Finite Group Databasebeta

← C41×#21937 #23798138

Subgroups — C41×#21937 #23798138

Order 10496.

1030 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#408C212yesmaximal
2C41×#2297C211yesmaximal, characteristic
3C41×#1851C214yesmaximal, complemented
4C41×#1850C214yesmaximal, complemented
5C41×#1798C212yesmaximal, complemented
6C41×#1797C212yesmaximal, complemented
7C22×#41×C41C2211yescharacteristic
8C22×M16×C41C2212yes—
9C23×C8×C41C2212yes—
10C2×#117×C41C2211yescharacteristic
11C22×C42×C41C2211yescharacteristic
12C2×C4⋊C8×C41C2214yes—
13C2×C4⋊C8×C41C2214yes—
14C41×#408—28no—
15C2×C22⋊C8×C41C2214yes—
16C2×C22⋊C8×C41C2214yes—
17C41×#391C412yes—
18C41×#390C412yes—
19C41×#386C412yes—
20C41×#386C412yes—
21C4×C22⋊C4×C41C2214yes—
22C41×#336C2212yes—
23C41×#336C2212yes—
24C41×#336C2212yes—
25C41×#336C2212yes—
26C2×#41×C41—42no—
27C2×#41×C41—42no—
28C2×#41×C41D414yes—
29C2×#41×C41Q814yes—
30C22×Q8×C41C2×C411yescharacteristic
31C22×D4×C41C2×C412yes—
32C22×D4×C41C2×C411yescharacteristic
33C23×C4×C41C2×C411yescharacteristic
34C23×C4×C41C2×C411yescharacteristic
35C23×C4×C41C2311yescharacteristic
36C23×C4×C41C2312yes—
37C2×M16×C41—24no—
38C2×M16×C41—42no—
39C2×M16×C41—42no—
40C22×C8×C41—24no—
41C22×C8×C41—42no—
42C22×C8×C41—42no—
43C22×C8×C41C2314yes—
44C22×C8×C41C2314yes—
45#117×C41—42no—
46C2×C4⋊C4×C41C2×C412yes—
47C2×C22⋊C4×C41C2×C414yes—
48C2×C22⋊C4×C41C2×C412yes—
49C2×C22⋊C4×C41C2×C414yes—
50C2×C42×C41—42no—
51C2×C42×C41C2×C412yes—
52C2×C42×C41C2312yes—
53C2×C42×C41C2312yes—
54C4⋊C8×C41—44no—
55C4⋊C8×C41—44no—
56C22⋊C8×C41—28no—
57C22⋊C8×C41—28no—
58#95×C41C2×C414yes—
59#95×C41C2×C414yes—
60C24×C41C22×C412yes—
61C24×C41C22×C411yescharacteristic
62#41×C41—48no—
63#41×C41—48no—
64C2×Q8×C41—41no—
65C2×Q8×C41—41no—
66C2×Q8×C41C4⋊C414yes—
67C2×D4×C41—41no—
68C2×D4×C41—41no—
69C2×D4×C41—42no—
70C2×D4×C41—42no—
71C2×D4×C41C4⋊C418yes—
72C2×D4×C41C4⋊C414yes—
73C22×C4×C41—22no—
74C22×C4×C41—22no—
75C22×C4×C41—22no—
76C22×C4×C41—22no—
77C22×C4×C41—22no—
78C22×C4×C41—22no—
79C22×C4×C41—24no—
80C22×C4×C41—41no—
81C22×C4×C41—41no—
82C22×C4×C41—42no—
83C22×C4×C41C22×C412yes—
84C22×C4×C41C22×C414yes—
85C22×C4×C41C22×C412yes—
86C22×C4×C41C22×C411yescharacteristic
87C22×C4×C41C22×C412yes—
88C22×C4×C41C2×D412yes—
89C22×C4×C41C2×D414yes—
90C22×C4×C41C2×Q812yes—
91C22×C4×C41C2×Q814yes—
92C22×C4×C41C2411yescharacteristic
93M16×C41—48no—
94C2×C8×C41—24no—
95C2×C8×C41—24no—
96C2×C8×C41—24no—
97C2×C8×C41—24no—
98C2×C8×C41—24no—
99C2×C8×C41—24no—
100C2×C8×C41—48no—
101C4⋊C4×C41—42no—
102C22⋊C4×C41—28no—
103C22⋊C4×C41—44no—
104C22⋊C4×C41—42no—
105C42×C41—24no—
106C42×C41—24no—
107C42×C41—42no—
108C23×C41—21no—
109C23×C41—21no—
110C23×C41—22no—
111C23×C41—22no—
112C23×C41—24no—
113C23×C41—22no—
114C23×C41—24no—
115C23×C41—22no—
116C23×C41C2×C4⋊C412yes—
