Finite Group Databasebeta

← C41×#19155 #23795356

Subgroups — C41×#19155 #23795356

Order 10496.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3131C211yesmaximal, characteristic
2C41×#3104C211yesmaximal, characteristic, complemented
3C41×#3103C211yesmaximal, characteristic
4C2×C41×#446C211yesmaximal, characteristic, complemented
5C41×#1704C212yesmaximal, complemented
6C41×#1702C212yesmaximal, complemented
7C41×#1700C212yesmaximal, complemented
8C41×#1698C212yesmaximal, complemented
9C41×#1564C211yesmaximal, characteristic, complemented
10C41×#1542C211yesmaximal, characteristic, complemented
11C41×#1540C211yesmaximal, characteristic
12C41×#533C2211yescharacteristic
13C41×#532C2211yescharacteristic
14C2×C4×Q8×C41C2211yescharacteristic
15C41×#488—21no—
16C41×#488—21no—
17C41×#487C2211yescharacteristic
18C41×#487C2211yescharacteristic
19C41×#486C2211yescharacteristic
20C41×#486C2211yescharacteristic
21C41×#484—21no—
22C41×#481—21no—
23C41×#477C2212yes—
24C41×#475C2212yes—
25C41×#462C2212yes—
26C41×#460C2212yes—
27C41×#451—21no—
28C41×#448—21no—
29C41×#446—21no—
30C41×#446—21no—
31C41×#446C2212yes—
32C41×#446C2212yes—
33C4×Q16×C41—22no—
34C4×SD16×C41—22no—
35C41×#431C2211yescharacteristic
36C41×#431C2211yescharacteristic
37C2×C4⋊C8×C41—21no—
38C2×C4⋊C8×C41C2211yescharacteristic
39C41×#416—21no—
40C41×#416—21no—
41C2×#97×C41—21no—
42C2×C4×C8×C41C2211yescharacteristic
43C41×#335C2212yes—
44C41×#334C2212yes—
45C41×#333C2212yes—
46C41×#332C2212yes—
47C41×#332C2212yes—
48C41×#331C2212yes—
49C2×#41×C41—21no—
50C22×Q8×C41D411yescharacteristic
51C2×Q16×C41—22no—
52C2×SD16×C41—22no—
53C22×C8×C41—21no—
54C22×C8×C41D411yescharacteristic
55C22×C8×C41D411yescharacteristic
56C4⋊Q8×C41C2311yescharacteristic
57C4⋊Q8×C41C2311yescharacteristic
58C4⋊Q8×C41C2311yescharacteristic
59#127×C41C2311yescharacteristic
60#125×C41—21no—
61#124×C41—21no—
62C22⋊Q8×C41—21no—
63C22⋊Q8×C41—21no—
64#121×C41—21no—
65#121×C41—21no—
66C4×Q8×C41—21no—
67C4×Q8×C41—21no—
68C4×Q8×C41—21no—
69C4×Q8×C41—21no—
70C4×Q8×C41D412yes—
71C4×Q8×C41C2312yes—
72C4×D4×C41—21no—
73C4×D4×C41—21no—
74#117×C41—21no—
75C2×C4⋊C4×C41—21no—
76C2×C4⋊C4×C41D411yescharacteristic
77C2×C42×C41—21no—
78C2×C42×C41C2311yescharacteristic
79#107×C41—22no—
80#106×C41—22no—
81C4⋊C8×C41—22no—
82C4⋊C8×C41—22no—
83C4⋊C8×C41—21no—
84C4⋊C8×C41C2312yes—
85C4⋊C8×C41C2312yes—
86C4⋊C8×C41C2312yes—
87#103×C41—22no—
88#103×C41—22no—
89#103×C41—21no—
90#103×C41—21no—
91#103×C41—21no—
92#103×C41—21no—
93#103×C41—22no—
94#102×C41—21no—
95#102×C41—21no—
96#102×C41—21no—
97#102×C41—21no—
98#102×C41—22no—
99C22⋊C8×C41—21no—
100C22⋊C8×C41—21no—
101#97×C41—22no—
102#97×C41—22no—
103C4×C8×C41—21no—
104C4×C8×C41—21no—
