Finite Group Databasebeta

← C41×#9590 #23785791

Subgroups — C41×#9590 #23785791

Order 10496.

364 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#1980C211yesmaximal, characteristic
2C41×#1950C211yesmaximal, characteristic, complemented
3C41×#1540C211yesmaximal, characteristic
4C41×#1492C211yesmaximal, characteristic
5C8×M16×C41C211yesmaximal, characteristic, complemented
6C41×#1303C211yesmaximal, characteristic, complemented
7C41×#1279C211yesmaximal, characteristic, complemented
8C41×#532C2211yescharacteristic
9C41×#431C2211yescharacteristic
10C2×#108×C41—21no—
11C41×#423C2211yescharacteristic
12C2×C4⋊C8×C41C2211yescharacteristic
13C2×#104×C41—21no—
14C2×#104×C41—21no—
15C4×M16×C41C2211yescharacteristic
16C2×C4×C8×C41C2211yescharacteristic
17C4×C4⋊C4×C41C2211yescharacteristic
18C41×#341—21no—
19C41×#332C411yescharacteristic, complemented
20C41×#332C411yescharacteristic, complemented
21C41×#331C411yescharacteristic, complemented
22C41×#331C411yescharacteristic, complemented
23C41×D4⋊C8—21no—
24C41×D4⋊C8—21no—
25C41×#322—21no—
26C82×C41—21no—
27C2×#41×C41—21no—
28C2×M16×C41—21no—
29C2×M16×C41D411yescharacteristic
30C2×M16×C41D411yescharacteristic
31C22×C8×C41—21no—
32C22×C8×C41—21no—
33C4⋊Q8×C41C2×C411yescharacteristic
34#127×C41C2×C411yescharacteristic
35#124×C41—21no—
36#121×C41—21no—
37#121×C41—21no—
38C4×D4×C41—21no—
39C4×D4×C41—21no—
40C2×C4⋊C4×C41—21no—
41C2×C42×C41—21no—
42C2×C42×C41C2311yescharacteristic
43#108×C41—42no—
44C4⋊C8×C41—21no—
45C4⋊C8×C41—21no—
46C4⋊C8×C41—21no—
47C4⋊C8×C41C2×C411yescharacteristic
48C4⋊C8×C41C2×C411yescharacteristic
49C4⋊C8×C41C2×C411yescharacteristic
50C4⋊C8×C41C2×C411yescharacteristic
51#104×C41—42no—
52#104×C41—42no—
53C22⋊C8×C41—21no—
54#97×C41—21no—
55C4×C8×C41—21no—
56C4×C8×C41—21no—
57C4×C8×C41—21no—
58C4×C8×C41D411yescharacteristic
59C4×C8×C41D411yescharacteristic
60#95×C41—21no—
61#41×C41—41no—
62#41×C41—41no—
63#41×C41—41no—
64#41×C41—41no—
65C2×Q8×C41—21no—
66C2×D4×C41—21no—
67C2×D4×C41—21no—
68C2×D4×C41—21no—
69C2×D4×C41—41no—
70C22×C4×C41—41no—
71C22×C4×C41—41no—
72C22×C4×C41C2×D411yescharacteristic
73C22×C4×C41#4111yescharacteristic
74C22×C4×C41#4111yescharacteristic
75M16×C41—21no—
76M16×C41—21no—
77M16×C41—41no—
78M16×C41—41no—
79M16×C41D812yes—
80M16×C41SD1612yes—
81C2×C8×C41—21no—
82C2×C8×C41—21no—
83C2×C8×C41—21no—
84C2×C8×C41—21no—
85C2×C8×C41—21no—
86C2×C8×C41—21no—
87C2×C8×C41—21no—
88C2×C8×C41—21no—
89C2×C8×C41—42no—
90C2×C8×C41—41no—
91C2×C8×C41—41no—
92C2×C8×C41—41no—
93C4⋊C4×C41—22no—
94C4⋊C4×C41—21no—
95C4⋊C4×C41—21no—
96C4⋊C4×C41—41no—
97C22⋊C4×C41—41no—
98C22⋊C4×C41—41no—
99C42×C41—41no—
100C42×C41—41no—
101C42×C41C22×C411yescharacteristic
102C42×C41C2×D411yescharacteristic
103C42×C41#4111yescharacteristic
104C42×C41#4111yescharacteristic
105C23×C41—41no—
106C23×C41#12411yescharacteristic
107Q8×C41—41no—
108Q8×C41—41no—
109D4×C41—41no—
