Finite Group Databasebeta

← C41×#25429 #23801630

Subgroups — C41×#25429 #23801630

Order 10496.

1034 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×#495C211yesmaximal, characteristic, complemented
2C2×C41×#468C211yesmaximal, characteristic, complemented
3C2×C41×#468C211yesmaximal, characteristic, complemented
4C2×C41×#440C211yesmaximal, characteristic, complemented
5C41×#2427C211yesmaximal, characteristic, complemented
6C41×#2426C211yesmaximal, characteristic, complemented
7C41×#2042C211yesmaximal, characteristic, complemented
8C41×#2042C211yesmaximal, characteristic, complemented
9C41×#2001C211yesmaximal, characteristic, complemented
10C41×#1999C211yesmaximal, characteristic
11C41×#1973C211yesmaximal, characteristic, complemented
12C41×#1942C211yesmaximal, characteristic, complemented
13C41×#1879C211yesmaximal, characteristic, complemented
14C41×#1878C211yesmaximal, characteristic, complemented
15C41×#1753C211yesmaximal, characteristic, complemented
16C22×Q16×C41C2211yescharacteristic
17C22×SD16×C41C2211yescharacteristic
18C22×SD16×C41C2211yescharacteristic
19C22×D8×C41C2211yescharacteristic
20C22×M16×C41C2211yescharacteristic
21C2×#124×C41C2211yescharacteristic
22C2×#124×C41C2211yescharacteristic
23C2×C22⋊Q8×C41C2211yescharacteristic
24C2×C22⋊Q8×C41C2211yescharacteristic
25C2×#121×C41C2211yescharacteristic
26C2×#121×C41C2211yescharacteristic
27C2×C4×Q8×C41C2211yescharacteristic
28C2×C4×D4×C41C2211yescharacteristic
29C41×#495—24no—
30C41×#468—24no—
31C41×#468—24no—
32C41×#440—24no—
33C2×#107×C41C2211yescharacteristic
34C2×#107×C41C2211yescharacteristic
35C2×#103×C41C2211yescharacteristic
36C2×#103×C41C2211yescharacteristic
37C2×#103×C41C2211yescharacteristic
38C2×#103×C41C2211yescharacteristic
39C2×#102×C41C2211yescharacteristic
40C2×#102×C41C2211yescharacteristic
41C2×#102×C41C2211yescharacteristic
42C2×#102×C41C2211yescharacteristic
43C2×C22⋊C8×C41C2211yescharacteristic
44C2×#97×C41C2211yescharacteristic
45C2×C4×C8×C41C2211yescharacteristic
46C41×#397—21no—
47C41×#396—21no—
48C41×#394—21no—
49C41×#394—21no—
50C41×#391C2211yescharacteristic
51C41×#390—21no—
52C41×#390C2211yescharacteristic
53C41×#389C2211yescharacteristic
54C41×#389C2211yescharacteristic
55C41×#388—21no—
56C41×#386—21no—
57C41×#380—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×C41C2311yescharacteristic
68C22×D4×C41C2311yescharacteristic
69C23×C4×C41—21no—
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—22no—
77C2×SD16×C41—22no—
78C2×SD16×C41—22no—
79C2×SD16×C41D414yescomplemented
80C2×D8×C41—22no—
81C2×D8×C41—22no—
82C2×D8×C41—41no—
83C2×M16×C41—22no—
84C2×M16×C41—22no—
85C2×M16×C41—22no—
86C22×C8×C41C2311yescharacteristic
87C22×C8×C41C2311yescharacteristic
88C22×C8×C41C2311yescharacteristic
89C22×C8×C41C2311yescharacteristic
90#124×C41—22no—
91#124×C41—22no—
92#124×C41—41no—
93#124×C41—41no—
94C22⋊Q8×C41—22no—
95C22⋊Q8×C41—22no—
96C22⋊Q8×C41—41no—
97C22⋊Q8×C41—41no—
98#121×C41—22no—
99#121×C41—22no—
100#121×C41—41no—
101#121×C41—41no—
102C4×Q8×C41—22no—
103C4×Q8×C41—41no—
104C4×D4×C41—22no—
105C4×D4×C41—41no—
106C2×C4⋊C4×C41—21no—
107C2×C4⋊C4×C41—21no—
108C2×C4⋊C4×C41—21no—
109C2×C4⋊C4×C41—21no—
110C2×C4⋊C4×C41—21no—
111C2×C4⋊C4×C41C2311yescharacteristic
112C2×C4⋊C4×C41C2311yescharacteristic
113C2×C4⋊C4×C41C2311yescharacteristic
114C2×C4⋊C4×C41C2311yescharacteristic
115C2×C22⋊C4×C41—21no—
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×C41C2311yescharacteristic
130C2×C42×C41C2311yescharacteristic
131#107×C41—22no—
132#107×C41D414yescomplemented
133#103×C41—22no—
134#103×C41—22no—
135#103×C41—22no—
136#103×C41—41no—
137#102×C41—22no—
