Finite Group Databasebeta

← C41×#33122 #23809323

Subgroups — C41×#33122 #23809323

Order 10496.

782 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3095C211yesmaximal, characteristic, complemented
2C41×#3094C211yesmaximal, characteristic
3C2×C41×#465C211yesmaximal, characteristic
4C2×C41×#405C211yesmaximal, characteristic, complemented
5C41×#1977C212yesmaximal, complemented
6C41×#1951C212yesmaximal, complemented
7C41×#1931C212yesmaximal, complemented
8C41×#1930C212yesmaximal, complemented
9C41×#1901C211yesmaximal, characteristic, complemented
10C41×#1900C211yesmaximal, characteristic
11C41×#1810C211yesmaximal, characteristic, complemented
12C22×SD16×C41C2211yescharacteristic
13C22×M16×C41C2211yescharacteristic
14C23×C8×C41C2211yescharacteristic
15C2×C22⋊Q8×C41C2211yescharacteristic
16C2×#121×C41C2211yescharacteristic
17C2×#117×C41C2211yescharacteristic
18C41×#485—22no—
19C41×#484—21no—
20C41×#483—21no—
21C41×#482—22no—
22C41×#481—21no—
23C41×#480—21no—
24C41×#465—21no—
25C41×#465—21no—
26C41×#465—21no—
27C41×#465—21no—
28C2×#108×C41C2212yes—
29C41×#428C2212yes—
30C41×#428C2212yes—
31C2×#106×C41C2211yescharacteristic
32C41×#419C2212yes—
33C41×#418C2212yes—
34C2×#103×C41C2211yescharacteristic
35C2×#102×C41C2211yescharacteristic
36C2×#101×C41C2212yes—
37C2×#100×C41C2212yes—
38C41×#407C2211yescharacteristic
39C41×#407C2211yescharacteristic
40C41×#405—21no—
41C41×#405—21no—
42C41×#405C2212yes—
43C41×#405C2212yes—
44C2×#97×C41—21no—
45C2×C4×C8×C41—21no—
46C41×#343C2212yes—
47C41×#343C2212yes—
48C41×#341C2212yes—
49C22×Q8×C41C2311yescharacteristic
50C22×D4×C41—21no—
51C22×D4×C41C2311yescharacteristic
52C23×C4×C41C2311yescharacteristic
53C2×SD16×C41—21no—
54C2×SD16×C41—21no—
55C2×SD16×C41—24no—
56C2×M16×C41—21no—
57C2×M16×C41—24no—
58C2×M16×C41C2312yes—
59C2×M16×C41C2312yes—
60C2×M16×C41C2312yes—
61C22×C8×C41—21no—
62C22×C8×C41—24no—
63C22×C8×C41D411yescharacteristic
64C22×C8×C41D411yescharacteristic
65C22×C8×C41D411yescharacteristic
66C22×C8×C41D411yescharacteristic
67C22×C8×C41C2311yescharacteristic
68C22×C8×C41C2311yescharacteristic
69C22⋊Q8×C41—21no—
70C22⋊Q8×C41—21no—
71C22⋊Q8×C41—21no—
72C22⋊Q8×C41—21no—
73#121×C41—21no—
74#121×C41—21no—
75#121×C41—21no—
76#121×C41—21no—
77#117×C41—21no—
78#117×C41—21no—
79#117×C41D412yes—
80#117×C41C2312yes—
81C2×C4⋊C4×C41—21no—
82C2×C4⋊C4×C41D411yescharacteristic
83C2×C4⋊C4×C41D411yescharacteristic
84C2×C4⋊C4×C41C2311yescharacteristic
85C2×C4⋊C4×C41C2311yescharacteristic
86C2×C22⋊C4×C41—21no—
87C2×C22⋊C4×C41—21no—
88C2×C22⋊C4×C41—21no—
89C2×C42×C41—21no—
90#108×C41—24no—
91#107×C41—22no—
92#107×C41—22no—
93#106×C41—21no—
94#106×C41—21no—
95#106×C41—22no—
96#106×C41—22no—
97#103×C41—21no—
98#103×C41—21no—
99#103×C41—22no—
100#103×C41—22no—
101#102×C41—21no—
102#102×C41—21no—
103#102×C41—22no—
104#102×C41—22no—
105#101×C41—24no—
106#100×C41—24no—
107C22⋊C8×C41—21no—
108C22⋊C8×C41—21no—
109C22⋊C8×C41—21no—
110C22⋊C8×C41—21no—
111#97×C41—22no—
