Finite Group Databasebeta

← C41×#26815 #23803016

Subgroups — C41×#26815 #23803016

Order 10496.

874 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#482C211yesmaximal, characteristic, complemented
2C2×C41×#478C211yesmaximal, characteristic, complemented
3C41×#2490C211yesmaximal, characteristic, complemented
4C41×#2363C211yesmaximal, characteristic, complemented
5C41×#2067C211yesmaximal, characteristic, complemented
6C41×#2059C211yesmaximal, characteristic, complemented
7C41×#2033C211yesmaximal, characteristic, complemented
8C41×#1999C211yesmaximal, characteristic
9C41×#1972C211yesmaximal, characteristic, complemented
10C41×#1925C211yesmaximal, characteristic, complemented
11C41×#1925C211yesmaximal, characteristic, complemented
12C41×#1924C211yesmaximal, characteristic, complemented
13C41×#1879C211yesmaximal, characteristic, complemented
14C41×#1854C211yesmaximal, characteristic, complemented
15C41×#1776C211yesmaximal, characteristic, complemented
16C22×D8×C41C2211yescharacteristic
17C2×#125×C41C2211yescharacteristic
18C2×#121×C41C2211yescharacteristic
19C2×#121×C41C2211yescharacteristic
20C2×C4×D4×C41C2211yescharacteristic
21C2×#117×C41C2211yescharacteristic
22C41×#482—24no—
23C41×#478—24no—
24C2×#107×C41C2211yescharacteristic
25C2×#107×C41C2211yescharacteristic
26C2×#107×C41C2211yescharacteristic
27C2×#106×C41C2211yescharacteristic
28C2×#106×C41C2211yescharacteristic
29C2×C4⋊C8×C41C2211yescharacteristic
30C2×#102×C41C2211yescharacteristic
31C2×#102×C41C2211yescharacteristic
32C2×#102×C41C2211yescharacteristic
33C2×#102×C41C2211yescharacteristic
34C2×#102×C41C2211yescharacteristic
35C2×#102×C41C2211yescharacteristic
36C2×C22⋊C8×C41C2211yescharacteristic
37C2×C22⋊C8×C41C2211yescharacteristic
38C2×#97×C41C2211yescharacteristic
39C41×#397—21no—
40C41×#394—21no—
41C41×#390—21no—
42C41×#390—21no—
43C41×#390C2211yescharacteristic
44C41×#390C2211yescharacteristic
45C41×#390C2211yescharacteristic
46C41×#389C2211yescharacteristic
47C41×#388—21no—
48C41×#388—21no—
49C41×#386—21no—
50C41×#380C2211yescharacteristic
51C4×C4⋊C4×C41C2211yescharacteristic
52C4×C4⋊C4×C41C2211yescharacteristic
53C4×C22⋊C4×C41—21no—
54C4×C22⋊C4×C41C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#336C2211yescharacteristic
60C41×#336C2211yescharacteristic
61C22×D4×C41—21no—
62C22×D4×C41—21no—
63C22×D4×C41C2311yescharacteristic
64C22×D4×C41C2311yescharacteristic
65C23×C4×C41—21no—
66C23×C4×C41C2311yescharacteristic
67C2×D8×C41—22no—
68C2×D8×C41—22no—
69C2×D8×C41—41no—
70C22×C8×C41C2311yescharacteristic
71C22×C8×C41C2311yescharacteristic
72C22×C8×C41C2311yescharacteristic
73C22×C8×C41C2311yescharacteristic
74#125×C41—22no—
75#125×C41—41no—
76#121×C41—22no—
77#121×C41—22no—
78#121×C41—22no—
79#121×C41—41no—
80C4×D4×C41—22no—
81C4×D4×C41—41no—
82#117×C41—22no—
83#117×C41—41no—
84C2×C4⋊C4×C41—21no—
85C2×C4⋊C4×C41—21no—
86C2×C4⋊C4×C41—21no—
87C2×C4⋊C4×C41C2311yescharacteristic
88C2×C4⋊C4×C41C2311yescharacteristic
89C2×C4⋊C4×C41C2311yescharacteristic
90C2×C4⋊C4×C41C2311yescharacteristic
91C2×C4⋊C4×C41C2311yescharacteristic
92C2×C4⋊C4×C41C2311yescharacteristic
93C2×C22⋊C4×C41—21no—
