Finite Group Databasebeta

← C41×#36692 #23812893

Subgroups — C41×#36692 #23812893

Order 10496.

1716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#2837C214yesmaximal, complemented
2C41×#2836C214yesmaximal, complemented
3C41×#2829C214yesmaximal, complemented
4C41×#2828C214yesmaximal, complemented
5C41×#2402C211yesmaximal, characteristic, complemented
6C41×#2397C211yesmaximal, characteristic, complemented
7C41×#2395C214yesmaximal, complemented
8C41×#2392C212yesmaximal, complemented
9C41×#2392C214yesmaximal, complemented
10C41×#2298C211yesmaximal, characteristic, complemented
11C41×#2293C212yesmaximal, complemented
12C2×C4×D4×C41C2212yes—
13C2×C4×D4×C41C2214yes—
14C2×C4×D4×C41C2214yes—
15C2×#117×C41C2211yescharacteristic
16C2×#117×C41C2214yes—
17C41×#400C2214yes—
18C41×#400C2214yes—
19C41×#399C2214yes—
20C41×#399C2214yes—
21C41×#398C2214yes—
22C41×#398C2214yes—
23C41×#398C2212yes—
24C41×#398C2214yes—
25C41×#397C2214yes—
26C41×#397C2214yes—
27C41×#397C2214yes—
28C41×#397C2214yes—
29C41×#397C2212yes—
30C41×#396C2214yes—
31C41×#396C2214yes—
32C41×#396C2214yes—
33C41×#394C2214yes—
34C41×#394C2214yes—
35C41×#394C2214yes—
36C41×#394C2214yes—
37C41×#394C2214yes—
38C41×#394C2214yes—
39C41×#394C2212yes—
40C41×#392C2212yes—
41C41×#392C2214yes—
42C41×#392C2214yes—
43C41×#390C2214yes—
44C41×#389C2214yes—
45C41×#388C2214yes—
46C41×#388C2214yes—
47C41×#388C2214yes—
48C41×#387C2214yes—
49C4×C4⋊C4×C41C2212yes—
50C4×C4⋊C4×C41C2212yes—
51C4×C4⋊C4×C41C2214yes—
52C4×C22⋊C4×C41C2214yes—
53C4×C22⋊C4×C41C2212yes—
54C4×C22⋊C4×C41C2214yes—
55C41×#376C2211yescharacteristic
56C43×C41C2211yescharacteristic
57C22×D4×C41C2312yes—
58C22×D4×C41C2314yes—
59C22×D4×C41C2314yes—
60C23×C4×C41C2311yescharacteristic
61C23×C4×C41C2314yes—
62C4×D4×C41—28no—
63C4×D4×C41—48no—
64C4×D4×C41—48no—
65#117×C41—24no—
66#117×C41—48no—
67C2×C4⋊C4×C41C2312yes—
68C2×C4⋊C4×C41C2312yes—
69C2×C4⋊C4×C41C2314yes—
70C2×C4⋊C4×C41C2314yes—
71C2×C4⋊C4×C41C2314yes—
72C2×C4⋊C4×C41C2314yes—
73C2×C4⋊C4×C41C2314yes—
74C2×C4⋊C4×C41C2314yes—
75C2×C4⋊C4×C41C2314yes—
76C2×C4⋊C4×C41C2314yes—
77C2×C22⋊C4×C41C2312yes—
78C2×C22⋊C4×C41C2314yes—
79C2×C22⋊C4×C41C2314yes—
80C2×C22⋊C4×C41C2314yes—
81C2×C22⋊C4×C41C2314yes—
82C2×C22⋊C4×C41C2314yes—
83C2×C22⋊C4×C41C2314yes—
84C2×C22⋊C4×C41C2314yes—
85C2×C22⋊C4×C41C2314yes—
86C2×C22⋊C4×C41C2314yes—
87C2×C22⋊C4×C41C2314yes—
88C2×C22⋊C4×C41C2314yes—
89C2×C22⋊C4×C41C2314yes—
90C2×C42×C41C2312yes—
91C2×C42×C41C2314yes—
92C2×C42×C41C2311yescharacteristic
93C2×C42×C41C2312yes—
94C2×C42×C41C2314yes—
95C2×C42×C41C2311yescharacteristic
96#95×C41C2314yes—
97#95×C41C2314yes—
98#95×C41C2314yes—
99#95×C41C2314yes—
100#95×C41C2314yes—
