Finite Group Databasebeta

← C107×#9430 #41035394

Subgroups — C107×#9430 #41035394

Order 27392.

444 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3141C211yesmaximal, characteristic
2C107×#2381C211yesmaximal, characteristic, complemented
3C107×#1556C211yesmaximal, characteristic, complemented
4C107×#1514C211yesmaximal, characteristic
5C107×#1514C211yesmaximal, characteristic
6C107×#1288C211yesmaximal, characteristic, complemented
7C107×#1288C211yesmaximal, characteristic, complemented
8#532×C107C2211yescharacteristic
9C2×C4⋊Q8×C107C2211yescharacteristic
10#489×C107—22no—
11#487×C107C412yescomplemented
12#486×C107C412yescomplemented
13#432×C107C2211yescharacteristic
14#432×C107C2211yescharacteristic
15#417×C107—22no—
16C4×M16×C107C2211yescharacteristic
17#391×C107—22no—
18#387×C107—22no—
19#387×C107—22no—
20#383×C107C2211yescharacteristic
21#383×C107C2211yescharacteristic
22#332×C107—22no—
23#327×C107—22no—
24#327×C107—22no—
25C2×#41×C107—21no—
26C22×Q8×C107—21no—
27C2×M16×C107—21no—
28C4⋊Q8×C107—21no—
29C4⋊Q8×C107—21no—
30C4⋊Q8×C107C2×C411yescharacteristic
31C4⋊Q8×C107C2×C412yes—
32C4⋊Q8×C107D412yes—
33#127×C107C2×C411yescharacteristic
34#124×C107—21no—
35#121×C107—21no—
36#121×C107—21no—
37C4×D4×C107—21no—
38C4×D4×C107—21no—
39C2×C4⋊C4×C107—21no—
40C2×C4⋊C4×C107—22no—
41C2×C4⋊C4×C107D412yes—
42C2×C42×C107—22no—
43C2×C42×C107C2311yescharacteristic
44C4⋊C8×C107—21no—
45C4⋊C8×C107—21no—
46#103×C107—24no—
47#102×C107—24no—
48C22⋊C8×C107—21no—
49C22⋊C8×C107—21no—
50#97×C107—21no—
51#97×C107—21no—
52#97×C107—21no—
53C4×C8×C107C2×C412yes—
54#95×C107—24no—
55#95×C107—21no—
56#95×C107—21no—
57#95×C107—21no—
58#95×C107—21no—
59#95×C107D412yes—
60#95×C107D412yes—
61#41×C107—44no—
62C2×Q8×C107—22no—
63C2×Q8×C107—22no—
64C2×Q8×C107—21no—
65C2×Q8×C107—81no—
66C2×Q8×C107—81no—
67C2×D4×C107—21no—
68C2×D4×C107—21no—
69C2×D4×C107—21no—
70C2×D4×C107—41no—
71C22×C4×C107—22no—
72C22×C4×C107—22no—
73C22×C4×C107—22no—
74C22×C4×C107—41no—
75C22×C4×C107C2×D411yescharacteristic
76C22×C4×C107C2×D411yescharacteristic
77C22×C4×C107C2×D411yescharacteristic
78M16×C107—42no—
79C2×C8×C107—22no—
80C2×C8×C107—41no—
81C2×C8×C107—41no—
82C4⋊C4×C107—22no—
83C4⋊C4×C107—22no—
84C4⋊C4×C107—22no—
85C4⋊C4×C107—21no—
86C4⋊C4×C107—21no—
87C4⋊C4×C107—82no—
88C4⋊C4×C107C22⋊C414yes—
89C22⋊C4×C107—41no—
90C22⋊C4×C107—41no—
91C42×C107—82no—
92C42×C107C22×C411yescharacteristic
93C42×C107C2×D411yescharacteristic
94C42×C107#4111yescharacteristic
95C42×C107#4111yescharacteristic
96C23×C107—41no—
97C23×C107#12011yescharacteristic
98Q8×C107—42no—
99Q8×C107—82no—
100Q8×C107—82no—
101D4×C107—42no—
102D4×C107—81no—
103D4×C107—81no—
104D4×C107—82no—
105C2×C4×C107—22no—
106C2×C4×C107—24no—
107C2×C4×C107—41no—
108C2×C4×C107—41no—
109C2×C4×C107—42no—
110C2×C4×C107—42no—
111C2×C4×C107—42no—
112C2×C4×C107—42no—
113C2×C4×C107—42no—
114C2×C4×C107—42no—
115C2×C4×C107—41no—
116C2×C4×C107—42no—
117C2×C4×C107—42no—
118C2×C4×C107—82no—
119C2×C4×C107C2×C22⋊C411yescharacteristic
120C2×C4×C107C4×D411yescharacteristic
121C2×C4×C107C4×D411yescharacteristic
122C2×C4×C107#12111yescharacteristic
123C2×C4×C107#12111yescharacteristic
124C2×C4×C107#12311yescharacteristic
125C8×C107—42no—
126C8×C107—81no—
127C8×C107—81no—
128C22×C107—21no—
129C22×C107—21no—
130C22×C107—81no—
131C22×C107—81no—
132C22×C107—81no—
133C22×C107#38611yescharacteristic
134C22×C107#45412yes—
135C4×C107—21no—
136C4×C107—21no—
137C4×C107—21no—
138C4×C107—21no—
139C4×C107—21no—
140C4×C107—21no—
141C4×C107—44no—
142C4×C107—82no—
143C4×C107—82no—
144C4×C107—81no—
145#9430C10711yesmaximal, characteristic, direct product factor, Sylow
146C2×C107—22no—
147C2×C107—161no—
148C2×C107#188811yescharacteristic
