Finite Group Databasebeta

← C41×#8877 #23785078

Subgroups — C41×#8877 #23785078

Order 10496.

360 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2992C211yesmaximal, characteristic
2C41×#1832C211yesmaximal, characteristic, complemented
3C41×#1573C211yesmaximal, characteristic, complemented
4C41×#1500C211yesmaximal, characteristic
5C41×#1483C211yesmaximal, characteristic
6C41×#1300C211yesmaximal, characteristic, complemented
7C41×#1283C211yesmaximal, characteristic, complemented
8C41×#529C2211yescharacteristic
9C41×#446—21no—
10C41×#435—21no—
11C41×#435—21no—
12C8×D4×C41—21no—
13C41×#433—21no—
14C41×#432C2211yescharacteristic
15C41×#431C2211yescharacteristic
16C41×#424—21no—
17C2×C4⋊C8×C41C2211yescharacteristic
18C2×C4⋊C8×C41C2211yescharacteristic
19C4×M16×C41C2211yescharacteristic
20C41×#376C2211yescharacteristic
21C41×#336—21no—
22C41×#336—21no—
23C41×#335—21no—
24C41×#334—21no—
25C41×#328C411yescharacteristic
26C41×#328C411yescharacteristic
27C41×#327C411yescharacteristic
28C41×#327C411yescharacteristic
29C41×Q8⋊C8—21no—
30C41×D4⋊C8—21no—
31C2×M16×C41—21no—
32C2×M16×C41—21no—
33C22×C8×C41—21no—
34C22×C8×C41—21no—
35C22×C8×C41D411yescharacteristic
36C22×C8×C41D411yescharacteristic
37#126×C41—21no—
38#125×C41Q811yescharacteristic
39#124×C41Q811yescharacteristic
40#123×C41—21no—
41C22⋊Q8×C41C2×C411yescharacteristic
42#121×C41C2×C411yescharacteristic
43C4×Q8×C41D411yescharacteristic
44C4×D4×C41—21no—
45C4×D4×C41D411yescharacteristic
46#117×C41—21no—
47C2×C42×C41—21no—
48C2×C42×C41C2311yescharacteristic
49C4⋊C8×C41—21no—
50C4⋊C8×C41—21no—
51C4⋊C8×C41—21no—
52C4⋊C8×C41—21no—
53C4⋊C8×C41—21no—
54C4⋊C8×C41—21no—
55C4⋊C8×C41—21no—
56C4⋊C8×C41D411yescharacteristic
57C4⋊C8×C41D411yescharacteristic
58C22⋊C8×C41—21no—
59C22⋊C8×C41—21no—
60C22⋊C8×C41—21no—
61C22⋊C8×C41C2×C411yescharacteristic
62C22⋊C8×C41C2×C411yescharacteristic
63#97×C41—21no—
64#97×C41—21no—
65#97×C41—21no—
66C4×C8×C41—21no—
67C4×C8×C41—21no—
68C4×C8×C41—21no—
69#95×C41—21no—
70#95×C41C2×C411yescharacteristic
71#95×C41C2×C411yescharacteristic
72C2×Q8×C41C4⋊C411yescharacteristic
73C2×D4×C41—21no—
74C2×D4×C41C4⋊C411yescharacteristic
75C22×C4×C41—21no—
76C22×C4×C41—21no—
77C22×C4×C41—21no—
78C22×C4×C41C22×C411yescharacteristic
79C22×C4×C41C2×D411yescharacteristic
80C22×C4×C41#4111yescharacteristic
81M16×C41—22no—
82M16×C41—41no—
83M16×C41—81no—
84C2×C8×C41—21no—
85C2×C8×C41—21no—
86C2×C8×C41—21no—
87C2×C8×C41—21no—
88C2×C8×C41—21no—
89C2×C8×C41—21no—
90C2×C8×C41—41no—
91C2×C8×C41—41no—
92C2×C8×C41—41no—
93C2×C8×C41—42no—
94C2×C8×C41—41no—
95C2×C8×C41—81no—
96C4⋊C4×C41—21no—
97C4⋊C4×C41—21no—
98C4⋊C4×C41—21no—
99C4⋊C4×C41—21no—
100C4⋊C4×C41C4⋊C411yescharacteristic
101C4⋊C4×C41C4⋊C411yescharacteristic
102C22⋊C4×C41—21no—
103C22⋊C4×C41—21no—