101#95×C41C2314yes—
102#95×C41C2314yes—
103#95×C41C2312yes—
104#95×C41C2312yes—
105#95×C41C2314yes—
106#95×C41C2314yes—
107C24×C41C2411yescharacteristic
108C24×C41C2414yes—
109C2×D4×C41—24no—
110C2×D4×C41—44no—
111C2×D4×C41—44no—
112C2×D4×C41—44no—
113C2×D4×C41—44no—
114C2×D4×C41—44no—
115C2×D4×C41—44no—
116C2×D4×C41—44no—
117C22×C4×C41—22no—
118C22×C4×C41—28no—
119C22×C4×C41—28no—
120C22×C4×C41—24no—
121C22×C4×C41—28no—
122C22×C4×C41C2412yes—
123C22×C4×C41C2414yes—
124C22×C4×C41C2414yes—
125C22×C4×C41C2414yes—
126C22×C4×C41C2414yes—
127C22×C4×C41C2414yes—
128C22×C4×C41C2411yescharacteristic
129C22×C4×C41C2412yes—
130C22×C4×C41C2411yescharacteristic
131C4⋊C4×C41—24no—
132C4⋊C4×C41—24no—
133C4⋊C4×C41—44no—
134C4⋊C4×C41—44no—
135C4⋊C4×C41—44no—
136C4⋊C4×C41—44no—
137C4⋊C4×C41—44no—
138C4⋊C4×C41—44no—
139C4⋊C4×C41—44no—
140C4⋊C4×C41—44no—
141C22⋊C4×C41—24no—
142C22⋊C4×C41—28no—
143C22⋊C4×C41—44no—
144C22⋊C4×C41—44no—
145C22⋊C4×C41—44no—
146C22⋊C4×C41—44no—
147C22⋊C4×C41—44no—
148C22⋊C4×C41—44no—
149C22⋊C4×C41—44no—
150C22⋊C4×C41—44no—
151C22⋊C4×C41—44no—
152C22⋊C4×C41—44no—
153C22⋊C4×C41—44no—
154C42×C41—22no—
155C42×C41—24no—
156C42×C41—28no—
157C42×C41—24no—
158C42×C41—44no—
159C42×C41#4114yes—
160C23×C41—21no—
161C23×C41—24no—
162C23×C41—24no—
163C23×C41—22no—
164C23×C41—24no—
165C23×C41—24no—
166C23×C41—24no—
167C23×C41—24no—
168C23×C41—24no—
169C23×C41—24no—
170C23×C41C2511yescharacteristic
171D4×C41—48no—
172D4×C41—416no—
173D4×C41—416no—
174C2×C4×C41—24no—
175C2×C4×C41—22no—
176C2×C4×C41—24no—
177C2×C4×C41—21no—
178C2×C4×C41—24no—
179C2×C4×C41—24no—
180C2×C4×C41—24no—
181C2×C4×C41—24no—
182C2×C4×C41—24no—
183C2×C4×C41—22no—
184C2×C4×C41—24no—
185C2×C4×C41—24no—
186C2×C4×C41—24no—
187C2×C4×C41—24no—
188C2×C4×C41—24no—
189C2×C4×C41—24no—
190C2×C4×C41—24no—
191C2×C4×C41—24no—
192C2×C4×C41—24no—
193C2×C4×C41—24no—
194C2×C4×C41—44no—
195C2×C4×C41—416no—
196C2×C4×C41C2×#4114yes—
197C2×C4×C41C2×#4112yes—
198C2×C4×C41H(5,𝔽2)14yes—
199#36692C4111yesmaximal, characteristic, direct product factor, Sylow
200C22×C41—41no—
201C22×C41—44no—
202C22×C41—44no—
203C22×C41—42no—
204C22×C41—44no—
205C22×C41—44no—
206C22×C41—44no—
207C22×C41—44no—
208C22×C41—44no—
209C22×C41—44no—
210C22×C41C22×#4111yescharacteristic
211C22×C41C2×H(5,𝔽2)12yes—
212C22×C41#58514yes—
213C4×C41—24no—
214C4×C41—44no—
215C4×C41—41no—
216C4×C41—42no—
217C4×C41—44no—
218C4×C41—44no—
219C4×C41—44no—
220C4×C41—44no—
221C4×C41#54014yes—
222#2837C2×C4114yescomplemented
223#2836C2×C4114yescomplemented
224#2829C2×C4114yescomplemented
225#2828C2×C4114yescomplemented
226#2402C2×C4111yescharacteristic, complemented
