×#1844C211yesmaximal, characteristic, complemented
3C107×#1802C212yesmaximal, complemented
4C2×D4⋊C8×C107C212yesmaximal, complemented
5C107×#1296C211yesmaximal, characteristic, complemented
6C2×#121×C107—22no—
7C2×C4×D4×C107C2212yes—
8C2×#106×C107—22no—
9C2×C4⋊C8×C107C2212yes—
10C2×#102×C107—22no—
11C2×C4×C8×C107C2211yescharacteristic
12#394×C107—22no—
13#384×C107C2211yescharacteristic
14#384×C107C2211yescharacteristic
15#380×C107—22no—
16#340×C107—22no—
17D4⋊C8×C107—24no—
18C22×D4×C107—22no—
19C22×D4×C107D412yes—
20C23×C4×C107—22no—
21C22×C8×C107—21no—
22C22×C8×C107—22no—
23#121×C107—44no—
24#121×C107—44no—
25C4×D4×C107—22no—
26C4×D4×C107—22no—
27C4×D4×C107—22no—
28C4×D4×C107—22no—
29C2×C4⋊C4×C107—22no—
30C2×C4⋊C4×C107—22no—
31C2×C4⋊C4×C107—21no—
32C2×C4⋊C4×C107D412yes—
33C2×C4⋊C4×C107D412yes—
34C2×C22⋊C4×C107—24no—
35C2×C22⋊C4×C107—22no—
36C2×C42×C107C2311yescharacteristic
37#106×C107—44no—
38C4⋊C8×C107—22no—
39C4⋊C8×C107—22no—
40#102×C107—44no—
41C4×C8×C107—21no—
42C4×C8×C107D412yescomplemented
43#95×C107—22no—
44C24×C107—22no—
45C2×D4×C107—22no—
46C2×D4×C107—22no—
47C2×D4×C107—22no—
48C2×D4×C107—22no—
49C2×D4×C107—22no—
50C2×D4×C107—48no—
51C2×D4×C107—82no—
52C2×D4×C107SD1614yes—
53C22×C4×C107—22no—
54C22×C4×C107—22no—
55C22×C4×C107—42no—
56C22×C4×C107—42no—
57C22×C4×C107—42no—
58C22×C4×C107—42no—
59C22×C4×C107—42no—
60C22×C4×C107—42no—
61C22×C4×C107—41no—
62C22×C4×C107C2×D411yescharacteristic
63C22×C4×C107C2×D412yes—
64C2×C8×C107—22no—
65C2×C8×C107—22no—
66C2×C8×C107—22no—
67C2×C8×C107—42no—
68C2×C8×C107—42no—
69C2×C8×C107—42no—
70C4⋊C4×C107—22no—
71C4⋊C4×C107—22no—
72C4⋊C4×C107—42no—
73C4⋊C4×C107—42no—
74C4⋊C4×C107—42no—
75C4⋊C4×C107—42no—
76C4⋊C4×C107—42no—
77C4⋊C4×C107—42no—
78C22⋊C4×C107—48no—
79C22⋊C4×C107—42no—
80C22⋊C4×C107—42no—
81C42×C107C2×D411yescharacteristic
82C42×C107#4111yescharacteristic
83C42×C107#4112yes—
84C23×C107—24no—
85C23×C107—42no—
86C23×C107—42no—
87C23×C107—42no—
88C23×C107—42no—
89C23×C107—42no—
90C23×C107—42no—
91C23×C107#12011yescharacteristic
92D4×C107—24no—
93D4×C107—24no—
94D4×C107—42no—
95D4×C107—42no—
96D4×C107—88no—
97C2×C4×C107—21no—
98C2×C4×C107—21no—
99C2×C4×C107—42no—
100C2×C4×C107—42no—
101C2×C4×C107—42no—
102C2×C4×C107—44no—
103C2×C4×C107—42no—
104C2×C4×C107—82no—
105C2×C4×C107—82no—
106C2×C4×C107—82no—
107C2×C4×C107—82no—
108C2×C4×C107—82no—
109C2×C4×C107—81no—
110C2×C4×C107#12111yescharacteristic
111C2×C4×C107#12112yes—
112C2×C4×C107#12312yes—
113C2×C4×C107#12411yescharacteristic
114C2×C4×C107C2×SD1612yes—
115C2×C4×C107#13512yes—
116C2×C4×C107AGL(1,ℤ/8)12yes—
117C2×C4×C107AGL(1,ℤ/8)12yes—
118C8×C107—24no—
119C8×C107—82no—
120C22×C107—44no—
121C22×C107—44no—
122C22×C107—44no—
123C22×C107—82no—
124C22×C107—82no—
125C22×C107—82no—
126C22×C107—82no—
127C22×C107#39411yescharacteristic
128C22×C107#44912yes—
129C22×C107#45012yes—
130C22×C107#45311yescharacteristic
131C22×C107#45611yescharacteristic
132C4×C107—21no—
133C4×C107—21no—
134C4×C107—82no—
135C4×C107—82no—
136C4×C107—161no—
137C4×C107#46512yes—
138C4×C107#46912yes—
139C4×C107#48112yes—
140C4×C107#48212yes—
141#10432C10711yesmaximal, characteristic, direct product factor, Sylow
142C2×C107—84no—
143C2×C107#162411yescharacteristic
144C2×C107#162911yescharacteristic
145C2×C107#165412yes—
146C2×C107#203412yes—
147C2×C107#203911yescharacteristic
