Finite Group Databasebeta

← #27510472

Subgroups — #27510472

Order 13568.

894 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20279888C211yesmaximal, characteristic, complemented
2#20276152C211yesmaximal, characteristic, complemented
3#20276141C211yesmaximal, characteristic, complemented
4#20275908C211yesmaximal, characteristic, complemented
5#20275894C211yesmaximal, characteristic, complemented
6#20275856C211yesmaximal, characteristic, complemented
7#20275851C211yesmaximal, characteristic, complemented
8#20275353C211yesmaximal, characteristic, complemented
9#20275339C211yesmaximal, characteristic, complemented
10#20275154C211yesmaximal, characteristic, complemented
11#20275149C211yesmaximal, characteristic, complemented
12#20275013C211yesmaximal, characteristic, complemented
13#20274655C211yesmaximal, characteristic, complemented
14#20274655C211yesmaximal, characteristic, complemented
15C53×#2407C211yesmaximal, characteristic
16C22×#11719917C2211yescharacteristic
17C2×#13133217C2211yescharacteristic
18C2×#13133150C2211yescharacteristic
19C2×#13133148C2211yescharacteristic
20C2×#13133141C2211yescharacteristic
21C2×#13133141C2211yescharacteristic
22C2×#13133141C2211yescharacteristic
23C2×#13133141C2211yescharacteristic
24C2×#13133138C2211yescharacteristic
25C2×#13133138C2211yescharacteristic
26C2×#13133138C2211yescharacteristic
27C2×#13133138C2211yescharacteristic
28C2×C22⋊#88322C2211yescharacteristic
29C2×C22⋊#88322C2211yescharacteristic
30C2×C22⋊#88322C2211yescharacteristic
31#16810535—21no—
32#16810535—21no—
33#16810526—21no—
34#16810488—21no—
35#16810483C2211yescharacteristic
36#16810483C2211yescharacteristic
37#16810483C2211yescharacteristic
38#16810483C2211yescharacteristic
39C4×C4⋊Dic53C2211yescharacteristic
40#16810385C2211yescharacteristic
41#16810385C2211yescharacteristic
42#16810385C2211yescharacteristic
43#16810385C2211yescharacteristic
44#16810385C2211yescharacteristic
45#16810385C2211yescharacteristic
46#16810378C2211yescharacteristic
47#16810378C2211yescharacteristic
48C22×#41×C53C2211yescharacteristic
49C2×C22⋊Q8×C53C2211yescharacteristic
50C2×#121×C53C2211yescharacteristic
51C2×C4×D4×C53C2211yescharacteristic
52C53×#394—21no—
53C53×#392—21no—
54C53×#391C2211yescharacteristic
55C53×#390C2211yescharacteristic
56C53×#386—21no—
57C53×#385—21no—
58C53×#380C2211yescharacteristic
59C22×Dic106—21no—
60C2×#11719917—41no—
61C2×#11719917—41no—
62C2×#11719917—41no—
63C22×#88322C2311yescharacteristic
64C22×#88322C2311yescharacteristic
65C22×#88322C2311yescharacteristic
66C22×#88322C2311yescharacteristic
67#13133217—41no—
68#13133217—41no—
69C2×C4⋊Dic53—21no—
70C2×C4⋊Dic53C2311yescharacteristic
71C2×C4⋊Dic53C2311yescharacteristic
72C2×C4⋊Dic53C2311yescharacteristic
73C2×C4⋊Dic53C2311yescharacteristic
74C2×C22⋊Dic53—21no—
75C2×C22⋊Dic53—21no—
76C2×C22⋊Dic53—21no—
77C2×C22⋊Dic53—21no—
78C2×C4×Dic53—21no—
79#13133150—41no—
80#13133148—41no—