227#2397C2×C4111yescharacteristic, complemented
228#2395C2×C4114yescomplemented
229#2392C2×C4112yescomplemented
230#2392C2×C4114yescomplemented
231#2298C2×C4111yescharacteristic, complemented
232#2293C2×C4112yescomplemented
233C2×C41—84no—
234C2×C41—81no—
235C2×C41C2×#54011yescharacteristic
236C2×C41#345512yes—
237C2×C41#352914yes—
238C2×C4×D4C22×C4112yes—
239C2×C4×D4C22×C4114yes—
240C2×C4×D4C22×C4114yes—
241C2×#117C22×C4111yescharacteristic
242C2×#117C22×C4114yes—
243#400C22×C4114yes—
244#400C22×C4114yes—
245#399C22×C4114yes—
246#399C22×C4114yes—
247#398C22×C4114yes—
248#398C22×C4114yes—
249#398C22×C4112yes—
250#398C22×C4114yes—
251#397C22×C4114yes—
252#397C22×C4114yes—
253#397C22×C4114yes—
254#397C22×C4114yes—
255#397C22×C4112yes—
256#396C22×C4114yes—
257#396C22×C4114yes—
258#396C22×C4114yes—
259#394C22×C4114yes—
260#394C22×C4114yes—
261#394C22×C4114yes—
262#394C22×C4114yes—
263#394C22×C4114yes—
264#394C22×C4114yes—
265#394C22×C4112yes—
266#392C22×C4112yes—
267#392C22×C4114yes—
268#392C22×C4114yes—
269#390C22×C4114yes—
270#389C22×C4114yes—
271#388C22×C4114yes—
272#388C22×C4114yes—
273#388C22×C4114yes—
274#387C22×C4114yes—
275C4×C4⋊C4C22×C4114yes—
276C4×C4⋊C4C22×C4112yes—
277C4×C4⋊C4C22×C4112yes—
278C4×C22⋊C4C22×C4112yes—
279C4×C22⋊C4C22×C4114yes—
280C4×C22⋊C4C22×C4114yes—
281#376C22×C4111yescharacteristic
282C43C22×C4111yescharacteristic
283C41#3669211yescharacteristic, direct product factor, Sylow
284C22×D4C23×C4112yes—
285C22×D4C23×C4114yes—
286C22×D4C23×C4114yes—
287C23×C4C23×C4111yescharacteristic
288C23×C4C23×C4114yes—
289C4×D4—28no—
290C4×D4—48no—
291C4×D4—48no—
292#117—24no—
293#117—48no—
294C2×C4⋊C4C23×C4112yes—
295C2×C4⋊C4C23×C4112yes—
296C2×C4⋊C4C23×C4114yes—
297C2×C4⋊C4C23×C4114yes—
298C2×C4⋊C4C23×C4114yes—
299C2×C4⋊C4C23×C4114yes—
300C2×C4⋊C4C23×C4114yes—
301C2×C4⋊C4C23×C4114yes—
302C2×C4⋊C4C23×C4114yes—
303C2×C4⋊C4C23×C4114yes—
304C2×C22⋊C4C23×C4112yes—
305C2×C22⋊C4C23×C4114yes—
306C2×C22⋊C4C23×C4114yes—
307C2×C22⋊C4C23×C4114yes—
308C2×C22⋊C4C23×C4114yes—
309C2×C22⋊C4C23×C4114yes—
310C2×C22⋊C4C23×C4114yes—
311C2×C22⋊C4C23×C4114yes—
312C2×C22⋊C4C23×C4114yes—
313C2×C22⋊C4C23×C4114yes—
314C2×C22⋊C4C23×C4114yes—
315C2×C22⋊C4C23×C4114yes—
316C2×C22⋊C4C23×C4114yes—
317C2×C42C23×C4112yes—
318C2×C42C23×C4114yes—
319C2×C42C23×C4111yescharacteristic
320C2×C42C23×C4112yes—
321C2×C42C23×C4114yes—
322C2×C42C23×C4111yescharacteristic
323#95C23×C4114yes—
324#95C23×C4114yes—
325#95C23×C4114yes—
326#95C23×C4114yes—
327#95C23×C4114yes—
328#95C23×C4114yes—
329#95C23×C4114yes—
330#95C23×C4112yes—
331#95C23×C4112yes—
332#95C23×C4114yes—
333#95C23×C4114yes—
334C24C24×C4111yescharacteristic
335C24C24×C4114yes—
336C2×D4—24no—
