Finite Group Databasebeta

← C41×#25953 #23802154

Subgroups — C41×#25953 #23802154

Order 10496.

958 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#479C211yesmaximal, characteristic, complemented
2C2×C41×#416C211yesmaximal, characteristic
3C41×#2441C211yesmaximal, characteristic, complemented
4C41×#2341C211yesmaximal, characteristic
5C41×#2094C211yesmaximal, characteristic, complemented
6C41×#2067C211yesmaximal, characteristic, complemented
7C41×#2065C211yesmaximal, characteristic, complemented
8C41×#2025C211yesmaximal, characteristic, complemented
9C41×#1865C211yesmaximal, characteristic, complemented
10C41×#1865C211yesmaximal, characteristic, complemented
11C41×#1854C211yesmaximal, characteristic, complemented
12C41×#1850C211yesmaximal, characteristic, complemented
13C41×#1807C211yesmaximal, characteristic, complemented
14C41×#1803C211yesmaximal, characteristic, complemented
15C41×#1788C211yesmaximal, characteristic
16C22×#41×C41C2211yescharacteristic
17C23×C8×C41C2211yescharacteristic
18C2×#125×C41C2211yescharacteristic
19C2×C4×Q8×C41C2211yescharacteristic
20C2×C4×Q8×C41C2211yescharacteristic
21C2×#117×C41C2211yescharacteristic
22C41×#479—24no—
23C2×#107×C41C2211yescharacteristic
24C2×#106×C41C2211yescharacteristic
25C2×#106×C41C2211yescharacteristic
26C2×#106×C41C2211yescharacteristic
27C2×C4⋊C8×C41C2211yescharacteristic
28C2×C4⋊C8×C41C2211yescharacteristic
29C41×#416—24no—
30C2×#103×C41C2211yescharacteristic
31C2×#103×C41C2211yescharacteristic
32C2×#103×C41C2211yescharacteristic
33C2×#103×C41C2211yescharacteristic
34C2×#102×C41C2211yescharacteristic
35C2×#102×C41C2211yescharacteristic
36C2×#102×C41C2211yescharacteristic
37C2×#102×C41C2211yescharacteristic
38C2×C22⋊C8×C41C2211yescharacteristic
39C41×#399—21no—
40C41×#396—21no—
41C41×#390—21no—
42C41×#390—21no—
43C41×#390C2211yescharacteristic
44C41×#390C2211yescharacteristic
45C41×#389—21no—
46C41×#389C2211yescharacteristic
47C41×#389C2211yescharacteristic
48C41×#387—21no—
49C41×#384C2211yescharacteristic
50C41×#380—21no—
51C41×#380C2211yescharacteristic
52C41×#380C2211yescharacteristic
53C4×C22⋊C4×C41—21no—
54C4×C22⋊C4×C41C2211yescharacteristic
55C41×#340C2211yescharacteristic
56C41×#340C2211yescharacteristic
57C41×#340C2211yescharacteristic
58C41×#340C2211yescharacteristic
59C41×#336C2211yescharacteristic
60C41×#336C2211yescharacteristic
61C2×#41×C41—22no—
62C2×#41×C41—22no—
63C2×#41×C41—22no—
64C2×#41×C41—41no—
65C2×#41×C41—41no—
66C2×#41×C41Q814yes—
67C22×Q8×C41C2311yescharacteristic
68C22×D4×C41—21no—
69C22×D4×C41C2311yescharacteristic
70C23×C4×C41—21no—
71C23×C4×C41C2311yescharacteristic
72C22×C8×C41—22no—
73C22×C8×C41—22no—
74C22×C8×C41—41no—
75C22×C8×C41C2311yescharacteristic
76C22×C8×C41C2311yescharacteristic
77C22×C8×C41C2311yescharacteristic
78C22×C8×C41C2311yescharacteristic
79#125×C41—22no—
80#125×C41—41no—
81C4×Q8×C41—22no—
82C4×Q8×C41—22no—
83C4×Q8×C41—41no—
84C4×Q8×C41—41no—
85#117×C41—22no—
86#117×C41—41no—
87C2×C4⋊C4×C41—21no—
88C2×C4⋊C4×C41—21no—
89C2×C4⋊C4×C41—21no—
90C2×C4⋊C4×C41—21no—
91C2×C4⋊C4×C41—21no—
92C2×C4⋊C4×C41—21no—
93C2×C4⋊C4×C41—21no—
94C2×C4⋊C4×C41—21no—
