Finite Group Databasebeta

← C41×#11850 #23788051

Subgroups — C41×#11850 #23788051

Order 10496.

396 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2484C211yesmaximal, characteristic
2C41×#1821C211yesmaximal, characteristic
3C2×C41×#324C211yesmaximal, characteristic
4C41×#1353C212yesmaximal, complemented
5C41×#1346C212yesmaximal, complemented
6C2×#117×C41C411yescharacteristic
7C22×C4⋊C4×C41C2211yescharacteristic
8C41×#407—21no—
9C2×C22⋊C8×C41—21no—
10C41×#400C411yescharacteristic
11C41×#400C2211yescharacteristic
12C41×#398C411yescharacteristic
13C41×#398C2211yescharacteristic
14C41×#387—21no—
15C41×#387—21no—
16C41×#385—21no—
17C41×#381—21no—
18C41×#381C411yescharacteristic
19C41×#343—21no—
20C41×#343C2212yes—
21C41×#324—21no—
22C41×#324C2212yes—
23C23×C4×C41C2×C411yescharacteristic
24C23×C4×C41D411yescharacteristic
25C23×C4×C41D411yescharacteristic
26C2×M16×C41—22no—
27C22×C8×C41—41no—
28#117×C41—41no—
29#117×C41—41no—
30C2×C4⋊C4×C41—21no—
31C2×C4⋊C4×C41—21no—
32C2×C4⋊C4×C41—41no—
33C2×C4⋊C4×C41—41no—
34C2×C4⋊C4×C41C2×C411yescharacteristic
35C2×C4⋊C4×C41C2×C411yescharacteristic
36C2×C4⋊C4×C41C2×C411yescharacteristic
37C2×C4⋊C4×C41D411yescharacteristic
38C2×C4⋊C4×C41D411yescharacteristic
39C2×C4⋊C4×C41C2311yescharacteristic
40C2×C22⋊C4×C41—21no—
41C2×C22⋊C4×C41—21no—
42C2×C42×C41—21no—
43C22⋊C8×C41—22no—
44C22⋊C8×C41—41no—
45C22⋊C8×C41—41no—
46C22⋊C8×C41—41no—
47#95×C41—21no—
48#95×C41—21no—
49#95×C41—21no—
50#95×C41—21no—
51#95×C41—21no—
52#95×C41—21no—
53#95×C41—21no—
54#95×C41C2×C411yescharacteristic
55#95×C41C2×C411yescharacteristic
56C24×C41C22⋊C411yescharacteristic
57C22×C4×C41—21no—
58C22×C4×C41—21no—
59C22×C4×C41—21no—
60C22×C4×C41—21no—
61C22×C4×C41—21no—
62C22×C4×C41—21no—
63C22×C4×C41—22no—
64C22×C4×C41—21no—
65C22×C4×C41—21no—
66C22×C4×C41—21no—
67C22×C4×C41—21no—
68C22×C4×C41—41no—
69C22×C4×C41—42no—
70C22×C4×C41—42no—
71C22×C4×C41C22⋊C411yescharacteristic
72C22×C4×C41C22⋊C411yescharacteristic
73C22×C4×C41C22⋊C411yescharacteristic
74C22×C4×C41C22×C411yescharacteristic
75C22×C4×C41C2×D411yescharacteristic
76C22×C4×C41C2×D411yescharacteristic
77M16×C41—42no—
78M16×C41—42no—
79C2×C8×C41—42no—
80C2×C8×C41—42no—
81C2×C8×C41—82no—
82C4⋊C4×C41—41no—
83C4⋊C4×C41—41no—
84C4⋊C4×C41—41no—
85C4⋊C4×C41—41no—
86C4⋊C4×C41—41no—
87C4⋊C4×C41—41no—
88C4⋊C4×C41—42no—
89C4⋊C4×C41—42no—
90C22⋊C4×C41—42no—
91C22⋊C4×C41—41no—
92C22⋊C4×C41—41no—
93C42×C41—42no—
94C23×C41—22no—
95C23×C41—21no—
96C23×C41—21no—
97C23×C41—41no—
98C23×C41#9911yescharacteristic
99C23×C41#9911yescharacteristic
100C23×C41C2×C22⋊C411yescharacteristic
101C2×C4×C41—21no—
102C2×C4×C41—21no—
103C2×C4×C41—21no—
104C2×C4×C41—21no—
105C2×C4×C41—21no—
106C2×C4×C41—21no—
107C2×C4×C41—21no—
108C2×C4×C41—21no—
109C2×C4×C41—21no—
110C2×C4×C41—42no—
111C2×C4×C41—42no—
112C2×C4×C41—42no—
113C2×C4×C41—42no—
114C2×C4×C41—42no—
115C2×C4×C41—41no—
116C2×C4×C41—41no—
117C2×C4×C41—41no—
118C2×C4×C41—41no—
119C2×C4×C41—41no—
120C2×C4×C41—41no—
121C2×C4×C41—41no—
122C2×C4×C41—41no—
123C2×C4×C41—42no—
124C2×C4×C41—41no—
125C2×C4×C41—41no—
126C2×C4×C41—41no—
127C2×C4×C41—41no—
128C2×C4×C41—41no—
129C2×C4×C41—41no—
130C2×C4×C41—81no—
131C2×C4×C41#13512yes—
132C8×C41—82no—
133C8×C41—82no—
134#11850C4111yesmaximal, characteristic, direct product factor, Sylow
135C22×C41—21no—
136C22×C41—21no—
137C22×C41—21no—
138C22×C41—21no—
139C22×C41—21no—
140C22×C41—21no—
141C22×C41—21no—
142C22×C41—42no—
143C22×C41—42no—
