Finite Group Databasebeta

← C41×#19035 #23795236

Subgroups — C41×#19035 #23795236

Order 10496.

824 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C41×#3563C211yesmaximal, characteristic
2C41×#3239C211yesmaximal, characteristic
3C41×#3165C211yesmaximal, characteristic, complemented
4C2×C41×#491C211yesmaximal, characteristic, complemented
5C41×#1664C214yesmaximal, complemented
6C41×#1663C214yesmaximal, complemented
7C41×#1531C211yesmaximal, characteristic, complemented
8C41×#1528C211yesmaximal, characteristic, complemented
9C41×#1524C211yesmaximal, characteristic
10C41×#564C2212yes—
11C41×#563C2212yes—
12C41×#557—21no—
13C41×#554—21no—
14C41×#552—21no—
15C41×#552—22no—
16C41×#552—21no—
17C41×#544—21no—
18C41×#544—21no—
19C41×#541—21no—
20C41×#541—22no—
21C41×#539—21no—
22C41×#533C2211yescharacteristic
23C2×C4⋊Q8×C41C2211yescharacteristic
24C41×#529C2211yescharacteristic
25C2×#125×C41C2211yescharacteristic
26C41×#501C2214yes—
27C41×#501C2212yes—
28C41×#500—21no—
29C41×#498—21no—
30C41×#491—22no—
31C41×#491C2214yes—
32C41×#489C2212yes—
33C41×#484—21no—
34C41×#481—21no—
35C41×#475—21no—
36C41×#474—21no—
37C41×#432C2211yescharacteristic
38C41×#428—22no—
39C2×#103×C41—21no—
40C2×#103×C41—21no—
41C4×M16×C41C2211yescharacteristic
42C2×#97×C41C2211yescharacteristic
43C41×#330C2212yes—
44C41×#330C2214yes—
45C41×#330C2214yes—
46C41×#329C2212yes—
47C22×Q8×C41—21no—
48C2×M16×C41—21no—
49C22×C8×C41—21no—
50C4⋊Q8×C41—22no—
51C4⋊Q8×C41—21no—
52C4⋊Q8×C41—22no—
53C4⋊Q8×C41—21no—
54C4⋊Q8×C41—21no—
55C4⋊Q8×C41—21no—
56C4⋊Q8×C41D411yescharacteristic
57C4⋊Q8×C41D411yescharacteristic
58C4⋊Q8×C41C2312yes—
59#126×C41—22no—
60#126×C41—22no—
61#126×C41—22no—
62#126×C41—22no—
63#126×C41—21no—
64#125×C41—22no—
65#125×C41—22no—
66#125×C41—21no—
67#125×C41—22no—
68#125×C41—22no—
69#125×C41—22no—
70#125×C41—22no—
71#125×C41—22no—
72#125×C41—22no—
73#125×C41—21no—
74#125×C41—21no—
75#125×C41D412yes—
76#125×C41C2311yescharacteristic
77#125×C41C2312yes—
78#125×C41C2312yes—
79#124×C41C2311yescharacteristic
80#123×C41—22no—
81#123×C41—22no—
82#123×C41—21no—
83C22⋊Q8×C41—22no—
84C22⋊Q8×C41—21no—
85C22⋊Q8×C41—21no—
86C22⋊Q8×C41—22no—
87C22⋊Q8×C41—21no—
88C22⋊Q8×C41—21no—
89C22⋊Q8×C41—22no—
90C22⋊Q8×C41—22no—
91C22⋊Q8×C41D411yescharacteristic
92#121×C41D411yescharacteristic
93C4×Q8×C41—21no—
94C4×Q8×C41—22no—
95C4×Q8×C41—21no—
96C4×Q8×C41—21no—
97C4×Q8×C41—21no—
98C4×Q8×C41D411yescharacteristic
99C4×D4×C41—22no—
100C4×D4×C41—21no—
101C4×D4×C41D411yescharacteristic
102#117×C41—22no—
103#117×C41—21no—
104#117×C41—22no—
105#117×C41—21no—
106#117×C41D412yes—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41D411yescharacteristic
113C2×C4⋊C4×C41D411yescharacteristic
114C2×C42×C41C2311yescharacteristic
115#107×C41—24no—
116#107×C41—22no—
