Finite Group Databasebeta

← C101×#13134 #38795285

Subgroups — C101×#13134 #38795285

Order 25856.

324 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#368×C101C211yesmaximal, characteristic, complemented
2C2×#359×C101C211yesmaximal, characteristic
3C101×#2138C211yesmaximal, characteristic
4C101×#1974C211yesmaximal, characteristic
5C101×#1772C211yesmaximal, characteristic, complemented
6C101×#1382C211yesmaximal, characteristic, complemented
7C101×#1374C211yesmaximal, characteristic, complemented
8C2×#135×C101C2211yescharacteristic
9C22×C16×C101C2211yescharacteristic
10C22×C16×C101C2211yescharacteristic
11C2×#108×C101C2211yescharacteristic
12C2×#108×C101C2211yescharacteristic
13#427×C101C2211yescharacteristic
14C2×#104×C101—21no—
15#408×C101—21no—
16#405×C101—21no—
17C2×C4×C8×C101C2211yescharacteristic
18#368×C101—22no—
19#359×C101—22no—
20#358×C101C411yescharacteristic, complemented
21#358×C101C411yescharacteristic, complemented
22#357×C101C411yescharacteristic, complemented
23#357×C101C411yescharacteristic, complemented
24#339×C101—21no—
25C2×#41×C101—21no—
26#135×C101—21no—
27#135×C101—21no—
28#135×C101—21no—
29#135×C101—21no—
30C2×Q16×C101C2×C411yescharacteristic
31C2×SD16×C101—21no—
32C2×D8×C101C2×C411yescharacteristic
33C2×M16×C101—21no—
34C2×M16×C101—21no—
35C22×C8×C101D411yescharacteristic
36C22×C8×C101C2311yescharacteristic
37#117×C101—21no—
38C2×C42×C101D411yescharacteristic
39C2×C16×C101—21no—
40C2×C16×C101—21no—
41C2×C16×C101—21no—
42C2×C16×C101—21no—
43C2×C16×C101—21no—
44C2×C16×C101C2×C411yescharacteristic
45C2×C16×C101C2×C411yescharacteristic
46#108×C101—21no—
47#108×C101—21no—
48#108×C101—21no—
49#108×C101D412yes—
50#107×C101C2×C411yescharacteristic
51#107×C101C2×C411yescharacteristic
52#106×C101—21no—
53#104×C101—42no—
54C22⋊C8×C101—41no—
55C22⋊C8×C101—41no—
56#97×C101—41no—
57C4×C8×C101—21no—
58C4×C8×C101—21no—
59C4×C8×C101—41no—
60#41×C101—41no—
61#41×C101—41no—
62#41×C101—41no—
63#41×C101—41no—
64C2×Q8×C101—21no—
65C2×D4×C101—21no—
66C2×D4×C101—41no—
67C22×C4×C101—21no—
68C22×C4×C101—41no—
69C22×C4×C101C2×D411yescharacteristic
70Q16×C101—21no—
71Q16×C101—21no—
72SD16×C101—41no—
73SD16×C101—41no—
74D8×C101—21no—
75D8×C101—21no—
76M16×C101—22no—
77M16×C101—41no—
78M16×C101—41no—
79M16×C101—41no—
80C2×C8×C101—21no—
81C2×C8×C101—21no—
82C2×C8×C101—41no—
83C2×C8×C101—41no—
84C2×C8×C101D811yescharacteristic
85C2×C8×C101D811yescharacteristic
86C2×C8×C101C22×C411yescharacteristic
87C2×C8×C101C2×D411yescharacteristic
88C2×C8×C101#4111yescharacteristic
89C2×C8×C101#4111yescharacteristic
90C2×C8×C101#4111yescharacteristic
91C2×C8×C101#4111yescharacteristic
92C4⋊C4×C101—21no—
93C4⋊C4×C101—21no—
94C22⋊C4×C101—41no—
95C42×C101—21no—
96C42×C101—21no—
97C42×C101—41no—
98C16×C101—21no—
99C16×C101—21no—
100C16×C101—41no—
101C23×C101—41no—
102C23×C101#13511yescharacteristic
103Q8×C101—41no—
104Q8×C101—41no—
105D4×C101—41no—
106D4×C101—41no—
107D4×C101—81no—
108D4×C101—81no—
109C2×C4×C101—22no—
110C2×C4×C101—41no—
111C2×C4×C101—41no—
112C2×C4×C101—41no—
113C2×C4×C101—41no—
114C2×C4×C101—41no—
115C2×C4×C101—81no—
116C2×C4×C101—81no—
117C2×C4×C101C4×D411yescharacteristic
118C2×C4×C101#12111yescharacteristic
119C2×C4×C101#12311yescharacteristic
120C2×C4×C101C2×D811yescharacteristic
121C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C101#13711yescharacteristic
123C8×C101—21no—
124C8×C101—21no—
125C8×C101—42no—
126C8×C101—81no—
127C8×C101#11711yescharacteristic
128C8×C101C4×D411yescharacteristic
129C8×C101#12411yescharacteristic
130C8×C101#12611yescharacteristic
131C22×C101—21no—
132C22×C101—21no—
133C22×C101—81no—
134C22×C101—81no—
135C22×C101—81no—
136C22×C101C4×D811yescharacteristic
137C22×C101#46411yescharacteristic
138C22×C101#48211yescharacteristic
139C4×C101—42no—
140C4×C101—81no—
141C4×C101—81no—
142C4×C101—81no—
143C4×C101#38811yescharacteristic
144C4×C101#44011yescharacteristic
145C4×C101#45911yescharacteristic
146C4×C101#48011yescharacteristic
147#13134C10111yesmaximal, characteristic, direct product factor, Sylow
148C2×C101—21no—
149C2×C101—21no—
150C2×C101—161no—
151C2×C101#192511yescharacteristic
152C2×C101#217811yescharacteristic
153C2×C101#217911yescharacteristic
154C2×#368C2×C10111yescharacteristic, complemented
155C2×#359C2×C10111yescharacteristic
156#2138C2×C10111yescharacteristic
