Finite Group Databasebeta

← C107×#9202 #41035166

Subgroups — C107×#9202 #41035166

Order 27392.

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

normal subgroups only

This group has 516 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×#2627C211yesmaximal, characteristic
2C107×#2313C211yesmaximal, characteristic
3C107×#1520C212yesmaximal
4C2×#324×C107C211yesmaximal, characteristic
5C107×#1289C212yesmaximal
6C2×C22⋊Q8×C107C2211yescharacteristic
7C22×C4⋊C4×C107C2211yescharacteristic
8C2×C22⋊C8×C107C2212yes—
9#400×C107C412yescomplemented
10#398×C107—22no—
11#395×C107C412yescomplemented
12#387×C107—24no—
13#385×C107—21no—
14#381×C107—21no—
15#381×C107—21no—
16#380×C107C2211yescharacteristic
17#380×C107C2212yes—
18C4×C22⋊C4×C107—21no—
19#328×C107—24no—
20#324×C107—22no—
21C22×Q8×C107C2×C411yescharacteristic
22C23×C4×C107D411yescharacteristic
23C23×C4×C107D411yescharacteristic
24C23×C4×C107C2311yescharacteristic
25C22×C8×C107—22no—
26C22⋊Q8×C107—22no—
27C22⋊Q8×C107—22no—
28C2×C4⋊C4×C107—22no—
29C2×C4⋊C4×C107—22no—
30C2×C4⋊C4×C107—21no—
31C2×C4⋊C4×C107—22no—
32C2×C4⋊C4×C107—22no—
33C2×C4⋊C4×C107—21no—
34C2×C4⋊C4×C107C2×C411yescharacteristic
35C2×C4⋊C4×C107C2×C412yes—
36C2×C4⋊C4×C107D412yes—
37C2×C22⋊C4×C107—22no—
38C2×C22⋊C4×C107—21no—
39C2×C22⋊C4×C107—21no—
40C2×C42×C107—22no—
41C22⋊C8×C107—22no—
42C22⋊C8×C107—22no—
43#95×C107—22no—
44#95×C107—24no—
45#95×C107—22no—
46#95×C107—22no—
47#95×C107—22no—
48#95×C107C2×C412yes—
49#95×C107D414yes—
50C24×C107C2×D411yescharacteristic
51C2×Q8×C107—22no—
52C2×Q8×C107—81no—
53C22×C4×C107—21no—
54C22×C4×C107—21no—
55C22×C4×C107—21no—
56C22×C4×C107—22no—
57C22×C4×C107—22no—
58C22×C4×C107—21no—
59C22×C4×C107—21no—
60C22×C4×C107—22no—
61C22×C4×C107—21no—
62C22×C4×C107—24no—
63C22×C4×C107—81no—
64C22×C4×C107—81no—
65C22×C4×C107C22⋊C412yes—
66C22×C4×C107C22⋊C412yes—
67C22×C4×C107C22×C411yescharacteristic
68C22×C4×C107C2×D412yes—
69C22×C4×C107C2×D411yescharacteristic
70C22×C4×C107#4112yes—
71C2×C8×C107—42no—
72C2×C8×C107—82no—
73C4⋊C4×C107—24no—
74C4⋊C4×C107—24no—
75C4⋊C4×C107—22no—
76C4⋊C4×C107—42no—
77C4⋊C4×C107—82no—
78C4⋊C4×C107—81no—
79C4⋊C4×C107—82no—
80C22⋊C4×C107—41no—
81C22⋊C4×C107—41no—
82C22⋊C4×C107—42no—
83C22⋊C4×C107—42no—
84C22⋊C4×C107—42no—
85C42×C107—82no—
86C23×C107—41no—
87C23×C107—41no—
88C23×C107C2×C22⋊C411yescharacteristic
89C23×C107#12011yescharacteristic
90C23×C107#12311yescharacteristic
91C23×C107#13512yes—
92C23×C107#13712yes—
93Q8×C107—82no—
94C2×C4×C107—22no—
95C2×C4×C107—22no—
96C2×C4×C107—22no—
97C2×C4×C107—22no—
98C2×C4×C107—41no—
99C2×C4×C107—42no—
100C2×C4×C107—42no—
101C2×C4×C107—41no—
102C2×C4×C107—42no—
103C2×C4×C107—42no—
104C2×C4×C107—42no—
105C2×C4×C107—42no—
106C2×C4×C107—44no—
107C2×C4×C107—42no—
108C2×C4×C107—42no—
109C2×C4×C107—42no—
110C2×C4×C107—44no—
111C2×C4×C107—42no—
112C2×C4×C107—41no—
113C2×C4×C107—41no—
114C2×C4×C107—42no—
115C2×C4×C107—44no—
116C2×C4×C107—81no—
117C2×C4×C107C4×D412yes—
118C2×C4×C107#12112yes—
119C8×C107—82no—
120C22×C107—21no—
121C22×C107—21no—
122C22×C107—21no—
123C22×C107—21no—
124C22×C107—21no—
125C22×C107—21no—
126C22×C107—42no—
127C22×C107—42no—
128C22×C107#38611yescharacteristic
129C22×C107#41611yescharacteristic
130C22×C107#41911yescharacteristic
131C22×C107#45212yes—
132C22×C107#48512yes—
