Finite Group Databasebeta

← C101×#7732 #38789883

Subgroups — C101×#7732 #38789883

Order 25856.

420 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×#2860C211yesmaximal, characteristic
2C101×#1831C211yesmaximal, characteristic, complemented
3C101×#1831C211yesmaximal, characteristic, complemented
4C101×#1271C212yesmaximal, complemented
5C101×#1270C212yesmaximal
6C2×#126×C101—21no—
7C2×C4⋊C8×C101—21no—
8C2×C4⋊C8×C101—21no—
9#390×C101C411yescharacteristic
10#390×C101C411yescharacteristic
11#390×C101C2211yescharacteristic
12#389×C101C411yescharacteristic
13#389×C101C411yescharacteristic
14#389×C101C2211yescharacteristic
15#388×C101—21no—
16#388×C101—21no—
17#388×C101—21no—
18C43×C101C2211yescharacteristic
19#336×C101—21no—
20#336×C101—21no—
21#336×C101C2212yes—
22#336×C101C2212yes—
23C22×D4×C101C2×C411yescharacteristic
24C22×C8×C101—22no—
25C22×C8×C101—22no—
26#126×C101—42no—
27#126×C101—42no—
28C2×C4⋊C4×C101—21no—
29C2×C4⋊C4×C101—21no—
30C2×C4⋊C4×C101—21no—
31C2×C4⋊C4×C101C2×C411yescharacteristic
32C2×C4⋊C4×C101C2×C411yescharacteristic
33C2×C4⋊C4×C101C2×C411yescharacteristic
34C2×C22⋊C4×C101—21no—
35C2×C22⋊C4×C101—21no—
36C2×C22⋊C4×C101—21no—
37C2×C22⋊C4×C101—21no—
38C2×C22⋊C4×C101—21no—
39C2×C22⋊C4×C101—21no—
40C2×C42×C101C2×C411yescharacteristic
41C2×C42×C101C2×C411yescharacteristic
42C2×C42×C101D411yescharacteristic
43C2×C42×C101D411yescharacteristic
44C2×C42×C101D411yescharacteristic
45C2×C42×C101D411yescharacteristic
46C2×C42×C101C2311yescharacteristic
47C4⋊C8×C101—42no—
48C4⋊C8×C101—42no—
49#95×C101—21no—
50#95×C101—21no—
51#95×C101—21no—
52C24×C101—21no—
53C2×D4×C101—22no—
54C2×D4×C101—41no—
55C2×D4×C101—41no—
56C22×C4×C101—21no—
57C22×C4×C101—21no—
58C22×C4×C101—21no—
59C22×C4×C101C22⋊C411yescharacteristic
60C22×C4×C101C22⋊C411yescharacteristic
61C22×C4×C101C22⋊C411yescharacteristic
62C22×C4×C101C22⋊C411yescharacteristic
63C22×C4×C101C22×C411yescharacteristic
64C22×C4×C101C2×D411yescharacteristic
65C22×C4×C101C2×D411yescharacteristic
66C2×C8×C101—42no—
67C2×C8×C101—42no—
68C2×C8×C101—42no—
69C2×C8×C101—42no—
70C2×C8×C101—42no—
71C2×C8×C101—42no—
72C4⋊C4×C101—22no—
73C4⋊C4×C101—41no—
74C4⋊C4×C101—41no—
75C4⋊C4×C101—42no—
76C4⋊C4×C101—42no—
77C4⋊C4×C101—41no—
78C4⋊C4×C101—41no—
79C22⋊C4×C101—42no—
80C22⋊C4×C101—42no—
81C22⋊C4×C101—42no—
82C22⋊C4×C101—42no—
83C22⋊C4×C101—41no—
84C22⋊C4×C101—41no—
85C22⋊C4×C101—41no—
86C22⋊C4×C101—41no—
87C42×C101—22no—
88C42×C101—21no—
89C42×C101—21no—
90C42×C101—41no—
91C42×C101—41no—
92C42×C101—41no—
93C42×C101—41no—
94C42×C101D812yes—
95C42×C101SD1612yes—
96C23×C101—41no—
97C23×C101—41no—
98C23×C101—41no—
99C23×C101—41no—
100C23×C101—41no—
101C23×C101—41no—
102C23×C101—41no—
103C23×C101C2×C22⋊C411yescharacteristic
104D4×C101—82no—
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—21no—
118C2×C4×C101—21no—
119C2×C4×C101—21no—
120C2×C4×C101—21no—
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#10212yes—
131C2×C4×C101#10212yes—
132C2×C4×C101#13112yes—
133C2×C4×C101C2×D811yescharacteristic
134C2×C4×C101C2×SD1611yescharacteristic
135C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C101#13711yescharacteristic
137C8×C101—82no—
138C8×C101—82no—
139C22×C101—81no—
140C22×C101—81no—
141C22×C101—81no—
142C22×C101—81no—
143C22×C101—81no—
144C22×C101—81no—
145C22×C101—81no—
146C22×C101#40811yescharacteristic
147C22×C101#41011yescharacteristic
148C22×C101#41311yescharacteristic
149C22×C101C2×#10211yescharacteristic
150C22×C101#41711yescharacteristic
151C22×C101#42111yescharacteristic
152C22×C101#42111yescharacteristic
153C4×C101—22no—
154C4×C101—22no—
155C4×C101—22no—
156C4×C101—21no—
157C4×C101—21no—
158C4×C101—21no—
159C4×C101—21no—
160C4×C101—41no—
161C4×C101—41no—
162C4×C101—81no—
163C4×C101—81no—
164C4×C101—81no—
165#7732C10111yesmaximal, characteristic, direct product factor, Sylow
