Finite Group Databasebeta

← C41×#25391 #23801592

Subgroups — C41×#25391 #23801592

Order 10496.

1020 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C41×#470C211yesmaximal, characteristic, complemented
2C2×C41×#468C211yesmaximal, characteristic, complemented
3C2×C41×#464C211yesmaximal, characteristic, complemented
4C2×C41×#436C211yesmaximal, characteristic, complemented
5C41×#2540C211yesmaximal, characteristic
6C41×#2536C211yesmaximal, characteristic, complemented
7C41×#2036C211yesmaximal, characteristic, complemented
8C41×#2034C211yesmaximal, characteristic, complemented
9C41×#2001C211yesmaximal, characteristic, complemented
10C41×#2000C211yesmaximal, characteristic, complemented
11C41×#1958C211yesmaximal, characteristic, complemented
12C41×#1949C211yesmaximal, characteristic, complemented
13C41×#1895C211yesmaximal, characteristic, complemented
14C41×#1894C211yesmaximal, characteristic, complemented
15C4×#103×C41C211yesmaximal, characteristic, complemented
16C22×Q16×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic
18C22×M16×C41C2211yescharacteristic
19C22×M16×C41C2211yescharacteristic
20C2×#124×C41C2211yescharacteristic
21C2×C22⋊Q8×C41C2211yescharacteristic
22C2×C22⋊Q8×C41C2211yescharacteristic
23C2×C22⋊Q8×C41C2211yescharacteristic
24C2×C22⋊Q8×C41C2211yescharacteristic
25C2×#121×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×C4×Q8×C41C2211yescharacteristic
28C2×C4×D4×C41C2211yescharacteristic
29C41×#470—24no—
30C41×#468—24no—
31C41×#464—24no—
32C41×#436—24no—
33C2×#107×C41C2211yescharacteristic
34C2×#106×C41C2211yescharacteristic
35C2×C4⋊C8×C41C2211yescharacteristic
36C2×#103×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#103×C41C2211yescharacteristic
40C2×#103×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×#102×C41C2211yescharacteristic
44C2×C22⋊C8×C41C2211yescharacteristic
45C2×C22⋊C8×C41C2211yescharacteristic
46C2×C4×C8×C41C2211yescharacteristic
47C41×#399—21no—
48C41×#398—21no—
49C41×#394—21no—
50C41×#392—21no—
51C41×#390—21no—
52C41×#390—21no—
53C41×#388—21no—
54C41×#388—21no—
55C41×#382C2211yescharacteristic
56C41×#380C2211yescharacteristic
57C41×#380C2211yescharacteristic
58C4×C4⋊C4×C41C2211yescharacteristic
59C41×#340C2211yescharacteristic
60C41×#340C2211yescharacteristic
61C41×#340C2211yescharacteristic
62C41×#340C2211yescharacteristic
63C22×Q8×C41C2311yescharacteristic
64C22×Q8×C41C2311yescharacteristic
65C22×D4×C41—21no—
66C22×D4×C41—21no—
67C22×D4×C41D411yescharacteristic
68C22×D4×C41C2311yescharacteristic
69C23×C4×C41C2311yescharacteristic
70C23×C4×C41C2311yescharacteristic
71C2×Q16×C41—22no—
72C2×Q16×C41—22no—
73C2×Q16×C41—41no—
74C2×SD16×C41—22no—
75C2×SD16×C41—22no—
76C2×SD16×C41—41no—
77C2×M16×C41—22no—
78C2×M16×C41—22no—
79C2×M16×C41—22no—
80C2×M16×C41—22no—
81C2×M16×C41—41no—
82C2×M16×C41—41no—
83C22×C8×C41C2311yescharacteristic
84C22×C8×C41C2311yescharacteristic
85C22×C8×C41C2311yescharacteristic
86C22×C8×C41C2311yescharacteristic
87#124×C41—22no—
88#124×C41—22no—
89C22⋊Q8×C41—22no—
90C22⋊Q8×C41—22no—
91C22⋊Q8×C41—22no—
92C22⋊Q8×C41—22no—
93C22⋊Q8×C41—41no—
94C22⋊Q8×C41—41no—
95C22⋊Q8×C41—41no—
96C22⋊Q8×C41—41no—
97#121×C41—22no—
98#121×C41—22no—
99#121×C41—41no—
100#121×C41—41no—
101C4×Q8×C41—22no—
102C4×Q8×C41—22no—
103C4×D4×C41—22no—