149C2×C107#190411yescharacteristic
150C2×C107#190511yescharacteristic
151#3141C2×C10711yescharacteristic
152#2381C2×C10711yescharacteristic, complemented
153#1556C2×C10711yescharacteristic, complemented
154#1514C2×C10711yescharacteristic
155#1514C2×C10711yescharacteristic
156#1288C2×C10711yescharacteristic, complemented
157#1288C2×C10711yescharacteristic, complemented
158C107#943011yescharacteristic, direct product factor, Sylow
159#532C22×C10711yescharacteristic
160C2×C4⋊Q8C22×C10711yescharacteristic
161#489—22no—
162#487C4×C10712yescomplemented
163#486C4×C10712yescomplemented
164#432C22×C10711yescharacteristic
165#432C22×C10711yescharacteristic
166#417—22no—
167C4×M16C22×C10711yescharacteristic
168#391—22no—
169#387—22no—
170#387—22no—
171#383C22×C10711yescharacteristic
172#383C22×C10711yescharacteristic
173#332—22no—
174#327—22no—
175#327—22no—
176C2×#41—21no—
177C22×Q8—21no—
178C2×M16—21no—
179C4⋊Q8—21no—
180C4⋊Q8—21no—
181C4⋊Q8C2×C4×C10711yescharacteristic
182C4⋊Q8C2×C4×C10712yes—
183C4⋊Q8D4×C10712yes—
184#127C2×C4×C10711yescharacteristic
185#124—21no—
186#121—21no—
187#121—21no—
188C4×D4—21no—
189C4×D4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4D4×C10712yes—
193C2×C42—22no—
194C2×C42C23×C10711yescharacteristic
195C4⋊C8—21no—
196C4⋊C8—21no—
197#103—24no—
198#102—24no—
199C22⋊C8—21no—
200C22⋊C8—21no—
201#97—21no—
202#97—21no—
203#97—21no—
204C4×C8C2×C4×C10712yes—
205#95—24no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95D4×C10712yes—
211#95D4×C10712yes—
212#41—44no—
213C2×Q8—22no—
214C2×Q8—22no—
215C2×Q8—21no—
216C2×Q8—81no—
217C2×Q8—81no—
218C2×D4—21no—
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—41no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—41no—
226C22×C4C2×D4×C10711yescharacteristic
227C22×C4C2×D4×C10711yescharacteristic
228C22×C4C2×D4×C10711yescharacteristic
229M16—42no—
230C2×C8—22no—
231C2×C8—41no—
232C2×C8—41no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—82no—
239C4⋊C4C22⋊C4×C10714yes—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C42—82no—
243C42C22×C4×C10711yescharacteristic
244C42C2×D4×C10711yescharacteristic
245C42#41×C10711yescharacteristic
246C42#41×C10711yescharacteristic
247C23—41no—
248C23#120×C10711yescharacteristic
249Q8—42no—
250Q8—82no—
251Q8—82no—
252D4—42no—
253D4—81no—
254D4—81no—
255D4—82no—
256C2×C4—22no—
257C2×C4—24no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—82no—
270C2×C4C2×C22⋊C4×C10711yescharacteristic
271C2×C4C4×D4×C10711yescharacteristic
272C2×C4C4×D4×C10711yescharacteristic
273C2×C4#121×C10711yescharacteristic
274C2×C4#121×C10711yescharacteristic
275C2×C4#123×C10711yescharacteristic
276C8—42no—
277C8—81no—
278C8—81no—
279C22—21no—
280C22—21no—
281C22—81no—
282C22—81no—
283C22—81no—
284C22#386×C10711yescharacteristic
285C22#454×C10712yes—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—44no—
293C4—82no—
294C4—82no—
295C4—81no—
296C2—22no—
297C2—161no—
298C2C107×#188811yescharacteristic
299C2C107×#190411yescharacteristic
300C2C107×#190511yescharacteristic
subgroupG/H
center, socleC22×C107#386
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
prime radical#532×C107C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2381C2semidirect
3. C107×#1556C2semidirect
6. C107×#1288C2semidirect
7. C107×#1288C2semidirect
11. #487×C107C4semidirect
12. #486×C107C4semidirect
145. #9430C107direct (N × H)
152. #2381C2×C107semidirect
153. #1556C2×C107semidirect
156. #1288C2×C107semidirect
157. #1288C2×C107semidirect
158. C107#9430direct (N × H)
162. #487C4×C107semidirect
163. #486C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#31412
C107×#23812
C107×#15562
C107×#15142
C107×#12882
#9430107