166C2×C101—161no—
167C2×C101#147311yescharacteristic
168C2×C101#148011yescharacteristic
169C2×C101#149511yescharacteristic
170C2×C101#151211yescharacteristic
171C2×C101#151711yescharacteristic
172C2×C101#153511yescharacteristic
173C2×C101#154711yescharacteristic
174#2860C2×C10111yescharacteristic
175#1831C2×C10111yescharacteristic, complemented
176#1831C2×C10111yescharacteristic, complemented
177#1271C2×C10112yescomplemented
178#1270C2×C10112yes—
179C101#773211yescharacteristic, direct product factor, Sylow
180C2×#126—21no—
181C2×C4⋊C8—21no—
182C2×C4⋊C8—21no—
183#390C4×C10111yescharacteristic
184#390C4×C10111yescharacteristic
185#390C22×C10111yescharacteristic
186#389C4×C10111yescharacteristic
187#389C4×C10111yescharacteristic
188#389C22×C10111yescharacteristic
189#388—21no—
190#388—21no—
191#388—21no—
192C43C22×C10111yescharacteristic
193#336—21no—
194#336—21no—
195#336C22×C10112yes—
196#336C22×C10112yes—
197C22×D4C2×C4×C10111yescharacteristic
198C22×C8—22no—
199C22×C8—22no—
200#126—42no—
201#126—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×C4×C10111yescharacteristic
206C2×C4⋊C4C2×C4×C10111yescharacteristic
207C2×C4⋊C4C2×C4×C10111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42C2×C4×C10111yescharacteristic
215C2×C42C2×C4×C10111yescharacteristic
216C2×C42D4×C10111yescharacteristic
217C2×C42D4×C10111yescharacteristic
218C2×C42D4×C10111yescharacteristic
219C2×C42D4×C10111yescharacteristic
220C2×C42C23×C10111yescharacteristic
221C4⋊C8—42no—
222C4⋊C8—42no—
223#95—21no—
224#95—21no—
225#95—21no—
226C24—21no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4C22⋊C4×C10111yescharacteristic
234C22×C4C22⋊C4×C10111yescharacteristic
235C22×C4C22⋊C4×C10111yescharacteristic
236C22×C4C22⋊C4×C10111yescharacteristic
237C22×C4C22×C4×C10111yescharacteristic
238C22×C4C2×D4×C10111yescharacteristic
239C22×C4C2×D4×C10111yescharacteristic
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C4⋊C4—22no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C42—22no—
262C42—21no—
263C42—21no—
264C42—41no—
265C42—41no—
266C42—41no—
267C42—41no—
268C42D8×C10112yes—
269C42SD16×C10112yes—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23C2×C22⋊C4×C10111yescharacteristic
278D4—82no—
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—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
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#102×C10112yes—
305C2×C4#102×C10112yes—
306C2×C4#131×C10112yes—
307C2×C4C2×D8×C10111yescharacteristic
308C2×C4C2×SD16×C10111yescharacteristic
309C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
310C2×C4#137×C10111yescharacteristic
311C8—82no—
312C8—82no—
313C22—81no—
314C22—81no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22#408×C10111yescharacteristic
321C22#410×C10111yescharacteristic
322C22#413×C10111yescharacteristic
323C22C2×#102×C10111yescharacteristic
324C22#417×C10111yescharacteristic
325C22#421×C10111yescharacteristic
326C22#421×C10111yescharacteristic
327C4—22no—
328C4—22no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C2—161no—
340C2C101×#147311yescharacteristic
341C2C101×#148011yescharacteristic
342C2C101×#149511yescharacteristic
343C2C101×#151211yescharacteristic
344C2C101×#151711yescharacteristic
345C2C101×#153511yescharacteristic
346C2C101×#154711yescharacteristic
subgroupG/H
center, socleC23×C101C2×C22⋊C4
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC22×D4×C101C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C43×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#1831C2semidirect
3. C101×#1831C2semidirect
4. C101×#1271C2semidirect
165. #7732C101direct (N × H)
175. #1831C2×C101semidirect
176. #1831C2×C101semidirect
177. #1271C2×C101semidirect
179. C101#7732direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#28602
C101×#18312
C101×#12712
C101×#12702
#7732101