148#2537C2×C10711yescharacteristic
149#1844C2×C10711yescharacteristic, complemented
150#1802C2×C10712yescomplemented
151C2×D4⋊C8C2×C10712yescomplemented
152#1296C2×C10711yescharacteristic, complemented
153C107#1043211yescharacteristic, direct product factor, Sylow
154C2×#121—22no—
155C2×C4×D4C22×C10712yes—
156C2×#106—22no—
157C2×C4⋊C8C22×C10712yes—
158C2×#102—22no—
159C2×C4×C8C22×C10711yescharacteristic
160#394—22no—
161#384C22×C10711yescharacteristic
162#384C22×C10711yescharacteristic
163#380—22no—
164#340—22no—
165D4⋊C8—24no—
166C22×D4—22no—
167C22×D4D4×C10712yes—
168C23×C4—22no—
169C22×C8—21no—
170C22×C8—22no—
171#121—44no—
172#121—44no—
173C4×D4—22no—
174C4×D4—22no—
175C4×D4—22no—
176C4×D4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4D4×C10712yes—
181C2×C4⋊C4D4×C10712yes—
182C2×C22⋊C4—24no—
183C2×C22⋊C4—22no—
184C2×C42C23×C10711yescharacteristic
185#106—44no—
186C4⋊C8—22no—
187C4⋊C8—22no—
188#102—44no—
189C4×C8—21no—
190C4×C8D4×C10712yescomplemented
191#95—22no—
192C24—22no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4—48no—
199C2×D4—82no—
200C2×D4SD16×C10714yes—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—42no—
204C22×C4—42no—
205C22×C4—42no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—41no—
210C22×C4C2×D4×C10711yescharacteristic
211C22×C4C2×D4×C10712yes—
212C2×C8—22no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—42no—
216C2×C8—42no—
217C2×C8—42no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C22⋊C4—48no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C42C2×D4×C10711yescharacteristic
230C42#41×C10711yescharacteristic
231C42#41×C10712yes—
232C23—24no—
233C23—42no—
234C23—42no—
235C23—42no—
236C23—42no—
237C23—42no—
238C23—42no—
239C23#120×C10711yescharacteristic
240D4—24no—
241D4—24no—
242D4—42no—
243D4—42no—
244D4—88no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—44no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—81no—
258C2×C4#121×C10711yescharacteristic
259C2×C4#121×C10712yes—
260C2×C4#123×C10712yes—
261C2×C4#124×C10711yescharacteristic
262C2×C4C2×SD16×C10712yes—
263C2×C4#135×C10712yes—
264C2×C4AGL(1,ℤ/8)×C10712yes—
265C2×C4AGL(1,ℤ/8)×C10712yes—
266C8—24no—
267C8—82no—
268C22—44no—
269C22—44no—
270C22—44no—
271C22—82no—
272C22—82no—
273C22—82no—
274C22—82no—
275C22#394×C10711yescharacteristic
276C22#449×C10712yes—
277C22#450×C10712yes—
278C22#453×C10711yescharacteristic
279C22#456×C10711yescharacteristic
280C4—21no—
281C4—21no—
282C4—82no—
283C4—82no—
284C4—161no—
285C4#465×C10712yes—
286C4#469×C10712yes—
287C4#481×C10712yes—
288C4#482×C10712yes—
289C2—84no—
290C2C107×#162411yescharacteristic
291C2C107×#162911yescharacteristic
292C2C107×#165412yes—
293C2C107×#203412yes—
294C2C107×#203911yescharacteristic
subgroupG/H
center, socleC23×C107#120
commutator, Frattini, cosocleC2×C42C23×C107
prime radicalC107×#2537C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#1844C2semidirect
3. C107×#1802C2semidirect
4. C2×D4⋊C8×C107C2semidirect
5. C107×#1296C2semidirect
42. C4×C8×C107D4semidirect
141. #10432C107direct (N × H)
149. #1844C2×C107semidirect
150. #1802C2×C107semidirect
151. C2×D4⋊C8C2×C107semidirect
152. #1296C2×C107semidirect
153. C107#10432direct (N × H)
190. C4×C8D4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#25372
C107×#18442
C107×#18022
C2×D4⋊C8×C1072
C107×#12962
#10432107