Finite Group Databasebeta

← C41×#34594 #23810795

Subgroups — C41×#34594 #23810795

Order 10496.

2362 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#529C212yesmaximal, complemented
2C41×#2664C214yesmaximal, complemented
3C41×#2662C214yesmaximal, complemented
4C41×#2659C211yesmaximal, characteristic, complemented
5C41×#2656C211yesmaximal, characteristic
6C41×#2639C212yesmaximal, complemented
7C41×#2618C214yesmaximal, complemented
8C41×#2396C214yesmaximal, complemented
9C41×#2392C214yesmaximal, complemented
10C4×#121×C41C214yesmaximal, complemented
11C2×C4×C4⋊C4×C41C211yesmaximal, characteristic, complemented
12C41×#529—216no—
13C2×#126×C41C2214yes—
14C2×#125×C41C2212yes—
15C2×#124×C41C2212yes—
16C2×#123×C41C2214yes—
17C2×C22⋊Q8×C41C2212yes—
18C2×#121×C41C2214yes—
19C2×#121×C41C2212yes—
20C2×C4×Q8×C41C2212yes—
21C2×C4×D4×C41C2214yes—
22C2×C4×D4×C41C2212yes—
23C2×C4×D4×C41C2214yes—
24C2×#117×C41C2214yes—
25C22×C4⋊C4×C41C2212yes—
26C22×C42×C41C2212yes—
27C22×C42×C41C2211yescharacteristic
28C41×#400C2214yes—
29C41×#399C2214yes—
30C41×#398C2218yes—
31C41×#398C2214yes—
32C41×#397C2214yes—
33C41×#396C2218yes—
34C41×#396C2218yes—
35C41×#395C2214yes—
36C41×#394C2218yes—
37C41×#394C2214yes—
38C41×#393C2214yes—
39C41×#392C2214yes—
40C41×#390C2214yes—
41C41×#389C2214yes—
42C41×#388C2218yes—
43C41×#386C2218yes—
44C41×#380C2214yes—
45C4×C4⋊C4×C41C2214yes—
46C4×C4⋊C4×C41C2214yes—
47C4×C4⋊C4×C41C2214yes—
48C4×C22⋊C4×C41C2218yes—
49C2×#95×C41C2211yescharacteristic
50C2×#95×C41C2211yescharacteristic
51C22×Q8×C41C2312yes—
52C22×D4×C41C2314yes—
53C22×D4×C41C2312yes—
54C22×D4×C41C2314yes—
55C23×C4×C41C2314yes—
56C23×C4×C41C2311yescharacteristic
57C23×C4×C41C2311yescharacteristic
58C23×C4×C41C2312yes—
59C23×C4×C41C2311yescharacteristic
60C23×C4×C41C2312yes—
61#126×C41—216no—
62#125×C41—28no—
63#124×C41—28no—
64#123×C41—216no—
65C22⋊Q8×C41—28no—
66#121×C41—28no—
67#121×C41—216no—
68C4×Q8×C41—28no—
69C4×D4×C41—216no—
70C4×D4×C41—28no—
71C4×D4×C41—48no—
72#117×C41—216no—
73C2×C4⋊C4×C41—28no—
74C2×C4⋊C4×C41C2318yes—
75C2×C4⋊C4×C41C2314yes—
76C2×C4⋊C4×C41C2314yes—
77C2×C4⋊C4×C41C2312yes—
78C2×C4⋊C4×C41C2314yes—
79C2×C4⋊C4×C41C2312yes—
80C2×C4⋊C4×C41C2314yes—
81C2×C4⋊C4×C41C2314yes—
82C2×C4⋊C4×C41C2314yes—
83C2×C4⋊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×C41C2318yes—
90C2×C22⋊C4×C41C2318yes—
91C2×C22⋊C4×C41C2318yes—
92C2×C42×C41—44no—
93C2×C42×C41D418yescomplemented
94C2×C42×C41C2314yes—
95C2×C42×C41C2314yes—
96C2×C42×C41C2314yes—
97C2×C42×C41C2312yes—
98C2×C42×C41C2312yes—
99#95×C41C2314yes—
100#95×C41C2314yes—
101#95×C41C2318yes—
102#95×C41C2318yes—
103#95×C41C2318yes—
104C24×C41C2414yes—
105C24×C41C2411yescharacteristic
106C2×Q8×C41—24no—
107C2×Q8×C41—44no—
108C2×D4×C41—28no—
109C2×D4×C41—216no—
110C2×D4×C41—24no—
111C2×D4×C41—28no—
112C2×D4×C41—44no—
113C2×D4×C41—44no—