104C4×D4×C41—22no—
105C2×C4⋊C4×C41—21no—
106C2×C4⋊C4×C41—21no—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41D411yescharacteristic
111C2×C4⋊C4×C41C2311yescharacteristic
112C2×C4⋊C4×C41C2311yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C4⋊C4×C41C2311yescharacteristic
116C2×C22⋊C4×C41—21no—
117C2×C22⋊C4×C41—21no—
118C2×C22⋊C4×C41—21no—
119C2×C22⋊C4×C41—21no—
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×C41D411yescharacteristic
127C2×C22⋊C4×C41D411yescharacteristic
128C2×C42×C41—21no—
129C2×C42×C41—21no—
130C2×C42×C41C2311yescharacteristic
131#107×C41—22no—
132#106×C41—22no—
133C4⋊C8×C41D414yescomplemented
134#103×C41—22no—
135#103×C41—22no—
136#103×C41—22no—
137#103×C41—41no—
138#103×C41D414yescomplemented
139#102×C41—22no—
140#102×C41—22no—
141#102×C41—41no—
142C22⋊C8×C41—22no—
143C22⋊C8×C41—22no—
144C4×C8×C41—22no—
145#95×C41—21no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41—21no—
149#95×C41—21no—
150C24×C41—21no—
151C24×C41C2×D411yescharacteristic
152C24×C41C2×D411yescharacteristic
153C2×Q8×C41—21no—
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×C41C2×D412yes—
165C2×D4×C41—22no—
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—41no—
173C2×D4×C41—41no—
174C2×D4×C41—42no—
175C2×D4×C41—42no—
176C2×D4×C41—42no—
177C2×D4×C41—42no—
178C2×D4×C41—81no—
179C2×D4×C41—81no—
180C22×C4×C41—21no—
181C22×C4×C41—21no—
182C22×C4×C41—21no—
183C22×C4×C41—21no—
184C22×C4×C41—21no—
185C22×C4×C41—21no—
186C22×C4×C41—21no—
187C22×C4×C41—21no—
188C22×C4×C41—21no—
189C22×C4×C41—21no—
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×C41C2×D411yescharacteristic
200C22×C4×C41C2×D411yescharacteristic
201C22×C4×C41C2×D411yescharacteristic
202C22×C4×C41C2×D411yescharacteristic
203C22×C4×C41C2411yescharacteristic
204Q16×C41—44no—
205SD16×C41—44no—
206M16×C41—44no—
207M16×C41—44no—
208C2×C8×C41—21no—
209C2×C8×C41—21no—
210C2×C8×C41—21no—
211C2×C8×C41—21no—
212C2×C8×C41—21no—
213C2×C8×C41—21no—
214C2×C8×C41—21no—
215C2×C8×C41—21no—
216C2×C8×C41—21no—
217C2×C8×C41C2×D412yes—
218C2×C8×C41C2×D412yes—
219C2×C8×C41C2×D412yes—
220C4⋊C4×C41—22no—
221C4⋊C4×C41—21no—
222C4⋊C4×C41—21no—
223C4⋊C4×C41—21no—
224C4⋊C4×C41—21no—
225C4⋊C4×C41—21no—
226C4⋊C4×C41—21no—
227C4⋊C4×C41—21no—
228C4⋊C4×C41—21no—
229C4⋊C4×C41—42no—
230C4⋊C4×C41—42no—
231C4⋊C4×C41—42no—
232C4⋊C4×C41—42no—
233C4⋊C4×C41—42no—
234C4⋊C4×C41C2×D412yes—
235C4⋊C4×C41#4112yes—
236C22⋊C4×C41—22no—
237C22⋊C4×C41—22no—
238C22⋊C4×C41—42no—
239C22⋊C4×C41—42no—
240C22⋊C4×C41—42no—
241C22⋊C4×C41—42no—
242C22⋊C4×C41—42no—
243C22⋊C4×C41—42no—
244C22⋊C4×C41—42no—
245C22⋊C4×C41—42no—
246C22⋊C4×C41—42no—
247C22⋊C4×C41—42no—
248C42×C41—42no—
249C42×C41—81no—
250C42×C41C2×D412yes—
251C42×C41#4112yes—
252C23×C41—21no—
253C23×C41—21no—
254C23×C41—21no—
255C23×C41—21no—
256C23×C41—21no—
257C23×C41—21no—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—21no—
261C23×C41—21no—
262C23×C41—21no—
263C23×C41—21no—
264C23×C41—21no—
265C23×C41—21no—
266C23×C41—41no—
267C23×C41—41no—
268C23×C41—41no—
269C23×C41—41no—
270C23×C41—41no—
271C23×C41—41no—
272C23×C41—41no—
273C23×C41C22×D411yescharacteristic
274Q8×C41—22no—
275Q8×C41—22no—
276Q8×C41—41no—
277Q8×C41—41no—
278Q8×C41—41no—
279Q8×C41—41no—
280Q8×C41—41no—
281Q8×C41—41no—
282D4×C41—44no—
