Finite Group Databasebeta

← C41×#33632 #23809833

Subgroups — C41×#33632 #23809833

Order 10496.

520 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3164C211yesmaximal, characteristic
2C41×#2950C211yesmaximal, characteristic
3C41×#2229C212yesmaximal, complemented
4C41×#2229C212yesmaximal, complemented
5C41×#2227C212yesmaximal, complemented
6C41×#2225C212yesmaximal, complemented
7C41×#2159C211yesmaximal, characteristic
8C41×#2158C211yesmaximal, characteristic
9C41×#2151C211yesmaximal, characteristic
10C41×#2141C211yesmaximal, characteristic
11C2×C41×#358C211yesmaximal, characteristic
12C22×Q16×C41C2211yescharacteristic
13C41×#544—21no—
14C41×#519—21no—
15C2×M32×C41C2211yescharacteristic
16C22×C16×C41C2211yescharacteristic
17C41×#501—22no—
18C41×#500C2212yes—
19C41×#499C2212yes—
20C41×#441—22no—
21C4×Q16×C41C2212yes—
22C4×Q16×C41C2212yes—
23C41×#428—21no—
24C41×#427C2211yescharacteristic
25C41×#427C2211yescharacteristic
26C2×#107×C41C2211yescharacteristic
27C41×#419—21no—
28C41×#405C2211yescharacteristic
29C41×#367C2211yescharacteristic
30C41×#367C2211yescharacteristic
31C41×#367C2212yes—
32C41×#366C2211yescharacteristic
33C41×#366C2211yescharacteristic
34C41×#366C2212yes—
35C41×C4⋊C16C2212yes—
36C41×C4⋊C16C2212yes—
37C41×#358C2212yes—
38C41×#358C2212yes—
39C41×#358C2212yes—
40C41×#358C2212yes—
41C22×Q8×C41—21no—
42C2×Q16×C41—21no—
43C2×Q16×C41—22no—
44C2×Q16×C41Q814yescomplemented
45C2×Q16×C41C2312yes—
46C2×M16×C41D411yescharacteristic
47C22×C8×C41C2311yescharacteristic
48C4⋊Q8×C41—22no—
49C4⋊Q8×C41—41no—
50#125×C41—22no—
51#125×C41—41no—
52C22⋊Q8×C41—42no—
53C4×Q8×C41—22no—
54C4×Q8×C41—22no—
55C4×Q8×C41—41no—
56C4×Q8×C41—41no—
57#117×C41—21no—
58#117×C41—21no—
59#117×C41—42no—
60#117×C41D411yescharacteristic
61C2×C4⋊C4×C41—21no—
62M32×C41—22no—
63C2×C16×C41—22no—
64C2×C16×C41C2311yescharacteristic
65C2×C16×C41C2311yescharacteristic
66C2×C16×C41C2312yes—
67#107×C41—22no—
68#107×C41—21no—
69#107×C41C2311yescharacteristic
70#107×C41C2312yes—
71#107×C41C2311yescharacteristic
72#107×C41C2311yescharacteristic
73#107×C41C2311yescharacteristic
74#106×C41—21no—
75#106×C41—22no—
76#106×C41—21no—
77#103×C41—22no—
78#103×C41—22no—
79#97×C41D412yes—
80C4×C8×C41C2312yes—
81C2×Q8×C41—24no—
82C2×Q8×C41—22no—
83C2×Q8×C41—41no—
84C2×Q8×C41—42no—
85C2×Q8×C41—42no—
86C22×C4×C41—41no—
87C22×C4×C41—41no—
88C22×C4×C41C2×D411yescharacteristic
89Q16×C41—24no—
90Q16×C41—22no—
91Q16×C41C2×Q814yes—
92M16×C41—22no—
93C2×C8×C41C2×D412yes—
94C2×C8×C41C2×D411yescharacteristic
95C2×C8×C41C2×Q812yes—
96C2×C8×C41#4112yes—
97C2×C8×C41C2411yescharacteristic
98C4⋊C4×C41—21no—
99C4⋊C4×C41—21no—
100C4⋊C4×C41—21no—
101C4⋊C4×C41—22no—
102C4⋊C4×C41—21no—
103C4⋊C4×C41—41no—
104C4⋊C4×C41—42no—
105C4⋊C4×C41—42no—
106C4⋊C4×C41—42no—
107C4⋊C4×C41—42no—
108C4⋊C4×C41—42no—
