Finite Group Databasebeta

← C107×#8914 #41034878

Subgroups — C107×#8914 #41034878

Order 27392.

468 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2379C211yesmaximal, characteristic
2C107×#1959C211yesmaximal, characteristic
3C107×#1836C212yesmaximal, complemented
4C2×#329×C107C211yesmaximal, characteristic
5C107×#1295C212yesmaximal, complemented
6C2×#124×C107C2211yescharacteristic
7C2×#103×C107—21no—
8C2×#102×C107—21no—
9C2×#97×C107C2211yescharacteristic
10C2×#97×C107C2212yes—
11#391×C107—21no—
12#388×C107—22no—
13#386×C107—21no—
14#385×C107—22no—
15#384×C107C2211yescharacteristic
16#382×C107C2212yes—
17#340×C107—22no—
18#340×C107—22no—
19#329×C107C414yescomplemented
20C22×Q8×C107D411yescharacteristic
21C22×D4×C107D411yescharacteristic
22C23×C4×C107—21no—
23C22×C8×C107—22no—
24C22×C8×C107—21no—
25#124×C107—22no—
26#124×C107C2×C412yes—
27#124×C107Q812yes—
28C2×C4⋊C4×C107—22no—
29C2×C4⋊C4×C107—21no—
30C2×C4⋊C4×C107—21no—
31C2×C4⋊C4×C107D412yes—
32C2×C4⋊C4×C107D412yes—
33C2×C22⋊C4×C107—22no—
34C2×C22⋊C4×C107—22no—
35C2×C22⋊C4×C107—21no—
36C2×C42×C107—21no—
37C2×C42×C107C2311yescharacteristic
38#103×C107—42no—
39#102×C107—42no—
40#97×C107—22no—
41#97×C107—22no—
42#97×C107C2×C414yescomplemented
43#95×C107—22no—
44#95×C107—22no—
45#95×C107—22no—
46C24×C107—21no—
47C2×Q8×C107—21no—
48C2×Q8×C107—41no—
49C2×Q8×C107—41no—
50C2×Q8×C107C4⋊C412yes—
51C2×D4×C107—21no—
52C2×D4×C107—41no—
53C2×D4×C107—41no—
54C2×D4×C107C4⋊C412yes—
55C22×C4×C107—21no—
56C22×C4×C107—22no—
57C22×C4×C107—22no—
58C22×C4×C107—41no—
59C22×C4×C107—81no—
60C22×C4×C107—82no—
61C22×C4×C107C2×D411yescharacteristic
62C22×C4×C107C2×D412yes—
63C2×C8×C107—22no—
64C2×C8×C107—24no—
65C2×C8×C107—42no—
66C2×C8×C107—42no—
67C2×C8×C107—41no—
68C2×C8×C107—41no—
69C4⋊C4×C107—42no—
70C4⋊C4×C107—42no—
71C4⋊C4×C107—41no—
72C4⋊C4×C107—41no—
73C4⋊C4×C107—44no—
74C4⋊C4×C107—81no—
75C22⋊C4×C107—24no—
76C22⋊C4×C107—24no—
77C22⋊C4×C107—81no—
78C22⋊C4×C107—82no—
79C42×C107—81no—
80C42×C107C22×C411yescharacteristic
81C42×C107C2×Q811yescharacteristic
82C42×C107#4112yes—
83C23×C107—22no—
84C23×C107—41no—
85C23×C107—42no—
86C23×C107—42no—
87C23×C107—41no—
88C23×C107#12011yescharacteristic
89Q8×C107—42no—
90Q8×C107—81no—
91D4×C107—42no—
92D4×C107—81no—
93C2×C4×C107—21no—
94C2×C4×C107—22no—
95C2×C4×C107—22no—
96C2×C4×C107—21no—
97C2×C4×C107—22no—
98C2×C4×C107—41no—
99C2×C4×C107—41no—
100C2×C4×C107—42no—
101C2×C4×C107—42no—
102C2×C4×C107—42no—
103C2×C4×C107—42no—
104C2×C4×C107—42no—
105C2×C4×C107—42no—
106C2×C4×C107—84no—
107C2×C4×C107—81no—
108C2×C4×C107—82no—
109C2×C4×C107C2×C4⋊C411yescharacteristic
110C2×C4×C107C4×D412yes—
111C2×C4×C107C22⋊Q812yes—
112C2×C4×C107#12311yescharacteristic
113C8×C107—42no—
114C8×C107—44no—
115C22×C107—42no—
116C22×C107—44no—
117C22×C107—81no—
118C22×C107—81no—
119C22×C107—82no—
120C22×C107#38511yescharacteristic
121C22×C107#45311yescharacteristic
122C22×C107#45412yes—
123C22×C107#45511yescharacteristic
124C22×C107#45512yes—
125C4×C107—21no—
126C4×C107—21no—
127C4×C107—22no—
128C4×C107—22no—
129C4×C107—42no—
130C4×C107—82no—
131C4×C107—82no—
132C4×C107—161no—
133#8914C10711yesmaximal, characteristic, direct product factor, Sylow
134C2×C107—82no—
135C2×C107#165711yescharacteristic
136C2×C107#165911yescharacteristic
