Finite Group Databasebeta

← C107×#9577 #41035541

Subgroups — C107×#9577 #41035541

Order 27392.

376 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C107×#1962C211yesmaximal, characteristic
2C4×C4⋊C8×C107C211yesmaximal, characteristic, complemented
3C107×#1571C211yesmaximal, characteristic, complemented
4C107×#1540C211yesmaximal, characteristic
5C107×#1480C211yesmaximal, characteristic
6C107×#1301C211yesmaximal, characteristic, complemented
7C107×#1276C211yesmaximal, characteristic, complemented
8#532×C107C2211yescharacteristic
9#431×C107C2211yescharacteristic
10#431×C107C2211yescharacteristic
11#423×C107C2211yescharacteristic
12C2×C4⋊C8×C107C2211yescharacteristic
13C2×C4⋊C8×C107C2211yescharacteristic
14C2×#104×C107—21no—
15C2×#104×C107—21no—
16C2×C4×C8×C107—21no—
17C43×C107C2211yescharacteristic
18#336×C107—21no—
19#335×C107—22no—
20#332×C107C412yescomplemented
21#331×C107C412yescomplemented
22D4⋊C8×C107—22no—
23C2×#41×C107—21no—
24C2×M16×C107—21no—
25C22×C8×C107—21no—
26C22×C8×C107—21no—
27C4⋊Q8×C107C2×C411yescharacteristic
28#127×C107C2×C411yescharacteristic
29#124×C107—21no—
30#121×C107—21no—
31#121×C107—21no—
32C4×D4×C107—21no—
33C4×D4×C107—21no—
34C2×C42×C107—21no—
35C2×C42×C107—21no—
36C2×C42×C107D411yescharacteristic
37C2×C42×C107D411yescharacteristic
38C2×C42×C107C2311yescharacteristic
39C4⋊C8×C107—21no—
40C4⋊C8×C107—21no—
41C4⋊C8×C107—21no—
42C4⋊C8×C107—21no—
43C4⋊C8×C107—21no—
44C4⋊C8×C107C2×C412yes—
45C4⋊C8×C107C2×C412yes—
46C4⋊C8×C107D412yes—
47#104×C107—42no—
48#104×C107—42no—
49C22⋊C8×C107—21no—
50C22⋊C8×C107—21no—
51C4×C8×C107—21no—
52C4×C8×C107—21no—
53C4×C8×C107—42no—
54#41×C107—41no—
55#41×C107—41no—
56#41×C107—41no—
57#41×C107—41no—
58C2×Q8×C107—21no—
59C2×D4×C107—21no—
60C2×D4×C107—21no—
61C2×D4×C107—21no—
62C2×D4×C107—41no—
63C22×C4×C107—21no—
64C22×C4×C107—21no—
65C22×C4×C107—41no—
66C22×C4×C107C2×D411yescharacteristic
67C22×C4×C107#4111yescharacteristic
68C22×C4×C107#4111yescharacteristic
69M16×C107—41no—
70M16×C107—41no—
71C2×C8×C107—22no—
72C2×C8×C107—22no—
73C2×C8×C107—22no—
74C2×C8×C107—41no—
75C2×C8×C107—41no—
76C2×C8×C107—41no—
77C2×C8×C107—41no—
78C2×C8×C107—41no—
79C2×C8×C107—41no—
80C4⋊C4×C107—21no—
81C4⋊C4×C107—21no—
82C22⋊C4×C107—41no—
83C22⋊C4×C107—41no—
84C42×C107—24no—
85C42×C107—21no—
86C42×C107—21no—
87C42×C107—21no—
88C42×C107—42no—
89C42×C107D812yes—
90C42×C107C22×C411yescharacteristic
91C42×C107C2×D411yescharacteristic
92C42×C107#4111yescharacteristic
93C42×C107#4111yescharacteristic
94C23×C107—41no—
95C23×C107#12311yescharacteristic
96Q8×C107—41no—
97Q8×C107—41no—
98D4×C107—41no—
99D4×C107—41no—
100D4×C107—42no—
101D4×C107—81no—
102D4×C107—81no—
103D4×C107—81no—
104C2×C4×C107—22no—
105C2×C4×C107—22no—
106C2×C4×C107—22no—
107C2×C4×C107—22no—
108C2×C4×C107—22no—
109C2×C4×C107—41no—
110C2×C4×C107—41no—
111C2×C4×C107—41no—
112C2×C4×C107—41no—
113C2×C4×C107—81no—
114C2×C4×C107—81no—
115C2×C4×C107#11711yescharacteristic
116C2×C4×C107C4×D411yescharacteristic
117C2×C4×C107C4×D411yescharacteristic
118C2×C4×C107#12111yescharacteristic
119C2×C4×C107#12411yescharacteristic
120C2×C4×C107#12611yescharacteristic
121C2×C4×C107C2×D811yescharacteristic
122C2×C4×C107#13511yescharacteristic
123C2×C4×C107AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C107#13711yescharacteristic
125C8×C107—42no—
126C8×C107—42no—
127C8×C107—42no—
128C8×C107—81no—
129C8×C107—81no—
130C22×C107—21no—
131C22×C107—21no—
132C22×C107—81no—
133C22×C107—81no—
134C22×C107—81no—
135C22×C107#38811yescharacteristic
136C22×C107#48011yescharacteristic
137C22×C107#48211yescharacteristic
138C4×C107—24no—
139C4×C107—21no—
140C4×C107—21no—
141C4×C107—21no—
142C4×C107—42no—
143C4×C107—81no—
144C4×C107C4×D811yescharacteristic
145C4×C107#44011yescharacteristic
146C4×C107#44312yes—
147C4×C107#45911yescharacteristic
148C4×C107#46411yescharacteristic
149#9577C10711yesmaximal, characteristic, direct product factor, Sylow
150C2×C107—21no—
151C2×C107—21no—
152C2×C107—161no—