109C4⋊C4×C41D811yescharacteristic
110C4⋊C4×C41D811yescharacteristic
111C22⋊C4×C41—41no—
112C22⋊C4×C41—41no—
113C22⋊C4×C41D812yes—
114C42×C41—41no—
115C42×C41—41no—
116C42×C41—42no—
117C42×C41—42no—
118C42×C41C2×D412yes—
119C16×C41—21no—
120C16×C41—21no—
121C16×C41—22no—
122C23×C41C2×D811yescharacteristic
123Q8×C41—24no—
124Q8×C41—42no—
125Q8×C41—44no—
126Q8×C41—162no—
127C2×C4×C41—42no—
128C2×C4×C41—44no—
129C2×C4×C41—41no—
130C2×C4×C41—41no—
131C2×C4×C41—41no—
132C2×C4×C41—41no—
133C2×C4×C41—42no—
134C2×C4×C41—161no—
135C2×C4×C41C22⋊Q812yes—
136C2×C4×C41C2×D812yes—
137C2×C4×C41C2×D812yes—
138C2×C4×C41C2×D811yescharacteristic
139C2×C4×C41#13712yes—
140C2×C4×C41C22×D411yescharacteristic
141C8×C41—22no—
142C8×C41C22⋊Q812yes—
143C8×C41C22×Q811yescharacteristic
144C8×C41C2×#4111yescharacteristic
145#33632C4111yesmaximal, characteristic, direct product factor, Sylow
146C22×C41—21no—
147C22×C41—21no—
148C22×C41#47412yes—
149C22×C41C22×D811yescharacteristic
150C4×C41—22no—
151C4×C41—22no—
152C4×C41—44no—
153C4×C41—81no—
154C4×C41—82no—
155C4×C41—81no—
156C4×C41—81no—
157C4×C41—81no—
158C4×C41#47412yes—
159C4×C41C2×C22⋊Q811yescharacteristic
160C4×C41C2×#13711yescharacteristic
161#3164C2×C4111yescharacteristic
162#2950C2×C4111yescharacteristic
163#2229C2×C4112yescomplemented
164#2229C2×C4112yescomplemented
165#2227C2×C4112yescomplemented
166#2225C2×C4112yescomplemented
167#2159C2×C4111yescharacteristic
168#2158C2×C4111yescharacteristic
169#2151C2×C4111yescharacteristic
170#2141C2×C4111yescharacteristic
171C2×#358C2×C4111yescharacteristic
172C2×C41—22no—
173C2×C41C2×#47411yescharacteristic
174C2×C41#341611yescharacteristic
175C2×C41#341711yescharacteristic
176C22×Q16C22×C4111yescharacteristic
177#544—21no—
178#519—21no—
179C2×M32C22×C4111yescharacteristic
180C22×C16C22×C4111yescharacteristic
181#501—22no—
182#500C22×C4112yes—
183#499C22×C4112yes—
184#441—22no—
185C4×Q16C22×C4112yes—
186C4×Q16C22×C4112yes—
187#428—21no—
188#427C22×C4111yescharacteristic
189#427C22×C4111yescharacteristic
190C2×#107C22×C4111yescharacteristic
191#419—21no—
192#405C22×C4111yescharacteristic
193#367C22×C4111yescharacteristic
194#367C22×C4111yescharacteristic
195#367C22×C4112yes—
196#366C22×C4111yescharacteristic
197#366C22×C4111yescharacteristic
198#366C22×C4112yes—
199C4⋊C16C22×C4112yes—
200C4⋊C16C22×C4112yes—
201#358C22×C4112yes—
202#358C22×C4112yes—
203#358C22×C4112yes—
204#358C22×C4112yes—
205C41#3363211yescharacteristic, direct product factor, Sylow
206C22×Q8—21no—
207C2×Q16—21no—
208C2×Q16—22no—
209C2×Q16Q8×C4114yescomplemented
210C2×Q16C23×C4112yes—
211C2×M16D4×C4111yescharacteristic
212C22×C8C23×C4111yescharacteristic
213C4⋊Q8—22no—
214C4⋊Q8—41no—
215#125—22no—
216#125—41no—
217C22⋊Q8—42no—
218C4×Q8—22no—
219C4×Q8—22no—
220C4×Q8—41no—
221C4×Q8—41no—
222#117—21no—
223#117—21no—
