Finite Group Databasebeta

← C107×#8227 #41034191

Subgroups — C107×#8227 #41034191

Order 27392.

488 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#125×C107C211yesmaximal, characteristic
2C107×#1745C211yesmaximal, characteristic
3C4×#97×C107C211yesmaximal, characteristic
4C2×#330×C107C212yesmaximal
5C107×#1295C212yesmaximal
6C2×#125×C107C2211yescharacteristic
7C2×#97×C107—21no—
8C2×#97×C107C2212yes—
9C2×#97×C107C2212yes—
10C2×C4×C8×C107—21no—
11#389×C107C411yescharacteristic
12#389×C107C411yescharacteristic
13#387×C107—21no—
14#387×C107—21no—
15#382×C107C2211yescharacteristic
16C4×C4⋊C4×C107—21no—
17C4×C4⋊C4×C107—21no—
18C4×C4⋊C4×C107C411yescharacteristic
19C4×C4⋊C4×C107C411yescharacteristic
20C43×C107C2211yescharacteristic
21#336×C107—21no—
22#336×C107—21no—
23#330×C107C418yescomplemented
24C22×C8×C107—22no—
25C22×C8×C107—22no—
26#125×C107—22no—
27#125×C107C2×C414yes—
28C2×C4⋊C4×C107—21no—
29C2×C4⋊C4×C107—21no—
30C2×C4⋊C4×C107—21no—
31C2×C4⋊C4×C107—21no—
32C2×C4⋊C4×C107C2×C411yescharacteristic
33C2×C4⋊C4×C107C2×C411yescharacteristic
34C2×C4⋊C4×C107C2×C411yescharacteristic
35C2×C4⋊C4×C107C2×C411yescharacteristic
36C2×C42×C107—21no—
37C2×C42×C107—21no—
38C2×C42×C107C2×C411yescharacteristic
39C2×C42×C107C2×C411yescharacteristic
40C2×C42×C107D411yescharacteristic
41C2×C42×C107D411yescharacteristic
42C2×C42×C107D411yescharacteristic
43C2×C42×C107D411yescharacteristic
44C2×C42×C107C2311yescharacteristic
45#97×C107—24no—
46#97×C107—22no—
47#97×C107—22no—
48#97×C107C2×C414yes—
49#97×C107C2×C414yes—
50C4×C8×C107—24no—
51#95×C107—21no—
52#95×C107—21no—
53#95×C107—21no—
54#95×C107—21no—
55#95×C107—21no—
56#95×C107—21no—
57C22×C4×C107—21no—
58C22×C4×C107—21no—
59C22×C4×C107—21no—
60C22×C4×C107—21no—
61C22×C4×C107C22⋊C411yescharacteristic
62C22×C4×C107C22⋊C411yescharacteristic
63C22×C4×C107C22⋊C411yescharacteristic
64C22×C4×C107C22⋊C411yescharacteristic
65C22×C4×C107C22×C411yescharacteristic
66C22×C4×C107C2×D411yescharacteristic
67C22×C4×C107C2×D411yescharacteristic
68C2×C8×C107—24no—
69C2×C8×C107—24no—
70C2×C8×C107—24no—
71C2×C8×C107—24no—
72C2×C8×C107—42no—
73C2×C8×C107—42no—
74C4⋊C4×C107—21no—
75C4⋊C4×C107—21no—
76C4⋊C4×C107—24no—
77C4⋊C4×C107—24no—
78C4⋊C4×C107—41no—
79C4⋊C4×C107—41no—
80C4⋊C4×C107—42no—
81C4⋊C4×C107—42no—
82C4⋊C4×C107C4212yes—
83C4⋊C4×C107C4212yes—
84C42×C107—22no—
85C42×C107—22no—
86C42×C107—22no—
87C42×C107—41no—
88C42×C107—41no—
89C42×C107—41no—
90C42×C107—42no—
91C42×C107—42no—
92C42×C107C22×C412yes—
93C42×C107#4112yes—
94C23×C107C2×C22⋊C411yescharacteristic
95C2×C4×C107—21no—
96C2×C4×C107—21no—
97C2×C4×C107—21no—
98C2×C4×C107—21no—
99C2×C4×C107—21no—
100C2×C4×C107—21no—
101C2×C4×C107—21no—
102C2×C4×C107—21no—
103C2×C4×C107—21no—
104C2×C4×C107—21no—
105C2×C4×C107—21no—
106C2×C4×C107—21no—
107C2×C4×C107—22no—
108C2×C4×C107—22no—
109C2×C4×C107—21no—
110C2×C4×C107—21no—
111C2×C4×C107—21no—
112C2×C4×C107—41no—
113C2×C4×C107—41no—
114C2×C4×C107—41no—
115C2×C4×C107—41no—
116C2×C4×C107—41no—
117C2×C4×C107—41no—
118C2×C4×C107—41no—
119C2×C4×C107—41no—
120C2×C4×C107—41no—
121C2×C4×C107—41no—
122C2×C4×C107#10112yes—
123C2×C4×C107#10412yes—
124C2×C4×C107#10412yes—
125C2×C4×C107C2×C4211yescharacteristic
126C2×C4×C107#11711yescharacteristic
127C2×C4×C107C4×D412yes—
128C2×C4×C107C4×D412yes—
129C8×C107—28no—
130C8×C107—44no—
131C22×C107C4×C22⋊C411yescharacteristic
132C22×C107C2×#10111yescharacteristic
133C22×C107#41311yescharacteristic
134C22×C107C2×#10411yescharacteristic
135C22×C107C2×#10411yescharacteristic
136C22×C107#42111yescharacteristic
137C22×C107#42111yescharacteristic
138C4×C107—21no—
139C4×C107—21no—
140C4×C107—22no—
141C4×C107—22no—
142C4×C107—22no—
143C4×C107—22no—
144C4×C107—22no—
145C4×C107—42no—
146C4×C107—42no—
147C4×C107—41no—
148C4×C107—81no—
149C4×C107—81no—