138#102×C41—22no—
139#102×C41—22no—
140#102×C41—41no—
141C22⋊C8×C41—22no—
142#97×C41—22no—
143C4×C8×C41—22no—
144#95×C41—21no—
145#95×C41—21no—
146#95×C41—21no—
147#95×C41—21no—
148#95×C41D411yescharacteristic
149#95×C41D411yescharacteristic
150C24×C41—21no—
151C24×C41—21no—
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—21no—
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—42no—
177C2×D4×C41—42no—
178C2×D4×C41—42no—
179C2×D4×C41—42no—
180C2×D4×C41—81no—
181C2×D4×C41—81no—
182C2×D4×C41C2×D412yes—
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—42no—
196C22×C4×C41—42no—
197C22×C4×C41—81no—
198C22×C4×C41C2×D411yescharacteristic
199C22×C4×C41C2×D411yescharacteristic
200C22×C4×C41C2×D411yescharacteristic
201C22×C4×C41C2×D411yescharacteristic
202C22×C4×C41C2×D411yescharacteristic
203C22×C4×C41C2411yescharacteristic
204Q16×C41—44no—
205SD16×C41—28no—
206SD16×C41—44no—
207D8×C41—44no—
208M16×C41—44no—
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×C41#4112yes—
220C2×C8×C41#4112yes—
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—42no—
228C4⋊C4×C41—42no—
229C4⋊C4×C41—42no—
230C4⋊C4×C41—81no—
231C4⋊C4×C41—81no—
232C4⋊C4×C41C2×D412yes—
233C4⋊C4×C41C2×D412yes—
234C22⋊C4×C41—41no—
235C22⋊C4×C41—41no—
236C22⋊C4×C41—42no—
237C22⋊C4×C41—42no—
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—81no—
247C42×C41—21no—
248C42×C41—21no—
249C42×C41—21no—
250C42×C41—21no—
251C42×C41—42no—
252C23×C41—21no—
253C23×C41—22no—
254C23×C41—21no—
255C23×C41—21no—
256C23×C41—21no—
257C23×C41—21no—
258C23×C41—21no—
259C23×C41—21no—
260C23×C41—41no—
261C23×C41—41no—
262C23×C41—41no—
263C23×C41—41no—
264C23×C41—41no—
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×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—22no—
283D4×C41—22no—
284D4×C41—41no—
285D4×C41—41no—
286D4×C41—41no—
287D4×C41—41no—
288D4×C41—41no—
289D4×C41—41no—
290D4×C41—84no—
291D4×C41—84no—
292C2×C4×C41—21no—
293C2×C4×C41—21no—
294C2×C4×C41—21no—
295C2×C4×C41—21no—
296C2×C4×C41—21no—
297C2×C4×C41—22no—
298C2×C4×C41—22no—
299C2×C4×C41—22no—
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—21no—
307C2×C4×C41—21no—
308C2×C4×C41—21no—
309C2×C4×C41—21no—
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—41no—
329C2×C4×C41—84no—
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—41no—
338C8×C41—41no—
339C8×C41#12114yes—
340#25429C4111yesmaximal, characteristic, direct product factor, Sylow
341C22×C41—41no—
342C22×C41—41no—
343C22×C41—41no—
344C22×C41—42no—
345C22×C41—41no—
346C22×C41—42no—
347C22×C41—41no—
348C22×C41—42no—
349C22×C41—41no—
350C22×C41—41no—
351C22×C41—81no—
352C22×C41—81no—
353C22×C41—81no—
354C22×C41—81no—
355C22×C41—81no—
356C22×C41—81no—
357C22×C41—81no—
358C22×C41—81no—
359C22×C41—81no—
360C22×C41—81no—
361C22×C41—81no—
362C22×C41#53211yescharacteristic
363C22×C41D4211yescharacteristic
364C22×C41D4211yescharacteristic
365C22×C41#57511yescharacteristic
366C22×C41#57511yescharacteristic
367C22×C41#57611yescharacteristic
368C22×C41#57811yescharacteristic
369C4×C41—41no—
370C4×C41—42no—
371C4×C41—41no—
372C4×C41—41no—
373C4×C41—41no—
374C4×C41—42no—
375C4×C41—42no—
376C4×C41—41no—
377C4×C41—81no—
378C4×C41—81no—
379C4×C41—81no—
380C4×C41C2×#12111yescharacteristic
381C4×C41#54011yescharacteristic
382C4×C41#54611yescharacteristic
383C4×C41#55011yescharacteristic
384C2×#495C2×C4111yescharacteristic, complemented
385C2×#468C2×C4111yescharacteristic, complemented
386C2×#468C2×C4111yescharacteristic, complemented
387C2×#440C2×C4111yescharacteristic, complemented
388#2427C2×C4111yescharacteristic, complemented
389#2426C2×C4111yescharacteristic, complemented