224#117—42no—
225#117D4×C4111yescharacteristic
226C2×C4⋊C4—21no—
227M32—22no—
228C2×C16—22no—
229C2×C16C23×C4111yescharacteristic
230C2×C16C23×C4112yes—
231C2×C16C23×C4111yescharacteristic
232#107—21no—
233#107—22no—
234#107C23×C4112yes—
235#107C23×C4111yescharacteristic
236#107C23×C4111yescharacteristic
237#107C23×C4111yescharacteristic
238#107C23×C4111yescharacteristic
239#106—21no—
240#106—21no—
241#106—22no—
242#103—22no—
243#103—22no—
244#97D4×C4112yes—
245C4×C8C23×C4112yes—
246C2×Q8—24no—
247C2×Q8—22no—
248C2×Q8—41no—
249C2×Q8—42no—
250C2×Q8—42no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4C2×D4×C4111yescharacteristic
254Q16—24no—
255Q16—22no—
256Q16C2×Q8×C4114yes—
257M16—22no—
258C2×C8C2×D4×C4112yes—
259C2×C8C2×D4×C4111yescharacteristic
260C2×C8C2×Q8×C4112yes—
261C2×C8#41×C4112yes—
262C2×C8C24×C4111yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—22no—
267C4⋊C4—21no—
268C4⋊C4—41no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—42no—
274C4⋊C4D8×C4111yescharacteristic
275C4⋊C4D8×C4111yescharacteristic
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4D8×C4112yes—
279C42—41no—
280C42—41no—
281C42—42no—
282C42—42no—
283C42C2×D4×C4112yes—
284C16—21no—
285C16—21no—
286C16—22no—
287C23C2×D8×C4111yescharacteristic
288Q8—24no—
289Q8—42no—
290Q8—44no—
291Q8—162no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—161no—
300C2×C4C22⋊Q8×C4112yes—
301C2×C4C2×D8×C4112yes—
302C2×C4C2×D8×C4112yes—
303C2×C4C2×D8×C4111yescharacteristic
304C2×C4#137×C4112yes—
305C2×C4C22×D4×C4111yescharacteristic
306C8—22no—
307C8C22⋊Q8×C4112yes—
308C8C22×Q8×C4111yescharacteristic
309C8C2×#41×C4111yescharacteristic
310C22—21no—
311C22—21no—
312C22C41×#47412yes—
313C22C22×D8×C4111yescharacteristic
314C4—22no—
315C4—22no—
316C4—44no—
317C4—82no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4C41×#47412yes—
323C4C2×C22⋊Q8×C4111yescharacteristic
324C4C2×#137×C4111yescharacteristic
325C2—22no—
326C2C2×C41×#47411yescharacteristic
327C2C41×#341611yescharacteristic
328C2C41×#341711yescharacteristic
subgroupG/H
center, socleC22×C41C22×D8
commutator, Frattini, cosocleC2×C8C24×C41
prime radicalC23×C41C2×D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ #117×C41 ◁ C41×#405 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#2229C2semidirect
4. C41×#2229C2semidirect
5. C41×#2227C2semidirect
6. C41×#2225C2semidirect
44. C2×Q16×C41Q8semidirect
145. #33632C41direct (N × H)
163. #2229C2×C41semidirect
164. #2229C2×C41semidirect
165. #2227C2×C41semidirect
166. #2225C2×C41semidirect
205. C41#33632direct (N × H)
209. C2×Q16Q8×C41semidirect

Maximal subgroups

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

subgroupindex
C41×#31642
C41×#29502
C41×#22292
C41×#22272
C41×#22252
C41×#21592
C41×#21582
C41×#21512
C41×#21412
C2×C41×#3582
#3363241