Finite Group Databasebeta

← C101×#8880 #38791031

Subgroups — C101×#8880 #38791031

Order 25856.

432 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2932C211yesmaximal, characteristic
2C101×#1940C211yesmaximal, characteristic, complemented
3C101×#1570C211yesmaximal, characteristic, complemented
4C101×#1502C211yesmaximal, characteristic
5C101×#1480C211yesmaximal, characteristic
6C101×#1303C211yesmaximal, characteristic, complemented
7C101×#1281C211yesmaximal, characteristic, complemented
8C2×#131×C101—21no—
9#532×C101C2211yescharacteristic
10#435×C101—22no—
11#435×C101—22no—
12#431×C101C2211yescharacteristic
13#431×C101C2211yescharacteristic
14#423×C101C2211yescharacteristic
15C2×C4⋊C8×C101—21no—
16C2×C4⋊C8×C101C2211yescharacteristic
17#408×C101—21no—
18C2×#97×C101C2211yescharacteristic
19C4×C4⋊C4×C101C2211yescharacteristic
20#336×C101—21no—
21#334×C101—22no—
22#327×C101C412yes—
23#327×C101C412yes—
24D4⋊C8×C101—22no—
25C2×#41×C101—21no—
26#131×C101—42no—
27#131×C101—42no—
28C2×M16×C101—22no—
29C2×M16×C101—21no—
30C22×C8×C101—22no—
31C22×C8×C101—21no—
32C22×C8×C101D411yescharacteristic
33C22×C8×C101D411yescharacteristic
34C4⋊Q8×C101Q811yescharacteristic
35#127×C101Q811yescharacteristic
36#124×C101—21no—
37#121×C101—21no—
38#121×C101C2×C412yes—
39C4×D4×C101—21no—
40C4×D4×C101D412yes—
41C2×C4⋊C4×C101—21no—
42C2×C42×C101—21no—
43C2×C42×C101C2311yescharacteristic
44C4⋊C8×C101—21no—
45C4⋊C8×C101—21no—
46C4⋊C8×C101—21no—
47C4⋊C8×C101—21no—
48C4⋊C8×C101—21no—
49C4⋊C8×C101—42no—
50C4⋊C8×C101D412yes—
51C22⋊C8×C101—24no—
52C22⋊C8×C101—21no—
53C22⋊C8×C101C2×C412yes—
54#97×C101—21no—
55#97×C101—21no—
56C4×C8×C101—21no—
57C4×C8×C101—21no—
58#95×C101C2×C411yescharacteristic
59#95×C101C2×C411yescharacteristic
60#41×C101—41no—
61#41×C101—41no—
62#41×C101—41no—
63#41×C101—41no—
64C2×Q8×C101—21no—
65C2×D4×C101—22no—
66C2×D4×C101—21no—
67C2×D4×C101—21no—
68C2×D4×C101C4⋊C412yes—
69C22×C4×C101—21no—
70C22×C4×C101—22no—
71C22×C4×C101—21no—
72C22×C4×C101C22×C411yescharacteristic
73C22×C4×C101C2×D411yescharacteristic
74C22×C4×C101#4111yescharacteristic
75M16×C101—44no—
76M16×C101—41no—
77M16×C101—41no—
78C2×C8×C101—21no—
79C2×C8×C101—21no—
80C2×C8×C101—22no—
81C2×C8×C101—21no—
82C2×C8×C101—22no—
83C2×C8×C101—21no—
84C2×C8×C101—21no—
85C2×C8×C101—44no—
86C2×C8×C101—41no—
87C2×C8×C101—41no—
88C2×C8×C101—41no—
89C2×C8×C101—41no—
90C2×C8×C101SD1612yes—
91C4⋊C4×C101—21no—
92C4⋊C4×C101—42no—
93C4⋊C4×C101C4⋊C412yes—
94C22⋊C4×C101—22no—
95C22⋊C4×C101—22no—
96C42×C101—41no—
97C42×C101—41no—
98C42×C101C2×D411yescharacteristic
99C42×C101C2×D411yescharacteristic
100C42×C101C2×Q811yescharacteristic
101C42×C101#4111yescharacteristic
102C23×C101—22no—
103C23×C101C4×D411yescharacteristic
104Q8×C101—41no—
105Q8×C101—41no—
106D4×C101—42no—
107D4×C101—42no—
108D4×C101—42no—
109D4×C101—41no—
110D4×C101—41no—
111D4×C101—81no—
112C2×C4×C101—22no—
113C2×C4×C101—22no—
114C2×C4×C101—41no—
115C2×C4×C101—41no—
116C2×C4×C101—41no—
117C2×C4×C101—41no—
118C2×C4×C101—42no—
119C2×C4×C101—42no—
120C2×C4×C101—41no—
121C2×C4×C101—41no—
122C2×C4×C101—41no—
123C2×C4×C101C2×C4⋊C411yescharacteristic
124C2×C4×C101C4×D411yescharacteristic
125C2×C4×C101#12011yescharacteristic
126C2×C4×C101C22⋊Q811yescharacteristic
127C2×C4×C101C22⋊Q811yescharacteristic
128C2×C4×C101#12311yescharacteristic
129C2×C4×C101C2×SD1611yescharacteristic
130C2×C4×C101#13511yescharacteristic
131C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
133C8×C101—22no—
134C8×C101—42no—
135C8×C101—41no—
136C8×C101—42no—
137C8×C101—81no—
138C8×C101—81no—
139C22×C101—21no—
140C22×C101—21no—
141C22×C101—42no—
142C22×C101—42no—
143C22×C101—42no—
144C22×C101#38511yescharacteristic
145C22×C101C4×SD1611yescharacteristic
146C22×C101#44211yescharacteristic
147C4×C101—21no—
148C4×C101—21no—
149C4×C101—21no—
150C4×C101—21no—
151C4×C101—42no—
152C4×C101—42no—
153C4×C101—81no—
154C4×C101#44911yescharacteristic
155C4×C101#45011yescharacteristic
156C4×C101#47611yescharacteristic
157C4×C101#47811yescharacteristic
158#8880C10111yesmaximal, characteristic, direct product factor, Sylow
159C2×C101—21no—
160C2×C101—21no—
161C2×C101—82no—
162C2×C101#186111yescharacteristic
