Finite Group Databasebeta

← C41×#25428 #23801629

Subgroups — C41×#25428 #23801629

Order 10496.

1086 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#492C211yesmaximal, characteristic, complemented
2C2×C41×#468C211yesmaximal, characteristic, complemented
3C2×C41×#468C211yesmaximal, characteristic, complemented
4C2×C41×#440C211yesmaximal, characteristic, complemented
5C41×#2429C211yesmaximal, characteristic, complemented
6C41×#2428C211yesmaximal, characteristic
7C41×#2043C211yesmaximal, characteristic, complemented
8C41×#2041C211yesmaximal, characteristic, complemented
9C41×#2000C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic, complemented
11C41×#1973C211yesmaximal, characteristic, complemented
12C41×#1942C211yesmaximal, characteristic, complemented
13C41×#1880C211yesmaximal, characteristic, complemented
14C41×#1877C211yesmaximal, characteristic, complemented
15C41×#1753C211yesmaximal, characteristic, complemented
16C22×SD16×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic
19C22×SD16×C41C2211yescharacteristic
20C22×M16×C41C2211yescharacteristic
21C2×C4⋊Q8×C41C2211yescharacteristic
22C2×#127×C41C2211yescharacteristic
23C2×C22⋊Q8×C41C2211yescharacteristic
24C2×C22⋊Q8×C41C2211yescharacteristic
25C2×#121×C41—21no—
26C2×#121×C41C2211yescharacteristic
27C2×#121×C41C2211yescharacteristic
28C2×C4×Q8×C41C2211yescharacteristic
29C2×C4×D4×C41C2211yescharacteristic
30C41×#492—24no—
31C41×#468—24no—
32C41×#468—24no—
33C41×#440—24no—
34C2×#107×C41C2211yescharacteristic
35C2×#107×C41C2211yescharacteristic
36C2×#103×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#103×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×C22⋊C8×C41C2211yescharacteristic
45C2×#97×C41C2211yescharacteristic
46C2×C4×C8×C41C2211yescharacteristic
47C41×#398—21no—
48C41×#396—21no—
49C41×#394—21no—
50C41×#392—21no—
51C41×#391C2211yescharacteristic
52C41×#390C2211yescharacteristic
53C41×#389—21no—
54C41×#389C2211yescharacteristic
55C41×#389C2211yescharacteristic
56C41×#388—21no—
57C41×#386—21no—
58C4×C22⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#336C2211yescharacteristic
62C41×#336C2211yescharacteristic
63C22×Q8×C41C2311yescharacteristic
64C22×Q8×C41C2311yescharacteristic
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41—21no—
68C22×D4×C41—21no—
69C22×D4×C41C2311yescharacteristic
70C22×D4×C41C2311yescharacteristic
71C23×C4×C41—21no—
72C23×C4×C41C2311yescharacteristic
73C2×SD16×C41—22no—
74C2×SD16×C41—22no—
75C2×SD16×C41—22no—
76C2×SD16×C41—22no—
77C2×SD16×C41—22no—
78C2×SD16×C41—22no—
79C2×SD16×C41—22no—
80C2×SD16×C41—22no—
81C2×SD16×C41—22no—
82C2×SD16×C41—41no—
83C2×SD16×C41—41no—
84C2×SD16×C41D414yescomplemented
85C2×M16×C41—22no—
86C2×M16×C41—22no—
87C2×M16×C41—22no—
88C22×C8×C41C2311yescharacteristic
89C22×C8×C41C2311yescharacteristic
90C22×C8×C41C2311yescharacteristic
