Finite Group Databasebeta

← C41×#9201 #23785402

Subgroups — C41×#9201 #23785402

Order 10496.

612 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2626C211yesmaximal, characteristic
2C41×#2312C211yesmaximal, characteristic
3C41×#1520C212yesmaximal, complemented
4C2×C41×#323C211yesmaximal, characteristic
5C41×#1289C212yesmaximal, complemented
6C2×C22⋊Q8×C41C2211yescharacteristic
7C22×C22⋊C4×C41C2211yescharacteristic
8C2×C22⋊C8×C41C2212yes—
9C41×#399C412yescomplemented
10C41×#396—22no—
11C41×#393C412yescomplemented
12C41×#388—24no—
13C41×#385—21no—
14C41×#380C2211yescharacteristic
15C41×#380C2212yes—
16C41×#379—21no—
17C41×#379—21no—
18C4×C22⋊C4×C41—21no—
19C41×#328—24no—
20C41×#323—22no—
21C25×C41D411yescharacteristic
22C22×Q8×C41C2×C411yescharacteristic
23C23×C4×C41D411yescharacteristic
24C23×C4×C41C2311yescharacteristic
25C22×C8×C41—22no—
26C22⋊Q8×C41—22no—
27C22⋊Q8×C41—22no—
28C2×C4⋊C4×C41—21no—
29C2×C4⋊C4×C41—22no—
30C2×C4⋊C4×C41—22no—
31C2×C4⋊C4×C41—21no—
32C2×C4⋊C4×C41C2×C411yescharacteristic
33C2×C22⋊C4×C41—22no—
34C2×C22⋊C4×C41—22no—
35C2×C22⋊C4×C41—21no—
36C2×C22⋊C4×C41—22no—
37C2×C22⋊C4×C41—21no—
38C2×C22⋊C4×C41—22no—
39C2×C22⋊C4×C41—22no—
40C2×C22⋊C4×C41—22no—
41C2×C22⋊C4×C41—22no—
42C2×C22⋊C4×C41C2×C412yes—
43C2×C22⋊C4×C41D412yes—
44C2×C42×C41—22no—
45C22⋊C8×C41—22no—
46C22⋊C8×C41—22no—
47#95×C41—22no—
48#95×C41—22no—
49#95×C41C2×C412yes—
50#95×C41D414yes—
51C24×C41—21no—
52C24×C41—21no—
53C24×C41—22no—
54C24×C41—22no—
55C24×C41—81no—
56C24×C41—81no—
57C24×C41C22⋊C412yes—
58C24×C41C2×D411yescharacteristic
59C2×Q8×C41—22no—
60C2×Q8×C41—81no—
61C22×C4×C41—21no—
62C22×C4×C41—21no—
63C22×C4×C41—21no—
64C22×C4×C41—22no—
65C22×C4×C41—21no—
66C22×C4×C41—24no—
67C22×C4×C41—81no—
68C22×C4×C41—81no—
69C22×C4×C41C22⋊C412yes—
70C22×C4×C41C22×C411yescharacteristic
71C22×C4×C41C2×D412yes—
72C22×C4×C41C2×D411yescharacteristic
73C22×C4×C41#4112yes—
74C2×C8×C41—42no—
75C2×C8×C41—82no—
76C4⋊C4×C41—22no—
77C4⋊C4×C41—42no—
78C4⋊C4×C41—82no—
79C4⋊C4×C41—81no—
80C4⋊C4×C41—82no—
81C22⋊C4×C41—24no—
82C22⋊C4×C41—24no—
83C22⋊C4×C41—41no—
84C22⋊C4×C41—41no—
85C22⋊C4×C41—42no—
86C22⋊C4×C41—42no—
87C22⋊C4×C41—42no—
88C22⋊C4×C41—82no—
89C22⋊C4×C41—82no—
90C22⋊C4×C41—82no—
91C22⋊C4×C41—82no—
92C42×C41—82no—
93C23×C41—22no—
94C23×C41—22no—
95C23×C41—22no—
96C23×C41—41no—
97C23×C41—41no—
98C23×C41—42no—
99C23×C41—42no—
100C23×C41—42no—
101C23×C41—42no—
102C23×C41—42no—
103C23×C41—42no—
104C23×C41—81no—
105C23×C41—81no—
106C23×C41—84no—
107C23×C41—84no—
108C23×C41C2×C22⋊C411yescharacteristic
109C23×C41#12011yescharacteristic
110C23×C41#12311yescharacteristic
111C23×C41#13512yes—
112C23×C41#13712yes—
113Q8×C41—82no—
114C2×C4×C41—22no—
115C2×C4×C41—41no—
116C2×C4×C41—42no—
117C2×C4×C41—42no—
118C2×C4×C41—41no—
119C2×C4×C41—42no—
120C2×C4×C41—42no—
121C2×C4×C41—44no—
122C2×C4×C41—42no—
123C2×C4×C41—42no—
124C2×C4×C41—44no—
125C2×C4×C41—42no—
126C2×C4×C41—42no—
127C2×C4×C41—41no—
128C2×C4×C41—41no—
129C2×C4×C41—42no—
130C2×C4×C41—44no—
131C2×C4×C41—81no—
132C2×C4×C41C4×D412yes—
133C2×C4×C41#12112yes—
134C8×C41—82no—
135#9201C4111yesmaximal, characteristic, direct product factor, Sylow
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—44no—
145C22×C41—42no—
146C22×C41—42no—
147C22×C41—42no—
148C22×C41—82no—
149C22×C41—84no—
150C22×C41—84no—
151C22×C41#38611yescharacteristic
152C22×C41#41611yescharacteristic
153C22×C41#41911yescharacteristic
154C22×C41#45212yes—
155C22×C41#48512yes—
156C4×C41—22no—
157C4×C41—22no—
158C4×C41—42no—
159C4×C41—82no—
160C4×C41—84no—
161C4×C41—81no—
162C4×C41—81no—