110D4×C41—41no—
111D4×C41—41no—
112D4×C41—41no—
113D4×C41—81no—
114D4×C41—81no—
115D4×C41—81no—
116C2×C4×C41—21no—
117C2×C4×C41—21no—
118C2×C4×C41—41no—
119C2×C4×C41—42no—
120C2×C4×C41—41no—
121C2×C4×C41—81no—
122C2×C4×C41—81no—
123C2×C4×C41—81no—
124C2×C4×C41—81no—
125C2×C4×C41#11711yescharacteristic
126C2×C4×C41C4×D411yescharacteristic
127C2×C4×C41C4×D411yescharacteristic
128C2×C4×C41#12111yescharacteristic
129C2×C4×C41#12311yescharacteristic
130C2×C4×C41#12611yescharacteristic
131C2×C4×C41C2×D811yescharacteristic
132C2×C4×C41C2×SD1611yescharacteristic
133C2×C4×C41#13511yescharacteristic
134C2×C4×C41#13511yescharacteristic
135C8×C41—22no—
136C8×C41—22no—
137C8×C41—22no—
138C8×C41—41no—
139C8×C41—41no—
140C8×C41—41no—
141C8×C41—41no—
142C8×C41—41no—
143C8×C41—81no—
144#9590C4111yesmaximal, characteristic, direct product factor, Sylow
145C22×C41—21no—
146C22×C41—21no—
147C22×C41—81no—
148C22×C41—81no—
149C22×C41—81no—
150C22×C41#38811yescharacteristic
151C22×C41#48611yescharacteristic
152C22×C41#48811yescharacteristic
153C4×C41—21no—
154C4×C41—21no—
155C4×C41—21no—
156C4×C41—82no—
157C4×C41—81no—
158C4×C41C4×D811yescharacteristic
159C4×C41C4×SD1611yescharacteristic
160C4×C41#44311yescharacteristic
161C4×C41#44411yescharacteristic
162C4×C41#46511yescharacteristic
163C4×C41#46611yescharacteristic
164#1980C2×C4111yescharacteristic
165#1950C2×C4111yescharacteristic, complemented
166#1540C2×C4111yescharacteristic
167#1492C2×C4111yescharacteristic
168C8×M16C2×C4111yescharacteristic, complemented
169#1303C2×C4111yescharacteristic, complemented
170#1279C2×C4111yescharacteristic, complemented
171C2×C41—21no—
172C2×C41—21no—
173C2×C41—161no—
174C2×C41#192911yescharacteristic
175C2×C41#193211yescharacteristic
176C2×C41#193411yescharacteristic
177#532C22×C4111yescharacteristic
178#431C22×C4111yescharacteristic
179C2×#108—21no—
180#423C22×C4111yescharacteristic
181C2×C4⋊C8C22×C4111yescharacteristic
182C2×#104—21no—
183C2×#104—21no—
184C4×M16C22×C4111yescharacteristic
185C2×C4×C8C22×C4111yescharacteristic
186C4×C4⋊C4C22×C4111yescharacteristic
187#341—21no—
188#332C4×C4111yescharacteristic, complemented
189#332C4×C4111yescharacteristic, complemented
190#331C4×C4111yescharacteristic, complemented
191#331C4×C4111yescharacteristic, complemented
192D4⋊C8—21no—
193D4⋊C8—21no—
194#322—21no—
195C82—21no—
196C41#959011yescharacteristic, direct product factor, Sylow
197C2×#41—21no—
198C2×M16—21no—
199C2×M16D4×C4111yescharacteristic
200C2×M16D4×C4111yescharacteristic
201C22×C8—21no—
202C22×C8—21no—
203C4⋊Q8C2×C4×C4111yescharacteristic
204#127C2×C4×C4111yescharacteristic
205#124—21no—
206#121—21no—
207#121—21no—
208C4×D4—21no—
209C4×D4—21no—
210C2×C4⋊C4—21no—
211C2×C42—21no—
212C2×C42C23×C4111yescharacteristic
213#108—42no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8C2×C4×C4111yescharacteristic
218C4⋊C8C2×C4×C4111yescharacteristic