337C2×D4—44no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4—44no—
343C2×D4—44no—
344C22×C4—22no—
345C22×C4—28no—
346C22×C4—28no—
347C22×C4—24no—
348C22×C4—28no—
349C22×C4C24×C4112yes—
350C22×C4C24×C4114yes—
351C22×C4C24×C4114yes—
352C22×C4C24×C4114yes—
353C22×C4C24×C4114yes—
354C22×C4C24×C4114yes—
355C22×C4C24×C4111yescharacteristic
356C22×C4C24×C4112yes—
357C22×C4C24×C4111yescharacteristic
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—44no—
361C4⋊C4—44no—
362C4⋊C4—44no—
363C4⋊C4—44no—
364C4⋊C4—44no—
365C4⋊C4—44no—
366C4⋊C4—44no—
367C4⋊C4—44no—
368C22⋊C4—24no—
369C22⋊C4—28no—
370C22⋊C4—44no—
371C22⋊C4—44no—
372C22⋊C4—44no—
373C22⋊C4—44no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—44no—
377C22⋊C4—44no—
378C22⋊C4—44no—
379C22⋊C4—44no—
380C22⋊C4—44no—
381C42—22no—
382C42—24no—
383C42—28no—
384C42—24no—
385C42—44no—
386C42#41×C4114yes—
387C23—21no—
388C23—24no—
389C23—24no—
390C23—22no—
391C23—24no—
392C23—24no—
393C23—24no—
394C23—24no—
395C23—24no—
396C23—24no—
397C23C25×C4111yescharacteristic
398D4—48no—
399D4—416no—
400D4—416no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—21no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—44no—
422C2×C4—416no—
423C2×C4C2×#41×C4114yes—
424C2×C4C2×#41×C4112yes—
425C2×C4H(5,𝔽2)×C4114yes—
426C22—41no—
427C22—44no—
428C22—44no—
429C22—42no—
430C22—44no—
431C22—44no—
432C22—44no—
433C22—44no—
434C22—44no—
435C22—44no—
436C22C22×#41×C4111yescharacteristic
437C22C2×H(5,𝔽2)×C4112yes—
438C22C41×#58514yes—
439C4—24no—
440C4—44no—
441C4—41no—
442C4—42no—
443C4—44no—
444C4—44no—
445C4—44no—
446C4—44no—
447C4C41×#54014yes—
448C2—84no—
449C2—81no—
450C2C2×C41×#54011yescharacteristic
451C2C41×#345512yes—
452C2C41×#352914yes—
subgroupG/H
centerC22×C4×C41C24
commutator, Frattini, cosocleC23C25×C41
socleC23×C41C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#2837C2semidirect
2. C41×#2836C2semidirect
3. C41×#2829C2semidirect
4. C41×#2828C2semidirect
5. C41×#2402C2semidirect
6. C41×#2397C2semidirect
7. C41×#2395C2semidirect
8. C41×#2392C2semidirect
9. C41×#2392C2semidirect
10. C41×#2298C2semidirect
11. C41×#2293C2semidirect
199. #36692C41direct (N × H)
222. #2837C2×C41semidirect
223. #2836C2×C41semidirect
224. #2829C2×C41semidirect
225. #2828C2×C41semidirect
226. #2402C2×C41semidirect
227. #2397C2×C41semidirect
228. #2395C2×C41semidirect
229. #2392C2×C41semidirect
230. #2392C2×C41semidirect
231. #2298C2×C41semidirect
232. #2293C2×C41semidirect
283. C41#36692direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#28372
C41×#28362
C41×#28292
C41×#28282
C41×#24022
C41×#23972
C41×#23952
C41×#23922
C41×#22982
C41×#22932
#3669241