163C2×C101#186411yescharacteristic
164C2×C101#186811yescharacteristic
165#2932C2×C10111yescharacteristic
166#1940C2×C10111yescharacteristic, complemented
167#1570C2×C10111yescharacteristic, complemented
168#1502C2×C10111yescharacteristic
169#1480C2×C10111yescharacteristic
170#1303C2×C10111yescharacteristic, complemented
171#1281C2×C10111yescharacteristic, complemented
172C101#888011yescharacteristic, direct product factor, Sylow
173C2×#131—21no—
174#532C22×C10111yescharacteristic
175#435—22no—
176#435—22no—
177#431C22×C10111yescharacteristic
178#431C22×C10111yescharacteristic
179#423C22×C10111yescharacteristic
180C2×C4⋊C8—21no—
181C2×C4⋊C8C22×C10111yescharacteristic
182#408—21no—
183C2×#97C22×C10111yescharacteristic
184C4×C4⋊C4C22×C10111yescharacteristic
185#336—21no—
186#334—22no—
187#327C4×C10112yes—
188#327C4×C10112yes—
189D4⋊C8—22no—
190C2×#41—21no—
191#131—42no—
192#131—42no—
193C2×M16—22no—
194C2×M16—21no—
195C22×C8—22no—
196C22×C8—21no—
197C22×C8D4×C10111yescharacteristic
198C22×C8D4×C10111yescharacteristic
199C4⋊Q8Q8×C10111yescharacteristic
200#127Q8×C10111yescharacteristic
201#124—21no—
202#121—21no—
203#121C2×C4×C10112yes—
204C4×D4—21no—
205C4×D4D4×C10112yes—
206C2×C4⋊C4—21no—
207C2×C42—21no—
208C2×C42C23×C10111yescharacteristic
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—42no—
215C4⋊C8D4×C10112yes—
216C22⋊C8—24no—
217C22⋊C8—21no—
218C22⋊C8C2×C4×C10112yes—
219#97—21no—
220#97—21no—
221C4×C8—21no—
222C4×C8—21no—
223#95C2×C4×C10111yescharacteristic
224#95C2×C4×C10111yescharacteristic
225#41—41no—
226#41—41no—
227#41—41no—
228#41—41no—
229C2×Q8—21no—
230C2×D4—22no—
231C2×D4—21no—
232C2×D4—21no—
233C2×D4C4⋊C4×C10112yes—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4C22×C4×C10111yescharacteristic
238C22×C4C2×D4×C10111yescharacteristic
239C22×C4#41×C10111yescharacteristic
240M16—44no—
241M16—41no—
242M16—41no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—22no—
246C2×C8—21no—
247C2×C8—22no—
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—44no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8SD16×C10112yes—
256C4⋊C4—21no—
257C4⋊C4—42no—
258C4⋊C4C4⋊C4×C10112yes—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C42—41no—
262C42—41no—
263C42C2×D4×C10111yescharacteristic
264C42C2×D4×C10111yescharacteristic
265C42C2×Q8×C10111yescharacteristic
266C42#41×C10111yescharacteristic
267C23—22no—
268C23C4×D4×C10111yescharacteristic
269Q8—41no—
270Q8—41no—
271D4—42no—
272D4—42no—
273D4—42no—
274D4—41no—
275D4—41no—
276D4—81no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4C2×C4⋊C4×C10111yescharacteristic
289C2×C4C4×D4×C10111yescharacteristic
290C2×C4#120×C10111yescharacteristic
291C2×C4C22⋊Q8×C10111yescharacteristic
292C2×C4C22⋊Q8×C10111yescharacteristic
293C2×C4#123×C10111yescharacteristic
294C2×C4C2×SD16×C10111yescharacteristic
295C2×C4#135×C10111yescharacteristic
296C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
297C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
298C8—22no—
299C8—42no—
300C8—41no—
301C8—42no—
302C8—81no—
303C8—81no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22#385×C10111yescharacteristic
310C22C4×SD16×C10111yescharacteristic
311C22#442×C10111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—42no—
318C4—81no—
319C4#449×C10111yescharacteristic
320C4#450×C10111yescharacteristic
321C4#476×C10111yescharacteristic
322C4#478×C10111yescharacteristic
323C2—21no—
324C2—21no—
325C2—82no—
326C2C101×#186111yescharacteristic
327C2C101×#186411yescharacteristic
328C2C101×#186811yescharacteristic
subgroupG/H
centerC2×C4×C101#120
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×C42C23×C101
socleC22×C101#385
prime radical#532×C101C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#1940C2semidirect
3. C101×#1570C2semidirect
6. C101×#1303C2semidirect
7. C101×#1281C2semidirect
158. #8880C101direct (N × H)
166. #1940C2×C101semidirect
167. #1570C2×C101semidirect
170. #1303C2×C101semidirect
171. #1281C2×C101semidirect
172. C101#8880direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#29322
C101×#19402
C101×#15702
C101×#15022
C101×#14802
C101×#13032
C101×#12812
#8880101