117C23×C41C2×C4⋊C414yes—
118C23×C41C23×C411yescharacteristic
119Q8×C41—44no—
120D4×C41—44no—
121D4×C41—48no—
122C2×C4×C41—22no—
123C2×C4×C41—21no—
124C2×C4×C41—21no—
125C2×C4×C41—22no—
126C2×C4×C41—22no—
127C2×C4×C41—22no—
128C2×C4×C41—24no—
129C2×C4×C41—24no—
130C2×C4×C41—24no—
131C2×C4×C41—24no—
132C2×C4×C41—24no—
133C2×C4×C41—24no—
134C2×C4×C41—22no—
135C2×C4×C41—24no—
136C2×C4×C41—24no—
137C2×C4×C41—22no—
138C2×C4×C41—24no—
139C2×C4×C41—22no—
140C2×C4×C41—44no—
141C2×C4×C41—44no—
142C2×C4×C41C2×C4⋊C414yes—
143C2×C4×C41C2×C4⋊C412yes—
144C2×C4×C41#13114yes—
145C2×C4×C41C22×D411yescharacteristic
146C2×C4×C41C22×Q811yescharacteristic
147C2×C4×C41H(5,𝔽2)12yes—
148C2×C4×C41H(5,𝔽2)12yes—
149C8×C41—44no—
150C8×C41—44no—
151#21937C4111yesmaximal, characteristic, direct product factor, Sylow
152C22×C41—24no—
153C22×C41—22no—
154C22×C41—28no—
155C22×C41—24no—
156C22×C41—41no—
157C22×C41—42no—
158C22×C41—41no—
159C22×C41—42no—
160C22×C41—42no—
161C22×C41—44no—
162C22×C41C22×C4⋊C411yescharacteristic
163C22×C41#51811yescharacteristic
164C22×C41#51811yescharacteristic
165C22×C41C2×#13112yes—
166C22×C41#56812yes—
167C4×C41—22no—
168C4×C41—24no—
169C4×C41—24no—
170C4×C41—42no—
171C4×C41—44no—
172C4×C41#53412yes—
173C4×C41#54312yes—
174C2×#408C2×C4112yes—
175#2297C2×C4111yescharacteristic
176#1851C2×C4114yescomplemented
177#1850C2×C4114yescomplemented
178#1798C2×C4112yescomplemented
179#1797C2×C4112yescomplemented
180C2×C41—42no—
181C2×C41—44no—
182C2×C41#231511yescharacteristic
183C2×C41#290612yes—
184C2×C41#297711yescharacteristic
185C2×C41#297811yescharacteristic
186C2×C41#298112yes—
187C22×#41C22×C4111yescharacteristic
188C22×M16C22×C4112yes—
189C23×C8C22×C4112yes—
190C2×#117C22×C4111yescharacteristic
191C22×C42C22×C4111yescharacteristic
192C2×C4⋊C8C22×C4114yes—
193C2×C4⋊C8C22×C4114yes—
194#408—28no—
195C2×C22⋊C8C22×C4114yes—
196C2×C22⋊C8C22×C4114yes—
197#391C4×C4112yes—
198#390C4×C4112yes—
199#386C4×C4112yes—
200#386C4×C4112yes—
201C4×C22⋊C4C22×C4114yes—
202#336C22×C4112yes—
203#336C22×C4112yes—
204#336C22×C4112yes—
205#336C22×C4112yes—
206C41#2193711yescharacteristic, direct product factor, Sylow
207C2×#41—42no—
208C2×#41—42no—
209C2×#41D4×C4114yes—
210C2×#41Q8×C4114yes—
211C22×Q8C2×C4×C4111yescharacteristic
212C22×D4C2×C4×C4112yes—
213C22×D4C2×C4×C4111yescharacteristic
214C23×C4C2×C4×C4111yescharacteristic
215C23×C4C2×C4×C4111yescharacteristic
216C23×C4C23×C4111yescharacteristic
217C23×C4C23×C4112yes—
218C2×M16—24no—
219C2×M16—42no—
220C2×M16—42no—
221C22×C8—24no—
222C22×C8—42no—
223C22×C8—42no—
224C22×C8C23×C4114yes—
225C22×C8C23×C4114yes—
226#117—42no—
227C2×C4⋊C4C2×C4×C4112yes—
228C2×C22⋊C4C2×C4×C4114yes—
229C2×C22⋊C4C2×C4×C4112yes—
230C2×C22⋊C4C2×C4×C4114yes—
231C2×C42—42no—
232C2×C42C2×C4×C4112yes—