104C22⋊C4×C41—21no—
105C22⋊C4×C41—21no—
106C22⋊C4×C41—21no—
107C42×C41—21no—
108C42×C41—41no—
109C42×C41—41no—
110C42×C41C2×D411yescharacteristic
111C42×C41C2×D411yescharacteristic
112C42×C41C2×Q811yescharacteristic
113C42×C41#4111yescharacteristic
114C23×C41—21no—
115C23×C41C4×D411yescharacteristic
116Q8×C41—41no—
117D4×C41—41no—
118D4×C41—41no—
119D4×C41—41no—
120C2×C4×C41—21no—
121C2×C4×C41—21no—
122C2×C4×C41—21no—
123C2×C4×C41—21no—
124C2×C4×C41—21no—
125C2×C4×C41—21no—
126C2×C4×C41—21no—
127C2×C4×C41—41no—
128C2×C4×C41—41no—
129C2×C4×C41—41no—
130C2×C4×C41—41no—
131C2×C4×C41—41no—
132C2×C4×C41—41no—
133C2×C4×C41—41no—
134C2×C4×C41—41no—
135C2×C4×C41—41no—
136C2×C4×C41C2×C4⋊C411yescharacteristic
137C2×C4×C41C4×D411yescharacteristic
138C2×C4×C41#12011yescharacteristic
139C2×C4×C41C22⋊Q811yescharacteristic
140C2×C4×C41C22⋊Q811yescharacteristic
141C2×C4×C41#12311yescharacteristic
142C8×C41—41no—
143C8×C41—41no—
144C8×C41—42no—
145C8×C41—41no—
146C8×C41—41no—
147C8×C41—41no—
148C8×C41—41no—
149C8×C41—81no—
150#8877C4111yesmaximal, characteristic, direct product factor, Sylow
151C22×C41—21no—
152C22×C41—21no—
153C22×C41—41no—
154C22×C41—41no—
155C22×C41—41no—
156C22×C41#38511yescharacteristic
157C22×C41#44311yescharacteristic
158C22×C41#44411yescharacteristic
159C4×C41—21no—
160C4×C41—21no—
161C4×C41—21no—
162C4×C41—21no—
163C4×C41—21no—
164C4×C41—41no—
165C4×C41—41no—
166C4×C41—41no—
167C4×C41—81no—
168C4×C41—81no—
169C4×C41#45411yescharacteristic
170C4×C41#45511yescharacteristic
171#2992C2×C4111yescharacteristic
172#1832C2×C4111yescharacteristic, complemented
173#1573C2×C4111yescharacteristic, complemented
174#1500C2×C4111yescharacteristic
175#1483C2×C4111yescharacteristic
176#1300C2×C4111yescharacteristic, complemented
177#1283C2×C4111yescharacteristic, complemented
178C2×C41—21no—
179C2×C41—21no—
180C2×C41—81no—
181C2×C41#186011yescharacteristic
182C2×C41#186611yescharacteristic
183C2×C41#186811yescharacteristic
184#529C22×C4111yescharacteristic
185#446—21no—
186#435—21no—
187#435—21no—
188C8×D4—21no—
189#433—21no—
190#432C22×C4111yescharacteristic
191#431C22×C4111yescharacteristic
192#424—21no—
193C2×C4⋊C8C22×C4111yescharacteristic
194C2×C4⋊C8C22×C4111yescharacteristic
195C4×M16C22×C4111yescharacteristic
196#376C22×C4111yescharacteristic
197#336—21no—
198#336—21no—
199#335—21no—
200#334—21no—
201#328C4×C4111yescharacteristic
202#328C4×C4111yescharacteristic
203#327C4×C4111yescharacteristic
204#327C4×C4111yescharacteristic
205Q8⋊C8—21no—
206D4⋊C8—21no—
207C41#887711yescharacteristic, direct product factor, Sylow
208C2×M16—21no—
209C2×M16—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8D4×C4111yescharacteristic
213C22×C8D4×C4111yescharacteristic
214#126—21no—
215#125Q8×C4111yescharacteristic