91C22×C8×C41C2311yescharacteristic
92C4⋊Q8×C41—22no—
93C4⋊Q8×C41—41no—
94#127×C41—22no—
95#127×C41—41no—
96C22⋊Q8×C41—22no—
97C22⋊Q8×C41—22no—
98C22⋊Q8×C41—41no—
99C22⋊Q8×C41—41no—
100#121×C41—22no—
101#121×C41—22no—
102#121×C41—44no—
103#121×C41—41no—
104#121×C41—41no—
105C4×Q8×C41—22no—
106C4×Q8×C41—41no—
107C4×D4×C41—22no—
108C4×D4×C41—41no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41—21no—
112C2×C4⋊C4×C41—21no—
113C2×C4⋊C4×C41—21no—
114C2×C4⋊C4×C41—21no—
115C2×C4⋊C4×C41—21no—
116C2×C4⋊C4×C41C2311yescharacteristic
117C2×C4⋊C4×C41C2311yescharacteristic
118C2×C4⋊C4×C41C2311yescharacteristic
119C2×C4⋊C4×C41C2311yescharacteristic
120C2×C22⋊C4×C41—21no—
121C2×C22⋊C4×C41—21no—
122C2×C22⋊C4×C41—21no—
123C2×C22⋊C4×C41—21no—
124C2×C22⋊C4×C41—21no—
125C2×C22⋊C4×C41—21no—
126C2×C22⋊C4×C41—21no—
127C2×C22⋊C4×C41D411yescharacteristic
128C2×C22⋊C4×C41D411yescharacteristic
129C2×C42×C41—21no—
130C2×C42×C41C2311yescharacteristic
131C2×C42×C41C2311yescharacteristic
132#107×C41—22no—
133#107×C41D414yescomplemented
134#103×C41—22no—
135#103×C41—22no—
136#103×C41—22no—
137#103×C41—41no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—41no—
142C22⋊C8×C41—22no—
143#97×C41—22no—
144C4×C8×C41—22no—
145#95×C41—21no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41—21no—
149#95×C41D411yescharacteristic
150#95×C41D411yescharacteristic
151C24×C41—21no—
152C24×C41—21no—
153C24×C41C2×D411yescharacteristic
154C2×Q8×C41—21no—
155C2×Q8×C41—21no—
156C2×Q8×C41—21no—
157C2×Q8×C41—21no—
158C2×Q8×C41—21no—
159C2×Q8×C41—21no—
160C2×Q8×C41—21no—
161C2×Q8×C41—21no—
162C2×Q8×C41—21no—
163C2×Q8×C41—21no—
164C2×Q8×C41—21no—
165C2×Q8×C41C2×D412yes—
166C2×D4×C41—21no—
167C2×D4×C41—21no—
168C2×D4×C41—21no—
169C2×D4×C41—21no—
170C2×D4×C41—21no—
171C2×D4×C41—21no—
172C2×D4×C41—21no—
173C2×D4×C41—21no—
174C2×D4×C41—21no—
175C2×D4×C41—21no—
176C2×D4×C41—21no—
177C2×D4×C41—42no—
178C2×D4×C41—42no—
179C2×D4×C41—42no—
180C2×D4×C41—42no—
181C2×D4×C41—42no—
182C2×D4×C41—42no—
183C2×D4×C41—42no—
184C2×D4×C41—42no—
185C2×D4×C41—81no—
186C2×D4×C41—81no—
187C2×D4×C41—81no—
188C2×D4×C41—81no—
189C2×D4×C41C2×D412yes—
190C22×C4×C41—21no—
191C22×C4×C41—21no—
192C22×C4×C41—21no—
193C22×C4×C41—21no—
194C22×C4×C41—21no—
195C22×C4×C41—21no—
196C22×C4×C41—21no—
197C22×C4×C41—21no—
198C22×C4×C41—21no—
199C22×C4×C41—21no—
200C22×C4×C41—21no—
201C22×C4×C41—21no—
202C22×C4×C41—42no—
203C22×C4×C41—42no—
204C22×C4×C41—81no—
205C22×C4×C41C2×D411yescharacteristic
206C22×C4×C41C2×D411yescharacteristic
207C22×C4×C41C2×D411yescharacteristic
208C22×C4×C41C2×D411yescharacteristic
209C22×C4×C41C2×D411yescharacteristic
210C22×C4×C41C2411yescharacteristic
211SD16×C41—28no—
212SD16×C41—44no—
213SD16×C41—44no—
214SD16×C41—44no—
215M16×C41—44no—
216C2×C8×C41—21no—
217C2×C8×C41—21no—
218C2×C8×C41—21no—
219C2×C8×C41—21no—
220C2×C8×C41—21no—
221C2×C8×C41—21no—
222C2×C8×C41—21no—