390#2042C2×C4111yescharacteristic, complemented
391#2042C2×C4111yescharacteristic, complemented
392#2001C2×C4111yescharacteristic, complemented
393#1999C2×C4111yescharacteristic
394#1973C2×C4111yescharacteristic, complemented
395#1942C2×C4111yescharacteristic, complemented
396#1879C2×C4111yescharacteristic, complemented
397#1878C2×C4111yescharacteristic, complemented
398#1753C2×C4111yescharacteristic, complemented
399C2×C41—81no—
400C2×C41—82no—
401C2×C41—161no—
402C2×C41#242811yescharacteristic
403C2×C41#317511yescharacteristic
404C2×C41#318311yescharacteristic
405C2×C41#326811yescharacteristic
406C2×C41#326911yescharacteristic
407C2×C41#327311yescharacteristic
408C2×C41#327711yescharacteristic
409C22×Q16C22×C4111yescharacteristic
410C22×SD16C22×C4111yescharacteristic
411C22×SD16C22×C4111yescharacteristic
412C22×D8C22×C4111yescharacteristic
413C22×M16C22×C4111yescharacteristic
414C2×#124C22×C4111yescharacteristic
415C2×#124C22×C4111yescharacteristic
416C2×C22⋊Q8C22×C4111yescharacteristic
417C2×C22⋊Q8C22×C4111yescharacteristic
418C2×#121C22×C4111yescharacteristic
419C2×#121C22×C4111yescharacteristic
420C2×C4×Q8C22×C4111yescharacteristic
421C2×C4×D4C22×C4111yescharacteristic
422#495—24no—
423#468—24no—
424#468—24no—
425#440—24no—
426C2×#107C22×C4111yescharacteristic
427C2×#107C22×C4111yescharacteristic
428C2×#103C22×C4111yescharacteristic
429C2×#103C22×C4111yescharacteristic
430C2×#103C22×C4111yescharacteristic
431C2×#103C22×C4111yescharacteristic
432C2×#102C22×C4111yescharacteristic
433C2×#102C22×C4111yescharacteristic
434C2×#102C22×C4111yescharacteristic
435C2×#102C22×C4111yescharacteristic
436C2×C22⋊C8C22×C4111yescharacteristic
437C2×#97C22×C4111yescharacteristic
438C2×C4×C8C22×C4111yescharacteristic
439#397—21no—
440#396—21no—
441#394—21no—
442#394—21no—
443#391C22×C4111yescharacteristic
444#390—21no—
445#390C22×C4111yescharacteristic
446#389C22×C4111yescharacteristic
447#389C22×C4111yescharacteristic
448#388—21no—
449#386—21no—
450#380—21no—
451C4×C22⋊C4C22×C4111yescharacteristic
452#340C22×C4111yescharacteristic
453#340C22×C4111yescharacteristic
454#336C22×C4111yescharacteristic
455#336C22×C4111yescharacteristic
456C41#2542911yescharacteristic, direct product factor, Sylow
457C22×Q8C23×C4111yescharacteristic
458C22×Q8C23×C4111yescharacteristic
459C22×D4—21no—
460C22×D4—21no—
461C22×D4C23×C4111yescharacteristic
462C22×D4C23×C4111yescharacteristic
463C23×C4—21no—
464C23×C4C23×C4111yescharacteristic
465C2×Q16—22no—
466C2×Q16—22no—
467C2×Q16—41no—
468C2×SD16—22no—
469C2×SD16—22no—
470C2×SD16—22no—
471C2×SD16—22no—
472C2×SD16—22no—
473C2×SD16D4×C4114yescomplemented
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—41no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C22×C8C23×C4111yescharacteristic
481C22×C8C23×C4111yescharacteristic
482C22×C8C23×C4111yescharacteristic
483C22×C8C23×C4111yescharacteristic
484#124—22no—
485#124—22no—
486#124—41no—
487#124—41no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—41no—
491C22⋊Q8—41no—
492#121—22no—
493#121—22no—
494#121—41no—
495#121—41no—
496C4×Q8—22no—
497C4×Q8—41no—
498C4×D4—22no—
499C4×D4—41no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C4111yescharacteristic
506C2×C4⋊C4C23×C4111yescharacteristic
507C2×C4⋊C4C23×C4111yescharacteristic
508C2×C4⋊C4C23×C4111yescharacteristic
509C2×C22⋊C4—21no—
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×C42C23×C4111yescharacteristic
524C2×C42C23×C4111yescharacteristic
525#107—22no—
526#107D4×C4114yescomplemented
527#103—22no—
528#103—22no—
529#103—22no—
530#103—41no—
531#102—22no—
532#102—22no—
533#102—22no—