112#97×C41—22no—
113C4×C8×C41—22no—
114C4×C8×C41—22no—
115C24×C41—21no—
116C24×C41#4111yescharacteristic
117C2×Q8×C41—21no—
118C2×Q8×C41—21no—
119C2×Q8×C41—22no—
120C2×Q8×C41—22no—
121C2×D4×C41—21no—
122C2×D4×C41—21no—
123C2×D4×C41—22no—
124C2×D4×C41—22no—
125C2×D4×C41—41no—
126C2×D4×C41—41no—
127C2×D4×C41—82no—
128C22×C4×C41—22no—
129C22×C4×C41—22no—
130C22×C4×C41—21no—
131C22×C4×C41—21no—
132C22×C4×C41—21no—
133C22×C4×C41—21no—
134C22×C4×C41—21no—
135C22×C4×C41C2×D411yescharacteristic
136C22×C4×C41C2×D411yescharacteristic
137C22×C4×C41C2×D411yescharacteristic
138C22×C4×C41C2×D411yescharacteristic
139C22×C4×C41#4111yescharacteristic
140C22×C4×C41C2411yescharacteristic
141SD16×C41—42no—
142SD16×C41—42no—
143M16×C41—24no—
144M16×C41—22no—
145M16×C41—22no—
146M16×C41—22no—
147M16×C41—22no—
148M16×C41—22no—
149M16×C41#4114yes—
150C2×C8×C41—24no—
151C2×C8×C41—22no—
152C2×C8×C41—22no—
153C2×C8×C41—22no—
154C2×C8×C41—22no—
155C2×C8×C41—22no—
156C2×C8×C41—22no—
157C2×C8×C41—22no—
158C2×C8×C41—22no—
159C2×C8×C41C2×D411yescharacteristic
160C2×C8×C41C2×D411yescharacteristic
161C2×C8×C41C2×D411yescharacteristic
162C2×C8×C41C2×D411yescharacteristic
163C2×C8×C41#4114yes—
164C4⋊C4×C41—21no—
165C4⋊C4×C41—21no—
166C4⋊C4×C41—21no—
167C4⋊C4×C41—21no—
168C4⋊C4×C41—21no—
169C4⋊C4×C41—21no—
170C4⋊C4×C41—41no—
171C4⋊C4×C41—41no—
172C4⋊C4×C41C2×D412yes—
173C4⋊C4×C41C2×D412yes—
174C22⋊C4×C41—22no—
175C22⋊C4×C41—22no—
176C22⋊C4×C41—41no—
177C22⋊C4×C41—41no—
178C22⋊C4×C41—41no—
179C22⋊C4×C41—41no—
180C42×C41—22no—
181C42×C41—22no—
182C23×C41—22no—
183C23×C41—22no—
184C23×C41—41no—
185C23×C41—41no—
186C23×C41—42no—
187C23×C41—81no—
188C23×C41—81no—
189C23×C41#12111yescharacteristic
190C23×C41#12111yescharacteristic
191C23×C41C2×#4111yescharacteristic
192Q8×C41—41no—
193Q8×C41—41no—
194Q8×C41—42no—
195D4×C41—41no—
196D4×C41—41no—
197D4×C41—42no—
198D4×C41—82no—
199D4×C41—82no—
200C2×C4×C41—22no—
201C2×C4×C41—21no—
202C2×C4×C41—21no—
203C2×C4×C41—21no—
204C2×C4×C41—21no—
205C2×C4×C41—22no—
206C2×C4×C41—22no—
207C2×C4×C41—22no—
208C2×C4×C41—22no—
209C2×C4×C41—42no—
210C2×C4×C41—42no—
211C2×C4×C41—41no—
212C2×C4×C41—41no—
213C2×C4×C41—41no—
214C2×C4×C41—42no—
215C2×C4×C41—81no—
216C2×C4×C41—81no—
217C2×C4×C41#12111yescharacteristic
218C2×C4×C41#12111yescharacteristic
219C2×C4×C41C22×D411yescharacteristic
220C2×C4×C41C22×D411yescharacteristic
221C2×C4×C41C2×#4112yes—
222C2×C4×C41C2×#4112yes—
223C8×C41—21no—
224C8×C41—21no—
225C8×C41—24no—
226C8×C41—42no—
227C8×C41—42no—
228C8×C41#12312yes—
229C8×C41#12312yes—
230#33122C4111yesmaximal, characteristic, direct product factor, Sylow
231C22×C41—21no—
232C22×C41—21no—
233C22×C41—21no—
234C22×C41—21no—
235C22×C41—21no—
236C22×C41—21no—
237C22×C41—21no—
238C22×C41—44no—
239C22×C41—81no—
240C22×C41—81no—
241C22×C41—81no—
242C22×C41—162no—
243C22×C41#47112yes—
244C22×C41C2×#12111yescharacteristic
245C22×C41#52912yes—
246C4×C41—21no—
247C4×C41—21no—
248C4×C41—42no—
249C4×C41—42no—