223C2×C8×C41—21no—
224C2×C8×C41C2×D412yes—
225C2×C8×C41C2×D412yes—
226C2×C8×C41#4112yes—
227C2×C8×C41#4112yes—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—21no—
230C4⋊C4×C41—21no—
231C4⋊C4×C41—21no—
232C4⋊C4×C41—21no—
233C4⋊C4×C41—21no—
234C4⋊C4×C41—42no—
235C4⋊C4×C41—42no—
236C4⋊C4×C41—42no—
237C4⋊C4×C41—42no—
238C4⋊C4×C41—42no—
239C4⋊C4×C41—42no—
240C4⋊C4×C41—42no—
241C4⋊C4×C41C2×D412yes—
242C4⋊C4×C41C2×D412yes—
243C22⋊C4×C41—22no—
244C22⋊C4×C41—22no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—42no—
247C22⋊C4×C41—42no—
248C22⋊C4×C41—42no—
249C22⋊C4×C41—42no—
250C22⋊C4×C41—42no—
251C22⋊C4×C41—81no—
252C42×C41—21no—
253C42×C41—21no—
254C42×C41—21no—
255C42×C41—21no—
256C42×C41—42no—
257C23×C41—21no—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—22no—
261C23×C41—21no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—41no—
266C23×C41—41no—
267C23×C41—41no—
268C23×C41—41no—
269C23×C41—41no—
270C23×C41—41no—
271C23×C41—41no—
272C23×C41—41no—
273C23×C41—41no—
274C23×C41—41no—
275C23×C41—41no—
276C23×C41—41no—
277C23×C41—41no—
278C23×C41C22×D411yescharacteristic
279Q8×C41—22no—
280Q8×C41—22no—
281Q8×C41—41no—
282Q8×C41—41no—
283Q8×C41—41no—
284Q8×C41—41no—
285Q8×C41—41no—
286Q8×C41—41no—
287D4×C41—22no—
288D4×C41—22no—
289D4×C41—41no—
290D4×C41—41no—
291D4×C41—41no—
292D4×C41—41no—
293D4×C41—41no—
294D4×C41—41no—
295D4×C41—84no—
296D4×C41—84no—
297D4×C41—84no—
298D4×C41—84no—
299C2×C4×C41—21no—
300C2×C4×C41—21no—
301C2×C4×C41—21no—
302C2×C4×C41—21no—
303C2×C4×C41—21no—
304C2×C4×C41—21no—
305C2×C4×C41—21no—
306C2×C4×C41—22no—
307C2×C4×C41—22no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
310C2×C4×C41—22no—
311C2×C4×C41—21no—
312C2×C4×C41—21no—
313C2×C4×C41—21no—
314C2×C4×C41—21no—
315C2×C4×C41—41no—
316C2×C4×C41—41no—
317C2×C4×C41—41no—
318C2×C4×C41—41no—
319C2×C4×C41—41no—
320C2×C4×C41—41no—
321C2×C4×C41—41no—
322C2×C4×C41—41no—
323C2×C4×C41—41no—
324C2×C4×C41—41no—
325C2×C4×C41—41no—
326C2×C4×C41—41no—
327C2×C4×C41—41no—
328C2×C4×C41—41no—
329C2×C4×C41—41no—
330C2×C4×C41—41no—
331C2×C4×C41—41no—
332C2×C4×C41—41no—
333C2×C4×C41—41no—
334C2×C4×C41—84no—
335C2×C4×C41AGL(1,ℤ/8)12yes—
336C2×C4×C41#13712yes—
337C2×C4×C41C22×D411yescharacteristic
338C2×C4×C41C22×D411yescharacteristic
339C2×C4×C41C2×#4111yescharacteristic
340C2×C4×C41C2×#4111yescharacteristic
341C2×C4×C41H(5,𝔽2)11yescharacteristic
342C2×C4×C41H(5,𝔽2)11yescharacteristic
343C8×C41—22no—
344C8×C41—41no—
345C8×C41—41no—
346C8×C41#12114yescomplemented
347#25428C4111yesmaximal, characteristic, direct product factor, Sylow
348C22×C41—41no—
349C22×C41—41no—
350C22×C41—41no—
351C22×C41—42no—
352C22×C41—41no—
353C22×C41—42no—
354C22×C41—42no—
355C22×C41—41no—
356C22×C41—41no—
357C22×C41—41no—
358C22×C41—81no—
359C22×C41—81no—
360C22×C41—81no—
361C22×C41—81no—
362C22×C41—81no—
363C22×C41—81no—
364C22×C41—81no—