283D4×C41—41no—
284D4×C41—41no—
285D4×C41—41no—
286D4×C41—41no—
287D4×C41—84no—
288D4×C41—84no—
289C2×C4×C41—21no—
290C2×C4×C41—21no—
291C2×C4×C41—21no—
292C2×C4×C41—21no—
293C2×C4×C41—21no—
294C2×C4×C41—21no—
295C2×C4×C41—22no—
296C2×C4×C41—21no—
297C2×C4×C41—22no—
298C2×C4×C41—21no—
299C2×C4×C41—22no—
300C2×C4×C41—21no—
301C2×C4×C41—21no—
302C2×C4×C41—41no—
303C2×C4×C41—41no—
304C2×C4×C41—41no—
305C2×C4×C41—41no—
306C2×C4×C41—41no—
307C2×C4×C41—41no—
308C2×C4×C41—41no—
309C2×C4×C41—41no—
310C2×C4×C41—41no—
311C2×C4×C41—41no—
312C2×C4×C41—41no—
313C2×C4×C41—41no—
314C2×C4×C41—41no—
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#12112yes—
329C2×C4×C41#12112yes—
330C2×C4×C41C22×D411yescharacteristic
331C2×C4×C41C22×D411yescharacteristic
332C2×C4×C41C2×#4111yescharacteristic
333C2×C4×C41C2×#4111yescharacteristic
334C2×C4×C41H(5,𝔽2)11yescharacteristic
335C2×C4×C41H(5,𝔽2)11yescharacteristic
336C8×C41—22no—
337C8×C41—22no—
338C8×C41—22no—
339C8×C41—41no—
340#25391C4111yesmaximal, characteristic, direct product factor, Sylow
341C22×C41—41no—
342C22×C41—41no—
343C22×C41—41no—
344C22×C41—41no—
345C22×C41—41no—
346C22×C41—41no—
347C22×C41—41no—
348C22×C41—41no—
349C22×C41—41no—
350C22×C41—41no—
351C22×C41—41no—
352C22×C41—41no—
353C22×C41—41no—
354C22×C41—41no—
355C22×C41—81no—
356C22×C41—81no—
357C22×C41—81no—
358C22×C41—81no—
359C22×C41—81no—
360C22×C41—81no—
361C22×C41—81no—
362C22×C41C2×#12111yescharacteristic
363C22×C41D4211yescharacteristic
364C22×C41#54611yescharacteristic
365C22×C41#57511yescharacteristic
366C22×C41#57511yescharacteristic
367C22×C41#57711yescharacteristic
368C22×C41#57811yescharacteristic
369C4×C41—22no—
370C4×C41—22no—
371C4×C41—41no—
372C4×C41—41no—
373C4×C41—42no—
374C4×C41—42no—
375C4×C41—42no—
376C4×C41—81no—
377C4×C41—81no—
378C4×C41—81no—
379C4×C41—81no—
380C4×C41#53211yescharacteristic
381C4×C41#54011yescharacteristic
382C4×C41D4211yescharacteristic
383C4×C41#55011yescharacteristic
384C2×#470C2×C4111yescharacteristic, complemented
385C2×#468C2×C4111yescharacteristic, complemented
386C2×#464C2×C4111yescharacteristic, complemented
387C2×#436C2×C4111yescharacteristic, complemented
388#2540C2×C4111yescharacteristic
389#2536C2×C4111yescharacteristic, complemented
390#2036C2×C4111yescharacteristic, complemented
391#2034C2×C4111yescharacteristic, complemented
392#2001C2×C4111yescharacteristic, complemented
393#2000C2×C4111yescharacteristic, complemented
394#1958C2×C4111yescharacteristic, complemented
395#1949C2×C4111yescharacteristic, complemented
396#1895C2×C4111yescharacteristic, complemented
397#1894C2×C4111yescharacteristic, complemented
398C4×#103C2×C4111yescharacteristic, complemented
399C2×C41—81no—
400C2×C41—81no—
401C2×C41—161no—
402C2×C41#242811yescharacteristic
403C2×C41#305411yescharacteristic
404C2×C41#306311yescharacteristic
405C2×C41#327511yescharacteristic
406C2×C41#327711yescharacteristic
407C2×C41#332311yescharacteristic
408C2×C41#332711yescharacteristic
409C22×Q16C22×C4111yescharacteristic
410C22×SD16C22×C4111yescharacteristic
411C22×M16C22×C4111yescharacteristic
412C22×M16C22×C4111yescharacteristic
413C2×#124C22×C4111yescharacteristic
414C2×C22⋊Q8C22×C4111yescharacteristic
415C2×C22⋊Q8C22×C4111yescharacteristic
416C2×C22⋊Q8C22×C4111yescharacteristic