117#106×C41—24no—
118#106×C41—22no—
119C4⋊C8×C41—21no—
120#103×C41—22no—
121#103×C41—24no—
122#103×C41—24no—
123#102×C41—22no—
124C22⋊C8×C41—21no—
125#97×C41—21no—
126#97×C41C2312yes—
127#97×C41C2312yes—
128#97×C41C2312yes—
129C4×C8×C41—21no—
130C2×Q8×C41—22no—
131C2×Q8×C41—21no—
132C2×Q8×C41—21no—
133C2×Q8×C41—22no—
134C2×Q8×C41—44no—
135C2×Q8×C41—41no—
136C2×Q8×C41C2×D411yescharacteristic
137C2×D4×C41—21no—
138C2×D4×C41C2×D411yescharacteristic
139C22×C4×C41—21no—
140C22×C4×C41—22no—
141C22×C4×C41—21no—
142C22×C4×C41—21no—
143C22×C4×C41—41no—
144C22×C4×C41C2×D411yescharacteristic
145C22×C4×C41C2×D411yescharacteristic
146C22×C4×C41C2×D411yescharacteristic
147M16×C41—24no—
148C2×C8×C41—22no—
149C2×C8×C41—22no—
150C2×C8×C41—22no—
151C2×C8×C41—42no—
152C4⋊C4×C41—22no—
153C4⋊C4×C41—22no—
154C4⋊C4×C41—22no—
155C4⋊C4×C41—22no—
156C4⋊C4×C41—22no—
157C4⋊C4×C41—22no—
158C4⋊C4×C41—22no—
159C4⋊C4×C41—22no—
160C4⋊C4×C41—21no—
161C4⋊C4×C41—21no—
162C4⋊C4×C41—22no—
163C4⋊C4×C41—22no—
164C4⋊C4×C41—21no—
165C4⋊C4×C41—21no—
166C4⋊C4×C41—21no—
167C4⋊C4×C41—21no—
168C4⋊C4×C41—22no—
169C4⋊C4×C41—22no—
170C4⋊C4×C41—21no—
171C4⋊C4×C41—21no—
172C4⋊C4×C41—22no—
173C4⋊C4×C41—22no—
174C4⋊C4×C41—22no—
175C4⋊C4×C41—22no—
176C4⋊C4×C41—41no—
177C4⋊C4×C41—41no—
178C4⋊C4×C41C2×D412yes—
179C4⋊C4×C41C2×D412yes—
180C4⋊C4×C41C2×D412yes—
181C4⋊C4×C41C2×D411yescharacteristic
182C4⋊C4×C41C2×D412yes—
183C4⋊C4×C41C2×D411yescharacteristic
184C22⋊C4×C41—22no—
185C22⋊C4×C41—22no—
186C22⋊C4×C41—22no—
187C22⋊C4×C41—21no—
188C22⋊C4×C41—22no—
189C22⋊C4×C41—21no—
190C22⋊C4×C41—21no—
191C22⋊C4×C41—21no—
192C22⋊C4×C41—21no—
193C42×C41—22no—
194C42×C41—22no—
195C42×C41—22no—
196C42×C41—22no—
197C42×C41—21no—
198C42×C41C2×D411yescharacteristic
199C42×C41C2×D411yescharacteristic
200C42×C41C2×D411yescharacteristic
201C42×C41C2411yescharacteristic
202C23×C41—21no—
203C23×C41#12011yescharacteristic
204Q8×C41—41no—
205Q8×C41—44no—
206Q8×C41—42no—
207Q8×C41—81no—
208Q8×C41—82no—
209Q8×C41—82no—
210D4×C41—41no—
211D4×C41—42no—
212C2×C4×C41—22no—
213C2×C4×C41—22no—
214C2×C4×C41—22no—
215C2×C4×C41—21no—
216C2×C4×C41—21no—
217C2×C4×C41—21no—
218C2×C4×C41—22no—
219C2×C4×C41—22no—
220C2×C4×C41—22no—
221C2×C4×C41—41no—
222C2×C4×C41—42no—
223C2×C4×C41—42no—
224C2×C4×C41—42no—
225C2×C4×C41—81no—
226C2×C4×C41—82no—
227C2×C4×C41—82no—
228C2×C4×C41#12011yescharacteristic
229C2×C4×C41#12011yescharacteristic
230C2×C4×C41#12011yescharacteristic
231C2×C4×C41C22×D411yescharacteristic
232C2×C4×C41C22×D411yescharacteristic
233C2×C4×C41C22×D411yescharacteristic
234C8×C41—24no—
235C8×C41—42no—
236C8×C41—42no—
237#19035C4111yesmaximal, characteristic, direct product factor, Sylow
238C22×C41—21no—
239C22×C41—21no—
240C22×C41—41no—
241C22×C41—41no—
242C22×C41—41no—
243C22×C41#45612yes—
