Finite Group Databasebeta

← C101×#7577 #38789728

Subgroups — C101×#7577 #38789728

Order 25856.

444 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2295C211yesmaximal, characteristic
2C101×#1831C211yesmaximal, characteristic
3C4×C4⋊C8×C101C211yesmaximal, characteristic
4C101×#1272C212yesmaximal
5C101×#1271C212yesmaximal
6C2×C4×Q8×C101C411yescharacteristic
7C2×C4⋊C8×C101—21no—
8C2×C4⋊C8×C101—21no—
9C2×C4×C8×C101—21no—
10#391×C101C411yescharacteristic
11#391×C101C2211yescharacteristic
12#389×C101C411yescharacteristic
13#389×C101C2211yescharacteristic
14#387×C101—21no—
15#387×C101—21no—
16C4×C4⋊C4×C101—21no—
17C4×C4⋊C4×C101C411yescharacteristic
18#376×C101—21no—
19C43×C101C2211yescharacteristic
20#336×C101—21no—
21#336×C101C2212yes—
22#336×C101C2212yes—
23C22×Q8×C101C2×C411yescharacteristic
24C22×C8×C101—22no—
25C22×C8×C101—22no—
26C4×Q8×C101—22no—
27C4×Q8×C101C814yescomplemented
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×C42×C101—21no—
35C2×C42×C101—21no—
36C2×C42×C101C2×C411yescharacteristic
37C2×C42×C101C2×C411yescharacteristic
38C2×C42×C101D411yescharacteristic
39C2×C42×C101D411yescharacteristic
40C2×C42×C101D411yescharacteristic
41C2×C42×C101D411yescharacteristic
42C2×C42×C101C2311yescharacteristic
43C4⋊C8×C101—24no—
44C4⋊C8×C101—42no—
45C4×C8×C101—42no—
46#95×C101—21no—
47#95×C101—21no—
48#95×C101—21no—
49#95×C101—21no—
50#95×C101—21no—
51#95×C101—21no—
52#95×C101—21no—
53C2×Q8×C101—21no—
54C2×Q8×C101—41no—
55C2×Q8×C101—41no—
56C2×Q8×C101C2×C812yes—
57C22×C4×C101—21no—
58C22×C4×C101—21no—
59C22×C4×C101—21no—
60C22×C4×C101—21no—
61C22×C4×C101C22⋊C411yescharacteristic
62C22×C4×C101C22⋊C411yescharacteristic
63C22×C4×C101C22⋊C411yescharacteristic
64C22×C4×C101C22⋊C411yescharacteristic
65C22×C4×C101C22×C411yescharacteristic
66C22×C4×C101C2×D411yescharacteristic
67C22×C4×C101C2×D411yescharacteristic
68C2×C8×C101—24no—
69C2×C8×C101—42no—
70C2×C8×C101—42no—
71C2×C8×C101—42no—
72C2×C8×C101—42no—
73C2×C8×C101—42no—
74C4⋊C4×C101—24no—
75C4⋊C4×C101—21no—
76C4⋊C4×C101—41no—
77C4⋊C4×C101—41no—
78C4⋊C4×C101—42no—
79C4⋊C4×C101—41no—
80C4⋊C4×C101—41no—
81C4⋊C4×C101C2×C812yes—
82C42×C101—24no—
83C42×C101—22no—
84C42×C101—21no—
85C42×C101—21no—
86C42×C101—41no—
87C42×C101—41no—
88C42×C101—41no—
89C42×C101—42no—
90C42×C101C2×C812yes—
91C42×C101M1612yes—
92C42×C101SD1612yes—
93C42×C101Q1612yes—
94C23×C101C2×C22⋊C411yescharacteristic
95Q8×C101—42no—
96Q8×C101—42no—
97C2×C4×C101—21no—
98C2×C4×C101—21no—
99C2×C4×C101—21no—
100C2×C4×C101—21no—
101C2×C4×C101—21no—
102C2×C4×C101—21no—
103C2×C4×C101—21no—
104C2×C4×C101—21no—
105C2×C4×C101—21no—
106C2×C4×C101—21no—
107C2×C4×C101—22no—
108C2×C4×C101—22no—
109C2×C4×C101—21no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—41no—
113C2×C4×C101—41no—
114C2×C4×C101—41no—
115C2×C4×C101—41no—
116C2×C4×C101—41no—
117C2×C4×C101—41no—
118C2×C4×C101—41no—
119C2×C4×C101—41no—
120C2×C4×C101—41no—
121C2×C4×C101—41no—
122C2×C4×C101C22⋊C812yes—
123C2×C4×C101C22⋊C812yes—
124C2×C4×C101#10312yes—
125C2×C4×C101#10312yes—
126C2×C4×C101#10412yes—
127C2×C4×C101C22×C811yescharacteristic
128C2×C4×C101C2×M1611yescharacteristic
129C2×C4×C101C2×SD1611yescharacteristic
130C2×C4×C101C2×Q1611yescharacteristic
131C2×C4×C101AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C101#13711yescharacteristic
133C8×C101—44no—
134C8×C101—82no—
135C22×C101C2×C22⋊C811yescharacteristic
136C22×C101#41011yescharacteristic
137C22×C101#41311yescharacteristic
138C22×C101C2×#10311yescharacteristic
139C22×C101#41711yescharacteristic
140C22×C101C2×#10411yescharacteristic
141C22×C101#42111yescharacteristic
142C4×C101—22no—
143C4×C101—21no—
144C4×C101—21no—
145C4×C101—22no—
146C4×C101—21no—
147C4×C101—21no—
148C4×C101—21no—
149C4×C101—21no—
150C4×C101—42no—
151C4×C101—42no—
152C4×C101—41no—
153C4×C101—81no—
154C4×C101—81no—
155C4×C101Q8⋊C814yes—
156#7577C10111yesmaximal, characteristic, direct product factor, Sylow
157C2×C101#145811yescharacteristic