365C22×C41—81no—
366C22×C41—81no—
367C22×C41—81no—
368C22×C41—81no—
369C22×C41#53211yescharacteristic
370C22×C41D4211yescharacteristic
371C22×C41D4211yescharacteristic
372C22×C41C2×AGL(1,ℤ/8)11yescharacteristic
373C22×C41C2×#13711yescharacteristic
374C22×C41#57711yescharacteristic
375C22×C41#57711yescharacteristic
376C4×C41—22no—
377C4×C41—22no—
378C4×C41—41no—
379C4×C41—42no—
380C4×C41—41no—
381C4×C41—42no—
382C4×C41—42no—
383C4×C41—41no—
384C4×C41—81no—
385C4×C41—81no—
386C4×C41—81no—
387C4×C41C2×#12111yescharacteristic
388C4×C41#54011yescharacteristic
389C4×C41#54611yescharacteristic
390C4×C41#55011yescharacteristic
391C2×#492C2×C4111yescharacteristic, complemented
392C2×#468C2×C4111yescharacteristic, complemented
393C2×#468C2×C4111yescharacteristic, complemented
394C2×#440C2×C4111yescharacteristic, complemented
395#2429C2×C4111yescharacteristic, complemented
396#2428C2×C4111yescharacteristic
397#2043C2×C4111yescharacteristic, complemented
398#2041C2×C4111yescharacteristic, complemented
399#2000C2×C4111yescharacteristic, complemented
400#2000C2×C4111yescharacteristic, complemented
401#1973C2×C4111yescharacteristic, complemented
402#1942C2×C4111yescharacteristic, complemented
403#1880C2×C4111yescharacteristic, complemented
404#1877C2×C4111yescharacteristic, complemented
405#1753C2×C4111yescharacteristic, complemented
406C2×C41—81no—
407C2×C41—82no—
408C2×C41—161no—
409C2×C41#242811yescharacteristic
410C2×C41#317411yescharacteristic
411C2×C41#318211yescharacteristic
412C2×C41#326511yescharacteristic
413C2×C41#326611yescharacteristic
414C2×C41#327211yescharacteristic
415C2×C41#327811yescharacteristic
416C22×SD16C22×C4111yescharacteristic
417C22×SD16C22×C4111yescharacteristic
418C22×SD16C22×C4111yescharacteristic
419C22×SD16C22×C4111yescharacteristic
420C22×M16C22×C4111yescharacteristic
421C2×C4⋊Q8C22×C4111yescharacteristic
422C2×#127C22×C4111yescharacteristic
423C2×C22⋊Q8C22×C4111yescharacteristic
424C2×C22⋊Q8C22×C4111yescharacteristic
425C2×#121—21no—
426C2×#121C22×C4111yescharacteristic
427C2×#121C22×C4111yescharacteristic
428C2×C4×Q8C22×C4111yescharacteristic
429C2×C4×D4C22×C4111yescharacteristic
430#492—24no—
431#468—24no—
432#468—24no—
433#440—24no—
434C2×#107C22×C4111yescharacteristic
435C2×#107C22×C4111yescharacteristic
436C2×#103C22×C4111yescharacteristic
437C2×#103C22×C4111yescharacteristic
438C2×#103C22×C4111yescharacteristic
439C2×#103C22×C4111yescharacteristic
440C2×#102C22×C4111yescharacteristic
441C2×#102C22×C4111yescharacteristic
442C2×#102C22×C4111yescharacteristic
443C2×#102C22×C4111yescharacteristic
444C2×C22⋊C8C22×C4111yescharacteristic
445C2×#97C22×C4111yescharacteristic
446C2×C4×C8C22×C4111yescharacteristic
447#398—21no—
448#396—21no—
449#394—21no—
450#392—21no—
451#391C22×C4111yescharacteristic
452#390C22×C4111yescharacteristic
453#389—21no—
454#389C22×C4111yescharacteristic