95C2×C4⋊C4×C41C2311yescharacteristic
96C2×C4⋊C4×C41C2311yescharacteristic
97C2×C4⋊C4×C41C2311yescharacteristic
98C2×C4⋊C4×C41C2311yescharacteristic
99C2×C4⋊C4×C41C2311yescharacteristic
100C2×C4⋊C4×C41C2311yescharacteristic
101C2×C22⋊C4×C41—21no—
102C2×C22⋊C4×C41—21no—
103C2×C22⋊C4×C41—21no—
104C2×C22⋊C4×C41—21no—
105C2×C22⋊C4×C41—21no—
106C2×C22⋊C4×C41—21no—
107C2×C22⋊C4×C41—21no—
108C2×C22⋊C4×C41D411yescharacteristic
109C2×C22⋊C4×C41D411yescharacteristic
110C2×C42×C41—21no—
111C2×C42×C41—21no—
112C2×C42×C41—21no—
113C2×C42×C41C2311yescharacteristic
114C2×C42×C41C2311yescharacteristic
115#107×C41—22no—
116#106×C41—22no—
117#106×C41—41no—
118#106×C41—41no—
119C4⋊C8×C41—22no—
120C4⋊C8×C41—41no—
121#103×C41—22no—
122#103×C41—22no—
123#103×C41—22no—
124#103×C41D414yes—
125#102×C41—22no—
126#102×C41—22no—
127#102×C41—41no—
128#102×C41—41no—
129C22⋊C8×C41—22no—
130#95×C41—21no—
131#95×C41—21no—
132#95×C41—21no—
133#95×C41—21no—
134#95×C41D411yescharacteristic
135#95×C41D411yescharacteristic
136C24×C41—21no—
137C24×C41C2×D411yescharacteristic
138#41×C41—28no—
139#41×C41—44no—
140#41×C41—44no—
141#41×C41—44no—
142C2×Q8×C41—21no—
143C2×Q8×C41—21no—
144C2×Q8×C41—21no—
145C2×Q8×C41C2×D412yes—
146C2×Q8×C41C2×Q812yes—
147C2×Q8×C41#4112yes—
148C2×D4×C41—24no—
149C2×D4×C41—21no—
150C2×D4×C41—21no—
151C2×D4×C41—21no—
152C2×D4×C41—21no—
153C2×D4×C41—21no—
154C2×D4×C41—42no—
155C2×D4×C41—42no—
156C2×D4×C41C2×Q812yes—
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—24no—
164C22×C4×C41—21no—
165C22×C4×C41—21no—
166C22×C4×C41—21no—
167C22×C4×C41—21no—
168C22×C4×C41—21no—
169C22×C4×C41—42no—
170C22×C4×C41—42no—
171C22×C4×C41C2×D411yescharacteristic
172C22×C4×C41C2×D411yescharacteristic
173C22×C4×C41C2×D411yescharacteristic
174C22×C4×C41C2×D411yescharacteristic
175C22×C4×C41C2×D411yescharacteristic
176C22×C4×C41C2×Q812yes—
177C22×C4×C41#4112yes—
178C22×C4×C41C2411yescharacteristic
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×C41—21no—
186C2×C8×C41—21no—
187C2×C8×C41—21no—
188C2×C8×C41—21no—
189C2×C8×C41—21no—
190C2×C8×C41—44no—
191C2×C8×C41C2×D412yes—
192C4⋊C4×C41—21no—
193C4⋊C4×C41—21no—
194C4⋊C4×C41—21no—
195C4⋊C4×C41—21no—
196C4⋊C4×C41—21no—
197C4⋊C4×C41—21no—
198C4⋊C4×C41—21no—
199C4⋊C4×C41—21no—
200C4⋊C4×C41—21no—
201C4⋊C4×C41—21no—
202C4⋊C4×C41—21no—
203C4⋊C4×C41—42no—
204C4⋊C4×C41—42no—
205C4⋊C4×C41—42no—
206C4⋊C4×C41—42no—
207C4⋊C4×C41—42no—
208C4⋊C4×C41—42no—
209C4⋊C4×C41—81no—
210C4⋊C4×C41—81no—
211C4⋊C4×C41C2×D412yes—
212C22⋊C4×C41—22no—
213C22⋊C4×C41—41no—
214C22⋊C4×C41—42no—
215C22⋊C4×C41—42no—
216C22⋊C4×C41—42no—
217C22⋊C4×C41—81no—
218C22⋊C4×C41—81no—
219C22⋊C4×C41—81no—
220C22⋊C4×C41—81no—
221C42×C41—21no—
222C42×C41—21no—
223C42×C41—21no—
224C42×C41—21no—
225C42×C41—42no—
226C42×C41—42no—
227C42×C41—42no—
228C23×C41—21no—
229C23×C41—21no—
230C23×C41—21no—
231C23×C41—21no—
232C23×C41—21no—
233C23×C41—21no—
234C23×C41—22no—
235C23×C41—41no—
236C23×C41—41no—
237C23×C41—41no—
238C23×C41—41no—
239C23×C41—41no—
240C23×C41—41no—
241C23×C41C22⋊Q812yes—
242C23×C41C22×D411yescharacteristic
243Q8×C41—22no—
244Q8×C41—22no—
245Q8×C41—22no—
246Q8×C41C22⋊Q814yes—
