Finite Group Databasebeta

← C101×#7576 #38789727

Subgroups — C101×#7576 #38789727

Order 25856.

604 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C101C211yesmaximal, characteristic
2C101×#1797C211yesmaximal, characteristic
3C4×C22⋊C8×C101C211yesmaximal, characteristic
4C101×#1271C214yesmaximal, complemented
5C22×C4⋊C4×C101—21no—
6C22×C4⋊C4×C101C411yescharacteristic
7C22×C4⋊C4×C101C411yescharacteristic
8C22×C42×C101C2211yescharacteristic
9C2×C4⋊C8×C101—21no—
10C2×C22⋊C8×C101—21no—
11C2×C22⋊C8×C101—21no—
12C2×C4×C8×C101—21no—
13#389×C101—21no—
14#389×C101—21no—
15#389×C101C412yes—
16#389×C101C2212yes—
17C2×#95×C101—21no—
18#336×C101C2212yes—
19#336×C101C2212yes—
20C23×C4×C101—21no—
21C23×C4×C101—21no—
22C23×C4×C101C2×C411yescharacteristic
23C23×C4×C101D411yescharacteristic
24C23×C4×C101D411yescharacteristic
25C22×C8×C101—22no—
26C22×C8×C101—22no—
27C2×C4⋊C4×C101—21no—
28C2×C4⋊C4×C101—22no—
29C2×C4⋊C4×C101—22no—
30C2×C4⋊C4×C101—21no—
31C2×C4⋊C4×C101—22no—
32C2×C4⋊C4×C101—44no—
33C2×C4⋊C4×C101—42no—
34C2×C4⋊C4×C101C814yescomplemented
35C2×C4⋊C4×C101C2×C412yes—
36C2×C4⋊C4×C101C2×C412yes—
37C2×C42×C101—42no—
38C2×C42×C101C2×C411yescharacteristic
39C2×C42×C101D411yescharacteristic
40C2×C42×C101D411yescharacteristic
41C2×C42×C101C2311yescharacteristic
42C4⋊C8×C101—42no—
43C22⋊C8×C101—24no—
44C22⋊C8×C101—42no—
45C4×C8×C101—42no—
46#95×C101—22no—
47#95×C101—22no—
48C24×C101C22⋊C411yescharacteristic
49C22×C4×C101—22no—
50C22×C4×C101—22no—
51C22×C4×C101—24no—
52C22×C4×C101—22no—
53C22×C4×C101—22no—
54C22×C4×C101—22no—
55C22×C4×C101—22no—
56C22×C4×C101—41no—
57C22×C4×C101—41no—
58C22×C4×C101—41no—
59C22×C4×C101—42no—
60C22×C4×C101—42no—
61C22×C4×C101—42no—
62C22×C4×C101—42no—
63C22×C4×C101—42no—
64C22×C4×C101C22⋊C411yescharacteristic
65C22×C4×C101C22⋊C411yescharacteristic
66C22×C4×C101C22⋊C411yescharacteristic
67C22×C4×C101C2×C812yes—
68C22×C4×C101M1612yes—
69C22×C4×C101SD1612yes—
70C22×C4×C101Q1612yes—
71C22×C4×C101C22×C411yescharacteristic
72C22×C4×C101C2×D411yescharacteristic
73C22×C4×C101C2×D411yescharacteristic
74C2×C8×C101—24no—
75C2×C8×C101—42no—
76C2×C8×C101—42no—
77C2×C8×C101—42no—
78C2×C8×C101—42no—
79C2×C8×C101—42no—
80C4⋊C4×C101—24no—
81C4⋊C4×C101—22no—
82C4⋊C4×C101—42no—
83C4⋊C4×C101—44no—
84C4⋊C4×C101—42no—
85C4⋊C4×C101—44no—
86C4⋊C4×C101C2×C814yes—
87C42×C101—22no—
88C42×C101—22no—
89C42×C101—41no—
90C42×C101—41no—
91C23×C101—21no—
92C23×C101—21no—
93C23×C101—21no—
94C23×C101—21no—
95C23×C101C22⋊C812yes—
96C23×C101#10312yes—
97C23×C101#10412yes—
98C23×C101C2×C22⋊C411yescharacteristic
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—24no—
108C2×C4×C101—24no—
109C2×C4×C101—24no—
110C2×C4×C101—21no—
111C2×C4×C101—21no—
112C2×C4×C101—21no—
113C2×C4×C101—42no—
114C2×C4×C101—42no—
115C2×C4×C101—44no—
116C2×C4×C101—48no—
117C2×C4×C101—42no—
118C2×C4×C101—42no—
119C2×C4×C101—42no—
120C2×C4×C101—42no—
121C2×C4×C101—42no—
122C2×C4×C101—84no—
123C2×C4×C101C22⋊C812yes—
124C2×C4×C101#9912yes—
125C2×C4×C101#10112yes—
126C2×C4×C101#10312yes—
127C2×C4×C101C22×C811yescharacteristic
128C2×C4×C101C2×M1611yescharacteristic
129C2×C4×C101C2×SD1611yescharacteristic
130C2×C4×C101C2×Q1611yescharacteristic
131C2×C4×C101AGL(1,ℤ/8)12yes—
132C8×C101—44no—
133C8×C101—82no—
134C22×C101—22no—
135C22×C101—22no—
136C22×C101—22no—
137C22×C101—22no—
138C22×C101—22no—
139C22×C101—22no—
140C22×C101Q8⋊C814yes—
141C22×C101C2×C22⋊C811yescharacteristic
142C22×C101C2×#9911yescharacteristic
143C22×C101C2×#10111yescharacteristic
144C22×C101C2×#10311yescharacteristic
145C22×C101#41811yescharacteristic
146C22×C101C2×#10411yescharacteristic
147C22×C101#42111yescharacteristic
148C4×C101—21no—
149C4×C101—21no—
150C4×C101—22no—
151C4×C101—21no—
152C4×C101—22no—
153C4×C101—21no—
154C4×C101—44no—
155C4×C101—41no—
156C4×C101—82no—
157C4×C101#32414yes—
158#7576C10111yesmaximal, characteristic, direct product factor, Sylow
159C2×C101—24no—
160C2×C101C2×#32411yescharacteristic