105C4×C8×C41D411yescharacteristic
106C4×C8×C41D411yescharacteristic
107C4×C8×C41C2311yescharacteristic
108C4×C8×C41C2311yescharacteristic
109#41×C41—42no—
110#41×C41—42no—
111C2×Q8×C41—21no—
112C2×Q8×C41—21no—
113C2×Q8×C41—21no—
114C2×Q8×C41—21no—
115C2×Q8×C41—42no—
116C2×Q8×C41C2×D412yes—
117C2×D4×C41—21no—
118C2×D4×C41—21no—
119C2×D4×C41—21no—
120C2×D4×C41—41no—
121C22×C4×C41—21no—
122C22×C4×C41—21no—
123C22×C4×C41—41no—
124C22×C4×C41C2×D411yescharacteristic
125C22×C4×C41C2×D411yescharacteristic
126C22×C4×C41#4111yescharacteristic
127Q16×C41—44no—
128SD16×C41—44no—
129C2×C8×C41—22no—
130C2×C8×C41—22no—
131C2×C8×C41—22no—
132C2×C8×C41—22no—
133C2×C8×C41—22no—
134C2×C8×C41—42no—
135C2×C8×C41C2×D411yescharacteristic
136C2×C8×C41C2×D411yescharacteristic
137C2×C8×C41C2×D411yescharacteristic
138C2×C8×C41C2×D411yescharacteristic
139C4⋊C4×C41—22no—
140C4⋊C4×C41—21no—
141C4⋊C4×C41—22no—
142C4⋊C4×C41—21no—
143C4⋊C4×C41—21no—
144C4⋊C4×C41—21no—
145C4⋊C4×C41—21no—
146C4⋊C4×C41—21no—
147C4⋊C4×C41—21no—
148C4⋊C4×C41—41no—
149C4⋊C4×C41—41no—
150C4⋊C4×C41C2×D412yes—
151C22⋊C4×C41—41no—
152C22⋊C4×C41—41no—
153C22⋊C4×C41—41no—
154C42×C41—22no—
155C42×C41—22no—
156C42×C41—41no—
157C42×C41C2×D411yescharacteristic
158C42×C41C2×D411yescharacteristic
159C42×C41#4111yescharacteristic
160C42×C41C2411yescharacteristic
161C23×C41—41no—
162C23×C41#12111yescharacteristic
163Q8×C41—22no—
164Q8×C41—22no—
165Q8×C41—42no—
166Q8×C41—41no—
167Q8×C41—41no—
168Q8×C41—42no—
169Q8×C41—81no—
170D4×C41—41no—
171D4×C41—41no—
172D4×C41—42no—
173D4×C41—81no—
174D4×C41—82no—
175C2×C4×C41—22no—
176C2×C4×C41—22no—
177C2×C4×C41—22no—
178C2×C4×C41—41no—
179C2×C4×C41—42no—
180C2×C4×C41—42no—
181C2×C4×C41—41no—
182C2×C4×C41—41no—
183C2×C4×C41—41no—
184C2×C4×C41—82no—
185C2×C4×C41#12111yescharacteristic
186C2×C4×C41#12111yescharacteristic
187C2×C4×C41#12111yescharacteristic
188C2×C4×C41#13512yes—
189C2×C4×C41#13712yes—
190C2×C4×C41C22×D411yescharacteristic
191C2×C4×C41C22×D411yescharacteristic
192C2×C4×C41C2×#4111yescharacteristic
193C8×C41—21no—
194C8×C41—21no—
195C8×C41—21no—
196C8×C41—21no—
197C8×C41—42no—
198C8×C41—42no—
199C8×C41—42no—
200#19155C4111yesmaximal, characteristic, direct product factor, Sylow
201C22×C41—21no—
202C22×C41—21no—
203C22×C41—81no—
204C22×C41—81no—
205C22×C41—81no—
206C22×C41#46412yes—
207C22×C41C2×#12111yescharacteristic
208C4×C41—21no—
209C4×C41—21no—
210C4×C41—21no—
211C4×C41—42no—
212C4×C41—42no—
213C4×C41—81no—
214C4×C41—81no—
215C4×C41—81no—
216C4×C41#46412yes—
217C4×C41C2×#13511yescharacteristic
218C4×C41C2×#13711yescharacteristic
219C4×C41#57512yes—
220#3131C2×C4111yescharacteristic
221#3104C2×C4111yescharacteristic, complemented
