Finite Group Databasebeta

← C41×#15171 #23791372

Subgroups — C41×#15171 #23791372

Order 10496.

1302 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#401C211yesmaximal, characteristic, complemented
2C2×C41×#396C211yesmaximal, characteristic
3C41×#1442C213yesmaximal, complemented
4C41×#1440C213yesmaximal
5C41×#1437C213yesmaximal
6C41×#1436C213yesmaximal, complemented
7C4×#95×C41C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C41C2213yes—
9C22×C22⋊C4×C41C2211yescharacteristic
10C22×C22⋊C4×C41C2213yes—
11C22×C22⋊C4×C41C2213yes—
12C22×C42×C41C2213yes—
13C41×#401—24no—
14C41×#396—24no—
15C2×#95×C41C2213yes—
16C2×#95×C41C2213yes—
17C2×#95×C41C2213yes—
18C2×#95×C41C2213yes—
19C2×#95×C41C2213yes—
20C2×#95×C41C2213yes—
21C2×#95×C41C2213yes—
22C2×#95×C41C2211yescharacteristic
23C25×C41C2311yescharacteristic
24C23×C4×C41C2311yescharacteristic
25C23×C4×C41C2313yes—
26C23×C4×C41C2313yes—
27C23×C4×C41C2313yes—
28C23×C4×C41C2313yes—
29C23×C4×C41C2311yescharacteristic
30C2×C4⋊C4×C41—26no—
31C2×C4⋊C4×C41—26no—
32C2×C4⋊C4×C41—43no—
33C2×C22⋊C4×C41—26no—
34C2×C22⋊C4×C41—26no—
35C2×C22⋊C4×C41—26no—
36C2×C22⋊C4×C41—26no—
37C2×C22⋊C4×C41—26no—
38C2×C22⋊C4×C41—43no—
39C2×C22⋊C4×C41—43no—
40C2×C42×C41—26no—
41C2×C42×C41—43no—
42C2×C42×C41—43no—
43#95×C41—26no—
44#95×C41—26no—
45#95×C41—26no—
46#95×C41—26no—
47#95×C41—26no—
48#95×C41—26no—
49#95×C41—43no—
50#95×C41D414yes—
51C24×C41—21no—
52C24×C41—23no—
53C24×C41—23no—
54C24×C41—23no—
55C24×C41—23no—
56C24×C41—21no—
57C24×C41#4112yes—
58C24×C41C2411yescharacteristic
59C22×C4×C41—23no—
60C22×C4×C41—21no—
61C22×C4×C41—23no—
62C22×C4×C41—23no—
63C22×C4×C41—23no—
64C22×C4×C41—23no—
65C22×C4×C41—23no—
66C22×C4×C41—23no—
67C22×C4×C41—23no—
68C22×C4×C41—23no—
69C22×C4×C41—23no—
70C22×C4×C41—23no—
71C22×C4×C41—23no—
72C22×C4×C41—23no—
73C22×C4×C41—23no—
74C22×C4×C41—23no—
75C22×C4×C41—23no—
76C22×C4×C41—23no—
77C22×C4×C41—23no—
78C22×C4×C41—23no—
79C22×C4×C41—21no—
80C22×C4×C41—23no—
81C22×C4×C41—23no—
82C22×C4×C41—23no—
83C22×C4×C41—23no—
84C22×C4×C41—23no—
85C22×C4×C41—23no—
86C22×C4×C41—23no—
87C22×C4×C41—23no—
88C22×C4×C41—23no—
89C22×C4×C41C2×D416yes—
90C22×C4×C41#4116yes—
91C22×C4×C41#4116yes—
92C22×C4×C41#4116yes—
93C4⋊C4×C41—412no—
94C22⋊C4×C41—412no—
95C22⋊C4×C41—412no—
96C22⋊C4×C41—44no—
97C42×C41—412no—
98C23×C41—26no—
99C23×C41—22no—
100C23×C41—26no—
101C23×C41—41no—
102C23×C41—43no—
103C23×C41—43no—
104C23×C41—43no—
105C23×C41—43no—
106C23×C41—43no—
107C23×C41—43no—
108C23×C41—43no—
109C23×C41—43no—
110C23×C41—43no—
111C23×C41C22×D411yescharacteristic
112C23×C41C2×#4113yes—
113C23×C41C2×#4113yes—
114C23×C41C2×#4111yescharacteristic
115C23×C41C2×#4113yes—
116C23×C41H(5,𝔽2)13yes—
117C23×C412−1+411yescharacteristic
118C2×C4×C41—26no—
119C2×C4×C41—26no—