157#1974C2×C10111yescharacteristic
158#1772C2×C10111yescharacteristic, complemented
159#1382C2×C10111yescharacteristic, complemented
160#1374C2×C10111yescharacteristic, complemented
161C101#1313411yescharacteristic, direct product factor, Sylow
162C2×#135C22×C10111yescharacteristic
163C22×C16C22×C10111yescharacteristic
164C22×C16C22×C10111yescharacteristic
165C2×#108C22×C10111yescharacteristic
166C2×#108C22×C10111yescharacteristic
167#427C22×C10111yescharacteristic
168C2×#104—21no—
169#408—21no—
170#405—21no—
171C2×C4×C8C22×C10111yescharacteristic
172#368—22no—
173#359—22no—
174#358C4×C10111yescharacteristic, complemented
175#358C4×C10111yescharacteristic, complemented
176#357C4×C10111yescharacteristic, complemented
177#357C4×C10111yescharacteristic, complemented
178#339—21no—
179C2×#41—21no—
180#135—21no—
181#135—21no—
182#135—21no—
183#135—21no—
184C2×Q16C2×C4×C10111yescharacteristic
185C2×SD16—21no—
186C2×D8C2×C4×C10111yescharacteristic
187C2×M16—21no—
188C2×M16—21no—
189C22×C8D4×C10111yescharacteristic
190C22×C8C23×C10111yescharacteristic
191#117—21no—
192C2×C42D4×C10111yescharacteristic
193C2×C16—21no—
194C2×C16—21no—
195C2×C16—21no—
196C2×C16—21no—
197C2×C16—21no—
198C2×C16C2×C4×C10111yescharacteristic
199C2×C16C2×C4×C10111yescharacteristic
200#108—21no—
201#108—21no—
202#108—21no—
203#108D4×C10112yes—
204#107C2×C4×C10111yescharacteristic
205#107C2×C4×C10111yescharacteristic
206#106—21no—
207#104—42no—
208C22⋊C8—41no—
209C22⋊C8—41no—
210#97—41no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—41no—
214#41—41no—
215#41—41no—
216#41—41no—
217#41—41no—
218C2×Q8—21no—
219C2×D4—21no—
220C2×D4—41no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4C2×D4×C10111yescharacteristic
224Q16—21no—
225Q16—21no—
226SD16—41no—
227SD16—41no—
228D8—21no—
229D8—21no—
230M16—22no—
231M16—41no—
232M16—41no—
233M16—41no—
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8D8×C10111yescharacteristic
239C2×C8D8×C10111yescharacteristic
240C2×C8C22×C4×C10111yescharacteristic
241C2×C8C2×D4×C10111yescharacteristic
242C2×C8#41×C10111yescharacteristic
243C2×C8#41×C10111yescharacteristic
244C2×C8#41×C10111yescharacteristic
245C2×C8#41×C10111yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—21no—
248C22⋊C4—41no—
249C42—21no—
250C42—21no—
251C42—41no—
252C16—21no—
253C16—21no—
254C16—41no—
255C23—41no—
256C23#135×C10111yescharacteristic
257Q8—41no—
258Q8—41no—
259D4—41no—
260D4—41no—
261D4—81no—
262D4—81no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4C4×D4×C10111yescharacteristic
272C2×C4#121×C10111yescharacteristic
273C2×C4#123×C10111yescharacteristic
274C2×C4C2×D8×C10111yescharacteristic
275C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
276C2×C4#137×C10111yescharacteristic
277C8—21no—
278C8—21no—
279C8—42no—
280C8—81no—
281C8#117×C10111yescharacteristic
282C8C4×D4×C10111yescharacteristic
283C8#124×C10111yescharacteristic
284C8#126×C10111yescharacteristic
285C22—21no—
286C22—21no—
287C22—81no—
288C22—81no—
289C22—81no—
290C22C4×D8×C10111yescharacteristic
291C22#464×C10111yescharacteristic
292C22#482×C10111yescharacteristic
293C4—42no—
294C4—81no—
295C4—81no—
296C4—81no—
297C4#388×C10111yescharacteristic
298C4#440×C10111yescharacteristic
299C4#459×C10111yescharacteristic
300C4#480×C10111yescharacteristic
301C2—21no—
302C2—21no—
303C2—161no—
304C2C101×#192511yescharacteristic
305C2C101×#217811yescharacteristic
306C2C101×#217911yescharacteristic
subgroupG/H
centerC2×C4×C101C2×D8
commutatorC2×C8C22×C4×C101
Frattini, cosocleC22×C8C23×C101
socleC22×C101C4×D8
prime radicalC2×#135×C101C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C101 ◁ C22×C8×C101 ◁ C2×C4×C8×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#368×C101C2semidirect
5. C101×#1772C2semidirect
6. C101×#1382C2semidirect
7. C101×#1374C2semidirect
20. #358×C101C4semidirect
21. #358×C101C4semidirect
22. #357×C101C4semidirect
23. #357×C101C4semidirect
147. #13134C101direct (N × H)
154. C2×#368C2×C101semidirect
158. #1772C2×C101semidirect
159. #1382C2×C101semidirect
160. #1374C2×C101semidirect
161. C101#13134direct (N × H)
174. #358C4×C101semidirect
175. #358C4×C101semidirect
176. #357C4×C101semidirect
177. #357C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#368×C1012
C2×#359×C1012
C101×#21382
C101×#19742
C101×#17722
C101×#13822
C101×#13742
#13134101