137C2×C107#166212yes—
138C2×C107#185611yescharacteristic
139C2×C107#186012yes—
140#2379C2×C10711yescharacteristic
141#1959C2×C10711yescharacteristic
142#1836C2×C10712yescomplemented
143C2×#329C2×C10711yescharacteristic
144#1295C2×C10712yescomplemented
145C107#891411yescharacteristic, direct product factor, Sylow
146C2×#124C22×C10711yescharacteristic
147C2×#103—21no—
148C2×#102—21no—
149C2×#97C22×C10711yescharacteristic
150C2×#97C22×C10712yes—
151#391—21no—
152#388—22no—
153#386—21no—
154#385—22no—
155#384C22×C10711yescharacteristic
156#382C22×C10712yes—
157#340—22no—
158#340—22no—
159#329C4×C10714yescomplemented
160C22×Q8D4×C10711yescharacteristic
161C22×D4D4×C10711yescharacteristic
162C23×C4—21no—
163C22×C8—22no—
164C22×C8—21no—
165#124—22no—
166#124C2×C4×C10712yes—
167#124Q8×C10712yes—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4D4×C10712yes—
172C2×C4⋊C4D4×C10712yes—
173C2×C22⋊C4—22no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—21no—
176C2×C42—21no—
177C2×C42C23×C10711yescharacteristic
178#103—42no—
179#102—42no—
180#97—22no—
181#97—22no—
182#97C2×C4×C10714yescomplemented
183#95—22no—
184#95—22no—
185#95—22no—
186C24—21no—
187C2×Q8—21no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8C4⋊C4×C10712yes—
191C2×D4—21no—
192C2×D4—41no—
193C2×D4—41no—
194C2×D4C4⋊C4×C10712yes—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—41no—
199C22×C4—81no—
200C22×C4—82no—
201C22×C4C2×D4×C10711yescharacteristic
202C22×C4C2×D4×C10712yes—
203C2×C8—22no—
204C2×C8—24no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—41no—
208C2×C8—41no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—44no—
214C4⋊C4—81no—
215C22⋊C4—24no—
216C22⋊C4—24no—
217C22⋊C4—81no—
218C22⋊C4—82no—
219C42—81no—
220C42C22×C4×C10711yescharacteristic
221C42C2×Q8×C10711yescharacteristic
222C42#41×C10712yes—
223C23—22no—
224C23—41no—
225C23—42no—
226C23—42no—
227C23—41no—
228C23#120×C10711yescharacteristic
229Q8—42no—
230Q8—81no—
231D4—42no—
232D4—81no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—84no—
247C2×C4—81no—
248C2×C4—82no—
249C2×C4C2×C4⋊C4×C10711yescharacteristic
250C2×C4C4×D4×C10712yes—
251C2×C4C22⋊Q8×C10712yes—
252C2×C4#123×C10711yescharacteristic
253C8—42no—
254C8—44no—
255C22—42no—
256C22—44no—
257C22—81no—
258C22—81no—
259C22—82no—
260C22#385×C10711yescharacteristic
261C22#453×C10711yescharacteristic
262C22#454×C10712yes—
263C22#455×C10712yes—
264C22#455×C10711yescharacteristic
265C4—21no—
266C4—21no—
267C4—22no—
268C4—22no—
269C4—42no—
270C4—82no—
271C4—82no—
272C4—161no—
273C2—82no—
274C2C107×#165711yescharacteristic
275C2C107×#165911yescharacteristic
276C2C107×#166212yes—
277C2C107×#185611yescharacteristic
278C2C107×#186012yes—
subgroupG/H
center, socleC23×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radicalC22×D4×C107D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
3. C107×#1836C2semidirect
5. C107×#1295C2semidirect
19. #329×C107C4semidirect
42. #97×C107C2×C4semidirect
133. #8914C107direct (N × H)
142. #1836C2×C107semidirect
144. #1295C2×C107semidirect
145. C107#8914direct (N × H)
159. #329C4×C107semidirect
182. #97C2×C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#23792
C107×#19592
C107×#18362
C2×#329×C1072
C107×#12952
#8914107