Finite Group Databasebeta

← C41×#11885 #23788086

Subgroups — C41×#11885 #23788086

Order 10496.

422 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3050C211yesmaximal, characteristic
2C2×C41×C22⋊C16C211yesmaximal, characteristic, complemented
3C41×#1807C211yesmaximal, characteristic, complemented
4C41×#1348C212yesmaximal, complemented
5C41×#1347C212yesmaximal, complemented
6C2×#135×C41C411yescharacteristic, complemented
7C23×C8×C41C2211yescharacteristic
8C41×#525—21no—
9C22×C16×C41—21no—
10C41×#467C411yescharacteristic, complemented
11C41×#467C2211yescharacteristic
12C41×#466C411yescharacteristic, complemented
13C41×#466C2211yescharacteristic
14C41×#465—21no—
15C41×#465—21no—
16C41×#427C411yescharacteristic, complemented
17C2×#106×C41—21no—
18C41×#416—21no—
19C41×#380—21no—
20C41×C22⋊C16—21no—
21C41×C22⋊C16C2212yes—
22C41×#340C2212yes—
23C2×#41×C41—21no—
24C23×C4×C41D411yescharacteristic
25#135×C41—42no—
26C2×Q16×C41C2×C411yescharacteristic
27C2×SD16×C41—21no—
28C2×D8×C41C2×C411yescharacteristic
29C22×C8×C41—42no—
30C22×C8×C41C2×C411yescharacteristic
31C22×C8×C41C2×C411yescharacteristic
32C22×C8×C41D411yescharacteristic
33C22×C8×C41D411yescharacteristic
34C22×C8×C41D411yescharacteristic
35C22×C8×C41C2311yescharacteristic
36#123×C41—41no—
37C22⋊Q8×C41—21no—
38C22⋊Q8×C41—21no—
39#121×C41—21no—
40#121×C41—21no—
41#120×C41—41no—
42C4×D4×C41—41no—
43C4×D4×C41—41no—
44#117×C41—21no—
45C2×C4⋊C4×C41—22no—
46C2×C22⋊C4×C41—41no—
47C2×C16×C41—22no—
48C2×C16×C41—42no—
49#107×C41C2×C411yescharacteristic
50#107×C41C2×C411yescharacteristic
51#106×C41—21no—
52#106×C41—42no—
53#103×C41—21no—
54#103×C41—21no—
55#102×C41—21no—
56#102×C41—21no—
57#95×C41—41no—
58C24×C41D811yescharacteristic
59#41×C41—42no—
60#41×C41—42no—
61C2×Q8×C41—21no—
62C2×D4×C41—21no—
63C2×D4×C41—41no—
64C2×D4×C41—41no—
65C2×D4×C41—41no—
66C22×C4×C41—41no—
67C22×C4×C41—41no—
68C22×C4×C41—41no—
69C22×C4×C41—42no—
70C22×C4×C41C22⋊C411yescharacteristic
71C22×C4×C41C22⋊C411yescharacteristic
72C22×C4×C41D811yescharacteristic
73C22×C4×C41SD1611yescharacteristic
74C22×C4×C41SD1611yescharacteristic
75C22×C4×C41C2×D411yescharacteristic
76Q16×C41—41no—
77SD16×C41—42no—
78D8×C41—41no—
79C2×C8×C41—22no—
80C2×C8×C41—22no—
81C2×C8×C41—22no—
82C2×C8×C41—41no—
83C2×C8×C41—41no—
84C2×C8×C41—41no—
85C2×C8×C41C22⋊C411yescharacteristic
86C2×C8×C41C22⋊C411yescharacteristic
87C2×C8×C41C22×C411yescharacteristic
88C2×C8×C41C2×D411yescharacteristic
89C4⋊C4×C41—21no—
90C4⋊C4×C41—21no—
91C4⋊C4×C41—42no—
92C4⋊C4×C41—42no—
93C4⋊C4×C41—41no—
94C4⋊C4×C41—41no—
95C22⋊C4×C41—41no—
96C22⋊C4×C41—41no—
97C22⋊C4×C41—41no—
98C22⋊C4×C41—41no—
99C22⋊C4×C41—41no—
100C22⋊C4×C41—82no—
101C42×C41—41no—
102C16×C41—42no—
103C23×C41—22no—
104C23×C41—22no—
105C23×C41—41no—
106C23×C41—41no—
107C23×C41#10211yescharacteristic
108C23×C41#10211yescharacteristic
109C23×C41C2×D811yescharacteristic
110Q8×C41—41no—
111Q8×C41—41no—
112D4×C41—41no—
113D4×C41—41no—
114D4×C41—82no—
115D4×C41—82no—
116D4×C41—82no—
117C2×C4×C41—21no—
118C2×C4×C41—21no—
119C2×C4×C41—21no—
120C2×C4×C41—21no—
121C2×C4×C41—21no—
122C2×C4×C41—21no—
123C2×C4×C41—41no—
124C2×C4×C41—41no—
125C2×C4×C41—41no—
126C2×C4×C41—41no—
127C2×C4×C41—41no—
128C2×C4×C41—41no—
129C2×C4×C41—82no—
130C2×C4×C41—82no—
131C2×C4×C41—82no—
132C2×C4×C41—82no—
133C2×C4×C41#10211yescharacteristic
134C2×C4×C41#10211yescharacteristic
135C2×C4×C41C2×C22⋊C411yescharacteristic
136C2×C4×C41C2×SD1611yescharacteristic
137C8×C41—21no—
138C8×C41—21no—
139C8×C41—21no—
140C8×C41#9912yes—
141#11885C4111yesmaximal, characteristic, direct product factor, Sylow
142C22×C41—21no—
143C22×C41—21no—
144C22×C41—21no—
145C22×C41—21no—
146C22×C41—21no—
147C22×C41—21no—
148C22×C41—21no—
149C22×C41—44no—
150C22×C41—81no—
151C22×C41—81no—
152C22×C41—81no—
153C22×C41#36012yes—
154C22×C41C2×#10211yescharacteristic
155C22×C41#50812yes—
156C4×C41—21no—
157C4×C41—21no—
158C4×C41—21no—
159C4×C41—81no—
160C4×C41—81no—
161C4×C41—81no—
162C4×C41—162no—
163C4×C41C2×#9911yescharacteristic
164C4×C41#42111yescharacteristic
165#3050C2×C4111yescharacteristic
166C2×C22⋊C16C2×C4111yescharacteristic, complemented
