Finite Group Databasebeta

← C41×#19216 #23795417

Subgroups — C41×#19216 #23795417

Order 10496.

592 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3249C211yesmaximal, characteristic, complemented
2C41×#3246C211yesmaximal, characteristic
3C41×#3131C211yesmaximal, characteristic
4C41×#2960C211yesmaximal, characteristic, complemented
5C41×#1704C212yesmaximal, complemented
6C41×#1702C212yesmaximal, complemented
7C41×#1680C212yesmaximal, complemented
8C41×#1678C212yesmaximal, complemented
9C2×C41×#334C211yesmaximal, characteristic, complemented
10C41×#1550C211yesmaximal, characteristic, complemented
11C41×#1547C211yesmaximal, characteristic
12C41×#533C2211yescharacteristic
13C41×#533C2211yescharacteristic
14C41×#532C2211yescharacteristic
15C41×#488—21no—
16C41×#488—21no—
17C41×#487C2211yescharacteristic
18C41×#487C2211yescharacteristic
19C41×#486C2211yescharacteristic
20C41×#486C2211yescharacteristic
21C41×#477—21no—
22C41×#477C2212yes—
23C41×#476—21no—
24C41×#475C2212yes—
25C41×#467—22no—
26C41×#465—22no—
27C41×#462—21no—
28C41×#462C2212yes—
29C41×#461—21no—
30C41×#460C2212yes—
31C41×#446—21no—
32C41×#446C2212yes—
33C8×Q8×C41—21no—
34C8×Q8×C41C2212yes—
35C41×#424—21no—
36C41×#423C2211yescharacteristic
37C2×C4⋊C8×C41C2211yescharacteristic
38C2×C4⋊C8×C41C2211yescharacteristic
39C41×#416—21no—
40C41×#416—21no—
41C41×#405—21no—
42C2×C4×C8×C41C2211yescharacteristic
43C41×#334C2212yes—
44C41×#334C2212yes—
45C41×#333C2212yes—
46C41×#332C2212yes—
47C41×#332C2212yes—
48C41×#331C2212yes—
49C2×#41×C41—21no—
50C2×Q16×C41—22no—
51C2×SD16×C41—22no—
52C2×M16×C41—21no—
53C22×C8×C41—21no—
54C22×C8×C41—21no—
55C22×C8×C41D411yescharacteristic
56C22×C8×C41D411yescharacteristic
57C4⋊Q8×C41D411yescharacteristic
58C4⋊Q8×C41D411yescharacteristic
59C4⋊Q8×C41C2311yescharacteristic
60C4⋊Q8×C41C2311yescharacteristic
61C4⋊Q8×C41C2311yescharacteristic
62#127×C41C2311yescharacteristic
63#125×C41—21no—
64#125×C41—21no—
65#124×C41—21no—
66C22⋊Q8×C41—21no—
67C22⋊Q8×C41—21no—
68C22⋊Q8×C41—21no—
69C22⋊Q8×C41D412yes—
70#121×C41—21no—
71#121×C41—21no—
72C4×Q8×C41—21no—
73C4×Q8×C41—21no—
74C4×Q8×C41—21no—
75C4×Q8×C41C2312yes—
76C4×D4×C41—21no—
77C4×D4×C41—21no—
78#117×C41—21no—
79#117×C41—21no—
80C2×C42×C41C2311yescharacteristic
81#107×C41—22no—
82#106×C41—22no—
83C4⋊C8×C41—22no—
84C4⋊C8×C41—22no—
85C4⋊C8×C41—21no—
86C4⋊C8×C41—21no—
87C4⋊C8×C41—21no—
88C4⋊C8×C41C2312yes—
89C4⋊C8×C41C2312yes—
90C4⋊C8×C41C2312yes—
91#103×C41—22no—
92#103×C41—22no—
93#103×C41—21no—
94#103×C41—21no—
95#103×C41—21no—
96#103×C41—21no—
97#103×C41—22no—
98#102×C41—21no—
99#102×C41—21no—
100#102×C41—21no—
101#102×C41—21no—
102#102×C41—22no—
103#97×C41—22no—
104C4×C8×C41—22no—
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×C41C2×D412yes—
116C2×D4×C41—21no—
117C2×D4×C41—21no—
118C2×D4×C41—21no—
119C2×D4×C41—41no—
120C22×C4×C41—41no—
121C22×C4×C41C2×D411yescharacteristic
122C22×C4×C41C2×D411yescharacteristic
123C22×C4×C41#4111yescharacteristic
124Q16×C41—82no—
125SD16×C41—82no—
126M16×C41—42no—
127C2×C8×C41—22no—
128C2×C8×C41—22no—
129C2×C8×C41—22no—
130C2×C8×C41—22no—
131C2×C8×C41—22no—
132C2×C8×C41—81no—
133C2×C8×C41—81no—
134C2×C8×C41C2×D411yescharacteristic
135C2×C8×C41C2×D411yescharacteristic
136C2×C8×C41C2×D411yescharacteristic
137C2×C8×C41C2×D411yescharacteristic
138C4⋊C4×C41—21no—
139C4⋊C4×C41—21no—
140C4⋊C4×C41—21no—
141C4⋊C4×C41—22no—
142C4⋊C4×C41—22no—
143C4⋊C4×C41—21no—
144C4⋊C4×C41—21no—
145C4⋊C4×C41—21no—
146C4⋊C4×C41—21no—
147C4⋊C4×C41—21no—
148C4⋊C4×C41—21no—