417C2×C22⋊Q8C22×C4111yescharacteristic
418C2×#121C22×C4111yescharacteristic
419C2×#121C22×C4111yescharacteristic
420C2×C4×Q8C22×C4111yescharacteristic
421C2×C4×D4C22×C4111yescharacteristic
422#470—24no—
423#468—24no—
424#464—24no—
425#436—24no—
426C2×#107C22×C4111yescharacteristic
427C2×#106C22×C4111yescharacteristic
428C2×C4⋊C8C22×C4111yescharacteristic
429C2×#103C22×C4111yescharacteristic
430C2×#103C22×C4111yescharacteristic
431C2×#103C22×C4111yescharacteristic
432C2×#103C22×C4111yescharacteristic
433C2×#103C22×C4111yescharacteristic
434C2×#102C22×C4111yescharacteristic
435C2×#102C22×C4111yescharacteristic
436C2×#102C22×C4111yescharacteristic
437C2×C22⋊C8C22×C4111yescharacteristic
438C2×C22⋊C8C22×C4111yescharacteristic
439C2×C4×C8C22×C4111yescharacteristic
440#399—21no—
441#398—21no—
442#394—21no—
443#392—21no—
444#390—21no—
445#390—21no—
446#388—21no—
447#388—21no—
448#382C22×C4111yescharacteristic
449#380C22×C4111yescharacteristic
450#380C22×C4111yescharacteristic
451C4×C4⋊C4C22×C4111yescharacteristic
452#340C22×C4111yescharacteristic
453#340C22×C4111yescharacteristic
454#340C22×C4111yescharacteristic
455#340C22×C4111yescharacteristic
456C41#2539111yescharacteristic, direct product factor, Sylow
457C22×Q8C23×C4111yescharacteristic
458C22×Q8C23×C4111yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4D4×C4111yescharacteristic
462C22×D4C23×C4111yescharacteristic
463C23×C4C23×C4111yescharacteristic
464C23×C4C23×C4111yescharacteristic
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16—41no—
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16—41no—
471C2×M16—22no—
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—22no—
475C2×M16—41no—
476C2×M16—41no—
477C22×C8C23×C4111yescharacteristic
478C22×C8C23×C4111yescharacteristic
479C22×C8C23×C4111yescharacteristic
480C22×C8C23×C4111yescharacteristic
481#124—22no—
482#124—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—41no—
488C22⋊Q8—41no—
489C22⋊Q8—41no—
490C22⋊Q8—41no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495C4×Q8—22no—
496C4×Q8—22no—
497C4×D4—22no—
498C4×D4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4D4×C4111yescharacteristic
505C2×C4⋊C4C23×C4111yescharacteristic
506C2×C4⋊C4C23×C4111yescharacteristic
507C2×C4⋊C4C23×C4111yescharacteristic
508C2×C4⋊C4C23×C4111yescharacteristic
509C2×C4⋊C4C23×C4111yescharacteristic
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4D4×C4111yescharacteristic
521C2×C22⋊C4D4×C4111yescharacteristic
522C2×C42—21no—
523C2×C42—21no—
524C2×C42C23×C4111yescharacteristic
525#107—22no—
526#106—22no—
527C4⋊C8D4×C4114yescomplemented
528#103—22no—
529#103—22no—
530#103—22no—
531#103—41no—
532#103D4×C4114yescomplemented
533#102—22no—
534#102—22no—
535#102—41no—
536C22⋊C8—22no—
537C22⋊C8—22no—
538C4×C8—22no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544C24—21no—
545C24C2×D4×C4111yescharacteristic
546C24C2×D4×C4111yescharacteristic
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8C2×D4×C4112yes—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—81no—
573C2×D4—81no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4C2×D4×C4111yescharacteristic
594C22×C4C2×D4×C4111yescharacteristic
595C22×C4C2×D4×C4111yescharacteristic
596C22×C4C2×D4×C4111yescharacteristic