114C2×D4×C41—44no—
115C22×C4×C41—24no—
116C22×C4×C41—22no—
117C22×C4×C41—22no—
118C22×C4×C41—24no—
119C22×C4×C41—28no—
120C22×C4×C41—28no—
121C22×C4×C41—28no—
122C22×C4×C41—42no—
123C22×C4×C41—42no—
124C22×C4×C41—42no—
125C22×C4×C41—42no—
126C22×C4×C41—42no—
127C22×C4×C41C2×D414yes—
128C22×C4×C41C2×D414yes—
129C22×C4×C41C2×D414yes—
130C22×C4×C41#4118yes—
131C22×C4×C41C2414yes—
132C22×C4×C41C2414yes—
133C22×C4×C41C2414yes—
134C22×C4×C41C2414yes—
135C22×C4×C41C2412yes—
136C22×C4×C41C2411yescharacteristic
137C22×C4×C41C2412yes—
138C22×C4×C41C2414yes—
139C22×C4×C41C2411yescharacteristic
140C4⋊C4×C41—28no—
141C4⋊C4×C41—28no—
142C4⋊C4×C41—24no—
143C4⋊C4×C41—28no—
144C4⋊C4×C41—24no—
145C4⋊C4×C41—28no—
146C4⋊C4×C41—216no—
147C4⋊C4×C41—28no—
148C4⋊C4×C41—44no—
149C4⋊C4×C41—44no—
150C22⋊C4×C41—28no—
151C22⋊C4×C41—28no—
152C22⋊C4×C41—28no—
153C22⋊C4×C41—28no—
154C22⋊C4×C41—28no—
155C22⋊C4×C41—216no—
156C22⋊C4×C41—48no—
157C22⋊C4×C41—48no—
158C42×C41—28no—
159C42×C41—28no—
160C42×C41—44no—
161C42×C41C2×D418yes—
162C42×C41C2×D418yes—
163C23×C41—21no—
164C23×C41—21no—
165C23×C41—22no—
166C23×C41—24no—
167C23×C41—28no—
168C23×C41—24no—
169C23×C41—24no—
170C23×C41—28no—
171C23×C41C22×D412yes—
172C23×C41C2×#4114yes—
173C23×C41C2511yescharacteristic
174Q8×C41—48no—
175D4×C41—48no—
176D4×C41—416no—
177D4×C41—416no—
178C2×C4×C41—28no—
179C2×C4×C41—24no—
180C2×C4×C41—24no—
181C2×C4×C41—21no—
182C2×C4×C41—21no—
183C2×C4×C41—24no—
184C2×C4×C41—24no—
185C2×C4×C41—28no—
186C2×C4×C41—24no—
187C2×C4×C41—24no—
188C2×C4×C41—24no—
189C2×C4×C41—28no—
190C2×C4×C41—24no—
191C2×C4×C41—24no—
192C2×C4×C41—24no—
193C2×C4×C41—24no—
194C2×C4×C41—24no—
195C2×C4×C41—28no—
196C2×C4×C41—44no—
197C2×C4×C41—48no—
198C2×C4×C41—48no—
199C2×C4×C41—416no—
200C2×C4×C41C22×D414yes—
201C2×C4×C41C22×D412yes—
202C2×C4×C41C22×D414yes—
203C2×C4×C41C22×D412yes—
204C2×C4×C41C2×#4118yes—
205C2×C4×C41H(5,𝔽2)12yes—
206C2×C4×C412−1+412yes—
207#34594C4111yesmaximal, characteristic, direct product factor, Sylow
208C22×C41—22no—
209C22×C41—22no—
210C22×C41—24no—
211C22×C41—24no—
212C22×C41—44no—
213C22×C41—44no—
214C22×C41—44no—
215C22×C41—48no—
216C22×C41—48no—
217C22×C41#53214yes—
218C22×C41C23×D411yescharacteristic
219C22×C41C22×#4112yes—
220C22×C41C2×H(5,𝔽2)11yescharacteristic
221C22×C41C2×2−1+411yescharacteristic
222C22×C41#58512yes—
223C4×C41—24no—
224C4×C41—22no—
225C4×C41—24no—
226C4×C41—28no—
227C4×C41—44no—
228C4×C41—44no—
229C4×C41—44no—
230C4×C41—44no—
231C4×C41#53714yes—
232C2×#529C2×C4112yescomplemented
233#2664C2×C4114yescomplemented
234#2662C2×C4114yescomplemented
235#2659C2×C4111yescharacteristic, complemented
236#2656C2×C4111yescharacteristic
237#2639C2×C4112yescomplemented
238#2618C2×C4114yescomplemented
239#2396C2×C4114yescomplemented
240#2392C2×C4114yescomplemented
241C4×#121C2×C4114yescomplemented