534#102—41no—
535C22⋊C8—22no—
536#97—22no—
537C4×C8—22no—
538#95—21no—
539#95—21no—
540#95—21no—
541#95—21no—
542#95D4×C4111yescharacteristic
543#95D4×C4111yescharacteristic
544C24—21no—
545C24—21no—
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—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—42no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4C2×D4×C4112yes—
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—42no—
590C22×C4—42no—
591C22×C4—81no—
592C22×C4C2×D4×C4111yescharacteristic
593C22×C4C2×D4×C4111yescharacteristic
594C22×C4C2×D4×C4111yescharacteristic
595C22×C4C2×D4×C4111yescharacteristic
596C22×C4C2×D4×C4111yescharacteristic
597C22×C4C24×C4111yescharacteristic
598Q16—44no—
599SD16—28no—
600SD16—44no—
601D8—44no—
602M16—44no—
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×C8#41×C4112yes—
614C2×C8#41×C4112yes—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—81no—
625C4⋊C4—81no—
626C4⋊C4C2×D4×C4112yes—
627C4⋊C4C2×D4×C4112yes—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C22⋊C4—42no—
631C22⋊C4—42no—
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—81no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—42no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
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—22no—
677D4—22no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—84no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
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—41no—
723C2×C4—84no—
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—41no—
732C8—41no—
733C8#121×C4114yes—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—42no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22C41×#53211yescharacteristic
756C22D42×C4111yescharacteristic
757C22D42×C4111yescharacteristic
758C22C41×#57511yescharacteristic
759C22C41×#57511yescharacteristic
760C22C41×#57611yescharacteristic
761C22C41×#57811yescharacteristic
762C4—41no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—42no—
769C4—41no—
770C4—81no—
771C4—81no—
772C4—81no—
773C4C2×#121×C4111yescharacteristic
774C4C41×#54011yescharacteristic
775C4C41×#54611yescharacteristic
776C4C41×#55011yescharacteristic
777C2—81no—
778C2—82no—
779C2—161no—
780C2C41×#242811yescharacteristic
781C2C41×#317511yescharacteristic
782C2C41×#318311yescharacteristic
783C2C41×#326811yescharacteristic
784C2C41×#326911yescharacteristic
785C2C41×#327311yescharacteristic
786C2C41×#327711yescharacteristic
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×#495C2semidirect
2. C2×C41×#468C2semidirect
3. C2×C41×#468C2semidirect
4. C2×C41×#440C2semidirect
5. C41×#2427C2semidirect
6. C41×#2426C2semidirect
7. C41×#2042C2semidirect
8. C41×#2042C2semidirect
9. C41×#2001C2semidirect
11. C41×#1973C2semidirect
12. C41×#1942C2semidirect
13. C41×#1879C2semidirect
14. C41×#1878C2semidirect
15. C41×#1753C2semidirect
79. C2×SD16×C41D4semidirect
132. #107×C41D4semidirect
340. #25429C41direct (N × H)
384. C2×#495C2×C41semidirect
385. C2×#468C2×C41semidirect
386. C2×#468C2×C41semidirect
387. C2×#440C2×C41semidirect
388. #2427C2×C41semidirect
389. #2426C2×C41semidirect
390. #2042C2×C41semidirect
391. #2042C2×C41semidirect
392. #2001C2×C41semidirect
394. #1973C2×C41semidirect
395. #1942C2×C41semidirect
396. #1879C2×C41semidirect
397. #1878C2×C41semidirect
398. #1753C2×C41semidirect
456. C41#25429direct (N × H)
473. C2×SD16D4×C41semidirect
526. #107D4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C41×#4952
C2×C41×#4682
C2×C41×#4402
C41×#24272
C41×#24262
C41×#20422
C41×#20012
C41×#19992
C41×#19732
C41×#19422
C41×#18792
C41×#18782
C41×#17532
#2542941