94C2×C22⋊C4×C41—21no—
95C2×C22⋊C4×C41—21no—
96C2×C22⋊C4×C41—21no—
97C2×C22⋊C4×C41—21no—
98C2×C22⋊C4×C41—21no—
99C2×C22⋊C4×C41—21no—
100C2×C22⋊C4×C41—21no—
101C2×C22⋊C4×C41—21no—
102C2×C22⋊C4×C41—21no—
103C2×C22⋊C4×C41—21no—
104C2×C22⋊C4×C41D411yescharacteristic
105C2×C22⋊C4×C41D411yescharacteristic
106C2×C42×C41—21no—
107C2×C42×C41—21no—
108C2×C42×C41—21no—
109C2×C42×C41C2311yescharacteristic
110C2×C42×C41C2311yescharacteristic
111#107×C41—22no—
112#107×C41—22no—
113#107×C41—22no—
114#106×C41—41no—
115#106×C41D414yescomplemented
116C4⋊C8×C41—22no—
117#102×C41—22no—
118#102×C41—22no—
119#102×C41—22no—
120#102×C41—22no—
121#102×C41—22no—
122#102×C41—22no—
123C22⋊C8×C41—22no—
124C22⋊C8×C41—22no—
125#97×C41—22no—
126#95×C41—21no—
127#95×C41—21no—
128#95×C41—21no—
129#95×C41—21no—
130#95×C41D411yescharacteristic
131#95×C41D411yescharacteristic
132C24×C41—21no—
133C24×C41—21no—
134C24×C41C2×D411yescharacteristic
135C2×D4×C41—24no—
136C2×D4×C41—21no—
137C2×D4×C41—21no—
138C2×D4×C41—21no—
139C2×D4×C41—21no—
140C2×D4×C41—21no—
141C2×D4×C41—21no—
142C2×D4×C41—21no—
143C2×D4×C41—21no—
144C2×D4×C41—21no—
145C2×D4×C41—21no—
146C2×D4×C41—21no—
147C2×D4×C41—42no—
148C2×D4×C41—42no—
149C2×D4×C41—81no—
150C2×D4×C41—81no—
151C2×D4×C41—81no—
152C2×D4×C41#4112yes—
153C22×C4×C41—21no—
154C22×C4×C41—21no—
155C22×C4×C41—21no—
156C22×C4×C41—21no—
157C22×C4×C41—21no—
158C22×C4×C41—21no—
159C22×C4×C41—21no—
160C22×C4×C41—21no—
161C22×C4×C41—21no—
162C22×C4×C41—21no—
163C22×C4×C41—21no—
164C22×C4×C41—21no—
165C22×C4×C41—42no—
166C22×C4×C41—42no—
167C22×C4×C41—81no—
168C22×C4×C41C2×D411yescharacteristic
169C22×C4×C41C2×D411yescharacteristic
170C22×C4×C41C2×D411yescharacteristic
171C22×C4×C41C2×D411yescharacteristic
172C22×C4×C41C2×D411yescharacteristic
173C22×C4×C41C2411yescharacteristic
174D8×C41—44no—
175C2×C8×C41—21no—
176C2×C8×C41—21no—
177C2×C8×C41—21no—
178C2×C8×C41—21no—
179C2×C8×C41—21no—
180C2×C8×C41—21no—
181C2×C8×C41—21no—
182C2×C8×C41—21no—
183C2×C8×C41—21no—
184C2×C8×C41—21no—
185C2×C8×C41C2×D412yes—
186C2×C8×C41#4112yes—
187C4⋊C4×C41—21no—
188C4⋊C4×C41—21no—
189C4⋊C4×C41—21no—
190C4⋊C4×C41—21no—
191C4⋊C4×C41—21no—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—21no—
194C4⋊C4×C41—21no—
195C4⋊C4×C41—21no—
196C4⋊C4×C41—42no—
197C4⋊C4×C41—42no—
198C4⋊C4×C41—81no—
199C4⋊C4×C41C2×D412yes—
200C4⋊C4×C41C2×D412yes—
201C4⋊C4×C41#4112yes—
202C22⋊C4×C41—24no—
203C22⋊C4×C41—41no—
204C22⋊C4×C41—41no—
205C22⋊C4×C41—42no—
206C22⋊C4×C41—42no—
207C22⋊C4×C41—42no—
208C22⋊C4×C41—42no—
209C22⋊C4×C41—42no—
210C22⋊C4×C41—81no—
211C22⋊C4×C41—81no—
212C22⋊C4×C41—81no—
213C22⋊C4×C41—81no—
214C22⋊C4×C41—81no—
215C42×C41—21no—
216C42×C41—21no—
217C42×C41—21no—
218C42×C41—21no—
219C42×C41—42no—
220C42×C41—81no—
221C42×C41—81no—
222C23×C41—22no—
223C23×C41—21no—
224C23×C41—21no—
225C23×C41—21no—
226C23×C41—21no—
227C23×C41—21no—
228C23×C41—21no—
229C23×C41—21no—
230C23×C41—41no—
231C23×C41—41no—
232C23×C41—41no—
233C23×C41—41no—
234C23×C41—41no—
235C23×C41—41no—
236C23×C41—41no—
237C23×C41—41no—
238C23×C41—41no—
239C23×C41—41no—
240C23×C41—41no—
241C23×C41—41no—
242C23×C41—41no—