250C4×C41—81no—
251C4×C41—81no—
252C4×C41—81no—
253C4×C41C2×#12311yescharacteristic
254C4×C41#52511yescharacteristic
255C4×C41#53212yes—
256#3095C2×C4111yescharacteristic, complemented
257#3094C2×C4111yescharacteristic
258C2×#465C2×C4111yescharacteristic
259C2×#405C2×C4111yescharacteristic, complemented
260#1977C2×C4112yescomplemented
261#1951C2×C4112yescomplemented
262#1931C2×C4112yescomplemented
263#1930C2×C4112yescomplemented
264#1901C2×C4111yescharacteristic, complemented
265#1900C2×C4111yescharacteristic
266#1810C2×C4111yescharacteristic, complemented
267C2×C41—22no—
268C2×C41—22no—
269C2×C41—41no—
270C2×C41—161no—
271C2×C41#285411yescharacteristic
272C2×C41C2×#47111yescharacteristic
273C2×C41#306711yescharacteristic
274C22×SD16C22×C4111yescharacteristic
275C22×M16C22×C4111yescharacteristic
276C23×C8C22×C4111yescharacteristic
277C2×C22⋊Q8C22×C4111yescharacteristic
278C2×#121C22×C4111yescharacteristic
279C2×#117C22×C4111yescharacteristic
280#485—22no—
281#484—21no—
282#483—21no—
283#482—22no—
284#481—21no—
285#480—21no—
286#465—21no—
287#465—21no—
288#465—21no—
289#465—21no—
290C2×#108C22×C4112yes—
291#428C22×C4112yes—
292#428C22×C4112yes—
293C2×#106C22×C4111yescharacteristic
294#419C22×C4112yes—
295#418C22×C4112yes—
296C2×#103C22×C4111yescharacteristic
297C2×#102C22×C4111yescharacteristic
298C2×#101C22×C4112yes—
299C2×#100C22×C4112yes—
300#407C22×C4111yescharacteristic
301#407C22×C4111yescharacteristic
302#405—21no—
303#405—21no—
304#405C22×C4112yes—
305#405C22×C4112yes—
306C2×#97—21no—
307C2×C4×C8—21no—
308#343C22×C4112yes—
309#343C22×C4112yes—
310#341C22×C4112yes—
311C41#3312211yescharacteristic, direct product factor, Sylow
312C22×Q8C23×C4111yescharacteristic
313C22×D4—21no—
314C22×D4C23×C4111yescharacteristic
315C23×C4C23×C4111yescharacteristic
316C2×SD16—21no—
317C2×SD16—21no—
318C2×SD16—24no—
319C2×M16—21no—
320C2×M16—24no—
321C2×M16C23×C4112yes—
322C2×M16C23×C4112yes—
323C2×M16C23×C4112yes—
324C22×C8—21no—
325C22×C8—24no—
326C22×C8D4×C4111yescharacteristic
327C22×C8D4×C4111yescharacteristic
328C22×C8D4×C4111yescharacteristic
329C22×C8D4×C4111yescharacteristic
330C22×C8C23×C4111yescharacteristic
331C22×C8C23×C4111yescharacteristic
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—21no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#117—21no—
341#117—21no—
342#117D4×C4112yes—
343#117C23×C4112yes—
344C2×C4⋊C4—21no—
345C2×C4⋊C4D4×C4111yescharacteristic
346C2×C4⋊C4D4×C4111yescharacteristic
347C2×C4⋊C4C23×C4111yescharacteristic
348C2×C4⋊C4C23×C4111yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—21no—
353#108—24no—
354#107—22no—
355#107—22no—
356#106—21no—
357#106—21no—
358#106—22no—
359#106—22no—
360#103—21no—
361#103—21no—
362#103—22no—
363#103—22no—
364#102—21no—
365#102—21no—
366#102—22no—
367#102—22no—
368#101—24no—
369#100—24no—
370C22⋊C8—21no—
371C22⋊C8—21no—
372C22⋊C8—21no—
373C22⋊C8—21no—
374#97—22no—
375#97—22no—
376C4×C8—22no—
377C4×C8—22no—
