Finite Group Databasebeta

← C101×#7620 #38789771

Subgroups — C101×#7620 #38789771

Order 25856.

590 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#121×C101C211yesmaximal, characteristic
2C101×#1817C211yesmaximal, characteristic, complemented
3C101×#1749C211yesmaximal, characteristic, complemented
4C101×#1271C212yesmaximal, complemented
5C101×#1270C212yesmaximal, complemented
6C2×#121×C101C411yescharacteristic
7C2×C4×D4×C101—21no—
8C2×C4×D4×C101C411yescharacteristic
9C22×C42×C101C2211yescharacteristic
10C2×C22⋊C8×C101—21no—
11C2×C22⋊C8×C101—21no—
12C2×#97×C101—21no—
13#390×C101C2211yescharacteristic
14#389×C101C2211yescharacteristic
15#388×C101—21no—
16#386×C101—21no—
17#380×C101C411yescharacteristic
18C4×C4⋊C4×C101C411yescharacteristic
19C4×C22⋊C4×C101—21no—
20#336×C101—21no—
21#336×C101C2212yes—
22#336×C101C2212yes—
23C22×D4×C101—21no—
24C22×D4×C101C2×C411yescharacteristic
25C23×C4×C101—21no—
26C23×C4×C101C2×C411yescharacteristic
27C23×C4×C101D411yescharacteristic
28C23×C4×C101D411yescharacteristic
29C22×C8×C101—22no—
30C22×C8×C101—22no—
31#121×C101—22no—
32#121×C101—22no—
33C4×D4×C101—42no—
34C4×D4×C101—44no—
35C2×C4⋊C4×C101—21no—
36C2×C4⋊C4×C101C2×C411yescharacteristic
37C2×C4⋊C4×C101C2×C411yescharacteristic
38C2×C4⋊C4×C101C2×C411yescharacteristic
39C2×C22⋊C4×C101—21no—
40C2×C22⋊C4×C101—21no—
41C2×C22⋊C4×C101—21no—
42C2×C22⋊C4×C101—21no—
43C2×C22⋊C4×C101—21no—
44C2×C42×C101—21no—
45C2×C42×C101—42no—
46C2×C42×C101C2×C411yescharacteristic
47C2×C42×C101D411yescharacteristic
48C2×C42×C101D411yescharacteristic
49C2×C42×C101C2311yescharacteristic
50C22⋊C8×C101—24no—
51C22⋊C8×C101—42no—
52#97×C101—42no—
53#95×C101—21no—
54#95×C101—21no—
55#95×C101—21no—
56C24×C101—21no—
57C24×C101C22⋊C411yescharacteristic
58C2×D4×C101—24no—
59C2×D4×C101—21no—
60C2×D4×C101—41no—
61C2×D4×C101—41no—
62C2×D4×C101—42no—
63C2×D4×C101—42no—
64C2×D4×C101M1612yes—
65C22×C4×C101—22no—
66C22×C4×C101—21no—
67C22×C4×C101—22no—
68C22×C4×C101—21no—
69C22×C4×C101—21no—
70C22×C4×C101—22no—
71C22×C4×C101—22no—
72C22×C4×C101—21no—
73C22×C4×C101—21no—
74C22×C4×C101—41no—
75C22×C4×C101—41no—
76C22×C4×C101—41no—
77C22×C4×C101—41no—
78C22×C4×C101—42no—
79C22×C4×C101—42no—
80C22×C4×C101—42no—
81C22×C4×C101C22⋊C411yescharacteristic
82C22×C4×C101C22⋊C411yescharacteristic
83C22×C4×C101C22⋊C411yescharacteristic
84C22×C4×C101C22×C411yescharacteristic
85C22×C4×C101C2×D411yescharacteristic
86C22×C4×C101C2×D411yescharacteristic
87C2×C8×C101—24no—
88C2×C8×C101—42no—
89C2×C8×C101—42no—
90C2×C8×C101—42no—
91C2×C8×C101—42no—
92C2×C8×C101—42no—
93C4⋊C4×C101—21no—
94C4⋊C4×C101—41no—
95C4⋊C4×C101—41no—
96C4⋊C4×C101—42no—
97C4⋊C4×C101M1612yes—
98C22⋊C4×C101—24no—
99C22⋊C4×C101—42no—
100C22⋊C4×C101—42no—
101C22⋊C4×C101—42no—
102C22⋊C4×C101—42no—
103C42×C101—22no—
104C42×C101—22no—
105C42×C101—41no—
106C42×C101—41no—
107C42×C101—42no—
108C23×C101—21no—
109C23×C101—21no—
110C23×C101—21no—
111C23×C101—21no—
112C23×C101—21no—
113C23×C101—21no—
114C23×C101—22no—