242C2×C4×C4⋊C4C2×C4111yescharacteristic, complemented
243C2×C41—24no—
244C2×C41—84no—
245C2×C41C2×#53211yescharacteristic
246C2×C41C2×#53711yescharacteristic
247C2×C41#344911yescharacteristic
248C2×C41#345912yes—
249C2×C41#346112yes—
250#529—216no—
251C2×#126C22×C4114yes—
252C2×#125C22×C4112yes—
253C2×#124C22×C4112yes—
254C2×#123C22×C4114yes—
255C2×C22⋊Q8C22×C4112yes—
256C2×#121C22×C4114yes—
257C2×#121C22×C4112yes—
258C2×C4×Q8C22×C4112yes—
259C2×C4×D4C22×C4112yes—
260C2×C4×D4C22×C4114yes—
261C2×C4×D4C22×C4114yes—
262C2×#117C22×C4114yes—
263C22×C4⋊C4C22×C4112yes—
264C22×C42C22×C4112yes—
265C22×C42C22×C4111yescharacteristic
266#400C22×C4114yes—
267#399C22×C4114yes—
268#398C22×C4118yes—
269#398C22×C4114yes—
270#397C22×C4114yes—
271#396C22×C4118yes—
272#396C22×C4118yes—
273#395C22×C4114yes—
274#394C22×C4118yes—
275#394C22×C4114yes—
276#393C22×C4114yes—
277#392C22×C4114yes—
278#390C22×C4114yes—
279#389C22×C4114yes—
280#388C22×C4118yes—
281#386C22×C4118yes—
282#380C22×C4114yes—
283C4×C4⋊C4C22×C4114yes—
284C4×C4⋊C4C22×C4114yes—
285C4×C4⋊C4C22×C4114yes—
286C4×C22⋊C4C22×C4118yes—
287C2×#95C22×C4111yescharacteristic
288C2×#95C22×C4111yescharacteristic
289C41#3459411yescharacteristic, direct product factor, Sylow
290C22×Q8C23×C4112yes—
291C22×D4C23×C4114yes—
292C22×D4C23×C4112yes—
293C22×D4C23×C4114yes—
294C23×C4C23×C4114yes—
295C23×C4C23×C4111yescharacteristic
296C23×C4C23×C4111yescharacteristic
297C23×C4C23×C4112yes—
298C23×C4C23×C4111yescharacteristic
299C23×C4C23×C4112yes—
300#126—216no—
301#125—28no—
302#124—28no—
303#123—216no—
304C22⋊Q8—28no—
305#121—28no—
306#121—216no—
307C4×Q8—28no—
308C4×D4—216no—
309C4×D4—28no—
310C4×D4—48no—
311#117—216no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4C23×C4118yes—
314C2×C4⋊C4C23×C4114yes—
315C2×C4⋊C4C23×C4114yes—
316C2×C4⋊C4C23×C4112yes—
317C2×C4⋊C4C23×C4114yes—
318C2×C4⋊C4C23×C4112yes—
319C2×C4⋊C4C23×C4114yes—
320C2×C4⋊C4C23×C4114yes—
321C2×C4⋊C4C23×C4114yes—
322C2×C4⋊C4C23×C4114yes—
323C2×C22⋊C4C23×C4114yes—
324C2×C22⋊C4C23×C4114yes—
325C2×C22⋊C4C23×C4114yes—
326C2×C22⋊C4C23×C4114yes—
327C2×C22⋊C4C23×C4114yes—
328C2×C22⋊C4C23×C4118yes—
329C2×C22⋊C4C23×C4118yes—
330C2×C22⋊C4C23×C4118yes—
331C2×C42—44no—
332C2×C42D4×C4118yescomplemented
333C2×C42C23×C4114yes—
334C2×C42C23×C4114yes—
335C2×C42C23×C4114yes—
336C2×C42C23×C4112yes—
337C2×C42C23×C4112yes—
338#95C23×C4114yes—
339#95C23×C4114yes—
340#95C23×C4118yes—
341#95C23×C4118yes—
342#95C23×C4118yes—
343C24C24×C4114yes—
344C24C24×C4111yescharacteristic
345C2×Q8—24no—
346C2×Q8—44no—
347C2×D4—28no—
348C2×D4—216no—
349C2×D4—24no—
350C2×D4—28no—
351C2×D4—44no—
352C2×D4—44no—
353C2×D4—44no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4—28no—
359C22×C4—28no—
360C22×C4—28no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4C2×D4×C4114yes—
367C22×C4C2×D4×C4114yes—
368C22×C4C2×D4×C4114yes—
369C22×C4#41×C4118yes—