144C22×C41#35212yes—
145C22×C41C2×#9911yescharacteristic
146C22×C41#41611yescharacteristic
147C22×C41#42111yescharacteristic
148C4×C41—22no—
149C4×C41—41no—
150C4×C41—41no—
151C4×C41—41no—
152C4×C41—41no—
153C4×C41—41no—
154C4×C41—81no—
155C4×C41—81no—
156C4×C41—81no—
157C4×C41—81no—
158#2484C2×C4111yescharacteristic
159#1821C2×C4111yescharacteristic
160C2×#324C2×C4111yescharacteristic
161#1353C2×C4112yescomplemented
162#1346C2×C4112yescomplemented
163C2×C41—21no—
164C2×C41—21no—
165C2×C41—22no—
166C2×C41—41no—
167C2×C41#151611yescharacteristic
168C2×C41C2×#35211yescharacteristic
169C2×C41#213311yescharacteristic
170C2×#117C4×C4111yescharacteristic
171C22×C4⋊C4C22×C4111yescharacteristic
172#407—21no—
173C2×C22⋊C8—21no—
174#400C4×C4111yescharacteristic
175#400C22×C4111yescharacteristic
176#398C4×C4111yescharacteristic
177#398C22×C4111yescharacteristic
178#387—21no—
179#387—21no—
180#385—21no—
181#381—21no—
182#381C4×C4111yescharacteristic
183#343—21no—
184#343C22×C4112yes—
185#324—21no—
186#324C22×C4112yes—
187C41#1185011yescharacteristic, direct product factor, Sylow
188C23×C4C2×C4×C4111yescharacteristic
189C23×C4D4×C4111yescharacteristic
190C23×C4D4×C4111yescharacteristic
191C2×M16—22no—
192C22×C8—41no—
193#117—41no—
194#117—41no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4C2×C4×C4111yescharacteristic
200C2×C4⋊C4C2×C4×C4111yescharacteristic
201C2×C4⋊C4C2×C4×C4111yescharacteristic
202C2×C4⋊C4D4×C4111yescharacteristic
203C2×C4⋊C4D4×C4111yescharacteristic
204C2×C4⋊C4C23×C4111yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C42—21no—
208C22⋊C8—22no—
209C22⋊C8—41no—
210C22⋊C8—41no—
211C22⋊C8—41no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95C2×C4×C4111yescharacteristic
220#95C2×C4×C4111yescharacteristic
221C24C22⋊C4×C4111yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4C22⋊C4×C4111yescharacteristic
237C22×C4C22⋊C4×C4111yescharacteristic
238C22×C4C22⋊C4×C4111yescharacteristic
239C22×C4C22×C4×C4111yescharacteristic
240C22×C4C2×D4×C4111yescharacteristic
241C22×C4C2×D4×C4111yescharacteristic
242M16—42no—
243M16—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—82no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C42—42no—
259C23—22no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23#99×C4111yescharacteristic
264C23#99×C4111yescharacteristic
265C23C2×C22⋊C4×C4111yescharacteristic
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—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—81no—
296C2×C4#135×C4112yes—
297C8—82no—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—42no—
307C22—42no—
308C22C41×#35212yes—
309C22C2×#99×C4111yescharacteristic
310C22C41×#41611yescharacteristic
311C22C41×#42111yescharacteristic
312C4—22no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C2—21no—
323C2—21no—
324C2—22no—
325C2—41no—
326C2C41×#151611yescharacteristic
327C2C2×C41×#35211yescharacteristic
328C2C41×#213311yescharacteristic
subgroupG/H
center, socleC22×C41C2×#99
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C4⋊C4C23×C41
prime radicalC24×C41C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C24×C41 ◁ C22×C4⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C41×#1353C2semidirect
5. C41×#1346C2semidirect
134. #11850C41direct (N × H)
161. #1353C2×C41semidirect
162. #1346C2×C41semidirect
187. C41#11850direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#24842
C41×#18212
C2×C41×#3242
C41×#13532
C41×#13462
#1185041