455#389C22×C4111yescharacteristic
456#388—21no—
457#386—21no—
458C4×C22⋊C4C22×C4111yescharacteristic
459#340C22×C4111yescharacteristic
460#340C22×C4111yescharacteristic
461#336C22×C4111yescharacteristic
462#336C22×C4111yescharacteristic
463C41#2542811yescharacteristic, direct product factor, Sylow
464C22×Q8C23×C4111yescharacteristic
465C22×Q8C23×C4111yescharacteristic
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—21no—
470C22×D4C23×C4111yescharacteristic
471C22×D4C23×C4111yescharacteristic
472C23×C4—21no—
473C23×C4C23×C4111yescharacteristic
474C2×SD16—22no—
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—22no—
478C2×SD16—22no—
479C2×SD16—22no—
480C2×SD16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×SD16—41no—
484C2×SD16—41no—
485C2×SD16D4×C4114yescomplemented
486C2×M16—22no—
487C2×M16—22no—
488C2×M16—22no—
489C22×C8C23×C4111yescharacteristic
490C22×C8C23×C4111yescharacteristic
491C22×C8C23×C4111yescharacteristic
492C22×C8C23×C4111yescharacteristic
493C4⋊Q8—22no—
494C4⋊Q8—41no—
495#127—22no—
496#127—41no—
497C22⋊Q8—22no—
498C22⋊Q8—22no—
499C22⋊Q8—41no—
500C22⋊Q8—41no—
501#121—22no—
502#121—22no—
503#121—44no—
504#121—41no—
505#121—41no—
506C4×Q8—22no—
507C4×Q8—41no—
508C4×D4—22no—
509C4×D4—41no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4C23×C4111yescharacteristic
518C2×C4⋊C4C23×C4111yescharacteristic
519C2×C4⋊C4C23×C4111yescharacteristic
520C2×C4⋊C4C23×C4111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4D4×C4111yescharacteristic
529C2×C22⋊C4D4×C4111yescharacteristic
530C2×C42—21no—
531C2×C42C23×C4111yescharacteristic
532C2×C42C23×C4111yescharacteristic
533#107—22no—
534#107D4×C4114yescomplemented
535#103—22no—
536#103—22no—
537#103—22no—
538#103—41no—
539#102—22no—
540#102—22no—
541#102—22no—
542#102—41no—
543C22⋊C8—22no—
544#97—22no—
545C4×C8—22no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95D4×C4111yescharacteristic
551#95D4×C4111yescharacteristic
552C24—21no—
553C24—21no—
554C24C2×D4×C4111yescharacteristic
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8C2×D4×C4112yes—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4C2×D4×C4112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4C2×D4×C4111yescharacteristic
607C22×C4C2×D4×C4111yescharacteristic
608C22×C4C2×D4×C4111yescharacteristic
609C22×C4C2×D4×C4111yescharacteristic
610C22×C4C2×D4×C4111yescharacteristic
611C22×C4C24×C4111yescharacteristic
612SD16—28no—
613SD16—44no—
614SD16—44no—
615SD16—44no—
616M16—44no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8C2×D4×C4112yes—
626C2×C8C2×D4×C4112yes—
627C2×C8#41×C4112yes—
628C2×C8#41×C4112yes—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—42no—
636C4⋊C4—42no—
637C4⋊C4—42no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—42no—
641C4⋊C4—42no—
642C4⋊C4C2×D4×C4112yes—