115C23×C101—41no—
116C23×C101—41no—
117C23×C101—41no—
118C23×C101—41no—
119C23×C101—41no—
120C23×C101—41no—
121C23×C101#10412yes—
122C23×C101C2×C22⋊C411yescharacteristic
123D4×C101—42no—
124D4×C101—42no—
125D4×C101—48no—
126C2×C4×C101—21no—
127C2×C4×C101—21no—
128C2×C4×C101—21no—
129C2×C4×C101—21no—
130C2×C4×C101—21no—
131C2×C4×C101—21no—
132C2×C4×C101—21no—
133C2×C4×C101—21no—
134C2×C4×C101—21no—
135C2×C4×C101—22no—
136C2×C4×C101—21no—
137C2×C4×C101—21no—
138C2×C4×C101—21no—
139C2×C4×C101—21no—
140C2×C4×C101—21no—
141C2×C4×C101—44no—
142C2×C4×C101—44no—
143C2×C4×C101—42no—
144C2×C4×C101—42no—
145C2×C4×C101—41no—
146C2×C4×C101—41no—
147C2×C4×C101—41no—
148C2×C4×C101—41no—
149C2×C4×C101—41no—
150C2×C4×C101—41no—
151C2×C4×C101—41no—
152C2×C4×C101—41no—
153C2×C4×C101—84no—
154C2×C4×C101#9912yes—
155C2×C4×C101C2×M1611yescharacteristic
156C2×C4×C101C2×M1611yescharacteristic
157C2×C4×C101#13512yes—
158C2×C4×C101AGL(1,ℤ/8)12yes—
159C8×C101—44no—
160C8×C101—82no—
161C22×C101—22no—
162C22×C101—22no—
163C22×C101—22no—
164C22×C101—41no—
165C22×C101—41no—
166C22×C101—41no—
167C22×C101—41no—
168C22×C101—42no—
169C22×C101—42no—
170C22×C101—42no—
171C22×C101—81no—
172C22×C101—81no—
173C22×C101—81no—
174C22×C101—81no—
175C22×C101#40711yescharacteristic
176C22×C101C2×#9911yescharacteristic
177C22×C101#41311yescharacteristic
178C22×C101#41611yescharacteristic
179C22×C101#41811yescharacteristic
180C22×C101C2×#10411yescharacteristic
181C22×C101#42111yescharacteristic
182C4×C101—21no—
183C4×C101—21no—
184C4×C101—22no—
185C4×C101—22no—
186C4×C101—22no—
187C4×C101—41no—
188C4×C101—42no—
189C4×C101—41no—
190C4×C101—81no—
191C4×C101—81no—
192#7620C10111yesmaximal, characteristic, direct product factor, Sylow
193C2×C101—42no—
194C2×C101—82no—
195C2×C101#146511yescharacteristic
196C2×C101#148811yescharacteristic
197C2×C101#149011yescharacteristic
198C2×C101#150111yescharacteristic
199C2×C101#151011yescharacteristic
200C2×C101#153211yescharacteristic
201C2×C101#155311yescharacteristic
202C4×#121C2×C10111yescharacteristic
203#1817C2×C10111yescharacteristic, complemented
204#1749C2×C10111yescharacteristic, complemented
205#1271C2×C10112yescomplemented
206#1270C2×C10112yescomplemented
207C101#762011yescharacteristic, direct product factor, Sylow
208C2×#121C4×C10111yescharacteristic
209C2×C4×D4—21no—
210C2×C4×D4C4×C10111yescharacteristic
211C22×C42C22×C10111yescharacteristic
212C2×C22⋊C8—21no—
213C2×C22⋊C8—21no—
214C2×#97—21no—
215#390C22×C10111yescharacteristic
216#389C22×C10111yescharacteristic
217#388—21no—
218#386—21no—
219#380C4×C10111yescharacteristic
220C4×C4⋊C4C4×C10111yescharacteristic
221C4×C22⋊C4—21no—
222#336—21no—
223#336C22×C10112yes—
224#336C22×C10112yes—
225C22×D4—21no—
226C22×D4C2×C4×C10111yescharacteristic
227C23×C4—21no—
228C23×C4C2×C4×C10111yescharacteristic
229C23×C4D4×C10111yescharacteristic
230C23×C4D4×C10111yescharacteristic
231C22×C8—22no—
232C22×C8—22no—
233#121—22no—
234#121—22no—
235C4×D4—42no—
