Finite Group Databasebeta

← C107×#8900 #41034864

Subgroups — C107×#8900 #41034864

Order 27392.

374 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#2990C211yesmaximal, characteristic
2C107×#1837C211yesmaximal, 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
15#423×C107C2211yescharacteristic
16#423×C107C2211yescharacteristic
17C2×C4⋊C8×C107—21no—
18C4×M16×C107C2211yescharacteristic
19C2×C4×C8×C107C2211yescharacteristic
20#341×C107—22no—
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
45C4⋊C8×C107—22no—
46C4⋊C8×C107—21no—
47C4⋊C8×C107—21no—
48C4⋊C8×C107—21no—
49C4⋊C8×C107—21no—
50C4⋊C8×C107C2×C411yescharacteristic
51C4⋊C8×C107C2×C411yescharacteristic
52C4⋊C8×C107D411yescharacteristic
53C4⋊C8×C107D411yescharacteristic
54C22⋊C8×C107—22no—
55C22⋊C8×C107—21no—
56C22⋊C8×C107—21no—
57#97×C107—22no—
58#97×C107—21no—
59C4×C8×C107—21no—
60C4×C8×C107—21no—
61C4×C8×C107—21no—
62C4×C8×C107—21no—
63C4×C8×C107C2×C411yescharacteristic
64C4×C8×C107C2×C411yescharacteristic
65#41×C107—22no—
66#41×C107—41no—
67C2×Q8×C107C4⋊C411yescharacteristic
68C2×D4×C107—21no—
69C2×D4×C107C4⋊C411yescharacteristic
70C22×C4×C107—21no—
71C22×C4×C107—21no—
72C22×C4×C107—21no—
73C22×C4×C107C2×D411yescharacteristic
74C22×C4×C107C2×Q811yescharacteristic
75C22×C4×C107#4111yescharacteristic
76M16×C107—22no—
77M16×C107—41no—
78M16×C107—42no—
79M16×C107—42no—
80C2×C8×C107—21no—
81C2×C8×C107—21no—
82C2×C8×C107—21no—
83C2×C8×C107—21no—
84C2×C8×C107—21no—
85C2×C8×C107—21no—
86C2×C8×C107—22no—
87C2×C8×C107—41no—
88C2×C8×C107—41no—
89C2×C8×C107—41no—
90C2×C8×C107—41no—
91C2×C8×C107—82no—
92C4⋊C4×C107—21no—
93C4⋊C4×C107—21no—
94C4⋊C4×C107C4⋊C411yescharacteristic
95C4⋊C4×C107C4⋊C411yescharacteristic
96C22⋊C4×C107—21no—
97C22⋊C4×C107—21no—
98C22⋊C4×C107—21no—
99C42×C107—21no—
100C42×C107—21no—
101C42×C107—21no—
102C42×C107C22×C411yescharacteristic
103C42×C107C2×D411yescharacteristic
104C42×C107C2×D411yescharacteristic
105C42×C107#4111yescharacteristic
106C23×C107—21no—
107C23×C107C22⋊Q811yescharacteristic
108Q8×C107—21no—
109Q8×C107—21no—
110D4×C107—21no—
111D4×C107—42no—
112D4×C107#10812yes—
113C2×C4×C107—21no—
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—42no—
123C2×C4×C107—41no—
124C2×C4×C107—41no—
125C2×C4×C107—41no—
126C2×C4×C107—41no—
127C2×C4×C107C2×C4⋊C411yescharacteristic
128C2×C4×C107C4×D411yescharacteristic
129C2×C4×C107C4×D411yescharacteristic
130C2×C4×C107#12011yescharacteristic
131C2×C4×C107C22⋊Q811yescharacteristic
132C2×C4×C107#12311yescharacteristic
133C8×C107—41no—
134C8×C107—41no—
135C8×C107—42no—
136C8×C107—41no—
137C8×C107—41no—
138C8×C107—41no—
139C8×C107—41no—
140C8×C107—42no—
141C8×C107—81no—
142C22×C107—21no—
143C22×C107—22no—
144C22×C107—21no—
145C22×C107—21no—
146C22×C107—41no—
147C22×C107—41no—
148C22×C107#38511yescharacteristic
149C4×C107—21no—
150C4×C107—21no—
151C4×C107—21no—
152C4×C107—41no—
153C4×C107—41no—
154C4×C107—41no—
155C4×C107C2×#10811yescharacteristic
156C4×C107#43011yescharacteristic
157C4×C107#44311yescharacteristic
158C4×C107#44411yescharacteristic
159C4×C107#45411yescharacteristic
160C4×C107#45511yescharacteristic
161#8900C10711yesmaximal, characteristic, direct product factor, Sylow
162C2×C107—41no—
163C2×C107—42no—
164C2×C107#185511yescharacteristic
165C2×C107#186011yescharacteristic
166C2×C107#186611yescharacteristic
167#2990C2×C10711yescharacteristic
168#1837C2×C10711yescharacteristic, complemented
169#1574C2×C10711yescharacteristic, complemented
170#1489C2×C10711yescharacteristic
171#1476C2×C10711yescharacteristic
172#1299C2×C10711yescharacteristic, complemented