643C4⋊C4C2×D4×C4112yes—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—81no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—42no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23C22×D4×C4111yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—41no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—41no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—84no—
697D4—84no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—84no—
736C2×C4AGL(1,ℤ/8)×C4112yes—
737C2×C4#137×C4112yes—
738C2×C4C22×D4×C4111yescharacteristic
739C2×C4C22×D4×C4111yescharacteristic
740C2×C4C2×#41×C4111yescharacteristic
741C2×C4C2×#41×C4111yescharacteristic
742C2×C4H(5,𝔽2)×C4111yescharacteristic
743C2×C4H(5,𝔽2)×C4111yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8#121×C4114yescomplemented
748C22—41no—
749C22—41no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C41×#53211yescharacteristic
770C22D42×C4111yescharacteristic
771C22D42×C4111yescharacteristic
772C22C2×AGL(1,ℤ/8)×C4111yescharacteristic
773C22C2×#137×C4111yescharacteristic
774C22C41×#57711yescharacteristic
775C22C41×#57711yescharacteristic
776C4—22no—
777C4—22no—
778C4—41no—
779C4—42no—
780C4—41no—
781C4—42no—
782C4—42no—
783C4—41no—
784C4—81no—
785C4—81no—
786C4—81no—
787C4C2×#121×C4111yescharacteristic
788C4C41×#54011yescharacteristic
789C4C41×#54611yescharacteristic
790C4C41×#55011yescharacteristic
791C2—81no—
792C2—82no—
793C2—161no—
794C2C41×#242811yescharacteristic
795C2C41×#317411yescharacteristic
796C2C41×#318211yescharacteristic
797C2C41×#326511yescharacteristic
798C2C41×#326611yescharacteristic
799C2C41×#327211yescharacteristic
800C2C41×#327811yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#2428C2
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×#492C2semidirect
2. C2×C41×#468C2semidirect
3. C2×C41×#468C2semidirect
4. C2×C41×#440C2semidirect
5. C41×#2429C2semidirect
7. C41×#2043C2semidirect
8. C41×#2041C2semidirect
9. C41×#2000C2semidirect
10. C41×#2000C2semidirect
11. C41×#1973C2semidirect
12. C41×#1942C2semidirect
13. C41×#1880C2semidirect
14. C41×#1877C2semidirect
15. C41×#1753C2semidirect
84. C2×SD16×C41D4semidirect
133. #107×C41D4semidirect
346. C8×C41#121semidirect
347. #25428C41direct (N × H)
391. C2×#492C2×C41semidirect
392. C2×#468C2×C41semidirect
393. C2×#468C2×C41semidirect
394. C2×#440C2×C41semidirect
395. #2429C2×C41semidirect
397. #2043C2×C41semidirect
398. #2041C2×C41semidirect
399. #2000C2×C41semidirect
400. #2000C2×C41semidirect
401. #1973C2×C41semidirect
402. #1942C2×C41semidirect
403. #1880C2×C41semidirect
404. #1877C2×C41semidirect
405. #1753C2×C41semidirect
463. C41#25428direct (N × H)
485. C2×SD16D4×C41semidirect
534. #107D4×C41semidirect
747. C8#121×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4922
C2×C41×#4682
C2×C41×#4402
C41×#24292
C41×#24282
C41×#20432
C41×#20412
C41×#20002
C41×#19732
C41×#19422
C41×#18802
C41×#18772
C41×#17532
#2542841