219C4⋊C8C2×C4×C4111yescharacteristic
220C4⋊C8C2×C4×C4111yescharacteristic
221#104—42no—
222#104—42no—
223C22⋊C8—21no—
224#97—21no—
225C4×C8—21no—
226C4×C8—21no—
227C4×C8—21no—
228C4×C8D4×C4111yescharacteristic
229C4×C8D4×C4111yescharacteristic
230#95—21no—
231#41—41no—
232#41—41no—
233#41—41no—
234#41—41no—
235C2×Q8—21no—
236C2×D4—21no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C2×D4×C4111yescharacteristic
243C22×C4#41×C4111yescharacteristic
244C22×C4#41×C4111yescharacteristic
245M16—21no—
246M16—21no—
247M16—41no—
248M16—41no—
249M16D8×C4112yes—
250M16SD16×C4112yes—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C4⋊C4—22no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C42—41no—
270C42—41no—
271C42C22×C4×C4111yescharacteristic
272C42C2×D4×C4111yescharacteristic
273C42#41×C4111yescharacteristic
274C42#41×C4111yescharacteristic
275C23—41no—
276C23#124×C4111yescharacteristic
277Q8—41no—
278Q8—41no—
279D4—41no—
280D4—41no—
281D4—41no—
282D4—41no—
283D4—81no—
284D4—81no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4#117×C4111yescharacteristic
296C2×C4C4×D4×C4111yescharacteristic
297C2×C4C4×D4×C4111yescharacteristic
298C2×C4#121×C4111yescharacteristic
299C2×C4#123×C4111yescharacteristic
300C2×C4#126×C4111yescharacteristic
301C2×C4C2×D8×C4111yescharacteristic
302C2×C4C2×SD16×C4111yescharacteristic
303C2×C4#135×C4111yescharacteristic
304C2×C4#135×C4111yescharacteristic
305C8—22no—
306C8—22no—
307C8—22no—
308C8—41no—
309C8—41no—
310C8—41no—
311C8—41no—
312C8—41no—
313C8—81no—
314C22—21no—
315C22—21no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22C41×#38811yescharacteristic
320C22C41×#48611yescharacteristic
321C22C41×#48811yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—82no—
326C4—81no—
327C4C4×D8×C4111yescharacteristic
328C4C4×SD16×C4111yescharacteristic
329C4C41×#44311yescharacteristic
330C4C41×#44411yescharacteristic
331C4C41×#46511yescharacteristic
332C4C41×#46611yescharacteristic
333C2—21no—
334C2—21no—
335C2—161no—
336C2C41×#192911yescharacteristic
337C2C41×#193211yescharacteristic
338C2C41×#193411yescharacteristic
subgroupG/H
centerC2×C4×C41#121
commutatorC42C22×C4×C41
Frattini, cosocleC2×C42C23×C41
socleC22×C41#388
prime radicalC41×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C41×#1950C2semidirect
5. C8×M16×C41C2semidirect
6. C41×#1303C2semidirect
7. C41×#1279C2semidirect
19. C41×#332C4semidirect
20. C41×#332C4semidirect
21. C41×#331C4semidirect
22. C41×#331C4semidirect
144. #9590C41direct (N × H)
165. #1950C2×C41semidirect
168. C8×M16C2×C41semidirect
169. #1303C2×C41semidirect
170. #1279C2×C41semidirect
188. #332C4×C41semidirect
189. #332C4×C41semidirect
190. #331C4×C41semidirect
191. #331C4×C41semidirect
196. C41#9590direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#19802
C41×#19502
C41×#15402
C41×#14922
C8×M16×C412
C41×#13032
C41×#12792
#959041