Finite Group Databasebeta

← C101×#7731 #38789882

Subgroups — C101×#7731 #38789882

Order 25856.

450 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2851C211yesmaximal, characteristic
2C101×#1817C211yesmaximal, characteristic
3C101×#1797C211yesmaximal, characteristic
4C101×#1271C212yesmaximal, complemented
5C101×#1271C212yesmaximal, complemented
6C2×#125×C101C411yescharacteristic
7C22×C42×C101C2211yescharacteristic
8C2×C4⋊C8×C101—21no—
9C2×C22⋊C8×C101—21no—
10C2×C22⋊C8×C101—21no—
11#389×C101C2211yescharacteristic
12#389×C101C2211yescharacteristic
13#387×C101—21no—
14#387×C101—21no—
15#385×C101—21no—
16#385×C101—21no—
17#382×C101C411yescharacteristic
18#380×C101C411yescharacteristic
19#380×C101C411yescharacteristic
20#336×C101—21no—
21#336×C101C2212yes—
22#336×C101C2212yes—
23C23×C4×C101C2×C411yescharacteristic
24C23×C4×C101D411yescharacteristic
25C23×C4×C101D411yescharacteristic
26C22×C8×C101—22no—
27C22×C8×C101—22no—
28#125×C101—42no—
29C2×C4⋊C4×C101—21no—
30C2×C4⋊C4×C101—21no—
31C2×C4⋊C4×C101—21no—
32C2×C4⋊C4×C101—21no—
33C2×C4⋊C4×C101C2×C411yescharacteristic
34C2×C4⋊C4×C101C2×C411yescharacteristic
35C2×C4⋊C4×C101C2×C411yescharacteristic
36C2×C4⋊C4×C101C2×C411yescharacteristic
37C2×C22⋊C4×C101—21no—
38C2×C22⋊C4×C101—21no—
39C2×C42×C101—42no—
40C2×C42×C101C2×C411yescharacteristic
41C2×C42×C101D411yescharacteristic
42C2×C42×C101D411yescharacteristic
43C2×C42×C101C2311yescharacteristic
44C4⋊C8×C101—42no—
45C22⋊C8×C101—42no—
46C22⋊C8×C101—42no—
47#95×C101—21no—
48#95×C101—21no—
49#95×C101—21no—
50#95×C101—21no—
51#95×C101—21no—
52#95×C101—21no—
53C24×C101C22⋊C411yescharacteristic
54C22×C4×C101—22no—
55C22×C4×C101—22no—
56C22×C4×C101—22no—
57C22×C4×C101—22no—
58C22×C4×C101—21no—
59C22×C4×C101—21no—
60C22×C4×C101—21no—
61C22×C4×C101—21no—
62C22×C4×C101—21no—
63C22×C4×C101—21no—
64C22×C4×C101—41no—
65C22×C4×C101—41no—
66C22×C4×C101—41no—
67C22×C4×C101—41no—
68C22×C4×C101C22⋊C411yescharacteristic
69C22×C4×C101C22⋊C411yescharacteristic
70C22×C4×C101C22⋊C411yescharacteristic
71C22×C4×C101C22×C411yescharacteristic
72C22×C4×C101C2×D411yescharacteristic
73C22×C4×C101C2×D411yescharacteristic
74C2×C8×C101—42no—
75C2×C8×C101—42no—
76C2×C8×C101—42no—
77C2×C8×C101—42no—
78C2×C8×C101—42no—
79C2×C8×C101—42no—
80C4⋊C4×C101—22no—
81C4⋊C4×C101—22no—
82C4⋊C4×C101—41no—
83C4⋊C4×C101—41no—
84C4⋊C4×C101—42no—
85C4⋊C4×C101—42no—
86C4⋊C4×C101—42no—
87C4⋊C4×C101—41no—
88C4⋊C4×C101—41no—
89C22⋊C4×C101—42no—
90C22⋊C4×C101—42no—
91C42×C101—22no—
92C42×C101—22no—
93C42×C101—41no—
94C42×C101—41no—
95C23×C101—21no—
96C23×C101—21no—
97C23×C101—21no—
98C23×C101—21no—
99C23×C101—21no—
100C23×C101—21no—
101C23×C101#10112yes—
102C23×C101C2×C22⋊C411yescharacteristic
103C2×C4×C101—21no—
104C2×C4×C101—21no—
105C2×C4×C101—21no—
106C2×C4×C101—21no—
107C2×C4×C101—21no—
108C2×C4×C101—21no—
109C2×C4×C101—21no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—21no—
114C2×C4×C101—21no—
115C2×C4×C101—21no—
116C2×C4×C101—21no—
117C2×C4×C101—44no—
118C2×C4×C101—44no—
119C2×C4×C101—42no—
120C2×C4×C101—42no—
121C2×C4×C101—41no—
122C2×C4×C101—41no—
123C2×C4×C101—41no—
124C2×C4×C101—41no—
125C2×C4×C101—41no—
126C2×C4×C101—41no—
127C2×C4×C101—41no—
128C2×C4×C101—41no—
129C2×C4×C101—41no—
130C2×C4×C101—41no—
131C2×C4×C101—41no—
132C2×C4×C101—41no—
133C2×C4×C101#9912yes—
134C2×C4×C101#13112yes—
135C2×C4×C101#13512yes—
136C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C101#13711yescharacteristic
138C8×C101—82no—
139C8×C101—82no—
140C22×C101—22no—
141C22×C101—22no—
142C22×C101—22no—
143C22×C101—41no—
144C22×C101—41no—
145C22×C101—41no—
146C22×C101—41no—
147C22×C101#40811yescharacteristic
148C22×C101C2×#9911yescharacteristic
149C22×C101C2×#10111yescharacteristic
150C22×C101#41611yescharacteristic
151C22×C101#41711yescharacteristic
152C22×C101#42111yescharacteristic
153C22×C101#42111yescharacteristic
