Finite Group Databasebeta

← C101×#13130 #38795281

Subgroups — C101×#13130 #38795281

Order 25856.

390 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#366×C101C211yesmaximal, characteristic, complemented
2C2×#357×C101C211yesmaximal, characteristic
3C2×#357×C101C211yesmaximal, characteristic
4C101×#1970C211yesmaximal, characteristic
5C4×#107×C101C211yesmaximal, characteristic, complemented
6C101×#1380C211yesmaximal, characteristic, complemented
7C101×#1374C211yesmaximal, characteristic, complemented
8C22×D8×C101C2211yescharacteristic
9C22×C16×C101C2211yescharacteristic
10C22×C16×C101C2211yescharacteristic
11C2×#107×C101C2211yescharacteristic
12C2×#107×C101C2211yescharacteristic
13C2×#107×C101C2211yescharacteristic
14C2×#102×C101—21no—
15C2×C4×C8×C101C2211yescharacteristic
16#390×C101—21no—
17C4×C4⋊C4×C101—21no—
18#366×C101—22no—
19#357×C101—22no—
20#357×C101C414yescomplemented
21#340×C101—21no—
22C22×D4×C101—21no—
23C2×D8×C101—21no—
24C2×D8×C101—21no—
25C2×D8×C101—21no—
26C2×D8×C101—21no—
27C2×D8×C101—21no—
28C2×D8×C101C2×C412yes—
29C22×C8×C101D411yescharacteristic
30C22×C8×C101C2311yescharacteristic
31C2×C4⋊C4×C101—21no—
32C2×C4⋊C4×C101—21no—
33C2×C4⋊C4×C101—21no—
34C2×C22⋊C4×C101—41no—
35C2×C22⋊C4×C101—41no—
36C2×C42×C101—41no—
37C2×C42×C101D411yescharacteristic
38C2×C16×C101—21no—
39C2×C16×C101—21no—
40C2×C16×C101—21no—
41C2×C16×C101—21no—
42C2×C16×C101—21no—
43C2×C16×C101C2×C412yes—
44#107×C101—21no—
45#107×C101—21no—
46#107×C101—21no—
47#107×C101—21no—
48#107×C101C2×C412yes—
49#107×C101D412yes—
50#102×C101—42no—
51C4×C8×C101—21no—
52C4×C8×C101—21no—
53#95×C101—41no—
54C24×C101—41no—
55C2×D4×C101—22no—
56C2×D4×C101—41no—
57C2×D4×C101—41no—
58C2×D4×C101—41no—
59C2×D4×C101—41no—
60C2×D4×C101—41no—
61C22×C4×C101—41no—
62C22×C4×C101—41no—
63C22×C4×C101—41no—
64C22×C4×C101D811yescharacteristic
65C22×C4×C101D811yescharacteristic
66C22×C4×C101C2×D411yescharacteristic
67D8×C101—22no—
68D8×C101—22no—
69D8×C101—41no—
70D8×C101—41no—
71C2×C8×C101—21no—
72C2×C8×C101—21no—
73C2×C8×C101—21no—
74C2×C8×C101C22×C411yescharacteristic
75C2×C8×C101C2×D411yescharacteristic
76C2×C8×C101#4111yescharacteristic
77C2×C8×C101#4111yescharacteristic
78C2×C8×C101#4111yescharacteristic
79C2×C8×C101#4111yescharacteristic
80C4⋊C4×C101—22no—
81C4⋊C4×C101—22no—
82C4⋊C4×C101—41no—
83C4⋊C4×C101—41no—
84C4⋊C4×C101—41no—
85C4⋊C4×C101—41no—
86C22⋊C4×C101—82no—
87C22⋊C4×C101—82no—
88C42×C101—21no—
89C42×C101—21no—
90C42×C101—82no—
91C16×C101—22no—
92C16×C101—41no—
93C23×C101—42no—
94C23×C101—81no—
95C23×C101—81no—
96C23×C101—81no—
97C23×C101—81no—
98C23×C101—81no—
99C23×C101—81no—
100C23×C101C2×D811yescharacteristic
101D4×C101—42no—
102D4×C101—42no—
103D4×C101—81no—
104D4×C101—81no—
105C2×C4×C101—21no—
106C2×C4×C101—21no—
107C2×C4×C101—21no—
108C2×C4×C101—21no—
109C2×C4×C101—21no—
110C2×C4×C101—42no—
111C2×C4×C101—42no—
112C2×C4×C101—81no—
113C2×C4×C101—81no—
114C2×C4×C101—81no—
115C2×C4×C101—81no—
116C2×C4×C101—81no—
117C2×C4×C101—81no—
118C2×C4×C101—81no—
119C2×C4×C101D1612yes—
120C2×C4×C101C4×D411yescharacteristic
121C2×C4×C101#12111yescharacteristic
122C2×C4×C101#12311yescharacteristic
123C2×C4×C101#13511yescharacteristic
124C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C101#13711yescharacteristic
126C8×C101—41no—
127C8×C101#11711yescharacteristic
128C8×C101C4×D411yescharacteristic
129C8×C101#12411yescharacteristic
130C8×C101#12611yescharacteristic
131C22×C101—82no—
132C22×C101—82no—
133C22×C101—82no—
134C22×C101—161no—
135C22×C101—161no—
136C22×C101—161no—
137C22×C101—161no—
138C22×C101C4×D811yescharacteristic
139C22×C101#45911yescharacteristic
140C22×C101#48011yescharacteristic
141C22×C101C2×D1611yescharacteristic
142C22×C101#50811yescharacteristic
143C22×C101#50911yescharacteristic
144C22×C101#51011yescharacteristic
145C4×C101—22no—
146C4×C101—41no—
147C4×C101—82no—
148C4×C101—82no—
149C4×C101—161no—
150C4×C101#38811yescharacteristic
151C4×C101#44011yescharacteristic
152C4×C101#46411yescharacteristic
153C4×C101#48211yescharacteristic
154#13130C10111yesmaximal, characteristic, direct product factor, Sylow
155C2×C101—162no—
156C2×C101#192511yescharacteristic
157C2×C101C4×D1611yescharacteristic
158C2×C101#217511yescharacteristic
159C2×C101#220611yescharacteristic