378C24—21no—
379C24#41×C4111yescharacteristic
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—82no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4C2×D4×C4111yescharacteristic
399C22×C4C2×D4×C4111yescharacteristic
400C22×C4C2×D4×C4111yescharacteristic
401C22×C4C2×D4×C4111yescharacteristic
402C22×C4#41×C4111yescharacteristic
403C22×C4C24×C4111yescharacteristic
404SD16—42no—
405SD16—42no—
406M16—24no—
407M16—22no—
408M16—22no—
409M16—22no—
410M16—22no—
411M16—22no—
412M16#41×C4114yes—
413C2×C8—24no—
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—22no—
421C2×C8—22no—
422C2×C8C2×D4×C4111yescharacteristic
423C2×C8C2×D4×C4111yescharacteristic
424C2×C8C2×D4×C4111yescharacteristic
425C2×C8C2×D4×C4111yescharacteristic
426C2×C8#41×C4114yes—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—41no—
434C4⋊C4—41no—
435C4⋊C4C2×D4×C4112yes—
436C4⋊C4C2×D4×C4112yes—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—41no—
443C42—22no—
444C42—22no—
445C23—22no—
446C23—22no—
447C23—41no—
448C23—41no—
449C23—42no—
450C23—81no—
451C23—81no—
452C23#121×C4111yescharacteristic
453C23#121×C4111yescharacteristic
454C23C2×#41×C4111yescharacteristic
455Q8—41no—
456Q8—41no—
457Q8—42no—
458D4—41no—
459D4—41no—
460D4—42no—
461D4—82no—
462D4—82no—
463C2×C4—22no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4#121×C4111yescharacteristic
481C2×C4#121×C4111yescharacteristic
482C2×C4C22×D4×C4111yescharacteristic
483C2×C4C22×D4×C4111yescharacteristic
484C2×C4C2×#41×C4112yes—
485C2×C4C2×#41×C4112yes—
486C8—21no—
487C8—21no—
488C8—24no—
489C8—42no—
490C8—42no—
491C8#123×C4112yes—
492C8#123×C4112yes—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—44no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—162no—
505C22C41×#47112yes—
506C22C2×#121×C4111yescharacteristic
507C22C41×#52912yes—
508C4—21no—
509C4—21no—
510C4—42no—
511C4—42no—
512C4—81no—
513C4—81no—
514C4—81no—
515C4C2×#123×C4111yescharacteristic
516C4C41×#52511yescharacteristic
517C4C41×#53212yes—
518C2—22no—
519C2—22no—
520C2—41no—
521C2—161no—
522C2C41×#285411yescharacteristic
523C2C2×C41×#47111yescharacteristic
524C2C41×#306711yescharacteristic
subgroupG/H
center, socleC22×C41C2×#121
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC2×#121×C41C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C41×#3095C2semidirect
4. C2×C41×#405C2semidirect
5. C41×#1977C2semidirect
6. C41×#1951C2semidirect
7. C41×#1931C2semidirect
8. C41×#1930C2semidirect
9. C41×#1901C2semidirect
11. C41×#1810C2semidirect
230. #33122C41direct (N × H)
256. #3095C2×C41semidirect
259. C2×#405C2×C41semidirect
260. #1977C2×C41semidirect
261. #1951C2×C41semidirect
262. #1931C2×C41semidirect
263. #1930C2×C41semidirect
264. #1901C2×C41semidirect
266. #1810C2×C41semidirect
311. C41#33122direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#30952
C41×#30942
C2×C41×#4652
C2×C41×#4052
C41×#19772
C41×#19512
C41×#19312
C41×#19302
C41×#19012
C41×#19002
C41×#18102
#3312241