Finite Group Databasebeta

← C101×#13008 #38795159

Subgroups — C101×#13008 #38795159

Order 25856.

516 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3054C211yesmaximal, characteristic
2C101×#2911C211yesmaximal, characteristic, complemented
3C101×#2145C212yesmaximal, complemented
4C2×#349×C101C211yesmaximal, characteristic, complemented
5C101×#1384C212yesmaximal, complemented
6C2×#135×C101C2211yescharacteristic
7C22×M16×C101C2211yescharacteristic
8#525×C101—21no—
9C2×#117×C101—21no—
10C2×M32×C101C2212yes—
11#470×C101C412yescomplemented
12#469×C101C412yescomplemented
13#468×C101—22no—
14#428×C101—24no—
15#427×C101—21no—
16#427×C101C2211yescharacteristic
17#427×C101C2212yes—
18#416×C101—21no—
19#360×C101—24no—
20#349×C101—22no—
21C2×#41×C101—21no—
22C23×C4×C101D411yescharacteristic
23#135×C101—22no—
24#135×C101—22no—
25C2×Q16×C101C2×C411yescharacteristic, complemented
26C2×SD16×C101—21no—
27C2×D8×C101C2×C411yescharacteristic, complemented
28C2×M16×C101—22no—
29C2×M16×C101—22no—
30C2×M16×C101C2×C412yes—
31C2×M16×C101D412yes—
32C22×C8×C101D411yescharacteristic
33C22×C8×C101C2311yescharacteristic
34#123×C101—41no—
35C22⋊Q8×C101—22no—
36#121×C101—22no—
37#120×C101—41no—
38C4×D4×C101—42no—
39#117×C101—22no—
40#117×C101—21no—
41#117×C101—22no—
42#117×C101—41no—
43#117×C101—41no—
44C2×C4⋊C4×C101—22no—
45C2×C22⋊C4×C101—41no—
46C2×C42×C101—41no—
47M32×C101—22no—
48M32×C101—22no—
49C2×C16×C101—22no—
50#107×C101—22no—
51#107×C101—22no—
52#107×C101—21no—
53#106×C101—22no—
54#106×C101C2×C412yescomplemented
55#106×C101D414yescomplemented
56#103×C101—22no—
57#102×C101—22no—
58C24×C101D811yescharacteristic
59#41×C101—41no—
60#41×C101—41no—
61#41×C101—41no—
62#41×C101—41no—
63C2×Q8×C101—21no—
64C2×D4×C101—21no—
65C2×D4×C101—42no—
66C2×D4×C101—41no—
67C22×C4×C101—21no—
68C22×C4×C101—21no—
69C22×C4×C101—21no—
70C22×C4×C101—21no—
71C22×C4×C101—42no—
72C22×C4×C101—41no—
73C22×C4×C101C22⋊C412yes—
74C22×C4×C101D811yescharacteristic
75C22×C4×C101SD1612yes—
76C22×C4×C101C2×D411yescharacteristic
77Q16×C101—22no—
78SD16×C101—42no—
79D8×C101—22no—
80M16×C101—24no—
81M16×C101—24no—
82C2×C8×C101—21no—
83C2×C8×C101—21no—
84C2×C8×C101C22⋊C412yes—
85C2×C8×C101C22×C411yescharacteristic
86C2×C8×C101C2×D412yes—
87C2×C8×C101C2×D411yescharacteristic
88C2×C8×C101#4112yes—
89C4⋊C4×C101—22no—
90C4⋊C4×C101—24no—
91C4⋊C4×C101—42no—
92C4⋊C4×C101—42no—
93C22⋊C4×C101—42no—
94C22⋊C4×C101—42no—
95C22⋊C4×C101—42no—
96C22⋊C4×C101—41no—
97C22⋊C4×C101—42no—
98C42×C101—42no—
99C42×C101—41no—
100C42×C101—42no—
101C16×C101—42no—
102C23×C101—21no—
103C23×C101—21no—
104C23×C101—41no—
105C23×C101—81no—
106C23×C101#10212yes—
107C23×C101C2×D811yescharacteristic
108Q8×C101—41no—
109Q8×C101—41no—
110D4×C101—41no—
111D4×C101—41no—
112D4×C101—84no—
113D4×C101—81no—
114D4×C101—81no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—22no—
118C2×C4×C101—22no—
119C2×C4×C101—22no—
120C2×C4×C101—22no—
121C2×C4×C101—42no—
122C2×C4×C101—41no—
123C2×C4×C101—44no—
124C2×C4×C101—84no—
125C2×C4×C101—81no—
126C2×C4×C101—81no—
127C2×C4×C101#10212yes—
128C2×C4×C101C2×C22⋊C411yescharacteristic
129C2×C4×C101#12011yescharacteristic
130C2×C4×C101#12311yescharacteristic
131C2×C4×C101C2×SD1611yescharacteristic
132C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C101#13711yescharacteristic
134C8×C101—22no—
135C8×C101C4×D412yes—
136C8×C101#12112yes—
137C22×C101—22no—
138C22×C101—41no—
139C22×C101—42no—
140C22×C101—42no—
141C22×C101—81no—
142C22×C101—82no—
143C22×C101—81no—
144C22×C101C2×#10211yescharacteristic
145C22×C101#44711yescharacteristic
146C22×C101#48011yescharacteristic
147C4×C101—22no—
148C4×C101—84no—
149C4×C101—82no—
150C4×C101—81no—
151C4×C101#38611yescharacteristic
152C4×C101#41711yescharacteristic
153C4×C101#44811yescharacteristic
154C4×C101#48111yescharacteristic
155#13008C10111yesmaximal, characteristic, direct product factor, Sylow
156C2×C101—21no—
157C2×C101—21no—
158C2×C101—21no—
159C2×C101—42no—
160C2×C101—161no—
161C2×C101#187411yescharacteristic
162#3054C2×C10111yescharacteristic
163#2911C2×C10111yescharacteristic, complemented