244C22×C41C2×#12011yescharacteristic
245C4×C41—21no—
246C4×C41—21no—
247C4×C41—21no—
248C4×C41—21no—
249C4×C41—21no—
250C4×C41—41no—
251C4×C41—42no—
252C4×C41—42no—
253C4×C41—41no—
254C4×C41—42no—
255C4×C41—42no—
256C4×C41—41no—
257C4×C41—82no—
258C4×C41#45412yes—
259#3563C2×C4111yescharacteristic
260#3239C2×C4111yescharacteristic
261#3165C2×C4111yescharacteristic, complemented
262C2×#491C2×C4111yescharacteristic, complemented
263#1664C2×C4114yescomplemented
264#1663C2×C4114yescomplemented
265#1531C2×C4111yescharacteristic, complemented
266#1528C2×C4111yescharacteristic, complemented
267#1524C2×C4111yescharacteristic
268C2×C41—22no—
269C2×C41—81no—
270C2×C41C2×#45411yescharacteristic
271C2×C41C2×#45611yescharacteristic
272C2×C41#302211yescharacteristic
273#564C22×C4112yes—
274#563C22×C4112yes—
275#557—21no—
276#554—21no—
277#552—21no—
278#552—22no—
279#552—21no—
280#544—21no—
281#544—21no—
282#541—21no—
283#541—22no—
284#539—21no—
285#533C22×C4111yescharacteristic
286C2×C4⋊Q8C22×C4111yescharacteristic
287#529C22×C4111yescharacteristic
288C2×#125C22×C4111yescharacteristic
289#501C22×C4114yes—
290#501C22×C4112yes—
291#500—21no—
292#498—21no—
293#491—22no—
294#491C22×C4114yes—
295#489C22×C4112yes—
296#484—21no—
297#481—21no—
298#475—21no—
299#474—21no—
300#432C22×C4111yescharacteristic
301#428—22no—
302C2×#103—21no—
303C2×#103—21no—
304C4×M16C22×C4111yescharacteristic
305C2×#97C22×C4111yescharacteristic
306#330C22×C4112yes—
307#330C22×C4114yes—
308#330C22×C4114yes—
309#329C22×C4112yes—
310C41#1903511yescharacteristic, direct product factor, Sylow
311C22×Q8—21no—
312C2×M16—21no—
313C22×C8—21no—
314C4⋊Q8—22no—
315C4⋊Q8—21no—
316C4⋊Q8—22no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8D4×C4111yescharacteristic
321C4⋊Q8D4×C4111yescharacteristic
322C4⋊Q8C23×C4112yes—
323#126—22no—
324#126—22no—
325#126—22no—
326#126—22no—
327#126—21no—
328#125—22no—
329#125—22no—
330#125—21no—
331#125—22no—
332#125—22no—
333#125—22no—
334#125—22no—
335#125—22no—
336#125—22no—
337#125—21no—
338#125—21no—
339#125D4×C4112yes—
340#125C23×C4112yes—
341#125C23×C4111yescharacteristic
342#125C23×C4112yes—
343#124C23×C4111yescharacteristic
344#123—22no—
345#123—22no—
346#123—21no—
347C22⋊Q8—22no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C22⋊Q8—22no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8D4×C4111yescharacteristic
356#121D4×C4111yescharacteristic
357C4×Q8—21no—
358C4×Q8—22no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8D4×C4111yescharacteristic
363C4×D4—22no—
364C4×D4—21no—
365C4×D4D4×C4111yescharacteristic
366#117—22no—
367#117—21no—
368#117—22no—
369#117—21no—
370#117D4×C4112yes—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4D4×C4111yescharacteristic
377C2×C4⋊C4D4×C4111yescharacteristic
378C2×C42C23×C4111yescharacteristic