81#13133141—22no—
82#13133141—41no—
83#13133141—41no—
84#13133141—41no—
85#13133138—22no—
86#13133138—41no—
87#13133138—41no—
88#13133138—41no—
89C22⋊#88322—41no—
90C22⋊#88322—41no—
91C22⋊#88322—41no—
92#13133124—21no—
93#13133124—21no—
94#13133124—21no—
95#13133124—21no—
96#13133124—21no—
97C2×#41×C53—22no—
98C2×#41×C53—22no—
99C2×#41×C53—41no—
100C2×#41×C53—41no—
101C2×#41×C53—41no—
102C2×#41×C53—41no—
103C22×Q8×C53C2311yescharacteristic
104C22×D4×C53—21no—
105C22×D4×C53—21no—
106C22×D4×C53D411yescharacteristic
107C22×D4×C53C2311yescharacteristic
108C23×C4×C53—21no—
109C23×C4×C53C2311yescharacteristic
110C23×C4×C53C2311yescharacteristic
111C22⋊Q8×C53—22no—
112C22⋊Q8×C53—41no—
113#121×C53—22no—
114#121×C53—41no—
115C4×D4×C53—41no—
116C4×D4×C53—41no—
117C2×C4⋊C4×C53—21no—
118C2×C4⋊C4×C53D411yescharacteristic
119C2×C4⋊C4×C53C2311yescharacteristic
120C2×C4⋊C4×C53C2311yescharacteristic
121C2×C22⋊C4×C53—21no—
122C2×C22⋊C4×C53—21no—
123C2×C22⋊C4×C53—21no—
124C2×C22⋊C4×C53—21no—
125C2×C22⋊C4×C53—21no—
126C2×C22⋊C4×C53D411yescharacteristic
127C2×C22⋊C4×C53D411yescharacteristic
128C2×C42×C53C2311yescharacteristic
129#95×C53—21no—
130#95×C53—21no—
131#95×C53—21no—
132C24×C53—21no—
133C24×C53C2×D411yescharacteristic
134C24×C53C2×D411yescharacteristic
135#41×C53—44no—
136#41×C53—44no—
137#41×C53—44no—
138#41×C53—44no—
139C2×Q8×C53—21no—
140C2×Q8×C53—21no—
141C2×Q8×C53—21no—
142C2×Q8×C53—21no—
143C2×Q8×C53—21no—
144C2×Q8×C53#4112yes—
145C2×D4×C53—22no—
146C2×D4×C53—21no—
147C2×D4×C53—21no—
148C2×D4×C53—21no—
149C2×D4×C53—21no—
150C2×D4×C53—21no—
151C2×D4×C53—41no—
152C2×D4×C53—41no—
153C2×D4×C53—42no—
154C2×D4×C53—42no—
155C2×D4×C53—42no—
156C2×D4×C53—42no—
157C2×D4×C53—42no—
158C2×D4×C53—81no—
159C2×D4×C53#4112yes—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—42no—
176C22×C4×C53—42no—
177C22×C4×C53—42no—
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D411yescharacteristic
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2411yescharacteristic
183C22×Dic53—21no—
184C22×Dic53—21no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C2×Dic106—42no—
188C2×Dic106—81no—
189C2×Dic106—81no—
190C4⋊C4×C53—21no—
191C4⋊C4×C53—21no—
192C4⋊C4×C53—21no—
193C4⋊C4×C53—21no—
194C4⋊C4×C53—41no—
195C4⋊C4×C53—42no—
196C22⋊C4×C53—41no—
197C22⋊C4×C53—41no—
198C22⋊C4×C53—42no—
199C22⋊C4×C53—42no—
200C22⋊C4×C53—42no—
201C22⋊C4×C53—81no—
202C22⋊C4×C53—81no—
203C42×C53—21no—
204C42×C53—21no—
205C22⋊Dic53—81no—
206C22⋊Dic53—81no—
207C22⋊Dic53—81no—
208C22⋊Dic53—81no—
209C4⋊Dic53—21no—
210C4⋊Dic53—21no—
211C4⋊Dic53—21no—
212C4⋊Dic53—21no—
213C4⋊Dic53—21no—
214C4⋊Dic53—21no—
215C4⋊Dic53—21no—
216C4⋊Dic53—21no—
217C4⋊Dic53—42no—
218C4×Dic53—42no—
219#11719917—44no—
220C2×#88322—21no—
221C2×#88322—21no—
222C2×#88322—21no—
223C2×#88322—21no—
224C2×#88322—21no—
225C2×#88322—21no—
226C2×#88322—21no—
227C2×#88322—21no—
228C2×#88322—21no—
229C2×#88322—21no—
230C2×#88322—21no—