243C23×C41C22×D411yescharacteristic
244D4×C41—22no—
245D4×C41—22no—
246D4×C41—41no—
247D4×C41—41no—
248D4×C41—41no—
249D4×C41—41no—
250D4×C41—41no—
251D4×C41—41no—
252D4×C41—84no—
253D4×C41—84no—
254C2×C4×C41—21no—
255C2×C4×C41—22no—
256C2×C4×C41—21no—
257C2×C4×C41—21no—
258C2×C4×C41—21no—
259C2×C4×C41—22no—
260C2×C4×C41—22no—
261C2×C4×C41—21no—
262C2×C4×C41—21no—
263C2×C4×C41—21no—
264C2×C4×C41—21no—
265C2×C4×C41—21no—
266C2×C4×C41—21no—
267C2×C4×C41—21no—
268C2×C4×C41—21no—
269C2×C4×C41—21no—
270C2×C4×C41—21no—
271C2×C4×C41—21no—
272C2×C4×C41—41no—
273C2×C4×C41—41no—
274C2×C4×C41—41no—
275C2×C4×C41—41no—
276C2×C4×C41—41no—
277C2×C4×C41—41no—
278C2×C4×C41—41no—
279C2×C4×C41—41no—
280C2×C4×C41—41no—
281C2×C4×C41—41no—
282C2×C4×C41—41no—
283C2×C4×C41—41no—
284C2×C4×C41—41no—
285C2×C4×C41—41no—
286C2×C4×C41—41no—
287C2×C4×C41—41no—
288C2×C4×C41—41no—
289C2×C4×C41—41no—
290C2×C4×C41—41no—
291C2×C4×C41—84no—
292C2×C4×C41C22×D411yescharacteristic
293C2×C4×C41C2×#4111yescharacteristic
294C2×C4×C41C2×#4111yescharacteristic
295C2×C4×C41C2×#4111yescharacteristic
296C2×C4×C41H(5,𝔽2)11yescharacteristic
297C2×C4×C412−1+411yescharacteristic
298C8×C41—22no—
299C8×C41—22no—
300C8×C41—41no—
301C8×C41—41no—
302#26815C4111yesmaximal, characteristic, direct product factor, Sylow
303C22×C41—41no—
304C22×C41—41no—
305C22×C41—41no—
306C22×C41—42no—
307C22×C41—41no—
308C22×C41—42no—
309C22×C41—41no—
310C22×C41—42no—
311C22×C41—41no—
312C22×C41—41no—
313C22×C41—81no—
314C22×C41—81no—
315C22×C41—81no—
316C22×C41—81no—
317C22×C41—81no—
318C22×C41—81no—
319C22×C41—81no—
320C22×C41—81no—
321C22×C41—81no—
322C22×C41—81no—
323C22×C41—81no—
324C22×C41#52511yescharacteristic
325C22×C41D4211yescharacteristic
326C22×C41#54711yescharacteristic
327C22×C41#57511yescharacteristic
328C22×C41#57511yescharacteristic
329C22×C41#57611yescharacteristic
330C22×C41#57611yescharacteristic
331C4×C41—41no—
332C4×C41—41no—
333C4×C41—42no—
334C4×C41—41no—
335C4×C41—41no—
336C4×C41—41no—
337C4×C41—42no—
338C4×C41—42no—
339C4×C41—81no—
340C4×C41—81no—
341C4×C41—81no—
342C4×C41#53211yescharacteristic
343C4×C41#54211yescharacteristic
344C4×C41#54811yescharacteristic
345C4×C41#55111yescharacteristic
346C2×#482C2×C4111yescharacteristic, complemented
347C2×#478C2×C4111yescharacteristic, complemented
348#2490C2×C4111yescharacteristic, complemented
349#2363C2×C4111yescharacteristic, complemented
350#2067C2×C4111yescharacteristic, complemented
351#2059C2×C4111yescharacteristic, complemented
352#2033C2×C4111yescharacteristic, complemented
353#1999C2×C4111yescharacteristic
354#1972C2×C4111yescharacteristic, complemented
355#1925C2×C4111yescharacteristic, complemented
356#1925C2×C4111yescharacteristic, complemented
357#1924C2×C4111yescharacteristic, complemented
358#1879C2×C4111yescharacteristic, complemented
359#1854C2×C4111yescharacteristic, complemented
360#1776C2×C4111yescharacteristic, complemented
361C2×C41—81no—
362C2×C41—82no—
363C2×C41—161no—
364C2×C41#246111yescharacteristic
365C2×C41#311111yescharacteristic
366C2×C41#312211yescharacteristic
367C2×C41#326811yescharacteristic
368C2×C41#326811yescharacteristic