370C22×C4C24×C4114yes—
371C22×C4C24×C4114yes—
372C22×C4C24×C4114yes—
373C22×C4C24×C4114yes—
374C22×C4C24×C4112yes—
375C22×C4C24×C4111yescharacteristic
376C22×C4C24×C4112yes—
377C22×C4C24×C4114yes—
378C22×C4C24×C4111yescharacteristic
379C4⋊C4—28no—
380C4⋊C4—28no—
381C4⋊C4—24no—
382C4⋊C4—28no—
383C4⋊C4—24no—
384C4⋊C4—28no—
385C4⋊C4—216no—
386C4⋊C4—28no—
387C4⋊C4—44no—
388C4⋊C4—44no—
389C22⋊C4—28no—
390C22⋊C4—28no—
391C22⋊C4—28no—
392C22⋊C4—28no—
393C22⋊C4—28no—
394C22⋊C4—216no—
395C22⋊C4—48no—
396C22⋊C4—48no—
397C42—28no—
398C42—28no—
399C42—44no—
400C42C2×D4×C4118yes—
401C42C2×D4×C4118yes—
402C23—21no—
403C23—21no—
404C23—22no—
405C23—24no—
406C23—28no—
407C23—24no—
408C23—24no—
409C23—28no—
410C23C22×D4×C4112yes—
411C23C2×#41×C4114yes—
412C23C25×C4111yescharacteristic
413Q8—48no—
414D4—48no—
415D4—416no—
416D4—416no—
417C2×C4—28no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—28no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—28no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—28no—
435C2×C4—44no—
436C2×C4—48no—
437C2×C4—48no—
438C2×C4—416no—
439C2×C4C22×D4×C4114yes—
440C2×C4C22×D4×C4112yes—
441C2×C4C22×D4×C4114yes—
442C2×C4C22×D4×C4112yes—
443C2×C4C2×#41×C4118yes—
444C2×C4H(5,𝔽2)×C4112yes—
445C2×C42−1+4×C4112yes—
446C22—22no—
447C22—22no—
448C22—24no—
449C22—24no—
450C22—44no—
451C22—44no—
452C22—44no—
453C22—48no—
454C22—48no—
455C22C41×#53214yes—
456C22C23×D4×C4111yescharacteristic
457C22C22×#41×C4112yes—
458C22C2×H(5,𝔽2)×C4111yescharacteristic
459C22C2×2−1+4×C4111yescharacteristic
460C22C41×#58512yes—
461C4—24no—
462C4—22no—
463C4—24no—
464C4—28no—
465C4—44no—
466C4—44no—
467C4—44no—
468C4—44no—
469C4C41×#53714yes—
470C2—24no—
471C2—84no—
472C2C2×C41×#53211yescharacteristic
473C2C2×C41×#53711yescharacteristic
474C2C41×#344911yescharacteristic
475C2C41×#345912yes—
476C2C41×#346112yes—
subgroupG/H
centerC22×C4×C41C24
commutator, Frattini, cosocleC23C25×C41
socleC23×C41C25
prime radicalC41×#2656C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#529C2semidirect
2. C41×#2664C2semidirect
3. C41×#2662C2semidirect
4. C41×#2659C2semidirect
6. C41×#2639C2semidirect
7. C41×#2618C2semidirect
8. C41×#2396C2semidirect
9. C41×#2392C2semidirect
10. C4×#121×C41C2semidirect
11. C2×C4×C4⋊C4×C41C2semidirect
93. C2×C42×C41D4semidirect
207. #34594C41direct (N × H)
232. C2×#529C2×C41semidirect
233. #2664C2×C41semidirect
234. #2662C2×C41semidirect
235. #2659C2×C41semidirect
237. #2639C2×C41semidirect
238. #2618C2×C41semidirect
239. #2396C2×C41semidirect
240. #2392C2×C41semidirect
241. C4×#121C2×C41semidirect
242. C2×C4×C4⋊C4C2×C41semidirect
289. C41#34594direct (N × H)
332. C2×C42D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#5292
C41×#26642
C41×#26622
C41×#26592
C41×#26562
C41×#26392
C41×#26182
C41×#23962
C41×#23922
C4×#121×C412
C2×C4×C4⋊C4×C412
#3459441