120C2×C4×C41—26no—
121C2×C4×C41—26no—
122C2×C4×C41—26no—
123C2×C4×C41—26no—
124C2×C4×C41—26no—
125C2×C4×C41—26no—
126C2×C4×C41—26no—
127C2×C4×C41—26no—
128C2×C4×C41—26no—
129C2×C4×C41—43no—
130C2×C4×C41—43no—
131C2×C4×C41—43no—
132C2×C4×C41—43no—
133C2×C4×C41—43no—
134C2×C4×C41—43no—
135C2×C4×C41—43no—
136C2×C4×C41—43no—
137C2×C4×C41—43no—
138C2×C4×C41—43no—
139C2×C4×C41—43no—
140C2×C4×C41—43no—
141C2×C4×C41—41no—
142C2×C4×C41—43no—
143C2×C4×C41—43no—
144C2×C4×C41—43no—
145C2×C4×C41—43no—
146C2×C4×C41—43no—
147C2×C4×C41—43no—
148C2×C4×C41—43no—
149C2×C4×C41—43no—
150C2×C4×C41—43no—
151C2×C4×C41#12614yes—
152#15171C4111yesmaximal, characteristic, direct product factor, Sylow
153C22×C41—46no—
154C22×C41—46no—
155C22×C41—42no—
156C22×C41—83no—
157C22×C41—81no—
158C22×C41—81no—
159C22×C41—83no—
160C22×C41C2×#12611yescharacteristic
161C22×C41#52913yes—
162C22×C41#52913yes—
163C22×C41#52913yes—
164C22×C41#53213yes—
165C22×C41#53813yes—
166C22×C41#53913yes—
167C22×C41#54613yes—
168C22×C41#54811yescharacteristic
169C22×C41#55113yes—
170C22×C41#55313yes—
171C22×C41#55313yes—
172C22×C41#55613yes—
173C4×C41—24no—
174C4×C41—46no—
175C4×C41—46no—
176C4×C41—46no—
177C4×C41—83no—
178C4×C41—81no—
179C2×#401C2×C4111yescharacteristic, complemented
180C2×#396C2×C4111yescharacteristic
181#1442C2×C4113yescomplemented
182#1440C2×C4113yes—
183#1437C2×C4113yes—
184#1436C2×C4113yescomplemented
185C4×#95C2×C4111yescharacteristic, complemented
186C2×C41—82no—
187C2×C41#240111yescharacteristic
188C2×C41#255913yes—
189C2×C41#256013yes—
190C2×C41#257613yes—
191C2×C41#259413yes—
192C2×C41#264311yescharacteristic
193C2×C41#286011yescharacteristic
194C22×C4⋊C4C22×C4113yes—
195C22×C22⋊C4C22×C4111yescharacteristic
196C22×C22⋊C4C22×C4113yes—
197C22×C22⋊C4C22×C4113yes—
198C22×C42C22×C4113yes—
199#401—24no—
200#396—24no—
201C2×#95C22×C4113yes—
202C2×#95C22×C4113yes—
203C2×#95C22×C4113yes—
204C2×#95C22×C4113yes—
205C2×#95C22×C4113yes—
206C2×#95C22×C4113yes—
207C2×#95C22×C4113yes—
208C2×#95C22×C4111yescharacteristic
209C41#1517111yescharacteristic, direct product factor, Sylow
210C25C23×C4111yescharacteristic
211C23×C4C23×C4111yescharacteristic
212C23×C4C23×C4113yes—
213C23×C4C23×C4113yes—
214C23×C4C23×C4113yes—
215C23×C4C23×C4113yes—
216C23×C4C23×C4111yescharacteristic
217C2×C4⋊C4—26no—
218C2×C4⋊C4—26no—
219C2×C4⋊C4—43no—
220C2×C22⋊C4—26no—
221C2×C22⋊C4—26no—
222C2×C22⋊C4—26no—
223C2×C22⋊C4—26no—
224C2×C22⋊C4—26no—
225C2×C22⋊C4—43no—
226C2×C22⋊C4—43no—
227C2×C42—26no—
228C2×C42—43no—
229C2×C42—43no—
230#95—26no—
231#95—26no—
232#95—26no—
233#95—26no—
234#95—26no—
235#95—26no—
236#95—43no—
237#95D4×C4114yes—
238C24—21no—
239C24—23no—
240C24—23no—
241C24—23no—
242C24—23no—
243C24—21no—
244C24#41×C4112yes—
245C24C24×C4111yescharacteristic