222#3103C2×C4111yescharacteristic
223C2×#446C2×C4111yescharacteristic, complemented
224#1704C2×C4112yescomplemented
225#1702C2×C4112yescomplemented
226#1700C2×C4112yescomplemented
227#1698C2×C4112yescomplemented
228#1564C2×C4111yescharacteristic, complemented
229#1542C2×C4111yescharacteristic, complemented
230#1540C2×C4111yescharacteristic
231C2×C41—22no—
232C2×C41—161no—
233C2×C41C2×#46411yescharacteristic
234C2×C41#305411yescharacteristic
235C2×C41#306711yescharacteristic
236#533C22×C4111yescharacteristic
237#532C22×C4111yescharacteristic
238C2×C4×Q8C22×C4111yescharacteristic
239#488—21no—
240#488—21no—
241#487C22×C4111yescharacteristic
242#487C22×C4111yescharacteristic
243#486C22×C4111yescharacteristic
244#486C22×C4111yescharacteristic
245#484—21no—
246#481—21no—
247#477C22×C4112yes—
248#475C22×C4112yes—
249#462C22×C4112yes—
250#460C22×C4112yes—
251#451—21no—
252#448—21no—
253#446—21no—
254#446—21no—
255#446C22×C4112yes—
256#446C22×C4112yes—
257C4×Q16—22no—
258C4×SD16—22no—
259#431C22×C4111yescharacteristic
260#431C22×C4111yescharacteristic
261C2×C4⋊C8—21no—
262C2×C4⋊C8C22×C4111yescharacteristic
263#416—21no—
264#416—21no—
265C2×#97—21no—
266C2×C4×C8C22×C4111yescharacteristic
267#335C22×C4112yes—
268#334C22×C4112yes—
269#333C22×C4112yes—
270#332C22×C4112yes—
271#332C22×C4112yes—
272#331C22×C4112yes—
273C41#1915511yescharacteristic, direct product factor, Sylow
274C2×#41—21no—
275C22×Q8D4×C4111yescharacteristic
276C2×Q16—22no—
277C2×SD16—22no—
278C22×C8—21no—
279C22×C8D4×C4111yescharacteristic
280C22×C8D4×C4111yescharacteristic
281C4⋊Q8C23×C4111yescharacteristic
282C4⋊Q8C23×C4111yescharacteristic
283C4⋊Q8C23×C4111yescharacteristic
284#127C23×C4111yescharacteristic
285#125—21no—
286#124—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289#121—21no—
290#121—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8—21no—
294C4×Q8—21no—
295C4×Q8D4×C4112yes—
296C4×Q8C23×C4112yes—
297C4×D4—21no—
298C4×D4—21no—
299#117—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4D4×C4111yescharacteristic
302C2×C42—21no—
303C2×C42C23×C4111yescharacteristic
304#107—22no—
305#106—22no—
306C4⋊C8—22no—
307C4⋊C8—22no—
308C4⋊C8—21no—
309C4⋊C8C23×C4112yes—
310C4⋊C8C23×C4112yes—
311C4⋊C8C23×C4112yes—
312#103—22no—
313#103—22no—
314#103—21no—
315#103—21no—
316#103—21no—
317#103—21no—
318#103—22no—
319#102—21no—
320#102—21no—
321#102—21no—
322#102—21no—
323#102—22no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326#97—22no—
327#97—22no—
328C4×C8—21no—
329C4×C8—21no—
330C4×C8D4×C4111yescharacteristic
331C4×C8D4×C4111yescharacteristic
332C4×C8C23×C4111yescharacteristic
333C4×C8C23×C4111yescharacteristic
334#41—42no—
335#41—42no—