158C2×C101C2×Q8⋊C811yescharacteristic
159C2×C101#147711yescharacteristic
160C2×C101#150911yescharacteristic
161C2×C101#151811yescharacteristic
162C2×C101#152911yescharacteristic
163C2×C101#155011yescharacteristic
164#2295C2×C10111yescharacteristic
165#1831C2×C10111yescharacteristic
166C4×C4⋊C8C2×C10111yescharacteristic
167#1272C2×C10112yes—
168#1271C2×C10112yes—
169C101#757711yescharacteristic, direct product factor, Sylow
170C2×C4×Q8C4×C10111yescharacteristic
171C2×C4⋊C8—21no—
172C2×C4⋊C8—21no—
173C2×C4×C8—21no—
174#391C4×C10111yescharacteristic
175#391C22×C10111yescharacteristic
176#389C4×C10111yescharacteristic
177#389C22×C10111yescharacteristic
178#387—21no—
179#387—21no—
180C4×C4⋊C4—21no—
181C4×C4⋊C4C4×C10111yescharacteristic
182#376—21no—
183C43C22×C10111yescharacteristic
184#336—21no—
185#336C22×C10112yes—
186#336C22×C10112yes—
187C22×Q8C2×C4×C10111yescharacteristic
188C22×C8—22no—
189C22×C8—22no—
190C4×Q8—22no—
191C4×Q8C8×C10114yescomplemented
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C2×C4×C10111yescharacteristic
196C2×C4⋊C4C2×C4×C10111yescharacteristic
197C2×C4⋊C4C2×C4×C10111yescharacteristic
198C2×C42—21no—
199C2×C42—21no—
200C2×C42C2×C4×C10111yescharacteristic
201C2×C42C2×C4×C10111yescharacteristic
202C2×C42D4×C10111yescharacteristic
203C2×C42D4×C10111yescharacteristic
204C2×C42D4×C10111yescharacteristic
205C2×C42D4×C10111yescharacteristic
206C2×C42C23×C10111yescharacteristic
207C4⋊C8—24no—
208C4⋊C8—42no—
209C4×C8—42no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217C2×Q8—21no—
218C2×Q8—41no—
219C2×Q8—41no—
220C2×Q8C2×C8×C10112yes—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4C22⋊C4×C10111yescharacteristic
226C22×C4C22⋊C4×C10111yescharacteristic
227C22×C4C22⋊C4×C10111yescharacteristic
228C22×C4C22⋊C4×C10111yescharacteristic
229C22×C4C22×C4×C10111yescharacteristic
230C22×C4C2×D4×C10111yescharacteristic
231C22×C4C2×D4×C10111yescharacteristic
232C2×C8—24no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C2×C8—42no—
237C2×C8—42no—
238C4⋊C4—24no—
239C4⋊C4—21no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4C2×C8×C10112yes—
246C42—24no—
247C42—22no—
248C42—21no—
249C42—21no—
250C42—41no—
251C42—41no—
252C42—41no—
253C42—42no—
254C42C2×C8×C10112yes—
255C42M16×C10112yes—
256C42SD16×C10112yes—
257C42Q16×C10112yes—
258C23C2×C22⋊C4×C10111yescharacteristic
259Q8—42no—
260Q8—42no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4C22⋊C8×C10112yes—
287C2×C4C22⋊C8×C10112yes—
288C2×C4#103×C10112yes—
289C2×C4#103×C10112yes—
290C2×C4#104×C10112yes—
291C2×C4C22×C8×C10111yescharacteristic
292C2×C4C2×M16×C10111yescharacteristic
293C2×C4C2×SD16×C10111yescharacteristic
294C2×C4C2×Q16×C10111yescharacteristic
295C2×C4AGL(1,ℤ/8)×C10111yescharacteristic
296C2×C4#137×C10111yescharacteristic
297C8—44no—
298C8—82no—
299C22C2×C22⋊C8×C10111yescharacteristic
300C22#410×C10111yescharacteristic
301C22#413×C10111yescharacteristic
302C22C2×#103×C10111yescharacteristic
303C22#417×C10111yescharacteristic
304C22C2×#104×C10111yescharacteristic
305C22#421×C10111yescharacteristic
306C4—21no—
307C4—21no—
308C4—22no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—22no—
314C4—42no—
315C4—42no—
316C4—41no—
317C4—81no—
318C4—81no—
319C4Q8⋊C8×C10114yes—
320C2C101×#145811yescharacteristic
321C2C2×Q8⋊C8×C10111yescharacteristic
322C2C101×#147711yescharacteristic
323C2C101×#150911yescharacteristic
324C2C101×#151811yescharacteristic
325C2C101×#152911yescharacteristic
326C2C101×#155011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C101C2×C22⋊C4
commutatorC2×C4C22×C8×C101
Frattini, cosocleC2×C42C23×C101
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C101 ◁ C43×C101 ◁ G

Complements

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

NH ≅ G/Ntype
27. C4×Q8×C101C8semidirect
156. #7577C101direct (N × H)
169. C101#7577direct (N × H)
191. C4×Q8C8×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#22952
C101×#18312
C4×C4⋊C8×C1012
C101×#12722
C101×#12712
#7577101