231C2×#88322—21no—
232C23×C53—21no—
233C23×C53—21no—
234C23×C53—21no—
235C23×C53—21no—
236C23×C53—21no—
237C23×C53—21no—
238C23×C53—22no—
239C23×C53—21no—
240C23×C53—21no—
241C23×C53—21no—
242C23×C53—21no—
243C23×C53—21no—
244C23×C53—21no—
245C23×C53—21no—
246C23×C53—21no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—41no—
250C23×C53—41no—
251C23×C53—41no—
252C23×C53—41no—
253C23×C53C22×D411yescharacteristic
254Q8×C53—22no—
255Q8×C53—22no—
256Q8×C53—41no—
257Q8×C53—41no—
258D4×C53—22no—
259D4×C53—22no—
260D4×C53—44no—
261D4×C53—48no—
262D4×C53—41no—
263D4×C53—41no—
264D4×C53—84no—
265C2×C4×C53—21no—
266C2×C4×C53—21no—
267C2×C4×C53—21no—
268C2×C4×C53—21no—
269C2×C4×C53—21no—
270C2×C4×C53—21no—
271C2×C4×C53—21no—
272C2×C4×C53—21no—
273C2×C4×C53—21no—
274C2×C4×C53—22no—
275C2×C4×C53—21no—
276C2×C4×C53—21no—
277C2×C4×C53—48no—
278C2×C4×C53—41no—
279C2×C4×C53—41no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—41no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—41no—
288C2×C4×C53—41no—
289C2×C4×C53—41no—
290C2×C4×C53—41no—
291C2×C4×C53—41no—
292C2×C4×C53—41no—
293C2×C4×C53—41no—
294C2×C4×C53#13712yes—
295C2×C4×C53C2×#4111yescharacteristic
296C2×C4×C53C2×#4111yescharacteristic
297C2×C4×C53H(5,𝔽2)11yescharacteristic
298C2×C4×C53H(5,𝔽2)11yescharacteristic
299C2×C4×C53H(5,𝔽2)11yescharacteristic
300C2×C4×C53H(5,𝔽2)11yescharacteristic
301C2×Dic53—41no—
302C2×Dic53—41no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—41no—
308C2×Dic53—41no—
309C2×Dic53—41no—
310C2×Dic53—41no—
311C2×Dic53—41no—
312C2×Dic53—41no—
313Dic106—84no—
314#88322—41no—
315#88322—41no—
316#88322—41no—
317#88322—41no—
318#31279—531nomaximal, Sylow
319C22×C53—41no—
320C22×C53—41no—
321C22×C53—42no—
322C22×C53—41no—
323C22×C53—41no—
324C22×C53—42no—
325C22×C53—41no—
326C22×C53—41no—
327C22×C53—41no—
328C22×C53—41no—
329C22×C53—41no—
330C22×C53—41no—
331C22×C53—41no—
332C22×C53—42no—
333C22×C53—41no—
334C22×C53—41no—
335C22×C53—41no—
336C22×C53—81no—
337C22×C53—81no—
338C22×C53—81no—
339C22×C53—81no—
340C22×C53#53411yescharacteristic
341C22×C53#54611yescharacteristic
342C22×C53#54611yescharacteristic
343C22×C53C2×#13711yescharacteristic
344C22×C53#57511yescharacteristic
345C22×C53#57611yescharacteristic
346C22×C53#57711yescharacteristic
347C4×C53—22no—
348C4×C53—41no—
349C4×C53—41no—
350C4×C53—42no—
351C4×C53—41no—
352C4×C53—81no—
353C4×C53—81no—
354C4×C53#53811yescharacteristic
355C4×C53#53811yescharacteristic
356C4×C53#55111yescharacteristic
357C4×C53H(3,𝔽4)11yescharacteristic
358Dic53—81no—
359Dic53—81no—
360Dic53—81no—
361Dic53—81no—
362#2563—531no—
363#2407D5311yescharacteristic
364#2077—531no—
365#2075—531no—
366#2035—531no—
367#2033—531no—
368#2024—531no—
369#2023—531no—
370#1928—531no—
371#1926—531no—
372#1895—531no—
373#1894—531no—
374#1870—531no—
375#1788—531no—
376#1788—531no—
377C2×C53—81no—
378C2×C53—81no—
379C2×C53—82no—
380C2×C53#268411yescharacteristic
