Finite Group Databasebeta

← C107×#9206 #41035170

Subgroups — C107×#9206 #41035170

Order 27392.

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

normal subgroups only

This group has 578 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×#2618C211yesmaximal, characteristic
2C107×#2313C211yesmaximal, characteristic, complemented
3C107×#1519C212yesmaximal
4C2×#324×C107C211yesmaximal, characteristic, complemented
5C107×#1289C212yesmaximal, complemented
6C2×#123×C107—21no—
7C2×#121×C107C2211yescharacteristic
8C22×C4⋊C4×C107C2211yescharacteristic
9C2×C22⋊C8×C107C2212yes—
10#398×C107C412yescomplemented
11#396×C107—22no—
12#394×C107C412yescomplemented
13#387×C107—24no—
14#386×C107—21no—
15#381×C107—21no—
16#380×C107C2211yescharacteristic
17#380×C107C2212yes—
18C4×C22⋊C4×C107—21no—
19#327×C107—24no—
20#324×C107—22no—
21C22×D4×C107—21no—
22C22×D4×C107C2×C411yescharacteristic
23C23×C4×C107D411yescharacteristic
24C23×C4×C107D411yescharacteristic
25C23×C4×C107C2311yescharacteristic
26C22×C8×C107—22no—
27#123×C107—44no—
28#121×C107—22no—
29#121×C107—22no—
30C2×C4⋊C4×C107—22no—
31C2×C4⋊C4×C107—22no—
32C2×C4⋊C4×C107—22no—
33C2×C4⋊C4×C107—22no—
34C2×C4⋊C4×C107—21no—
35C2×C4⋊C4×C107C2×C411yescharacteristic
36C2×C4⋊C4×C107C2×C412yes—
37C2×C4⋊C4×C107D412yes—
38C2×C22⋊C4×C107—22no—
39C2×C22⋊C4×C107—21no—
40C2×C22⋊C4×C107—22no—
41C2×C22⋊C4×C107—21no—
42C2×C22⋊C4×C107—22no—
43C2×C42×C107—22no—
44C22⋊C8×C107—22no—
45C22⋊C8×C107—22no—
46#95×C107—22no—
47#95×C107—24no—
48#95×C107—22no—
49#95×C107C2×C412yes—
50#95×C107D414yes—
51C24×C107—21no—
52C24×C107C2×D411yescharacteristic
53C2×D4×C107—22no—
54C2×D4×C107—41no—
55C2×D4×C107—41no—
56C2×D4×C107—42no—
57C2×D4×C107—42no—
58C2×D4×C107—81no—
59C22×C4×C107—21no—
60C22×C4×C107—21no—
61C22×C4×C107—21no—
62C22×C4×C107—22no—
63C22×C4×C107—22no—
64C22×C4×C107—21no—
65C22×C4×C107—21no—
66C22×C4×C107—22no—
67C22×C4×C107—24no—
68C22×C4×C107—81no—
69C22×C4×C107—81no—
70C22×C4×C107C22⋊C412yes—
71C22×C4×C107C22⋊C412yes—
72C22×C4×C107C22×C411yescharacteristic
73C22×C4×C107C2×D412yes—
74C22×C4×C107C2×D411yescharacteristic
75C22×C4×C107#4112yes—
76C2×C8×C107—42no—
77C2×C8×C107—82no—
78C4⋊C4×C107—24no—
79C4⋊C4×C107—24no—
80C4⋊C4×C107—22no—
81C4⋊C4×C107—44no—
82C4⋊C4×C107—82no—
83C4⋊C4×C107—81no—
84C22⋊C4×C107—44no—
85C22⋊C4×C107—42no—
86C22⋊C4×C107—42no—
87C22⋊C4×C107—42no—
88C22⋊C4×C107—42no—
89C22⋊C4×C107—82no—
90C42×C107—82no—
91C23×C107—41no—
92C23×C107—41no—
93C23×C107—42no—
94C23×C107—42no—
95C23×C107—41no—
96C23×C107—41no—
97C23×C107—41no—
98C23×C107C2×C22⋊C411yescharacteristic
99C23×C107#12011yescharacteristic
100C23×C107#12311yescharacteristic
101C23×C107#13512yes—
102C23×C107AGL(1,ℤ/8)12yes—
103D4×C107—82no—
104D4×C107—82no—
105D4×C107—82no—
106C2×C4×C107—22no—
107C2×C4×C107—22no—
108C2×C4×C107—22no—
109C2×C4×C107—22no—
110C2×C4×C107—41no—
111C2×C4×C107—42no—
112C2×C4×C107—42no—
113C2×C4×C107—41no—
114C2×C4×C107—42no—
115C2×C4×C107—42no—
116C2×C4×C107—42no—
117C2×C4×C107—42no—
118C2×C4×C107—44no—
119C2×C4×C107—42no—
120C2×C4×C107—44no—
121C2×C4×C107—42no—
122C2×C4×C107—41no—
123C2×C4×C107—41no—
124C2×C4×C107—42no—
125C2×C4×C107—41no—
126C2×C4×C107—44no—
127C2×C4×C107—81no—
128C2×C4×C107C4×D412yes—
129C2×C4×C107#12112yes—
130C8×C107—82no—
131C22×C107—21no—
132C22×C107—21no—
133C22×C107—21no—
134C22×C107—21no—
135C22×C107—21no—
136C22×C107—21no—
137C22×C107—42no—
138C22×C107—42no—
139C22×C107—82no—
140C22×C107—82no—
141C22×C107—81no—
142C22×C107—81no—
143C22×C107—81no—
144C22×C107#38611yescharacteristic
145C22×C107#41611yescharacteristic
146C22×C107#41811yescharacteristic
147C22×C107#44912yes—
148C22×C107#48212yes—
149C4×C107—22no—
150C4×C107—22no—
