Finite Group Databasebeta

← C101×#9015 #38791166

Subgroups — C101×#9015 #38791166

Order 25856.

800 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#395×C101C211yesmaximal, characteristic
2C101×#2316C211yesmaximal, characteristic
3C101×#1787C212yesmaximal
4C2×#324×C101C211yesmaximal, characteristic
5C101×#1294C212yesmaximal
6C23×Q8×C101C2211yescharacteristic
7C2×#117×C101—21no—
8C22×C4⋊C4×C101—21no—
9C22×C4⋊C4×C101C2211yescharacteristic
10C2×#103×C101—24no—
11C2×C22⋊C8×C101C2212yes—
12#395×C101—22no—
13#395×C101C414yescomplemented
14#389×C101—24no—
15#380×C101—21no—
16#380×C101C2212yes—
17C2×#95×C101—21no—
18C2×#95×C101C2211yescharacteristic
19#324×C101—22no—
20C22×Q8×C101—21no—
21C22×Q8×C101—22no—
22C22×Q8×C101—22no—
23C22×Q8×C101—44no—
24C22×Q8×C101C2×C412yes—
25C23×C4×C101—21no—
26C23×C4×C101—21no—
27C23×C4×C101D411yescharacteristic
28C23×C4×C101D411yescharacteristic
29C23×C4×C101C2311yescharacteristic
30C22×C8×C101—22no—
31#117×C101—42no—
32#117×C101—42no—
33C2×C4⋊C4×C101—22no—
34C2×C4⋊C4×C101—22no—
35C2×C4⋊C4×C101—22no—
36C2×C4⋊C4×C101—24no—
37C2×C4⋊C4×C101—22no—
38C2×C4⋊C4×C101—44no—
39C2×C4⋊C4×C101C2×C412yes—
40C2×C4⋊C4×C101D412yes—
41C2×C4⋊C4×C101D414yes—
42C2×C22⋊C4×C101—22no—
43C2×C42×C101—22no—
44#103×C101—48no—
45C22⋊C8×C101—22no—
46C22⋊C8×C101—22no—
47#95×C101—22no—
48#95×C101—24no—
49#95×C101—21no—
50#95×C101—22no—
51#95×C101C2×C412yes—
52C24×C101C2×D411yescharacteristic
53C2×Q8×C101—28no—
54C2×Q8×C101—24no—
55C2×Q8×C101—44no—
56C2×Q8×C101—44no—
57C2×Q8×C101—44no—
58C2×Q8×C101—48no—
59C2×Q8×C101—42no—
60C22×C4×C101—21no—
61C22×C4×C101—21no—
62C22×C4×C101—21no—
63C22×C4×C101—21no—
64C22×C4×C101—24no—
65C22×C4×C101—24no—
66C22×C4×C101—22no—
67C22×C4×C101—22no—
68C22×C4×C101—21no—
69C22×C4×C101—21no—
70C22×C4×C101—24no—
71C22×C4×C101—42no—
72C22×C4×C101—42no—
73C22×C4×C101—42no—
74C22×C4×C101—41no—
75C22×C4×C101—41no—
76C22×C4×C101—41no—
77C22×C4×C101—41no—
78C22×C4×C101—42no—
79C22×C4×C101C22⋊C412yes—
80C22×C4×C101C22⋊C412yes—
81C22×C4×C101SD1612yes—
82C22×C4×C101Q1612yes—
83C22×C4×C101C22×C411yescharacteristic
84C22×C4×C101C2×D412yes—
85C22×C4×C101C2×D411yescharacteristic
86C22×C4×C101#4112yes—
87C2×C8×C101—44no—
88C2×C8×C101—42no—
89C4⋊C4×C101—24no—
90C4⋊C4×C101—24no—
91C4⋊C4×C101—44no—
92C4⋊C4×C101—48no—
93C4⋊C4×C101—44no—
94C4⋊C4×C101—82no—
95C22⋊C4×C101—42no—
96C22⋊C4×C101—42no—
97C42×C101—44no—
98C23×C101—22no—
99C23×C101—22no—
100C23×C101C2×C22⋊C411yescharacteristic
101C23×C101#12011yescharacteristic
102C23×C101#12311yescharacteristic
103C23×C101C2×SD1611yescharacteristic
104C23×C101C2×Q1611yescharacteristic
105C23×C101AGL(1,ℤ/8)11yescharacteristic
106C23×C101#13711yescharacteristic
107Q8×C101—28no—
108Q8×C101—48no—
109Q8×C101—44no—
110C2×C4×C101—22no—
111C2×C4×C101—22no—
112C2×C4×C101—22no—
113C2×C4×C101—22no—
114C2×C4×C101—24no—
115C2×C4×C101—22no—
116C2×C4×C101—22no—
117C2×C4×C101—24no—
118C2×C4×C101—24no—
119C2×C4×C101—22no—
120C2×C4×C101—41no—
121C2×C4×C101—41no—
122C2×C4×C101—42no—
123C2×C4×C101—42no—
124C2×C4×C101—44no—
125C2×C4×C101—44no—
126C2×C4×C101—42no—
127C2×C4×C101—44no—
128C2×C4×C101—42no—
129C2×C4×C101—42no—
130C2×C4×C101—42no—
131C2×C4×C101—44no—
132C2×C4×C101—42no—
133C2×C4×C101—44no—
134C2×C4×C101—44no—
135C2×C4×C101—44no—
136C2×C4×C101—81no—
137C2×C4×C101#10314yescomplemented
138C2×C4×C101C4×D412yes—
139C2×C4×C101#12112yes—
140C8×C101—82no—
141C22×C101—22no—
142C22×C101—22no—
143C22×C101—22no—
144C22×C101—22no—
145C22×C101—21no—
146C22×C101—21no—
147C22×C101—21no—
148C22×C101—21no—
149C22×C101#38611yescharacteristic
150C22×C101C2×#10311yescharacteristic
151C22×C101#41711yescharacteristic
152C22×C101#45011yescharacteristic
153C22×C101#45111yescharacteristic
154C22×C101#45612yes—
155C22×C101B(4,𝔽2)12yes—
156C22×C101#48311yescharacteristic
157C22×C101#48411yescharacteristic
158C4×C101—24no—
159C4×C101—22no—
160C4×C101—22no—
161C4×C101—44no—
162C4×C101—44no—
163C4×C101—42no—
164C4×C101—84no—