379#107—24no—
380#107—22no—
381#106—24no—
382#106—22no—
383C4⋊C8—21no—
384#103—22no—
385#103—24no—
386#103—24no—
387#102—22no—
388C22⋊C8—21no—
389#97—21no—
390#97C23×C4112yes—
391#97C23×C4112yes—
392#97C23×C4112yes—
393C4×C8—21no—
394C2×Q8—22no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—44no—
399C2×Q8—41no—
400C2×Q8C2×D4×C4111yescharacteristic
401C2×D4—21no—
402C2×D4C2×D4×C4111yescharacteristic
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—41no—
408C22×C4C2×D4×C4111yescharacteristic
409C22×C4C2×D4×C4111yescharacteristic
410C22×C4C2×D4×C4111yescharacteristic
411M16—24no—
412C2×C8—22no—
413C2×C8—22no—
414C2×C8—22no—
415C2×C8—42no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4C2×D4×C4112yes—
443C4⋊C4C2×D4×C4112yes—
444C4⋊C4C2×D4×C4112yes—
445C4⋊C4C2×D4×C4111yescharacteristic
446C4⋊C4C2×D4×C4112yes—
447C4⋊C4C2×D4×C4111yescharacteristic
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—21no—
452C22⋊C4—22no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—22no—
461C42—21no—
462C42C2×D4×C4111yescharacteristic
463C42C2×D4×C4111yescharacteristic
464C42C2×D4×C4111yescharacteristic
465C42C24×C4111yescharacteristic
466C23—21no—
467C23#120×C4111yescharacteristic
468Q8—41no—
469Q8—44no—
470Q8—42no—
471Q8—81no—
472Q8—82no—
473Q8—82no—
474D4—41no—
475D4—42no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—81no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4#120×C4111yescharacteristic
493C2×C4#120×C4111yescharacteristic
494C2×C4#120×C4111yescharacteristic
495C2×C4C22×D4×C4111yescharacteristic
496C2×C4C22×D4×C4111yescharacteristic
497C2×C4C22×D4×C4111yescharacteristic
498C8—24no—
499C8—42no—
500C8—42no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22C41×#45612yes—
507C22C2×#120×C4111yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—42no—
515C4—42no—
516C4—41no—
517C4—42no—
518C4—42no—
519C4—41no—
520C4—82no—
521C4C41×#45412yes—
522C2—22no—
523C2—81no—
524C2C2×C41×#45411yescharacteristic
525C2C2×C41×#45611yescharacteristic
526C2C41×#302211yescharacteristic
subgroupG/H
center, socleC22×C41C2×#120
commutator, Frattini, cosocleC42C24×C41
prime radical#121×C41D4
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
3. C41×#3165C2semidirect
4. C2×C41×#491C2semidirect
5. C41×#1664C2semidirect
6. C41×#1663C2semidirect
7. C41×#1531C2semidirect
8. C41×#1528C2semidirect
237. #19035C41direct (N × H)
261. #3165C2×C41semidirect
262. C2×#491C2×C41semidirect
263. #1664C2×C41semidirect
264. #1663C2×C41semidirect
265. #1531C2×C41semidirect
266. #1528C2×C41semidirect
310. C41#19035direct (N × H)

Maximal subgroups

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

subgroupindex
C41×#35632
C41×#32392
C41×#31652
C2×C41×#4912
C41×#16642
C41×#16632
C41×#15312
C41×#15282
C41×#15242
#1903541