150#8227C10711yesmaximal, characteristic, direct product factor, Sylow
151C2×C107#152811yescharacteristic
152C2×C107#152911yescharacteristic
153C2×C107#153111yescharacteristic
154C2×C107#153211yescharacteristic
155C2×C107C4×#10111yescharacteristic
156C2×C107C4×#10411yescharacteristic
157C2×C107#175911yescharacteristic
158C4×#125C2×C10711yescharacteristic
159#1745C2×C10711yescharacteristic
160C4×#97C2×C10711yescharacteristic
161C2×#330C2×C10712yes—
162#1295C2×C10712yes—
163C107#822711yescharacteristic, direct product factor, Sylow
164C2×#125C22×C10711yescharacteristic
165C2×#97—21no—
166C2×#97C22×C10712yes—
167C2×#97C22×C10712yes—
168C2×C4×C8—21no—
169#389C4×C10711yescharacteristic
170#389C4×C10711yescharacteristic
171#387—21no—
172#387—21no—
173#382C22×C10711yescharacteristic
174C4×C4⋊C4—21no—
175C4×C4⋊C4—21no—
176C4×C4⋊C4C4×C10711yescharacteristic
177C4×C4⋊C4C4×C10711yescharacteristic
178C43C22×C10711yescharacteristic
179#336—21no—
180#336—21no—
181#330C4×C10718yescomplemented
182C22×C8—22no—
183C22×C8—22no—
184#125—22no—
185#125C2×C4×C10714yes—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×C4×C10711yescharacteristic
191C2×C4⋊C4C2×C4×C10711yescharacteristic
192C2×C4⋊C4C2×C4×C10711yescharacteristic
193C2×C4⋊C4C2×C4×C10711yescharacteristic
194C2×C42—21no—
195C2×C42—21no—
196C2×C42C2×C4×C10711yescharacteristic
197C2×C42C2×C4×C10711yescharacteristic
198C2×C42D4×C10711yescharacteristic
199C2×C42D4×C10711yescharacteristic
200C2×C42D4×C10711yescharacteristic
201C2×C42D4×C10711yescharacteristic
202C2×C42C23×C10711yescharacteristic
203#97—24no—
204#97—22no—
205#97—22no—
206#97C2×C4×C10714yes—
207#97C2×C4×C10714yes—
208C4×C8—24no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4C22⋊C4×C10711yescharacteristic
220C22×C4C22⋊C4×C10711yescharacteristic
221C22×C4C22⋊C4×C10711yescharacteristic
222C22×C4C22⋊C4×C10711yescharacteristic
223C22×C4C22×C4×C10711yescharacteristic
224C22×C4C2×D4×C10711yescharacteristic
225C22×C4C2×D4×C10711yescharacteristic
226C2×C8—24no—
227C2×C8—24no—
228C2×C8—24no—
229C2×C8—24no—
230C2×C8—42no—
231C2×C8—42no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4C42×C10712yes—
241C4⋊C4C42×C10712yes—
242C42—22no—
243C42—22no—
244C42—22no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—42no—
249C42—42no—
250C42C22×C4×C10712yes—
251C42#41×C10712yes—
252C23C2×C22⋊C4×C10711yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4#101×C10712yes—
281C2×C4#104×C10712yes—
282C2×C4#104×C10712yes—
283C2×C4C2×C42×C10711yescharacteristic
284C2×C4#117×C10711yescharacteristic
285C2×C4C4×D4×C10712yes—
286C2×C4C4×D4×C10712yes—
287C8—28no—
288C8—44no—
289C22C4×C22⋊C4×C10711yescharacteristic
290C22C2×#101×C10711yescharacteristic
291C22#413×C10711yescharacteristic
292C22C2×#104×C10711yescharacteristic
293C22C2×#104×C10711yescharacteristic
294C22#421×C10711yescharacteristic
295C22#421×C10711yescharacteristic
296C4—21no—
297C4—21no—
298C4—22no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—42no—
304C4—42no—
305C4—41no—
306C4—81no—
307C4—81no—
308C2C107×#152811yescharacteristic
309C2C107×#152911yescharacteristic
310C2C107×#153111yescharacteristic
311C2C107×#153211yescharacteristic
312C2C4×#101×C10711yescharacteristic
313C2C4×#104×C10711yescharacteristic
314C2C107×#175911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C107C2×C22⋊C4
commutatorC2×C4C2×C42×C107
Frattini, cosocleC2×C42C23×C107
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C107 ◁ C43×C107 ◁ G

Complements

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

NH ≅ G/Ntype
23. #330×C107C4semidirect
150. #8227C107direct (N × H)
163. C107#8227direct (N × H)
181. #330C4×C107semidirect

Maximal subgroups

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

subgroupindex
C4×#125×C1072
C107×#17452
C4×#97×C1072
C2×#330×C1072
C107×#12952
#8227107