233C2×C42C23×C4112yes—
234C2×C42C23×C4112yes—
235C4⋊C8—44no—
236C4⋊C8—44no—
237C22⋊C8—28no—
238C22⋊C8—28no—
239#95C2×C4×C4114yes—
240#95C2×C4×C4114yes—
241C24C22×C4×C4112yes—
242C24C22×C4×C4111yescharacteristic
243#41—48no—
244#41—48no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8C4⋊C4×C4114yes—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4C4⋊C4×C4118yes—
253C2×D4C4⋊C4×C4114yes—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—24no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4C22×C4×C4112yes—
265C22×C4C22×C4×C4114yes—
266C22×C4C22×C4×C4112yes—
267C22×C4C22×C4×C4111yescharacteristic
268C22×C4C22×C4×C4112yes—
269C22×C4C2×D4×C4112yes—
270C22×C4C2×D4×C4114yes—
271C22×C4C2×Q8×C4112yes—
272C22×C4C2×Q8×C4114yes—
273C22×C4C24×C4111yescharacteristic
274M16—48no—
275C2×C8—24no—
276C2×C8—24no—
277C2×C8—24no—
278C2×C8—24no—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—48no—
282C4⋊C4—42no—
283C22⋊C4—28no—
284C22⋊C4—42no—
285C22⋊C4—44no—
286C42—24no—
287C42—24no—
288C42—42no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—24no—
294C23—22no—
295C23—24no—
296C23—22no—
297C23C2×C4⋊C4×C4112yes—
298C23C2×C4⋊C4×C4114yes—
299C23C23×C4×C4111yescharacteristic
300Q8—44no—
301D4—44no—
302D4—48no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—22no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—22no—
319C2×C4—24no—
320C2×C4—22no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4C2×C4⋊C4×C4114yes—
324C2×C4C2×C4⋊C4×C4112yes—
325C2×C4#131×C4114yes—
326C2×C4C22×D4×C4111yescharacteristic
327C2×C4C22×Q8×C4111yescharacteristic
328C2×C4H(5,𝔽2)×C4112yes—
329C2×C4H(5,𝔽2)×C4112yes—
330C8—44no—
331C8—44no—
332C22—24no—
333C22—22no—
334C22—28no—
335C22—24no—
336C22—41no—
337C22—42no—
338C22—41no—
339C22—42no—
340C22—42no—
341C22—44no—
342C22C22×C4⋊C4×C4111yescharacteristic
343C22C41×#51811yescharacteristic
344C22C41×#51811yescharacteristic
345C22C2×#131×C4112yes—
346C22C41×#56812yes—
347C4—22no—
348C4—24no—
349C4—24no—
350C4—42no—
351C4—44no—
352C4C41×#53412yes—
353C4C41×#54312yes—
354C2—42no—
355C2—44no—
356C2C41×#231511yescharacteristic
357C2C41×#290612yes—
358C2C41×#297711yescharacteristic
359C2C41×#297811yescharacteristic
360C2C41×#298112yes—
subgroupG/H
centerC22×C4×C41C24
commutatorC23C23×C4×C41
Frattini, cosocleC22×C4C24×C41
socleC23×C41C23×C4
prime radicalC22×#41×C41C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
3. C41×#1851C2semidirect
4. C41×#1850C2semidirect
5. C41×#1798C2semidirect
6. C41×#1797C2semidirect
151. #21937C41direct (N × H)
176. #1851C2×C41semidirect
177. #1850C2×C41semidirect
178. #1798C2×C41semidirect
179. #1797C2×C41semidirect
206. C41#21937direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4082
C41×#22972
C41×#18512
C41×#18502
C41×#17982
C41×#17972
#2193741