216#124Q8×C4111yescharacteristic
217#123—21no—
218C22⋊Q8C2×C4×C4111yescharacteristic
219#121C2×C4×C4111yescharacteristic
220C4×Q8D4×C4111yescharacteristic
221C4×D4—21no—
222C4×D4D4×C4111yescharacteristic
223#117—21no—
224C2×C42—21no—
225C2×C42C23×C4111yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—21no—
233C4⋊C8D4×C4111yescharacteristic
234C4⋊C8D4×C4111yescharacteristic
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8C2×C4×C4111yescharacteristic
239C22⋊C8C2×C4×C4111yescharacteristic
240#97—21no—
241#97—21no—
242#97—21no—
243C4×C8—21no—
244C4×C8—21no—
245C4×C8—21no—
246#95—21no—
247#95C2×C4×C4111yescharacteristic
248#95C2×C4×C4111yescharacteristic
249C2×Q8C4⋊C4×C4111yescharacteristic
250C2×D4—21no—
251C2×D4C4⋊C4×C4111yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4C22×C4×C4111yescharacteristic
256C22×C4C2×D4×C4111yescharacteristic
257C22×C4#41×C4111yescharacteristic
258M16—22no—
259M16—41no—
260M16—81no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—42no—
271C2×C8—41no—
272C2×C8—81no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4C4⋊C4×C4111yescharacteristic
278C4⋊C4C4⋊C4×C4111yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C42—21no—
285C42—41no—
286C42—41no—
287C42C2×D4×C4111yescharacteristic
288C42C2×D4×C4111yescharacteristic
289C42C2×Q8×C4111yescharacteristic
290C42#41×C4111yescharacteristic
291C23—21no—
292C23C4×D4×C4111yescharacteristic
293Q8—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4C2×C4⋊C4×C4111yescharacteristic
314C2×C4C4×D4×C4111yescharacteristic
315C2×C4#120×C4111yescharacteristic
316C2×C4C22⋊Q8×C4111yescharacteristic
317C2×C4C22⋊Q8×C4111yescharacteristic
318C2×C4#123×C4111yescharacteristic
319C8—41no—
320C8—41no—
321C8—42no—
322C8—41no—
323C8—41no—
324C8—41no—
325C8—41no—
326C8—81no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22C41×#38511yescharacteristic
333C22C41×#44311yescharacteristic
334C22C41×#44411yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4C41×#45411yescharacteristic
346C4C41×#45511yescharacteristic
347C2—21no—
348C2—21no—
349C2—81no—
350C2C41×#186011yescharacteristic
351C2C41×#186611yescharacteristic
352C2C41×#186811yescharacteristic
subgroupG/H
centerC2×C4×C41#120
commutatorC22×C4C22×C4×C41
Frattini, cosocleC2×C42C23×C41
socleC22×C41#385
prime radical#121×C41C2×C4
LCSG ▷ C22×C4 ▷ 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×#1832C2semidirect
3. C41×#1573C2semidirect
6. C41×#1300C2semidirect
7. C41×#1283C2semidirect
150. #8877C41direct (N × H)
172. #1832C2×C41semidirect
173. #1573C2×C41semidirect
176. #1300C2×C41semidirect
177. #1283C2×C41semidirect
207. C41#8877direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#29922
C41×#18322
C41×#15732
C41×#15002
C41×#14832
C41×#13002
C41×#12832
#887741