247D4×C41—22no—
248D4×C41—22no—
249D4×C41—48no—
250D4×C41—41no—
251D4×C41—41no—
252C2×C4×C41—22no—
253C2×C4×C41—21no—
254C2×C4×C41—22no—
255C2×C4×C41—21no—
256C2×C4×C41—22no—
257C2×C4×C41—21no—
258C2×C4×C41—21no—
259C2×C4×C41—22no—
260C2×C4×C41—22no—
261C2×C4×C41—22no—
262C2×C4×C41—22no—
263C2×C4×C41—21no—
264C2×C4×C41—21no—
265C2×C4×C41—22no—
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—21no—
273C2×C4×C41—48no—
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×C41C22⋊Q812yes—
292C2×C4×C41#13512yes—
293C2×C4×C41C22×D411yescharacteristic
294C2×C4×C41C22×Q811yescharacteristic
295C2×C4×C41C2×#4111yescharacteristic
296C2×C4×C41C2×#4111yescharacteristic
297C2×C4×C41H(5,𝔽2)11yescharacteristic
298C2×C4×C41H(5,𝔽2)11yescharacteristic
299C8×C41—22no—
300C8×C41—41no—
301C8×C41—41no—
302C8×C41—41no—
303#25953C4111yesmaximal, characteristic, direct product factor, Sylow
304C22×C41—22no—
305C22×C41—22no—
306C22×C41—22no—
307C22×C41—41no—
308C22×C41—41no—
309C22×C41—41no—
310C22×C41—41no—
311C22×C41—42no—
312C22×C41—42no—
313C22×C41—42no—
314C22×C41—81no—
315C22×C41—81no—
316C22×C41—81no—
317C22×C41—81no—
318C22×C41C2×C22⋊Q811yescharacteristic
319C22×C41D4211yescharacteristic
320C22×C41#54611yescharacteristic
321C22×C41C2×#13511yescharacteristic
322C22×C41#57511yescharacteristic
323C22×C41#57711yescharacteristic
324C22×C41#57711yescharacteristic
325C4×C41—22no—
326C4×C41—24no—
327C4×C41—22no—
328C4×C41—41no—
329C4×C41—41no—
330C4×C41—42no—
331C4×C41—41no—
332C4×C41—81no—
333C4×C41—81no—
334C4×C41—81no—
335C4×C41—81no—
336C4×C41—81no—
337C4×C41C2×C22⋊Q811yescharacteristic
338C4×C41#54311yescharacteristic
339C4×C41#54611yescharacteristic
340C4×C41#55111yescharacteristic
341C2×#479C2×C4111yescharacteristic, complemented
342C2×#416C2×C4111yescharacteristic
343#2441C2×C4111yescharacteristic, complemented
344#2341C2×C4111yescharacteristic
345#2094C2×C4111yescharacteristic, complemented
346#2067C2×C4111yescharacteristic, complemented
347#2065C2×C4111yescharacteristic, complemented
348#2025C2×C4111yescharacteristic, complemented
349#1865C2×C4111yescharacteristic, complemented
350#1865C2×C4111yescharacteristic, complemented
351#1854C2×C4111yescharacteristic, complemented
352#1850C2×C4111yescharacteristic, complemented
353#1807C2×C4111yescharacteristic, complemented
354#1803C2×C4111yescharacteristic, complemented
355#1788C2×C4111yescharacteristic
356C2×C41—42no—
357C2×C41—82no—
358C2×C41#243711yescharacteristic
359C2×C41#307611yescharacteristic
360C2×C41#308411yescharacteristic
361C2×C41#327111yescharacteristic
362C2×C41#328411yescharacteristic
363C2×C41#330111yescharacteristic
364C2×C41#331711yescharacteristic
365C22×#41C22×C4111yescharacteristic
366C23×C8C22×C4111yescharacteristic
367C2×#125C22×C4111yescharacteristic
368C2×C4×Q8C22×C4111yescharacteristic
369C2×C4×Q8C22×C4111yescharacteristic
370C2×#117C22×C4111yescharacteristic
371#479—24no—
372C2×#107C22×C4111yescharacteristic
373C2×#106C22×C4111yescharacteristic
374C2×#106C22×C4111yescharacteristic
375C2×#106C22×C4111yescharacteristic
376C2×C4⋊C8C22×C4111yescharacteristic
377C2×C4⋊C8C22×C4111yescharacteristic