173#1278C2×C10711yescharacteristic, complemented
174C107#890011yescharacteristic, direct product factor, Sylow
175C4×#41C22×C10711yescharacteristic
176#446—21no—
177#435—22no—
178C8×D4—21no—
179#432—21no—
180#431C22×C10711yescharacteristic
181#431C22×C10711yescharacteristic
182#423C22×C10711yescharacteristic
183#423C22×C10711yescharacteristic
184C2×C4⋊C8—21no—
185C4×M16C22×C10711yescharacteristic
186C2×C4×C8C22×C10711yescharacteristic
187#341—22no—
188#335—21no—
189#334—21no—
190Q8⋊C8—21no—
191Q8⋊C8C4×C10711yescharacteristic
192Q8⋊C8C4×C10711yescharacteristic
193D4⋊C8—21no—
194D4⋊C8C4×C10711yescharacteristic
195D4⋊C8C4×C10711yescharacteristic
196C2×#41Q8×C10711yescharacteristic
197C2×M16—21no—
198C2×M16—21no—
199C2×M16D4×C10712yes—
200C22×C8—21no—
201C22×C8—22no—
202C4×Q8C2×C4×C10711yescharacteristic
203C4×Q8D4×C10711yescharacteristic
204C4×D4—21no—
205C4×D4—21no—
206C4×D4C2×C4×C10711yescharacteristic
207C4×D4D4×C10711yescharacteristic
208#117—21no—
209#117Q8×C10711yescharacteristic
210C2×C42—21no—
211C2×C42C23×C10711yescharacteristic
212C4⋊C8—22no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8C2×C4×C10711yescharacteristic
218C4⋊C8C2×C4×C10711yescharacteristic
219C4⋊C8D4×C10711yescharacteristic
220C4⋊C8D4×C10711yescharacteristic
221C22⋊C8—22no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224#97—22no—
225#97—21no—
226C4×C8—21no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8C2×C4×C10711yescharacteristic
231C4×C8C2×C4×C10711yescharacteristic
232#41—22no—
233#41—41no—
234C2×Q8C4⋊C4×C10711yescharacteristic
235C2×D4—21no—
236C2×D4C4⋊C4×C10711yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4C2×D4×C10711yescharacteristic
241C22×C4C2×Q8×C10711yescharacteristic
242C22×C4#41×C10711yescharacteristic
243M16—22no—
244M16—41no—
245M16—42no—
246M16—42no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—82no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4C4⋊C4×C10711yescharacteristic
262C4⋊C4C4⋊C4×C10711yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42C22×C4×C10711yescharacteristic
270C42C2×D4×C10711yescharacteristic
271C42C2×D4×C10711yescharacteristic
272C42#41×C10711yescharacteristic
273C23—21no—
274C23C22⋊Q8×C10711yescharacteristic
275Q8—21no—
276Q8—21no—
277D4—21no—
278D4—42no—
279D4#108×C10712yes—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4C2×C4⋊C4×C10711yescharacteristic
295C2×C4C4×D4×C10711yescharacteristic
296C2×C4C4×D4×C10711yescharacteristic
297C2×C4#120×C10711yescharacteristic
298C2×C4C22⋊Q8×C10711yescharacteristic
299C2×C4#123×C10711yescharacteristic
300C8—41no—
301C8—41no—
302C8—42no—
303C8—41no—
304C8—41no—
305C8—41no—
306C8—41no—
307C8—42no—
308C8—81no—
309C22—21no—
310C22—21no—
311C22—22no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22#385×C10711yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4C2×#108×C10711yescharacteristic
323C4#430×C10711yescharacteristic
324C4#443×C10711yescharacteristic
325C4#444×C10711yescharacteristic
326C4#454×C10711yescharacteristic
327C4#455×C10711yescharacteristic
328C2—41no—
329C2—42no—
330C2C107×#185511yescharacteristic
331C2C107×#186011yescharacteristic
332C2C107×#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×#1837C2semidirect
3. C107×#1574C2semidirect
6. C107×#1299C2semidirect
7. C107×#1278C2semidirect
161. #8900C107direct (N × H)
168. #1837C2×C107semidirect
169. #1574C2×C107semidirect
172. #1299C2×C107semidirect
173. #1278C2×C107semidirect
174. C107#8900direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#29902
C107×#18372
C107×#15742
C107×#14892
C107×#14762
C107×#12992
C107×#12782
#8900107