Finite Group Databasebeta

← C107×#8898 #41034862

Subgroups — C107×#8898 #41034862

Order 27392.

390 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2990C211yesmaximal, characteristic
2C107×#1848C211yesmaximal, characteristic, complemented
3C107×#1574C211yesmaximal, characteristic, complemented
4C107×#1489C211yesmaximal, characteristic
5C107×#1476C211yesmaximal, characteristic
6C107×#1299C211yesmaximal, characteristic, complemented
7C107×#1278C211yesmaximal, characteristic, complemented
8C4×#41×C107C2211yescharacteristic
9#446×C107—21no—
10#435×C107—22no—
11C8×D4×C107—21no—
12#432×C107—21no—
13#431×C107C2211yescharacteristic
14#431×C107C2211yescharacteristic
15C2×#108×C107—22no—
16#423×C107C2211yescharacteristic
17#423×C107C2211yescharacteristic
18C2×C4⋊C8×C107—21no—
19C4×M16×C107C2211yescharacteristic
20C2×C4×C8×C107C2211yescharacteristic
21#335×C107—21no—
22#334×C107—21no—
23Q8⋊C8×C107—21no—
24Q8⋊C8×C107C411yescharacteristic
25Q8⋊C8×C107C411yescharacteristic
26D4⋊C8×C107—21no—
27D4⋊C8×C107C411yescharacteristic
28D4⋊C8×C107C411yescharacteristic
29C2×#41×C107Q811yescharacteristic
30C2×M16×C107—21no—
31C2×M16×C107—21no—
32C2×M16×C107D412yes—
33C22×C8×C107—21no—
34C22×C8×C107—22no—
35C4×Q8×C107C2×C411yescharacteristic
36C4×Q8×C107D411yescharacteristic
37C4×D4×C107—21no—
38C4×D4×C107—21no—
39C4×D4×C107C2×C411yescharacteristic
40C4×D4×C107D411yescharacteristic
41#117×C107—21no—
42#117×C107Q811yescharacteristic
43C2×C42×C107—21no—
44C2×C42×C107C2311yescharacteristic
45#108×C107—44no—
46C4⋊C8×C107—22no—
47C4⋊C8×C107—21no—
48C4⋊C8×C107—21no—
49C4⋊C8×C107—21no—
50C4⋊C8×C107—21no—
51C4⋊C8×C107C2×C411yescharacteristic
52C4⋊C8×C107C2×C411yescharacteristic
53C4⋊C8×C107D411yescharacteristic
54C4⋊C8×C107D411yescharacteristic
55C22⋊C8×C107—22no—
56C22⋊C8×C107—21no—
57C22⋊C8×C107—21no—
58#97×C107—22no—
59#97×C107—21no—
60C4×C8×C107—21no—
61C4×C8×C107—21no—
62C4×C8×C107—21no—
63C4×C8×C107—21no—
64C4×C8×C107C2×C411yescharacteristic
65C4×C8×C107C2×C411yescharacteristic
66#41×C107—22no—
67#41×C107—41no—
68C2×Q8×C107C4⋊C411yescharacteristic
69C2×D4×C107—21no—
70C2×D4×C107C4⋊C411yescharacteristic
71C22×C4×C107—21no—
72C22×C4×C107—21no—
73C22×C4×C107—21no—
74C22×C4×C107C2×D411yescharacteristic
75C22×C4×C107C2×Q811yescharacteristic
76C22×C4×C107#4111yescharacteristic
77M16×C107—22no—
78M16×C107—41no—
79M16×C107—42no—
80M16×C107—42no—
81C2×C8×C107—22no—
82C2×C8×C107—22no—
83C2×C8×C107—21no—
84C2×C8×C107—21no—
85C2×C8×C107—21no—
86C2×C8×C107—21no—
87C2×C8×C107—21no—
88C2×C8×C107—21no—
89C2×C8×C107—22no—
90C2×C8×C107—41no—
91C2×C8×C107—41no—
92C2×C8×C107—82no—
93C4⋊C4×C107—21no—
94C4⋊C4×C107—21no—
95C4⋊C4×C107C4⋊C411yescharacteristic
96C4⋊C4×C107C4⋊C411yescharacteristic
97C22⋊C4×C107—21no—
98C22⋊C4×C107—21no—
99C22⋊C4×C107—21no—
100C42×C107—21no—
101C42×C107—21no—