154C4×C101—22no—
155C4×C101—21no—
156C4×C101—21no—
157C4×C101—22no—
158C4×C101—22no—
159C4×C101—41no—
160C4×C101—41no—
161C4×C101—81no—
162C4×C101—81no—
163C4×C101—81no—
164C4×C101—81no—
165#7731C10111yesmaximal, characteristic, direct product factor, Sylow
166C2×C101—42no—
167C2×C101#147211yescharacteristic
168C2×C101#148211yescharacteristic
169C2×C101#149511yescharacteristic
170C2×C101#151311yescharacteristic
171C2×C101#151611yescharacteristic
172C2×C101#153411yescharacteristic
173C2×C101#155211yescharacteristic
174#2851C2×C10111yescharacteristic
175#1817C2×C10111yescharacteristic
176#1797C2×C10111yescharacteristic
177#1271C2×C10112yescomplemented
178#1271C2×C10112yescomplemented
179C101#773111yescharacteristic, direct product factor, Sylow
180C2×#125C4×C10111yescharacteristic
181C22×C42C22×C10111yescharacteristic
182C2×C4⋊C8—21no—
183C2×C22⋊C8—21no—
184C2×C22⋊C8—21no—
185#389C22×C10111yescharacteristic
186#389C22×C10111yescharacteristic
187#387—21no—
188#387—21no—
189#385—21no—
190#385—21no—
191#382C4×C10111yescharacteristic
192#380C4×C10111yescharacteristic
193#380C4×C10111yescharacteristic
194#336—21no—
195#336C22×C10112yes—
196#336C22×C10112yes—
197C23×C4C2×C4×C10111yescharacteristic
198C23×C4D4×C10111yescharacteristic
199C23×C4D4×C10111yescharacteristic
200C22×C8—22no—
201C22×C8—22no—
202#125—42no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×C4×C10111yescharacteristic
208C2×C4⋊C4C2×C4×C10111yescharacteristic
209C2×C4⋊C4C2×C4×C10111yescharacteristic
210C2×C4⋊C4C2×C4×C10111yescharacteristic
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C42—42no—
214C2×C42C2×C4×C10111yescharacteristic
215C2×C42D4×C10111yescharacteristic
216C2×C42D4×C10111yescharacteristic
217C2×C42C23×C10111yescharacteristic
218C4⋊C8—42no—
219C22⋊C8—42no—
220C22⋊C8—42no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227C24C22⋊C4×C10111yescharacteristic
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C22⋊C4×C10111yescharacteristic
243C22×C4C22⋊C4×C10111yescharacteristic
244C22×C4C22⋊C4×C10111yescharacteristic
245C22×C4C22×C4×C10111yescharacteristic
246C22×C4C2×D4×C10111yescharacteristic
247C22×C4C2×D4×C10111yescharacteristic
248C2×C8—42no—
249C2×C8—42no—
250C2×C8—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C42—22no—
266C42—22no—
267C42—41no—
268C42—41no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23#101×C10112yes—
276C23C2×C22⋊C4×C10111yescharacteristic
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#99×C10112yes—
308C2×C4#131×C10112yes—
309C2×C4#135×C10112yes—
310C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
311C2×C4#137×C10111yescharacteristic
312C8—82no—
313C8—82no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22#408×C10111yescharacteristic
322C22C2×#99×C10111yescharacteristic
323C22C2×#101×C10111yescharacteristic
324C22#416×C10111yescharacteristic
325C22#417×C10111yescharacteristic
326C22#421×C10111yescharacteristic
327C22#421×C10111yescharacteristic
328C4—22no—
329C4—21no—
330C4—21no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—81no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—42no—
340C2C101×#147211yescharacteristic
341C2C101×#148211yescharacteristic
342C2C101×#149511yescharacteristic
343C2C101×#151311yescharacteristic
344C2C101×#151611yescharacteristic
345C2C101×#153411yescharacteristic
346C2C101×#155211yescharacteristic
subgroupG/H
center, socleC23×C101C2×C22⋊C4
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC24×C101C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C22×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
4. C101×#1271C2semidirect
5. C101×#1271C2semidirect
165. #7731C101direct (N × H)
177. #1271C2×C101semidirect
178. #1271C2×C101semidirect
179. C101#7731direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#28512
C101×#18172
C101×#17972
C101×#12712
#7731101