133C4×C107—22no—
134C4×C107—22no—
135C4×C107—42no—
136C4×C107—42no—
137C4×C107—82no—
138C4×C107—84no—
139C4×C107—81no—
140C4×C107—81no—
141#9202C10711yesmaximal, characteristic, direct product factor, Sylow
142C2×C107—21no—
143C2×C107—22no—
144C2×C107—21no—
145C2×C107—22no—
146C2×C107#187311yescharacteristic
147C2×C107#191211yescharacteristic
148C2×C107#191311yescharacteristic
149#2627C2×C10711yescharacteristic
150#2313C2×C10711yescharacteristic
151#1520C2×C10712yes—
152C2×#324C2×C10711yescharacteristic
153#1289C2×C10712yes—
154C107#920211yescharacteristic, direct product factor, Sylow
155C2×C22⋊Q8C22×C10711yescharacteristic
156C22×C4⋊C4C22×C10711yescharacteristic
157C2×C22⋊C8C22×C10712yes—
158#400C4×C10712yescomplemented
159#398—22no—
160#395C4×C10712yescomplemented
161#387—24no—
162#385—21no—
163#381—21no—
164#381—21no—
165#380C22×C10711yescharacteristic
166#380C22×C10712yes—
167C4×C22⋊C4—21no—
168#328—24no—
169#324—22no—
170C22×Q8C2×C4×C10711yescharacteristic
171C23×C4D4×C10711yescharacteristic
172C23×C4D4×C10711yescharacteristic
173C23×C4C23×C10711yescharacteristic
174C22×C8—22no—
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×C4×C10711yescharacteristic
184C2×C4⋊C4C2×C4×C10712yes—
185C2×C4⋊C4D4×C10712yes—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—21no—
189C2×C42—22no—
190C22⋊C8—22no—
191C22⋊C8—22no—
192#95—22no—
193#95—24no—
194#95—22no—
195#95—22no—
196#95—22no—
197#95C2×C4×C10712yes—
198#95D4×C10714yes—
199C24C2×D4×C10711yescharacteristic
200C2×Q8—22no—
201C2×Q8—81no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—24no—
212C22×C4—81no—
213C22×C4—81no—
214C22×C4C22⋊C4×C10712yes—
215C22×C4C22⋊C4×C10712yes—
216C22×C4C22×C4×C10711yescharacteristic
217C22×C4C2×D4×C10712yes—
218C22×C4C2×D4×C10711yescharacteristic
219C22×C4#41×C10712yes—
220C2×C8—42no—
221C2×C8—82no—
222C4⋊C4—24no—
223C4⋊C4—24no—
224C4⋊C4—22no—
225C4⋊C4—42no—
226C4⋊C4—82no—
227C4⋊C4—81no—
228C4⋊C4—82no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C22⋊C4—42no—
234C42—82no—
235C23—41no—
236C23—41no—
237C23C2×C22⋊C4×C10711yescharacteristic
238C23#120×C10711yescharacteristic
239C23#123×C10711yescharacteristic
240C23#135×C10712yes—
241C23#137×C10712yes—
242Q8—82no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—44no—
265C2×C4—81no—
266C2×C4C4×D4×C10712yes—
267C2×C4#121×C10712yes—
268C8—82no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—42no—
276C22—42no—
277C22#386×C10711yescharacteristic
278C22#416×C10711yescharacteristic
279C22#419×C10711yescharacteristic
280C22#452×C10712yes—
281C22#485×C10712yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—82no—
287C4—84no—
288C4—81no—
289C4—81no—
290C2—21no—
291C2—22no—
292C2—21no—
293C2—22no—
294C2C107×#187311yescharacteristic
295C2C107×#191211yescharacteristic
296C2C107×#191311yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC24×C107C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C23×C4×C107 ◁ G

Complements

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

NH ≅ G/Ntype
9. #400×C107C4semidirect
11. #395×C107C4semidirect
141. #9202C107direct (N × H)
154. C107#9202direct (N × H)
158. #400C4×C107semidirect
160. #395C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#26272
C107×#23132
C107×#15202
C2×#324×C1072
C107×#12892
#9202107