102C42×C107—21no—
103C42×C107C22×C411yescharacteristic
104C42×C107C2×D411yescharacteristic
105C42×C107C2×D411yescharacteristic
106C42×C107#4111yescharacteristic
107C23×C107—21no—
108C23×C107C22⋊Q811yescharacteristic
109Q8×C107—21no—
110Q8×C107—21no—
111D4×C107—21no—
112D4×C107—42no—
113D4×C107#10812yescomplemented
114C2×C4×C107—21no—
115C2×C4×C107—21no—
116C2×C4×C107—21no—
117C2×C4×C107—21no—
118C2×C4×C107—21no—
119C2×C4×C107—21no—
120C2×C4×C107—21no—
121C2×C4×C107—21no—
122C2×C4×C107—21no—
123C2×C4×C107—42no—
124C2×C4×C107—41no—
125C2×C4×C107—41no—
126C2×C4×C107—41no—
127C2×C4×C107—41no—
128C2×C4×C107C2×C4⋊C411yescharacteristic
129C2×C4×C107C4×D411yescharacteristic
130C2×C4×C107C4×D411yescharacteristic
131C2×C4×C107#12011yescharacteristic
132C2×C4×C107C22⋊Q811yescharacteristic
133C2×C4×C107#12311yescharacteristic
134C8×C107—22no—
135C8×C107—22no—
136C8×C107—42no—
137C8×C107—41no—
138C8×C107—41no—
139C8×C107—41no—
140C8×C107—42no—
141C8×C107—41no—
142C8×C107—81no—
143C22×C107—21no—
144C22×C107—22no—
145C22×C107—21no—
146C22×C107—21no—
147C22×C107—41no—
148C22×C107—41no—
149C22×C107#38511yescharacteristic
150C4×C107—21no—
151C4×C107—21no—
152C4×C107—21no—
153C4×C107—41no—
154C4×C107—41no—
155C4×C107—41no—
156C4×C107C2×#10811yescharacteristic
157C4×C107#43011yescharacteristic
158C4×C107#44311yescharacteristic
159C4×C107#44411yescharacteristic
160C4×C107#45311yescharacteristic
161C4×C107#45611yescharacteristic
162#8898C10711yesmaximal, characteristic, direct product factor, Sylow
163C2×C107—41no—
164C2×C107—42no—
165C2×C107#185511yescharacteristic
166C2×C107#185911yescharacteristic
167C2×C107#186611yescharacteristic
168#2990C2×C10711yescharacteristic
169#1848C2×C10711yescharacteristic, complemented
170#1574C2×C10711yescharacteristic, complemented
171#1489C2×C10711yescharacteristic
172#1476C2×C10711yescharacteristic
173#1299C2×C10711yescharacteristic, complemented
174#1278C2×C10711yescharacteristic, complemented
175C107#889811yescharacteristic, direct product factor, Sylow
176C4×#41C22×C10711yescharacteristic
177#446—21no—
178#435—22no—
179C8×D4—21no—
180#432—21no—
181#431C22×C10711yescharacteristic
182#431C22×C10711yescharacteristic
183C2×#108—22no—
184#423C22×C10711yescharacteristic
185#423C22×C10711yescharacteristic
186C2×C4⋊C8—21no—
187C4×M16C22×C10711yescharacteristic
188C2×C4×C8C22×C10711yescharacteristic
189#335—21no—
190#334—21no—
191Q8⋊C8—21no—
192Q8⋊C8C4×C10711yescharacteristic
193Q8⋊C8C4×C10711yescharacteristic
194D4⋊C8—21no—
195D4⋊C8C4×C10711yescharacteristic
196D4⋊C8C4×C10711yescharacteristic
197C2×#41Q8×C10711yescharacteristic
198C2×M16—21no—
199C2×M16—21no—
200C2×M16D4×C10712yes—
201C22×C8—21no—
202C22×C8—22no—
203C4×Q8C2×C4×C10711yescharacteristic
204C4×Q8D4×C10711yescharacteristic
205C4×D4—21no—
206C4×D4—21no—