165#9015C10111yesmaximal, characteristic, direct product factor, Sylow
166C2×C101—21no—
167C2×C101—21no—
168C2×C101—21no—
169C2×C101—21no—
170C2×C101#160412yes—
171C2×C101#160512yes—
172C2×C101#187211yescharacteristic
173C2×C101#188611yescharacteristic
174C2×C101#188911yescharacteristic
175C2×#395C2×C10111yescharacteristic
176#2316C2×C10111yescharacteristic
177#1787C2×C10112yes—
178C2×#324C2×C10111yescharacteristic
179#1294C2×C10112yes—
180C101#901511yescharacteristic, direct product factor, Sylow
181C23×Q8C22×C10111yescharacteristic
182C2×#117—21no—
183C22×C4⋊C4—21no—
184C22×C4⋊C4C22×C10111yescharacteristic
185C2×#103—24no—
186C2×C22⋊C8C22×C10112yes—
187#395—22no—
188#395C4×C10114yescomplemented
189#389—24no—
190#380—21no—
191#380C22×C10112yes—
192C2×#95—21no—
193C2×#95C22×C10111yescharacteristic
194#324—22no—
195C22×Q8—21no—
196C22×Q8—22no—
197C22×Q8—22no—
198C22×Q8—44no—
199C22×Q8C2×C4×C10112yes—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4D4×C10111yescharacteristic
203C23×C4D4×C10111yescharacteristic
204C23×C4C23×C10111yescharacteristic
205C22×C8—22no—
206#117—42no—
207#117—42no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—44no—
214C2×C4⋊C4C2×C4×C10112yes—
215C2×C4⋊C4D4×C10112yes—
216C2×C4⋊C4D4×C10114yes—
217C2×C22⋊C4—22no—
218C2×C42—22no—
219#103—48no—
220C22⋊C8—22no—
221C22⋊C8—22no—
222#95—22no—
223#95—24no—
224#95—21no—
225#95—22no—
226#95C2×C4×C10112yes—
227C24C2×D4×C10111yescharacteristic
228C2×Q8—28no—
229C2×Q8—24no—
230C2×Q8—44no—
231C2×Q8—44no—
232C2×Q8—44no—
233C2×Q8—48no—
234C2×Q8—42no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—24no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—42no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—42no—
254C22×C4C22⋊C4×C10112yes—
255C22×C4C22⋊C4×C10112yes—
256C22×C4SD16×C10112yes—
257C22×C4Q16×C10112yes—
258C22×C4C22×C4×C10111yescharacteristic
259C22×C4C2×D4×C10112yes—
260C22×C4C2×D4×C10111yescharacteristic
261C22×C4#41×C10112yes—
262C2×C8—44no—
263C2×C8—42no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—44no—
267C4⋊C4—48no—
268C4⋊C4—44no—
269C4⋊C4—82no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C42—44no—
273C23—22no—
274C23—22no—
275C23C2×C22⋊C4×C10111yescharacteristic
276C23#120×C10111yescharacteristic
277C23#123×C10111yescharacteristic
278C23C2×SD16×C10111yescharacteristic
279C23C2×Q16×C10111yescharacteristic
280C23AGL(1,ℤ/8)×C10111yescharacteristic
281C23#137×C10111yescharacteristic
282Q8—28no—
283Q8—48no—
284Q8—44no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—24no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—44no—
301C2×C4—44no—
302C2×C4—44no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—44no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—44no—
311C2×C4—81no—
312C2×C4#103×C10114yescomplemented
313C2×C4C4×D4×C10112yes—
314C2×C4#121×C10112yes—
315C8—82no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22#386×C10111yescharacteristic
325C22C2×#103×C10111yescharacteristic
326C22#417×C10111yescharacteristic
327C22#450×C10111yescharacteristic
328C22#451×C10111yescharacteristic
329C22#456×C10112yes—
330C22B(4,𝔽2)×C10112yes—
331C22#483×C10111yescharacteristic
332C22#484×C10111yescharacteristic
333C4—22no—
334C4—22no—
335C4—24no—
336C4—44no—
337C4—44no—
338C4—42no—
339C4—84no—
340C2—21no—
341C2—21no—
342C2—21no—
343C2—21no—
344C2C101×#160412yes—
345C2C101×#160512yes—
346C2C101×#187211yescharacteristic
347C2C101×#188611yescharacteristic
348C2C101×#188911yescharacteristic
subgroupG/H
center, socleC23×C101#120
commutatorC22×C4C22×C4×C101
Frattini, cosocleC23×C4C23×C101
prime radicalC24×C101C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
13. #395×C101C4semidirect
137. C2×C4×C101#103semidirect
165. #9015C101direct (N × H)
180. C101#9015direct (N × H)
188. #395C4×C101semidirect
312. C2×C4#103×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#395×C1012
C101×#23162
C101×#17872
C2×#324×C1012
C101×#12942
#9015101