151C4×C107—42no—
152C4×C107—42no—
153C4×C107—82no—
154C4×C107—84no—
155C4×C107—81no—
156#9206C10711yesmaximal, characteristic, direct product factor, Sylow
157C2×C107—21no—
158C2×C107—22no—
159C2×C107—21no—
160C2×C107—22no—
161C2×C107—161no—
162C2×C107#187511yescharacteristic
163C2×C107#191211yescharacteristic
164C2×C107#191311yescharacteristic
165#2618C2×C10711yescharacteristic
166#2313C2×C10711yescharacteristic, complemented
167#1519C2×C10712yes—
168C2×#324C2×C10711yescharacteristic, complemented
169#1289C2×C10712yescomplemented
170C107#920611yescharacteristic, direct product factor, Sylow
171C2×#123—21no—
172C2×#121C22×C10711yescharacteristic
173C22×C4⋊C4C22×C10711yescharacteristic
174C2×C22⋊C8C22×C10712yes—
175#398C4×C10712yescomplemented
176#396—22no—
177#394C4×C10712yescomplemented
178#387—24no—
179#386—21no—
180#381—21no—
181#380C22×C10711yescharacteristic
182#380C22×C10712yes—
183C4×C22⋊C4—21no—
184#327—24no—
185#324—22no—
186C22×D4—21no—
187C22×D4C2×C4×C10711yescharacteristic
188C23×C4D4×C10711yescharacteristic
189C23×C4D4×C10711yescharacteristic
190C23×C4C23×C10711yescharacteristic
191C22×C8—22no—
192#123—44no—
193#121—22no—
194#121—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4C2×C4×C10711yescharacteristic
201C2×C4⋊C4C2×C4×C10712yes—
202C2×C4⋊C4D4×C10712yes—
203C2×C22⋊C4—21no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—22no—
208C2×C42—22no—
209C22⋊C8—22no—
210C22⋊C8—22no—
211#95—22no—
212#95—24no—
213#95—22no—
214#95C2×C4×C10712yes—
215#95D4×C10714yes—
216C24—21no—
217C24C2×D4×C10711yescharacteristic
218C2×D4—22no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—42no—
222C2×D4—42no—
223C2×D4—81no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—81no—
234C22×C4—81no—
235C22×C4C22⋊C4×C10712yes—
236C22×C4C22⋊C4×C10712yes—
237C22×C4C22×C4×C10711yescharacteristic
238C22×C4C2×D4×C10712yes—
239C22×C4C2×D4×C10711yescharacteristic
240C22×C4#41×C10712yes—
241C2×C8—42no—
242C2×C8—82no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—22no—
246C4⋊C4—44no—
247C4⋊C4—82no—
248C4⋊C4—81no—
249C22⋊C4—44no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—82no—
255C42—82no—
256C23—41no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23C2×C22⋊C4×C10711yescharacteristic
264C23#120×C10711yescharacteristic
265C23#123×C10711yescharacteristic
266C23#135×C10712yes—
267C23AGL(1,ℤ/8)×C10712yes—
268D4—82no—
269D4—82no—
270D4—82no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—44no—
292C2×C4—81no—
293C2×C4C4×D4×C10712yes—
294C2×C4#121×C10712yes—
295C8—82no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—82no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#386×C10711yescharacteristic
310C22#416×C10711yescharacteristic
311C22#418×C10711yescharacteristic
312C22#449×C10712yes—
313C22#482×C10712yes—
314C4—22no—
315C4—22no—
316C4—42no—
317C4—42no—
318C4—82no—
319C4—84no—
320C4—81no—
321C2—21no—
322C2—22no—
323C2—21no—
324C2—22no—
325C2—161no—
326C2C107×#187511yescharacteristic
327C2C107×#191211yescharacteristic
328C2C107×#191311yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC22×C4C22×C4×C107
Frattini, cosocleC23×C4C23×C107
prime radicalC2×#121×C107C22
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
2. C107×#2313C2semidirect
4. C2×#324×C107C2semidirect
5. C107×#1289C2semidirect
10. #398×C107C4semidirect
12. #394×C107C4semidirect
156. #9206C107direct (N × H)
166. #2313C2×C107semidirect
168. C2×#324C2×C107semidirect
169. #1289C2×C107semidirect
170. C107#9206direct (N × H)
175. #398C4×C107semidirect
177. #394C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#26182
C107×#23132
C107×#15192
C2×#324×C1072
C107×#12892
#9206107