207C4×D4C2×C4×C10711yescharacteristic
208C4×D4D4×C10711yescharacteristic
209#117—21no—
210#117Q8×C10711yescharacteristic
211C2×C42—21no—
212C2×C42C23×C10711yescharacteristic
213#108—44no—
214C4⋊C8—22no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8C2×C4×C10711yescharacteristic
220C4⋊C8C2×C4×C10711yescharacteristic
221C4⋊C8D4×C10711yescharacteristic
222C4⋊C8D4×C10711yescharacteristic
223C22⋊C8—22no—
224C22⋊C8—21no—
225C22⋊C8—21no—
226#97—22no—
227#97—21no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8C2×C4×C10711yescharacteristic
233C4×C8C2×C4×C10711yescharacteristic
234#41—22no—
235#41—41no—
236C2×Q8C4⋊C4×C10711yescharacteristic
237C2×D4—21no—
238C2×D4C4⋊C4×C10711yescharacteristic
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×D4×C10711yescharacteristic
243C22×C4C2×Q8×C10711yescharacteristic
244C22×C4#41×C10711yescharacteristic
245M16—22no—
246M16—41no—
247M16—42no—
248M16—42no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—82no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4C4⋊C4×C10711yescharacteristic
264C4⋊C4C4⋊C4×C10711yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42C22×C4×C10711yescharacteristic
272C42C2×D4×C10711yescharacteristic
273C42C2×D4×C10711yescharacteristic
274C42#41×C10711yescharacteristic
275C23—21no—
276C23C22⋊Q8×C10711yescharacteristic
277Q8—21no—
278Q8—21no—
279D4—21no—
280D4—42no—
281D4#108×C10712yescomplemented
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4C2×C4⋊C4×C10711yescharacteristic
297C2×C4C4×D4×C10711yescharacteristic
298C2×C4C4×D4×C10711yescharacteristic
299C2×C4#120×C10711yescharacteristic
300C2×C4C22⋊Q8×C10711yescharacteristic
301C2×C4#123×C10711yescharacteristic
302C8—22no—
303C8—22no—
304C8—42no—
305C8—41no—
306C8—41no—
307C8—41no—
308C8—42no—
309C8—41no—
310C8—81no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22#385×C10711yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4C2×#108×C10711yescharacteristic
325C4#430×C10711yescharacteristic
326C4#443×C10711yescharacteristic
327C4#444×C10711yescharacteristic
328C4#453×C10711yescharacteristic
329C4#456×C10711yescharacteristic
330C2—41no—
331C2—42no—
332C2C107×#185511yescharacteristic
333C2C107×#185911yescharacteristic
334C2C107×#186611yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC22×C107#385
prime radicalC2×#41×C107Q8
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#1848C2semidirect
3. C107×#1574C2semidirect
6. C107×#1299C2semidirect
7. C107×#1278C2semidirect
113. D4×C107#108semidirect
162. #8898C107direct (N × H)
169. #1848C2×C107semidirect
170. #1574C2×C107semidirect
173. #1299C2×C107semidirect
174. #1278C2×C107semidirect
175. C107#8898direct (N × H)
281. D4#108×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#29902
C107×#18482
C107×#15742
C107×#14892
C107×#14762
C107×#12992
C107×#12782
#8898107