236C4×D4—44no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4C2×C4×C10111yescharacteristic
239C2×C4⋊C4C2×C4×C10111yescharacteristic
240C2×C4⋊C4C2×C4×C10111yescharacteristic
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C42—21no—
247C2×C42—42no—
248C2×C42C2×C4×C10111yescharacteristic
249C2×C42D4×C10111yescharacteristic
250C2×C42D4×C10111yescharacteristic
251C2×C42C23×C10111yescharacteristic
252C22⋊C8—24no—
253C22⋊C8—42no—
254#97—42no—
255#95—21no—
256#95—21no—
257#95—21no—
258C24—21no—
259C24C22⋊C4×C10111yescharacteristic
260C2×D4—24no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4M16×C10112yes—
267C22×C4—22no—
268C22×C4—21no—
269C22×C4—22no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4C22⋊C4×C10111yescharacteristic
284C22×C4C22⋊C4×C10111yescharacteristic
285C22×C4C22⋊C4×C10111yescharacteristic
286C22×C4C22×C4×C10111yescharacteristic
287C22×C4C2×D4×C10111yescharacteristic
288C22×C4C2×D4×C10111yescharacteristic
289C2×C8—24no—
290C2×C8—42no—
291C2×C8—42no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8—42no—
295C4⋊C4—21no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—42no—
299C4⋊C4M16×C10112yes—
300C22⋊C4—24no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—42no—
305C42—22no—
306C42—22no—
307C42—41no—
308C42—41no—
309C42—42no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—22no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23#104×C10112yes—
324C23C2×C22⋊C4×C10111yescharacteristic
325D4—42no—
326D4—42no—
327D4—48no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—84no—
356C2×C4#99×C10112yes—
357C2×C4C2×M16×C10111yescharacteristic
358C2×C4C2×M16×C10111yescharacteristic
359C2×C4#135×C10112yes—
360C2×C4AGL(1,ℤ/8)×C10112yes—
361C8—44no—
362C8—82no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22#407×C10111yescharacteristic
378C22C2×#99×C10111yescharacteristic
379C22#413×C10111yescharacteristic
380C22#416×C10111yescharacteristic
381C22#418×C10111yescharacteristic
382C22C2×#104×C10111yescharacteristic
383C22#421×C10111yescharacteristic
384C4—21no—
385C4—21no—
386C4—22no—
387C4—22no—
388C4—22no—
389C4—41no—
390C4—42no—
391C4—41no—
392C4—81no—
393C4—81no—
394C2—42no—
395C2—82no—
396C2C101×#146511yescharacteristic
397C2C101×#148811yescharacteristic
398C2C101×#149011yescharacteristic
399C2C101×#150111yescharacteristic
400C2C101×#151011yescharacteristic
401C2C101×#153211yescharacteristic
402C2C101×#155311yescharacteristic
subgroupG/H
center, socleC23×C101C2×C22⋊C4
commutatorC22×C4C22×C4×C101
Frattini, cosocleC2×C42C23×C101
prime radicalC2×#121×C101C4
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
2. C101×#1817C2semidirect
3. C101×#1749C2semidirect
4. C101×#1271C2semidirect
5. C101×#1270C2semidirect
192. #7620C101direct (N × H)
203. #1817C2×C101semidirect
204. #1749C2×C101semidirect
205. #1271C2×C101semidirect
206. #1270C2×C101semidirect
207. C101#7620direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#121×C1012
C101×#18172
C101×#17492
C101×#12712
C101×#12702
#7620101