161C2×C101C2×Q8⋊C811yescharacteristic
162C2×C101#147811yescharacteristic
163C2×C101#150711yescharacteristic
164C2×C101#152011yescharacteristic
165C2×C101#152811yescharacteristic
166C2×C101#154911yescharacteristic
167C2×#389C2×C10111yescharacteristic
168#1797C2×C10111yescharacteristic
169C4×C22⋊C8C2×C10111yescharacteristic
170#1271C2×C10114yescomplemented
171C101#757611yescharacteristic, direct product factor, Sylow
172C22×C4⋊C4—21no—
173C22×C4⋊C4C4×C10111yescharacteristic
174C22×C4⋊C4C4×C10111yescharacteristic
175C22×C42C22×C10111yescharacteristic
176C2×C4⋊C8—21no—
177C2×C22⋊C8—21no—
178C2×C22⋊C8—21no—
179C2×C4×C8—21no—
180#389—21no—
181#389—21no—
182#389C4×C10112yes—
183#389C22×C10112yes—
184C2×#95—21no—
185#336C22×C10112yes—
186#336C22×C10112yes—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4C2×C4×C10111yescharacteristic
190C23×C4D4×C10111yescharacteristic
191C23×C4D4×C10111yescharacteristic
192C22×C8—22no—
193C22×C8—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—44no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4C8×C10114yescomplemented
202C2×C4⋊C4C2×C4×C10112yes—
203C2×C4⋊C4C2×C4×C10112yes—
204C2×C42—42no—
205C2×C42C2×C4×C10111yescharacteristic
206C2×C42D4×C10111yescharacteristic
207C2×C42D4×C10111yescharacteristic
208C2×C42C23×C10111yescharacteristic
209C4⋊C8—42no—
210C22⋊C8—24no—
211C22⋊C8—42no—
212C4×C8—42no—
213#95—22no—
214#95—22no—
215C24C22⋊C4×C10111yescharacteristic
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—24no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—42no—
227C22×C4—42no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4C22⋊C4×C10111yescharacteristic
232C22×C4C22⋊C4×C10111yescharacteristic
233C22×C4C22⋊C4×C10111yescharacteristic
234C22×C4C2×C8×C10112yes—
235C22×C4M16×C10112yes—
236C22×C4SD16×C10112yes—
237C22×C4Q16×C10112yes—
238C22×C4C22×C4×C10111yescharacteristic
239C22×C4C2×D4×C10111yescharacteristic
240C22×C4C2×D4×C10111yescharacteristic
241C2×C8—24no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C4⋊C4—24no—
248C4⋊C4—22no—
249C4⋊C4—42no—
250C4⋊C4—44no—
251C4⋊C4—42no—
252C4⋊C4—44no—
253C4⋊C4C2×C8×C10114yes—
254C42—22no—
255C42—22no—
256C42—41no—
257C42—41no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23C22⋊C8×C10112yes—
263C23#103×C10112yes—
264C23#104×C10112yes—
265C23C2×C22⋊C4×C10111yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—44no—
283C2×C4—48no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—84no—
290C2×C4C22⋊C8×C10112yes—
291C2×C4#99×C10112yes—
292C2×C4#101×C10112yes—
293C2×C4#103×C10112yes—
294C2×C4C22×C8×C10111yescharacteristic
295C2×C4C2×M16×C10111yescharacteristic
296C2×C4C2×SD16×C10111yescharacteristic
297C2×C4C2×Q16×C10111yescharacteristic
298C2×C4AGL(1,ℤ/8)×C10112yes—
299C8—44no—
300C8—82no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22Q8⋊C8×C10114yes—
308C22C2×C22⋊C8×C10111yescharacteristic
309C22C2×#99×C10111yescharacteristic
310C22C2×#101×C10111yescharacteristic
311C22C2×#103×C10111yescharacteristic
312C22#418×C10111yescharacteristic
313C22C2×#104×C10111yescharacteristic
314C22#421×C10111yescharacteristic
315C4—21no—
316C4—21no—
317C4—22no—
318C4—21no—
319C4—22no—
320C4—21no—
321C4—44no—
322C4—41no—
323C4—82no—
324C4#324×C10114yes—
325C2—24no—
326C2C2×#324×C10111yescharacteristic
327C2C2×Q8⋊C8×C10111yescharacteristic
328C2C101×#147811yescharacteristic
329C2C101×#150711yescharacteristic
330C2C101×#152011yescharacteristic
331C2C101×#152811yescharacteristic
332C2C101×#154911yescharacteristic
subgroupG/H
center, socleC23×C101C2×C22⋊C4
commutatorC2×C4C22×C8×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC24×C101C22⋊C4
LCSG ▷ C2×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
34. C2×C4⋊C4×C101C8semidirect
158. #7576C101direct (N × H)
170. #1271C2×C101semidirect
171. C101#7576direct (N × H)
201. C2×C4⋊C4C8×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C1012
C101×#17972
C4×C22⋊C8×C1012
C101×#12712
#7576101