246C22×C4—23no—
247C22×C4—21no—
248C22×C4—23no—
249C22×C4—23no—
250C22×C4—23no—
251C22×C4—23no—
252C22×C4—23no—
253C22×C4—23no—
254C22×C4—23no—
255C22×C4—23no—
256C22×C4—23no—
257C22×C4—23no—
258C22×C4—23no—
259C22×C4—23no—
260C22×C4—23no—
261C22×C4—23no—
262C22×C4—23no—
263C22×C4—23no—
264C22×C4—23no—
265C22×C4—23no—
266C22×C4—21no—
267C22×C4—23no—
268C22×C4—23no—
269C22×C4—23no—
270C22×C4—23no—
271C22×C4—23no—
272C22×C4—23no—
273C22×C4—23no—
274C22×C4—23no—
275C22×C4—23no—
276C22×C4C2×D4×C4116yes—
277C22×C4#41×C4116yes—
278C22×C4#41×C4116yes—
279C22×C4#41×C4116yes—
280C4⋊C4—412no—
281C22⋊C4—412no—
282C22⋊C4—412no—
283C22⋊C4—44no—
284C42—412no—
285C23—26no—
286C23—22no—
287C23—26no—
288C23—41no—
289C23—43no—
290C23—43no—
291C23—43no—
292C23—43no—
293C23—43no—
294C23—43no—
295C23—43no—
296C23—43no—
297C23—43no—
298C23C22×D4×C4111yescharacteristic
299C23C2×#41×C4113yes—
300C23C2×#41×C4113yes—
301C23C2×#41×C4111yescharacteristic
302C23C2×#41×C4113yes—
303C23H(5,𝔽2)×C4113yes—
304C232−1+4×C4111yescharacteristic
305C2×C4—26no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—26no—
312C2×C4—26no—
313C2×C4—26no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—43no—
317C2×C4—43no—
318C2×C4—43no—
319C2×C4—43no—
320C2×C4—43no—
321C2×C4—43no—
322C2×C4—43no—
323C2×C4—43no—
324C2×C4—43no—
325C2×C4—43no—
326C2×C4—43no—
327C2×C4—43no—
328C2×C4—41no—
329C2×C4—43no—
330C2×C4—43no—
331C2×C4—43no—
332C2×C4—43no—
333C2×C4—43no—
334C2×C4—43no—
335C2×C4—43no—
336C2×C4—43no—
337C2×C4—43no—
338C2×C4#126×C4114yes—
339C22—46no—
340C22—46no—
341C22—42no—
342C22—83no—
343C22—83no—
344C22—81no—
345C22—81no—
346C22C2×#126×C4111yescharacteristic
347C22C41×#52913yes—
348C22C41×#52913yes—
349C22C41×#52913yes—
350C22C41×#53213yes—
351C22C41×#53813yes—
352C22C41×#53913yes—
353C22C41×#54613yes—
354C22C41×#54811yescharacteristic
355C22C41×#55113yes—
356C22C41×#55313yes—
357C22C41×#55313yes—
358C22C41×#55613yes—
359C4—24no—
360C4—46no—
361C4—46no—
362C4—46no—
363C4—83no—
364C4—81no—
365C2—82no—
366C2C41×#240111yescharacteristic
367C2C41×#255913yes—
368C2C41×#256013yes—
369C2C41×#257613yes—
370C2C41×#259413yes—
371C2C41×#264311yescharacteristic
372C2C41×#286011yescharacteristic
subgroupG/H
center, socleC24×C41C24
commutator, Frattini, cosocleC24C24×C41
prime radicalC25×C41C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#401C2semidirect
3. C41×#1442C2semidirect
6. C41×#1436C2semidirect
7. C4×#95×C41C2semidirect
152. #15171C41direct (N × H)
179. C2×#401C2×C41semidirect
181. #1442C2×C41semidirect
184. #1436C2×C41semidirect
185. C4×#95C2×C41semidirect
209. C41#15171direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4012
C2×C41×#3962
C41×#14422
C41×#14402
C41×#14372
C41×#14362
C4×#95×C412
#1517141