369C2×C41#334711yescharacteristic
370C2×C41#335511yescharacteristic
371C22×D8C22×C4111yescharacteristic
372C2×#125C22×C4111yescharacteristic
373C2×#121C22×C4111yescharacteristic
374C2×#121C22×C4111yescharacteristic
375C2×C4×D4C22×C4111yescharacteristic
376C2×#117C22×C4111yescharacteristic
377#482—24no—
378#478—24no—
379C2×#107C22×C4111yescharacteristic
380C2×#107C22×C4111yescharacteristic
381C2×#107C22×C4111yescharacteristic
382C2×#106C22×C4111yescharacteristic
383C2×#106C22×C4111yescharacteristic
384C2×C4⋊C8C22×C4111yescharacteristic
385C2×#102C22×C4111yescharacteristic
386C2×#102C22×C4111yescharacteristic
387C2×#102C22×C4111yescharacteristic
388C2×#102C22×C4111yescharacteristic
389C2×#102C22×C4111yescharacteristic
390C2×#102C22×C4111yescharacteristic
391C2×C22⋊C8C22×C4111yescharacteristic
392C2×C22⋊C8C22×C4111yescharacteristic
393C2×#97C22×C4111yescharacteristic
394#397—21no—
395#394—21no—
396#390—21no—
397#390—21no—
398#390C22×C4111yescharacteristic
399#390C22×C4111yescharacteristic
400#390C22×C4111yescharacteristic
401#389C22×C4111yescharacteristic
402#388—21no—
403#388—21no—
404#386—21no—
405#380C22×C4111yescharacteristic
406C4×C4⋊C4C22×C4111yescharacteristic
407C4×C4⋊C4C22×C4111yescharacteristic
408C4×C22⋊C4—21no—
409C4×C22⋊C4C22×C4111yescharacteristic
410#340C22×C4111yescharacteristic
411#340C22×C4111yescharacteristic
412#340C22×C4111yescharacteristic
413#340C22×C4111yescharacteristic
414#336C22×C4111yescharacteristic
415#336C22×C4111yescharacteristic
416C41#2681511yescharacteristic, direct product factor, Sylow
417C22×D4—21no—
418C22×D4—21no—
419C22×D4C23×C4111yescharacteristic
420C22×D4C23×C4111yescharacteristic
421C23×C4—21no—
422C23×C4C23×C4111yescharacteristic
423C2×D8—22no—
424C2×D8—22no—
425C2×D8—41no—
426C22×C8C23×C4111yescharacteristic
427C22×C8C23×C4111yescharacteristic
428C22×C8C23×C4111yescharacteristic
429C22×C8C23×C4111yescharacteristic
430#125—22no—
431#125—41no—
432#121—22no—
433#121—22no—
434#121—22no—
435#121—41no—
436C4×D4—22no—
437C4×D4—41no—
438#117—22no—
439#117—41no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4C23×C4111yescharacteristic
444C2×C4⋊C4C23×C4111yescharacteristic
445C2×C4⋊C4C23×C4111yescharacteristic
446C2×C4⋊C4C23×C4111yescharacteristic
447C2×C4⋊C4C23×C4111yescharacteristic
448C2×C4⋊C4C23×C4111yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4D4×C4111yescharacteristic
461C2×C22⋊C4D4×C4111yescharacteristic
462C2×C42—21no—
463C2×C42—21no—
464C2×C42—21no—
465C2×C42C23×C4111yescharacteristic
466C2×C42C23×C4111yescharacteristic
467#107—22no—
468#107—22no—
469#107—22no—
470#106—41no—
471#106D4×C4114yescomplemented
472C4⋊C8—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102—22no—
477#102—22no—
478#102—22no—
479C22⋊C8—22no—
480C22⋊C8—22no—
481#97—22no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95D4×C4111yescharacteristic
487#95D4×C4111yescharacteristic
488C24—21no—
489C24—21no—
490C24C2×D4×C4111yescharacteristic
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4#41×C4112yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4C2×D4×C4111yescharacteristic
525C22×C4C2×D4×C4111yescharacteristic