167#1807C2×C4111yescharacteristic, complemented
168#1348C2×C4112yescomplemented
169#1347C2×C4112yescomplemented
170C2×C41—22no—
171C2×C41—22no—
172C2×C41—41no—
173C2×C41—161no—
174C2×C41#151911yescharacteristic
175C2×C41#213811yescharacteristic
176C2×C41C2×#36011yescharacteristic
177C2×#135C4×C4111yescharacteristic, complemented
178C23×C8C22×C4111yescharacteristic
179#525—21no—
180C22×C16—21no—
181#467C4×C4111yescharacteristic, complemented
182#467C22×C4111yescharacteristic
183#466C4×C4111yescharacteristic, complemented
184#466C22×C4111yescharacteristic
185#465—21no—
186#465—21no—
187#427C4×C4111yescharacteristic, complemented
188C2×#106—21no—
189#416—21no—
190#380—21no—
191C22⋊C16—21no—
192C22⋊C16C22×C4112yes—
193#340C22×C4112yes—
194C41#1188511yescharacteristic, direct product factor, Sylow
195C2×#41—21no—
196C23×C4D4×C4111yescharacteristic
197#135—42no—
198C2×Q16C2×C4×C4111yescharacteristic
199C2×SD16—21no—
200C2×D8C2×C4×C4111yescharacteristic
201C22×C8—42no—
202C22×C8C2×C4×C4111yescharacteristic
203C22×C8C2×C4×C4111yescharacteristic
204C22×C8D4×C4111yescharacteristic
205C22×C8D4×C4111yescharacteristic
206C22×C8D4×C4111yescharacteristic
207C22×C8C23×C4111yescharacteristic
208#123—41no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211#121—21no—
212#121—21no—
213#120—41no—
214C4×D4—41no—
215C4×D4—41no—
216#117—21no—
217C2×C4⋊C4—22no—
218C2×C22⋊C4—41no—
219C2×C16—22no—
220C2×C16—42no—
221#107C2×C4×C4111yescharacteristic
222#107C2×C4×C4111yescharacteristic
223#106—21no—
224#106—42no—
225#103—21no—
226#103—21no—
227#102—21no—
228#102—21no—
229#95—41no—
230C24D8×C4111yescharacteristic
231#41—42no—
232#41—42no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4C22⋊C4×C4111yescharacteristic
243C22×C4C22⋊C4×C4111yescharacteristic
244C22×C4D8×C4111yescharacteristic
245C22×C4SD16×C4111yescharacteristic
246C22×C4SD16×C4111yescharacteristic
247C22×C4C2×D4×C4111yescharacteristic
248Q16—41no—
249SD16—42no—
250D8—41no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8C22⋊C4×C4111yescharacteristic
258C2×C8C22⋊C4×C4111yescharacteristic
259C2×C8C22×C4×C4111yescharacteristic
260C2×C8C2×D4×C4111yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—82no—
273C42—41no—
274C16—42no—
275C23—22no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23#102×C4111yescharacteristic
280C23#102×C4111yescharacteristic
281C23C2×D8×C4111yescharacteristic
282Q8—41no—
283Q8—41no—
284D4—41no—
285D4—41no—
286D4—82no—
287D4—82no—
288D4—82no—
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—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4#102×C4111yescharacteristic
306C2×C4#102×C4111yescharacteristic
307C2×C4C2×C22⋊C4×C4111yescharacteristic
308C2×C4C2×SD16×C4111yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8#99×C4112yes—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—44no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22C41×#36012yes—
325C22C2×#102×C4111yescharacteristic
326C22C41×#50812yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—162no—
334C4C2×#99×C4111yescharacteristic
335C4C41×#42111yescharacteristic
336C2—22no—
337C2—22no—
338C2—41no—
339C2—161no—
340C2C41×#151911yescharacteristic
341C2C41×#213811yescharacteristic
342C2C2×C41×#36011yescharacteristic
subgroupG/H
center, socleC22×C41C2×#102
commutatorC2×C8C22×C4×C41
Frattini, cosocleC22×C8C23×C41
prime radicalC41×#3050C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ C23×C8×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C41×C22⋊C16C2semidirect
3. C41×#1807C2semidirect
4. C41×#1348C2semidirect
5. C41×#1347C2semidirect
6. C2×#135×C41C4semidirect
10. C41×#467C4semidirect
12. C41×#466C4semidirect
16. C41×#427C4semidirect
141. #11885C41direct (N × H)
166. C2×C22⋊C16C2×C41semidirect
167. #1807C2×C41semidirect
168. #1348C2×C41semidirect
169. #1347C2×C41semidirect
177. C2×#135C4×C41semidirect
181. #467C4×C41semidirect
183. #466C4×C41semidirect
187. #427C4×C41semidirect
194. C41#11885direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#30502
C2×C41×C22⋊C162
C41×#18072
C41×#13482
C41×#13472
#1188541