160C2×C101#221111yescharacteristic
161C2×C101#223211yescharacteristic
162C2×C101#223411yescharacteristic
163C2×#366C2×C10111yescharacteristic, complemented
164C2×#357C2×C10111yescharacteristic
165C2×#357C2×C10111yescharacteristic
166#1970C2×C10111yescharacteristic
167C4×#107C2×C10111yescharacteristic, complemented
168#1380C2×C10111yescharacteristic, complemented
169#1374C2×C10111yescharacteristic, complemented
170C101#1313011yescharacteristic, direct product factor, Sylow
171C22×D8C22×C10111yescharacteristic
172C22×C16C22×C10111yescharacteristic
173C22×C16C22×C10111yescharacteristic
174C2×#107C22×C10111yescharacteristic
175C2×#107C22×C10111yescharacteristic
176C2×#107C22×C10111yescharacteristic
177C2×#102—21no—
178C2×C4×C8C22×C10111yescharacteristic
179#390—21no—
180C4×C4⋊C4—21no—
181#366—22no—
182#357—22no—
183#357C4×C10114yescomplemented
184#340—21no—
185C22×D4—21no—
186C2×D8—21no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8—21no—
190C2×D8—21no—
191C2×D8C2×C4×C10112yes—
192C22×C8D4×C10111yescharacteristic
193C22×C8C23×C10111yescharacteristic
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C22⋊C4—41no—
198C2×C22⋊C4—41no—
199C2×C42—41no—
200C2×C42D4×C10111yescharacteristic
201C2×C16—21no—
202C2×C16—21no—
203C2×C16—21no—
204C2×C16—21no—
205C2×C16—21no—
206C2×C16C2×C4×C10112yes—
207#107—21no—
208#107—21no—
209#107—21no—
210#107—21no—
211#107C2×C4×C10112yes—
212#107D4×C10112yes—
213#102—42no—
214C4×C8—21no—
215C4×C8—21no—
216#95—41no—
217C24—41no—
218C2×D4—22no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4D8×C10111yescharacteristic
228C22×C4D8×C10111yescharacteristic
229C22×C4C2×D4×C10111yescharacteristic
230D8—22no—
231D8—22no—
232D8—41no—
233D8—41no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8C22×C4×C10111yescharacteristic
238C2×C8C2×D4×C10111yescharacteristic
239C2×C8#41×C10111yescharacteristic
240C2×C8#41×C10111yescharacteristic
241C2×C8#41×C10111yescharacteristic
242C2×C8#41×C10111yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C22⋊C4—82no—
250C22⋊C4—82no—
251C42—21no—
252C42—21no—
253C42—82no—
254C16—22no—
255C16—41no—
256C23—42no—
257C23—81no—
258C23—81no—
259C23—81no—
260C23—81no—
261C23—81no—
262C23—81no—
263C23C2×D8×C10111yescharacteristic
264D4—42no—
265D4—42no—
266D4—81no—
267D4—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4D16×C10112yes—
283C2×C4C4×D4×C10111yescharacteristic
284C2×C4#121×C10111yescharacteristic
285C2×C4#123×C10111yescharacteristic
286C2×C4#135×C10111yescharacteristic
287C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
288C2×C4#137×C10111yescharacteristic
289C8—41no—
290C8#117×C10111yescharacteristic
291C8C4×D4×C10111yescharacteristic
292C8#124×C10111yescharacteristic
293C8#126×C10111yescharacteristic
294C22—82no—
295C22—82no—
296C22—82no—
297C22—161no—
298C22—161no—
299C22—161no—
300C22—161no—
301C22C4×D8×C10111yescharacteristic
302C22#459×C10111yescharacteristic
303C22#480×C10111yescharacteristic
304C22C2×D16×C10111yescharacteristic
305C22#508×C10111yescharacteristic
306C22#509×C10111yescharacteristic
307C22#510×C10111yescharacteristic
308C4—22no—
309C4—41no—
310C4—82no—
311C4—82no—
312C4—161no—
313C4#388×C10111yescharacteristic
314C4#440×C10111yescharacteristic
315C4#464×C10111yescharacteristic
316C4#482×C10111yescharacteristic
317C2—162no—
318C2C101×#192511yescharacteristic
319C2C4×D16×C10111yescharacteristic
320C2C101×#217511yescharacteristic
321C2C101×#220611yescharacteristic
322C2C101×#221111yescharacteristic
323C2C101×#223211yescharacteristic
324C2C101×#223411yescharacteristic
subgroupG/H
center, socleC23×C101C2×D8
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
prime radicalC22×D8×C101C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C42×C101 ◁ C2×C4×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#366×C101C2semidirect
5. C4×#107×C101C2semidirect
6. C101×#1380C2semidirect
7. C101×#1374C2semidirect
20. #357×C101C4semidirect
154. #13130C101direct (N × H)
163. C2×#366C2×C101semidirect
167. C4×#107C2×C101semidirect
168. #1380C2×C101semidirect
169. #1374C2×C101semidirect
170. C101#13130direct (N × H)
183. #357C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#366×C1012
C2×#357×C1012
C101×#19702
C4×#107×C1012
C101×#13802
C101×#13742
#13130101