153C2×C107#192511yescharacteristic
154C2×C107#193211yescharacteristic
155C2×C107#193711yescharacteristic
156#1962C2×C10711yescharacteristic
157C4×C4⋊C8C2×C10711yescharacteristic, complemented
158#1571C2×C10711yescharacteristic, complemented
159#1540C2×C10711yescharacteristic
160#1480C2×C10711yescharacteristic
161#1301C2×C10711yescharacteristic, complemented
162#1276C2×C10711yescharacteristic, complemented
163C107#957711yescharacteristic, direct product factor, Sylow
164#532C22×C10711yescharacteristic
165#431C22×C10711yescharacteristic
166#431C22×C10711yescharacteristic
167#423C22×C10711yescharacteristic
168C2×C4⋊C8C22×C10711yescharacteristic
169C2×C4⋊C8C22×C10711yescharacteristic
170C2×#104—21no—
171C2×#104—21no—
172C2×C4×C8—21no—
173C43C22×C10711yescharacteristic
174#336—21no—
175#335—22no—
176#332C4×C10712yescomplemented
177#331C4×C10712yescomplemented
178D4⋊C8—22no—
179C2×#41—21no—
180C2×M16—21no—
181C22×C8—21no—
182C22×C8—21no—
183C4⋊Q8C2×C4×C10711yescharacteristic
184#127C2×C4×C10711yescharacteristic
185#124—21no—
186#121—21no—
187#121—21no—
188C4×D4—21no—
189C4×D4—21no—
190C2×C42—21no—
191C2×C42—21no—
192C2×C42D4×C10711yescharacteristic
193C2×C42D4×C10711yescharacteristic
194C2×C42C23×C10711yescharacteristic
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8C2×C4×C10712yes—
201C4⋊C8C2×C4×C10712yes—
202C4⋊C8D4×C10712yes—
203#104—42no—
204#104—42no—
205C22⋊C8—21no—
206C22⋊C8—21no—
207C4×C8—21no—
208C4×C8—21no—
209C4×C8—42no—
210#41—41no—
211#41—41no—
212#41—41no—
213#41—41no—
214C2×Q8—21no—
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—21no—
218C2×D4—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4C2×D4×C10711yescharacteristic
223C22×C4#41×C10711yescharacteristic
224C22×C4#41×C10711yescharacteristic
225M16—41no—
226M16—41no—
227C2×C8—22no—
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C42—24no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—42no—
245C42D8×C10712yes—
246C42C22×C4×C10711yescharacteristic
247C42C2×D4×C10711yescharacteristic
248C42#41×C10711yescharacteristic
249C42#41×C10711yescharacteristic
250C23—41no—
251C23#123×C10711yescharacteristic
252Q8—41no—
253Q8—41no—
254D4—41no—
255D4—41no—
256D4—42no—
257D4—81no—
258D4—81no—
259D4—81no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4#117×C10711yescharacteristic
272C2×C4C4×D4×C10711yescharacteristic
273C2×C4C4×D4×C10711yescharacteristic
274C2×C4#121×C10711yescharacteristic
275C2×C4#124×C10711yescharacteristic
276C2×C4#126×C10711yescharacteristic
277C2×C4C2×D8×C10711yescharacteristic
278C2×C4#135×C10711yescharacteristic
279C2×C4AGL(1,ℤ/8)×C10711yescharacteristic
280C2×C4#137×C10711yescharacteristic
281C8—42no—
282C8—42no—
283C8—42no—
284C8—81no—
285C8—81no—
286C22—21no—
287C22—21no—
288C22—81no—
289C22—81no—
290C22—81no—
291C22#388×C10711yescharacteristic
292C22#480×C10711yescharacteristic
293C22#482×C10711yescharacteristic
294C4—24no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—42no—
299C4—81no—
300C4C4×D8×C10711yescharacteristic
301C4#440×C10711yescharacteristic
302C4#443×C10712yes—
303C4#459×C10711yescharacteristic
304C4#464×C10711yescharacteristic
305C2—21no—
306C2—21no—
307C2—161no—
308C2C107×#192511yescharacteristic
309C2C107×#193211yescharacteristic
310C2C107×#193711yescharacteristic
subgroupG/H
centerC2×C4×C107#121
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC22×C107#388
prime radical#532×C107C22
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. C4×C4⋊C8×C107C2semidirect
3. C107×#1571C2semidirect
6. C107×#1301C2semidirect
7. C107×#1276C2semidirect
20. #332×C107C4semidirect
21. #331×C107C4semidirect
149. #9577C107direct (N × H)
157. C4×C4⋊C8C2×C107semidirect
158. #1571C2×C107semidirect
161. #1301C2×C107semidirect
162. #1276C2×C107semidirect
163. C107#9577direct (N × H)
176. #332C4×C107semidirect
177. #331C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#19622
C4×C4⋊C8×C1072
C107×#15712
C107×#15402
C107×#14802
C107×#13012
C107×#12762
#9577107