149C4⋊C4×C41—41no—
150C4⋊C4×C41—41no—
151C4⋊C4×C41C2×D412yes—
152C22⋊C4×C41—22no—
153C22⋊C4×C41—41no—
154C22⋊C4×C41—41no—
155C22⋊C4×C41—41no—
156C42×C41—22no—
157C42×C41—41no—
158C42×C41C2×D411yescharacteristic
159C42×C41C2×D411yescharacteristic
160C42×C41#4111yescharacteristic
161C42×C41C2411yescharacteristic
162C23×C41—41no—
163C23×C41#12111yescharacteristic
164Q8×C41—22no—
165Q8×C41—22no—
166Q8×C41—42no—
167Q8×C41—41no—
168Q8×C41—41no—
169Q8×C41—41no—
170Q8×C41—41no—
171Q8×C41—81no—
172D4×C41—41no—
173D4×C41—41no—
174D4×C41—41no—
175D4×C41—41no—
176D4×C41—81no—
177D4×C41—82no—
178C2×C4×C41—21no—
179C2×C4×C41—21no—
180C2×C4×C41—22no—
181C2×C4×C41—22no—
182C2×C4×C41—41no—
183C2×C4×C41—41no—
184C2×C4×C41—41no—
185C2×C4×C41—41no—
186C2×C4×C41—82no—
187C2×C4×C41#12111yescharacteristic
188C2×C4×C41#12111yescharacteristic
189C2×C4×C41#12111yescharacteristic
190C2×C4×C41#13512yes—
191C2×C4×C41#13712yes—
192C2×C4×C41C22×D411yescharacteristic
193C2×C4×C41C22×D411yescharacteristic
194C2×C4×C41C2×#4111yescharacteristic
195C8×C41—21no—
196C8×C41—21no—
197C8×C41—21no—
198C8×C41—21no—
199C8×C41—42no—
200C8×C41—42no—
201C8×C41—42no—
202#19216C4111yesmaximal, characteristic, direct product factor, Sylow
203C22×C41—21no—
204C22×C41—21no—
205C22×C41—81no—
206C22×C41—81no—
207C22×C41—81no—
208C22×C41#46412yes—
209C22×C41C2×#12111yescharacteristic
210C4×C41—21no—
211C4×C41—21no—
212C4×C41—21no—
213C4×C41—42no—
214C4×C41—42no—
215C4×C41—81no—
216C4×C41—81no—
217C4×C41—81no—
218C4×C41#46412yes—
219C4×C41C2×#13511yescharacteristic
220C4×C41C2×#13711yescharacteristic
221C4×C41#57711yescharacteristic
222C4×C41#57711yescharacteristic
223#3249C2×C4111yescharacteristic, complemented
224#3246C2×C4111yescharacteristic
225#3131C2×C4111yescharacteristic
226#2960C2×C4111yescharacteristic, complemented
227#1704C2×C4112yescomplemented
228#1702C2×C4112yescomplemented
229#1680C2×C4112yescomplemented
230#1678C2×C4112yescomplemented
231C2×#334C2×C4111yescharacteristic, complemented
232#1550C2×C4111yescharacteristic, complemented
233#1547C2×C4111yescharacteristic
234C2×C41—22no—
235C2×C41—161no—
236C2×C41C2×#46411yescharacteristic
237C2×C41#306011yescharacteristic
238C2×C41#306711yescharacteristic
239#533C22×C4111yescharacteristic
240#533C22×C4111yescharacteristic
241#532C22×C4111yescharacteristic
242#488—21no—
243#488—21no—
244#487C22×C4111yescharacteristic
245#487C22×C4111yescharacteristic
246#486C22×C4111yescharacteristic
247#486C22×C4111yescharacteristic
248#477—21no—
249#477C22×C4112yes—
250#476—21no—
251#475C22×C4112yes—
252#467—22no—
253#465—22no—
254#462—21no—
255#462C22×C4112yes—
256#461—21no—
257#460C22×C4112yes—
258#446—21no—
259#446C22×C4112yes—
260C8×Q8—21no—
261C8×Q8C22×C4112yes—
262#424—21no—
263#423C22×C4111yescharacteristic
264C2×C4⋊C8C22×C4111yescharacteristic
265C2×C4⋊C8C22×C4111yescharacteristic
266#416—21no—
267#416—21no—
268#405—21no—
269C2×C4×C8C22×C4111yescharacteristic
270#334C22×C4112yes—
271#334C22×C4112yes—
272#333C22×C4112yes—
273#332C22×C4112yes—
274#332C22×C4112yes—
275#331C22×C4112yes—
276C41#1921611yescharacteristic, direct product factor, Sylow
277C2×#41—21no—
278C2×Q16—22no—
279C2×SD16—22no—
280C2×M16—21no—
281C22×C8—21no—
282C22×C8—21no—
283C22×C8D4×C4111yescharacteristic
284C22×C8D4×C4111yescharacteristic
285C4⋊Q8D4×C4111yescharacteristic
286C4⋊Q8D4×C4111yescharacteristic
287C4⋊Q8C23×C4111yescharacteristic
288C4⋊Q8C23×C4111yescharacteristic
289C4⋊Q8C23×C4111yescharacteristic
290#127C23×C4111yescharacteristic
291#125—21no—
292#125—21no—