378#416—24no—
379C2×#103C22×C4111yescharacteristic
380C2×#103C22×C4111yescharacteristic
381C2×#103C22×C4111yescharacteristic
382C2×#103C22×C4111yescharacteristic
383C2×#102C22×C4111yescharacteristic
384C2×#102C22×C4111yescharacteristic
385C2×#102C22×C4111yescharacteristic
386C2×#102C22×C4111yescharacteristic
387C2×C22⋊C8C22×C4111yescharacteristic
388#399—21no—
389#396—21no—
390#390—21no—
391#390—21no—
392#390C22×C4111yescharacteristic
393#390C22×C4111yescharacteristic
394#389—21no—
395#389C22×C4111yescharacteristic
396#389C22×C4111yescharacteristic
397#387—21no—
398#384C22×C4111yescharacteristic
399#380—21no—
400#380C22×C4111yescharacteristic
401#380C22×C4111yescharacteristic
402C4×C22⋊C4—21no—
403C4×C22⋊C4C22×C4111yescharacteristic
404#340C22×C4111yescharacteristic
405#340C22×C4111yescharacteristic
406#340C22×C4111yescharacteristic
407#340C22×C4111yescharacteristic
408#336C22×C4111yescharacteristic
409#336C22×C4111yescharacteristic
410C41#2595311yescharacteristic, direct product factor, Sylow
411C2×#41—22no—
412C2×#41—22no—
413C2×#41—22no—
414C2×#41—41no—
415C2×#41—41no—
416C2×#41Q8×C4114yes—
417C22×Q8C23×C4111yescharacteristic
418C22×D4—21no—
419C22×D4C23×C4111yescharacteristic
420C23×C4—21no—
421C23×C4C23×C4111yescharacteristic
422C22×C8—22no—
423C22×C8—22no—
424C22×C8—41no—
425C22×C8C23×C4111yescharacteristic
426C22×C8C23×C4111yescharacteristic
427C22×C8C23×C4111yescharacteristic
428C22×C8C23×C4111yescharacteristic
429#125—22no—
430#125—41no—
431C4×Q8—22no—
432C4×Q8—22no—
433C4×Q8—41no—
434C4×Q8—41no—
435#117—22no—
436#117—41no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4C23×C4111yescharacteristic
446C2×C4⋊C4C23×C4111yescharacteristic
447C2×C4⋊C4C23×C4111yescharacteristic
448C2×C4⋊C4C23×C4111yescharacteristic
449C2×C4⋊C4C23×C4111yescharacteristic
450C2×C4⋊C4C23×C4111yescharacteristic
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⋊C4D4×C4111yescharacteristic
459C2×C22⋊C4D4×C4111yescharacteristic
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—21no—
463C2×C42C23×C4111yescharacteristic
464C2×C42C23×C4111yescharacteristic
465#107—22no—
466#106—22no—
467#106—41no—
468#106—41no—
469C4⋊C8—22no—
470C4⋊C8—41no—
471#103—22no—
472#103—22no—
473#103—22no—
474#103D4×C4114yes—
475#102—22no—
476#102—22no—
477#102—41no—
478#102—41no—
479C22⋊C8—22no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95D4×C4111yescharacteristic
485#95D4×C4111yescharacteristic
486C24—21no—
487C24C2×D4×C4111yescharacteristic
488#41—28no—
489#41—44no—
490#41—44no—
491#41—44no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8C2×D4×C4112yes—
496C2×Q8C2×Q8×C4112yes—
497C2×Q8#41×C4112yes—
498C2×D4—24no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4C2×Q8×C4112yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—24no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4C2×D4×C4111yescharacteristic
522C22×C4C2×D4×C4111yescharacteristic
523C22×C4C2×D4×C4111yescharacteristic
524C22×C4C2×D4×C4111yescharacteristic
525C22×C4C2×D4×C4111yescharacteristic
526C22×C4C2×Q8×C4112yes—
527C22×C4#41×C4112yes—
528C22×C4C24×C4111yescharacteristic
529C2×C8—21no—
530C2×C8—21no—