163#2626C2×C4111yescharacteristic
164#2312C2×C4111yescharacteristic
165#1520C2×C4112yescomplemented
166C2×#323C2×C4111yescharacteristic
167#1289C2×C4112yescomplemented
168C2×C41—21no—
169C2×C41—22no—
170C2×C41—21no—
171C2×C41—22no—
172C2×C41—82no—
173C2×C41#187311yescharacteristic
174C2×C41#191111yescharacteristic
175C2×C41#191311yescharacteristic
176C2×C22⋊Q8C22×C4111yescharacteristic
177C22×C22⋊C4C22×C4111yescharacteristic
178C2×C22⋊C8C22×C4112yes—
179#399C4×C4112yescomplemented
180#396—22no—
181#393C4×C4112yescomplemented
182#388—24no—
183#385—21no—
184#380C22×C4111yescharacteristic
185#380C22×C4112yes—
186#379—21no—
187#379—21no—
188C4×C22⋊C4—21no—
189#328—24no—
190#323—22no—
191C41#920111yescharacteristic, direct product factor, Sylow
192C25D4×C4111yescharacteristic
193C22×Q8C2×C4×C4111yescharacteristic
194C23×C4D4×C4111yescharacteristic
195C23×C4C23×C4111yescharacteristic
196C22×C8—22no—
197C22⋊Q8—22no—
198C22⋊Q8—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×C4×C4111yescharacteristic
204C2×C22⋊C4—22no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4C2×C4×C4112yes—
214C2×C22⋊C4D4×C4112yes—
215C2×C42—22no—
216C22⋊C8—22no—
217C22⋊C8—22no—
218#95—22no—
219#95—22no—
220#95C2×C4×C4112yes—
221#95D4×C4114yes—
222C24—21no—
223C24—21no—
224C24—22no—
225C24—22no—
226C24—81no—
227C24—81no—
228C24C22⋊C4×C4112yes—
229C24C2×D4×C4111yescharacteristic
230C2×Q8—22no—
231C2×Q8—81no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—24no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4C22⋊C4×C4112yes—
241C22×C4C22×C4×C4111yescharacteristic
242C22×C4C2×D4×C4112yes—
243C22×C4C2×D4×C4111yescharacteristic
244C22×C4#41×C4112yes—
245C2×C8—42no—
246C2×C8—82no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—82no—
250C4⋊C4—81no—
251C4⋊C4—82no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—82no—
260C22⋊C4—82no—
261C22⋊C4—82no—
262C22⋊C4—82no—
263C42—82no—
264C23—22no—
265C23—22no—
266C23—22no—
267C23—41no—
268C23—41no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23—81no—
276C23—81no—
277C23—84no—
278C23—84no—
279C23C2×C22⋊C4×C4111yescharacteristic
280C23#120×C4111yescharacteristic
281C23#123×C4111yescharacteristic
282C23#135×C4112yes—
283C23#137×C4112yes—
284Q8—82no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—44no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—44no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—44no—
302C2×C4—81no—
303C2×C4C4×D4×C4112yes—
304C2×C4#121×C4112yes—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—42no—
313C22—42no—
314C22—44no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—82no—
319C22—84no—
320C22—84no—
321C22C41×#38611yescharacteristic
322C22C41×#41611yescharacteristic
323C22C41×#41911yescharacteristic
324C22C41×#45212yes—
325C22C41×#48512yes—
326C4—22no—
327C4—22no—
328C4—42no—
329C4—82no—
330C4—84no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—22no—
335C2—21no—
336C2—22no—
337C2—82no—
338C2C41×#187311yescharacteristic
339C2C41×#191111yescharacteristic
340C2C41×#191311yescharacteristic
subgroupG/H
center, socleC22×C41#386
commutatorC22×C4C22×C4×C41
Frattini, cosocleC23×C4C23×C41
prime radicalC25×C41D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#1520C2semidirect
5. C41×#1289C2semidirect
9. C41×#399C4semidirect
11. C41×#393C4semidirect
135. #9201C41direct (N × H)
165. #1520C2×C41semidirect
167. #1289C2×C41semidirect
179. #399C4×C41semidirect
181. #393C4×C41semidirect
191. C41#9201direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#26262
C41×#23122
C41×#15202
C2×C41×#3232
C41×#12892
#920141