293#124—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8D4×C4112yes—
298#121—21no—
299#121—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8C23×C4112yes—
304C4×D4—21no—
305C4×D4—21no—
306#117—21no—
307#117—21no—
308C2×C42C23×C4111yescharacteristic
309#107—22no—
310#106—22no—
311C4⋊C8—22no—
312C4⋊C8—22no—
313C4⋊C8—21no—
314C4⋊C8—21no—
315C4⋊C8—21no—
316C4⋊C8C23×C4112yes—
317C4⋊C8C23×C4112yes—
318C4⋊C8C23×C4112yes—
319#103—22no—
320#103—22no—
321#103—21no—
322#103—21no—
323#103—21no—
324#103—21no—
325#103—22no—
326#102—21no—
327#102—21no—
328#102—21no—
329#102—21no—
330#102—22no—
331#97—22no—
332C4×C8—22no—
333C4×C8D4×C4111yescharacteristic
334C4×C8D4×C4111yescharacteristic
335C4×C8C23×C4111yescharacteristic
336C4×C8C23×C4111yescharacteristic
337#41—42no—
338#41—42no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C2×D4×C4112yes—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—41no—
348C22×C4—41no—
349C22×C4C2×D4×C4111yescharacteristic
350C22×C4C2×D4×C4111yescharacteristic
351C22×C4#41×C4111yescharacteristic
352Q16—82no—
353SD16—82no—
354M16—42no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—81no—
361C2×C8—81no—
362C2×C8C2×D4×C4111yescharacteristic
363C2×C8C2×D4×C4111yescharacteristic
364C2×C8C2×D4×C4111yescharacteristic
365C2×C8C2×D4×C4111yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4C2×D4×C4112yes—
380C22⋊C4—22no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C42—22no—
385C42—41no—
386C42C2×D4×C4111yescharacteristic
387C42C2×D4×C4111yescharacteristic
388C42#41×C4111yescharacteristic
389C42C24×C4111yescharacteristic
390C23—41no—
391C23#121×C4111yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395Q8—41no—
396Q8—41no—
397Q8—41no—
398Q8—41no—
399Q8—81no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—81no—
405D4—82no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4#121×C4111yescharacteristic
416C2×C4#121×C4111yescharacteristic
417C2×C4#121×C4111yescharacteristic
418C2×C4#135×C4112yes—
419C2×C4#137×C4112yes—
420C2×C4C22×D4×C4111yescharacteristic
421C2×C4C22×D4×C4111yescharacteristic
422C2×C4C2×#41×C4111yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8—21no—
427C8—42no—
428C8—42no—
429C8—42no—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22C41×#46412yes—
436C22C2×#121×C4111yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—42no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4C41×#46412yes—
446C4C2×#135×C4111yescharacteristic
447C4C2×#137×C4111yescharacteristic
448C4C41×#57711yescharacteristic
449C4C41×#57711yescharacteristic
450C2—22no—
451C2—161no—
452C2C2×C41×#46411yescharacteristic
453C2C41×#306011yescharacteristic
454C2C41×#306711yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC42C24×C41
prime radicalC41×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C2×C42×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3249C2semidirect
4. C41×#2960C2semidirect
5. C41×#1704C2semidirect
6. C41×#1702C2semidirect
7. C41×#1680C2semidirect
8. C41×#1678C2semidirect
9. C2×C41×#334C2semidirect
10. C41×#1550C2semidirect
202. #19216C41direct (N × H)
223. #3249C2×C41semidirect
226. #2960C2×C41semidirect
227. #1704C2×C41semidirect
228. #1702C2×C41semidirect
229. #1680C2×C41semidirect
230. #1678C2×C41semidirect
231. C2×#334C2×C41semidirect
232. #1550C2×C41semidirect
276. C41#19216direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#32492
C41×#32462
C41×#31312
C41×#29602
C41×#17042
C41×#17022
C41×#16802
C41×#16782
C2×C41×#3342
C41×#15502
C41×#15472
#1921641