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—44no—
541C2×C8C2×D4×C4112yes—
542C4⋊C4—21no—
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—21no—
553C4⋊C4—42no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4—81no—
561C4⋊C4C2×D4×C4112yes—
562C22⋊C4—22no—
563C22⋊C4—41no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—42no—
576C42—42no—
577C42—42no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—22no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23C22⋊Q8×C4112yes—
592C23C22×D4×C4111yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—22no—
596Q8C22⋊Q8×C4114yes—
597D4—22no—
598D4—22no—
599D4—48no—
600D4—41no—
601D4—41no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—48no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
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×C4C22⋊Q8×C4112yes—
642C2×C4#135×C4112yes—
643C2×C4C22×D4×C4111yescharacteristic
644C2×C4C22×Q8×C4111yescharacteristic
645C2×C4C2×#41×C4111yescharacteristic
646C2×C4C2×#41×C4111yescharacteristic
647C2×C4H(5,𝔽2)×C4111yescharacteristic
648C2×C4H(5,𝔽2)×C4111yescharacteristic
649C8—22no—
650C8—41no—
651C8—41no—
652C8—41no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—41no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—42no—
662C22—42no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22C2×C22⋊Q8×C4111yescharacteristic
668C22D42×C4111yescharacteristic
669C22C41×#54611yescharacteristic
670C22C2×#135×C4111yescharacteristic
671C22C41×#57511yescharacteristic
672C22C41×#57711yescharacteristic
673C22C41×#57711yescharacteristic
674C4—22no—
675C4—22no—
676C4—24no—
677C4—41no—
678C4—41no—
679C4—41no—
680C4—42no—
681C4—81no—
682C4—81no—
683C4—81no—
684C4—81no—
685C4—81no—
686C4C2×C22⋊Q8×C4111yescharacteristic
687C4C41×#54311yescharacteristic
688C4C41×#54611yescharacteristic
689C4C41×#55111yescharacteristic
690C2—42no—
691C2—82no—
692C2C41×#243711yescharacteristic
693C2C41×#307611yescharacteristic
694C2C41×#308411yescharacteristic
695C2C41×#327111yescharacteristic
696C2C41×#328411yescharacteristic
697C2C41×#330111yescharacteristic
698C2C41×#331711yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC22×#41×C41C22
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×#479C2semidirect
3. C41×#2441C2semidirect
5. C41×#2094C2semidirect
6. C41×#2067C2semidirect
7. C41×#2065C2semidirect
8. C41×#2025C2semidirect
9. C41×#1865C2semidirect
10. C41×#1865C2semidirect
11. C41×#1854C2semidirect
12. C41×#1850C2semidirect
13. C41×#1807C2semidirect
14. C41×#1803C2semidirect
303. #25953C41direct (N × H)
341. C2×#479C2×C41semidirect
343. #2441C2×C41semidirect
345. #2094C2×C41semidirect
346. #2067C2×C41semidirect
347. #2065C2×C41semidirect
348. #2025C2×C41semidirect
349. #1865C2×C41semidirect
350. #1865C2×C41semidirect
351. #1854C2×C41semidirect
352. #1850C2×C41semidirect
353. #1807C2×C41semidirect
354. #1803C2×C41semidirect
410. C41#25953direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C41×#4792
C2×C41×#4162
C41×#24412
C41×#23412
C41×#20942
C41×#20672
C41×#20652
C41×#20252
C41×#18652
C41×#18542
C41×#18502
C41×#18072
C41×#18032
C41×#17882
#2595341