336C2×Q8—21no—
337C2×Q8—21no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—42no—
341C2×Q8C2×D4×C4112yes—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—41no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4C2×D4×C4111yescharacteristic
350C22×C4C2×D4×C4111yescharacteristic
351C22×C4#41×C4111yescharacteristic
352Q16—44no—
353SD16—44no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—42no—
360C2×C8C2×D4×C4111yescharacteristic
361C2×C8C2×D4×C4111yescharacteristic
362C2×C8C2×D4×C4111yescharacteristic
363C2×C8C2×D4×C4111yescharacteristic
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4C2×D4×C4112yes—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C42—22no—
380C42—22no—
381C42—41no—
382C42C2×D4×C4111yescharacteristic
383C42C2×D4×C4111yescharacteristic
384C42#41×C4111yescharacteristic
385C42C24×C4111yescharacteristic
386C23—41no—
387C23#121×C4111yescharacteristic
388Q8—22no—
389Q8—22no—
390Q8—42no—
391Q8—41no—
392Q8—41no—
393Q8—42no—
394Q8—81no—
395D4—41no—
396D4—41no—
397D4—42no—
398D4—81no—
399D4—82no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—82no—
410C2×C4#121×C4111yescharacteristic
411C2×C4#121×C4111yescharacteristic
412C2×C4#121×C4111yescharacteristic
413C2×C4#135×C4112yes—
414C2×C4#137×C4112yes—
415C2×C4C22×D4×C4111yescharacteristic
416C2×C4C22×D4×C4111yescharacteristic
417C2×C4C2×#41×C4111yescharacteristic
418C8—21no—
419C8—21no—
420C8—21no—
421C8—21no—
422C8—42no—
423C8—42no—
424C8—42no—
425C22—21no—
426C22—21no—
427C22—81no—
428C22—81no—
429C22—81no—
430C22C41×#46412yes—
431C22C2×#121×C4111yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4C41×#46412yes—
441C4C2×#135×C4111yescharacteristic
442C4C2×#137×C4111yescharacteristic
443C4C41×#57512yes—
444C2—22no—
445C2—161no—
446C2C2×C41×#46411yescharacteristic
447C2C41×#305411yescharacteristic
448C2C41×#306711yescharacteristic
subgroupG/H
centerC2×C4×C41#121
commutator, Frattini, cosocleC42C24×C41
socleC22×C41C2×#121
prime radicalC41×#532C22
LCSG ▷ C42 ▷ 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×#3104C2semidirect
4. C2×C41×#446C2semidirect
5. C41×#1704C2semidirect
6. C41×#1702C2semidirect
7. C41×#1700C2semidirect
8. C41×#1698C2semidirect
9. C41×#1564C2semidirect
10. C41×#1542C2semidirect
200. #19155C41direct (N × H)
221. #3104C2×C41semidirect
223. C2×#446C2×C41semidirect
224. #1704C2×C41semidirect
225. #1702C2×C41semidirect
226. #1700C2×C41semidirect
227. #1698C2×C41semidirect
228. #1564C2×C41semidirect
229. #1542C2×C41semidirect
273. C41#19155direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#31312
C41×#31042
C41×#31032
C2×C41×#4462
C41×#17042
C41×#17022
C41×#17002
C41×#16982
C41×#15642
C41×#15422
C41×#15402
#1915541