164#2145C2×C10112yescomplemented
165C2×#349C2×C10111yescharacteristic, complemented
166#1384C2×C10112yescomplemented
167C101#1300811yescharacteristic, direct product factor, Sylow
168C2×#135C22×C10111yescharacteristic
169C22×M16C22×C10111yescharacteristic
170#525—21no—
171C2×#117—21no—
172C2×M32C22×C10112yes—
173#470C4×C10112yescomplemented
174#469C4×C10112yescomplemented
175#468—22no—
176#428—24no—
177#427—21no—
178#427C22×C10111yescharacteristic
179#427C22×C10112yes—
180#416—21no—
181#360—24no—
182#349—22no—
183C2×#41—21no—
184C23×C4D4×C10111yescharacteristic
185#135—22no—
186#135—22no—
187C2×Q16C2×C4×C10111yescharacteristic, complemented
188C2×SD16—21no—
189C2×D8C2×C4×C10111yescharacteristic, complemented
190C2×M16—22no—
191C2×M16—22no—
192C2×M16C2×C4×C10112yes—
193C2×M16D4×C10112yes—
194C22×C8D4×C10111yescharacteristic
195C22×C8C23×C10111yescharacteristic
196#123—41no—
197C22⋊Q8—22no—
198#121—22no—
199#120—41no—
200C4×D4—42no—
201#117—22no—
202#117—22no—
203#117—21no—
204#117—41no—
205#117—41no—
206C2×C4⋊C4—22no—
207C2×C22⋊C4—41no—
208C2×C42—41no—
209M32—22no—
210M32—22no—
211C2×C16—22no—
212#107—22no—
213#107—22no—
214#107—21no—
215#106—22no—
216#106C2×C4×C10112yescomplemented
217#106D4×C10114yescomplemented
218#103—22no—
219#102—22no—
220C24D8×C10111yescharacteristic
221#41—41no—
222#41—41no—
223#41—41no—
224#41—41no—
225C2×Q8—21no—
226C2×D4—21no—
227C2×D4—42no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4C22⋊C4×C10112yes—
236C22×C4D8×C10111yescharacteristic
237C22×C4SD16×C10112yes—
238C22×C4C2×D4×C10111yescharacteristic
239Q16—22no—
240SD16—42no—
241D8—22no—
242M16—24no—
243M16—24no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8C22⋊C4×C10112yes—
247C2×C8C22×C4×C10111yescharacteristic
248C2×C8C2×D4×C10112yes—
249C2×C8C2×D4×C10111yescharacteristic
250C2×C8#41×C10112yes—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C42—42no—
261C42—41no—
262C42—42no—
263C16—42no—
264C23—21no—
265C23—21no—
266C23—41no—
267C23—81no—
268C23#102×C10112yes—
269C23C2×D8×C10111yescharacteristic
270Q8—41no—
271Q8—41no—
272D4—41no—
273D4—41no—
274D4—84no—
275D4—81no—
276D4—81no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—44no—
286C2×C4—84no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4#102×C10112yes—
290C2×C4C2×C22⋊C4×C10111yescharacteristic
291C2×C4#120×C10111yescharacteristic
292C2×C4#123×C10111yescharacteristic
293C2×C4C2×SD16×C10111yescharacteristic
294C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
295C2×C4#137×C10111yescharacteristic
296C8—22no—
297C8C4×D4×C10112yes—
298C8#121×C10112yes—
299C22—22no—
300C22—41no—
301C22—42no—
302C22—42no—
303C22—81no—
304C22—82no—
305C22—81no—
306C22C2×#102×C10111yescharacteristic
307C22#447×C10111yescharacteristic
308C22#480×C10111yescharacteristic
309C4—22no—
310C4—84no—
311C4—82no—
312C4—81no—
313C4#386×C10111yescharacteristic
314C4#417×C10111yescharacteristic
315C4#448×C10111yescharacteristic
316C4#481×C10111yescharacteristic
317C2—21no—
318C2—21no—
319C2—21no—
320C2—42no—
321C2—161no—
322C2C101×#187411yescharacteristic
subgroupG/H
centerC4×C101#481
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
socleC2×C101#1874
prime radicalC101×#3054C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C101 ◁ C22×C4×C101 ◁ C22×M16×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2911C2semidirect
3. C101×#2145C2semidirect
4. C2×#349×C101C2semidirect
5. C101×#1384C2semidirect
11. #470×C101C4semidirect
12. #469×C101C4semidirect
25. C2×Q16×C101C2×C4semidirect
27. C2×D8×C101C2×C4semidirect
54. #106×C101C2×C4semidirect
55. #106×C101D4semidirect
155. #13008C101direct (N × H)
163. #2911C2×C101semidirect
164. #2145C2×C101semidirect
165. C2×#349C2×C101semidirect
166. #1384C2×C101semidirect
167. C101#13008direct (N × H)
173. #470C4×C101semidirect
174. #469C4×C101semidirect
187. C2×Q16C2×C4×C101semidirect
189. C2×D8C2×C4×C101semidirect
216. #106C2×C4×C101semidirect
217. #106D4×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#30542
C101×#29112
C101×#21452
C2×#349×C1012
C101×#13842
#13008101