597C22×C4C24×C4111yescharacteristic
598Q16—44no—
599SD16—44no—
600M16—44no—
601M16—44no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8C2×D4×C4112yes—
612C2×C8C2×D4×C4112yes—
613C2×C8C2×D4×C4112yes—
614C4⋊C4—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—42no—
627C4⋊C4—42no—
628C4⋊C4C2×D4×C4112yes—
629C4⋊C4#41×C4112yes—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—42no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C42—42no—
643C42—81no—
644C42C2×D4×C4112yes—
645C42#41×C4112yes—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23C22×D4×C4111yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676D4—44no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—84no—
682D4—84no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4#121×C4112yes—
723C2×C4#121×C4112yes—
724C2×C4C22×D4×C4111yescharacteristic
725C2×C4C22×D4×C4111yescharacteristic
726C2×C4C2×#41×C4111yescharacteristic
727C2×C4C2×#41×C4111yescharacteristic
728C2×C4H(5,𝔽2)×C4111yescharacteristic
729C2×C4H(5,𝔽2)×C4111yescharacteristic
730C8—22no—
731C8—22no—
732C8—22no—
733C8—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C2×#121×C4111yescharacteristic
756C22D42×C4111yescharacteristic
757C22C41×#54611yescharacteristic
758C22C41×#57511yescharacteristic
759C22C41×#57511yescharacteristic
760C22C41×#57711yescharacteristic
761C22C41×#57811yescharacteristic
762C4—22no—
763C4—22no—
764C4—42no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—42no—
769C4—81no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4C41×#53211yescharacteristic
774C4C41×#54011yescharacteristic
775C4D42×C4111yescharacteristic
776C4C41×#55011yescharacteristic
777C2—81no—
778C2—81no—
779C2—161no—
780C2C41×#242811yescharacteristic
781C2C41×#305411yescharacteristic
782C2C41×#306311yescharacteristic
783C2C41×#327511yescharacteristic
784C2C41×#327711yescharacteristic
785C2C41×#332311yescharacteristic
786C2C41×#332711yescharacteristic
subgroupG/H
center, socleC23×C41C22×D4
commutator, Frattini, cosocleC22×C4C24×C41
prime radicalC41×#2540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C41 ◁ C2×C4×D4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C41×#470C2semidirect
2. C2×C41×#468C2semidirect
3. C2×C41×#464C2semidirect
4. C2×C41×#436C2semidirect
6. C41×#2536C2semidirect
7. C41×#2036C2semidirect
8. C41×#2034C2semidirect
9. C41×#2001C2semidirect
10. C41×#2000C2semidirect
11. C41×#1958C2semidirect
12. C41×#1949C2semidirect
13. C41×#1895C2semidirect
14. C41×#1894C2semidirect
15. C4×#103×C41C2semidirect
133. C4⋊C8×C41D4semidirect
138. #103×C41D4semidirect
340. #25391C41direct (N × H)
384. C2×#470C2×C41semidirect
385. C2×#468C2×C41semidirect
386. C2×#464C2×C41semidirect
387. C2×#436C2×C41semidirect
389. #2536C2×C41semidirect
390. #2036C2×C41semidirect
391. #2034C2×C41semidirect
392. #2001C2×C41semidirect
393. #2000C2×C41semidirect
394. #1958C2×C41semidirect
395. #1949C2×C41semidirect
396. #1895C2×C41semidirect
397. #1894C2×C41semidirect
398. C4×#103C2×C41semidirect
456. C41#25391direct (N × H)
527. C4⋊C8D4×C41semidirect
532. #103D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4702
C2×C41×#4682
C2×C41×#4642
C2×C41×#4362
C41×#25402
C41×#25362
C41×#20362
C41×#20342
C41×#20012
C41×#20002
C41×#19582
C41×#19492
C41×#18952
C41×#18942
C4×#103×C412
#2539141