526C22×C4C2×D4×C4111yescharacteristic
527C22×C4C2×D4×C4111yescharacteristic
528C22×C4C2×D4×C4111yescharacteristic
529C22×C4C24×C4111yescharacteristic
530D8—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8C2×D4×C4112yes—
542C2×C8#41×C4112yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4C2×D4×C4112yes—
556C4⋊C4C2×D4×C4112yes—
557C4⋊C4#41×C4112yes—
558C22⋊C4—24no—
559C22⋊C4—41no—
560C22⋊C4—41no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—42no—
576C42—81no—
577C42—81no—
578C23—22no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23C22×D4×C4111yescharacteristic
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609D4—84no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—84no—
648C2×C4C22×D4×C4111yescharacteristic
649C2×C4C2×#41×C4111yescharacteristic
650C2×C4C2×#41×C4111yescharacteristic
651C2×C4C2×#41×C4111yescharacteristic
652C2×C4H(5,𝔽2)×C4111yescharacteristic
653C2×C42−1+4×C4111yescharacteristic
654C8—22no—
655C8—22no—
656C8—41no—
657C8—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—42no—
662C22—41no—
663C22—42no—
664C22—41no—
665C22—42no—
666C22—41no—
667C22—41no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C41×#52511yescharacteristic
680C22D42×C4111yescharacteristic
681C22C41×#54711yescharacteristic
682C22C41×#57511yescharacteristic
683C22C41×#57511yescharacteristic
684C22C41×#57611yescharacteristic
685C22C41×#57611yescharacteristic
686C4—41no—
687C4—41no—
688C4—42no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—42no—
693C4—42no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C41×#53211yescharacteristic
698C4C41×#54211yescharacteristic
699C4C41×#54811yescharacteristic
700C4C41×#55111yescharacteristic
701C2—81no—
702C2—82no—
703C2—161no—
704C2C41×#246111yescharacteristic
705C2C41×#311111yescharacteristic
706C2C41×#312211yescharacteristic
707C2C41×#326811yescharacteristic
708C2C41×#326811yescharacteristic
709C2C41×#334711yescharacteristic
710C2C41×#335511yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C4×C22⋊C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#482C2semidirect
2. C2×C41×#478C2semidirect
3. C41×#2490C2semidirect
4. C41×#2363C2semidirect
5. C41×#2067C2semidirect
6. C41×#2059C2semidirect
7. C41×#2033C2semidirect
9. C41×#1972C2semidirect
10. C41×#1925C2semidirect
11. C41×#1925C2semidirect
12. C41×#1924C2semidirect
13. C41×#1879C2semidirect
14. C41×#1854C2semidirect
15. C41×#1776C2semidirect
115. #106×C41D4semidirect
302. #26815C41direct (N × H)
346. C2×#482C2×C41semidirect
347. C2×#478C2×C41semidirect
348. #2490C2×C41semidirect
349. #2363C2×C41semidirect
350. #2067C2×C41semidirect
351. #2059C2×C41semidirect
352. #2033C2×C41semidirect
354. #1972C2×C41semidirect
355. #1925C2×C41semidirect
356. #1925C2×C41semidirect
357. #1924C2×C41semidirect
358. #1879C2×C41semidirect
359. #1854C2×C41semidirect
360. #1776C2×C41semidirect
416. C41#26815direct (N × H)
471. #106D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4822
C2×C41×#4782
C41×#24902
C41×#23632
C41×#20672
C41×#20592
C41×#20332
C41×#19992
C41×#19722
C41×#19252
C41×#19242
C41×#18792
C41×#18542
C41×#17762
#2681541