381C2×C53#319611yescharacteristic
382C2×C53#319811yescharacteristic
383C2×C53#331911yescharacteristic
384C2×C53#332111yescharacteristic
385C2×C53#333111yescharacteristic
386C2×C53#333311yescharacteristic
387C22×#41C2×D5311yescharacteristic
388C22×M16—531no—
389C2×C4⋊Q8—531no—
390C2×C22⋊Q8C2×D5311yescharacteristic
391C2×#121C2×D5311yescharacteristic
392C2×C4×D4C2×D5311yescharacteristic
393C2×#107—531no—
394C2×#106—531no—
395C2×#103—531no—
396C2×#103—531no—
397C2×#103—531no—
398C2×#103—531no—
399C2×#102—531no—
400C2×#102—531no—
401C2×#102—531no—
402C2×#102—531no—
403C2×C22⋊C8—531no—
404C2×C22⋊C8—531no—
405C2×C22⋊C8—531no—
406#394—21no—
407#393—1061no—
408#393—1061no—
409#392—21no—
410#391C2×D5311yescharacteristic
411#390—1061no—
412#390C2×D5311yescharacteristic
413#386—21no—
414#385—21no—
415#382—1061no—
416#380—531no—
417#380—531no—
418#380—531no—
419#380—531no—
420#380C2×D5311yescharacteristic
421C4×C4⋊C4—531no—
422#340—531no—
423#340—531no—
424#340—531no—
425#340—531no—
426#340—531no—
427#340—531no—
428#336—531no—
429#336—531no—
430C53#3127911yescharacteristic, complemented, Sylow
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41—41no—
436C2×#41—41no—
437C22×Q8—1061no—
438C22×Q8C22×D5311yescharacteristic
439C22×D4—21no—
440C22×D4—21no—
441C22×D4C22⋊D5311yescharacteristic
442C22×D4C22×D5311yescharacteristic
443C23×C4—21no—
444C23×C4C22×D5311yescharacteristic
445C23×C4C22×D5311yescharacteristic
446C2×M16—2121no—
447C2×M16—2121no—
448C2×M16—2121no—
449C22×C8—531no—
450C22×C8—531no—
451C22×C8—531no—
452C22×C8—531no—
453C4⋊Q8—2121no—
454C4⋊Q8—2121no—
455C22⋊Q8—22no—
456C22⋊Q8—41no—
457#121—22no—
458#121—41no—
459C4×D4—41no—
460C4×D4—41no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—531no—
463C2×C4⋊C4—531no—
464C2×C4⋊C4—531no—
465C2×C4⋊C4—531no—
466C2×C4⋊C4—1061no—
467C2×C4⋊C4C22⋊D5311yescharacteristic
468C2×C4⋊C4C22×D5311yescharacteristic
469C2×C4⋊C4C22×D5311yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—1061no—
476C2×C22⋊C4—1061no—
477C2×C22⋊C4—1061no—
478C2×C22⋊C4—1061no—
479C2×C22⋊C4C22⋊D5311yescharacteristic
480C2×C22⋊C4C22⋊D5311yescharacteristic
481C2×C42—1061no—
482C2×C42C22×D5311yescharacteristic
483#107—2121no—
484#106—2121no—
485#103—1062no—
486#103—2121no—
487#103—2121no—
488#103—2121no—
489#102—1062no—
490#102—2121no—
491#102—2121no—
492#102—2121no—
493C22⋊C8—2121no—
494C22⋊C8—2121no—
495C22⋊C8—2121no—
496#95—21no—
497#95—21no—
498#95—21no—
499#95—1061no—
500#95—1061no—
501#95—1061no—
502#95—1061no—
503#95—1061no—
504C24—21no—
505C24C2×C22⋊D5311yescharacteristic
506C24C2×C22⋊D5311yescharacteristic
507#41—44no—
508#41—44no—
509#41—44no—
510#41—44no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—4241no—
517C2×Q8—4241no—
518C2×Q8—2122no—
519C2×Q8#1171994712yes—
520C2×D4—22no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—41no—
527C2×D4—41no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—81no—
534C2×D4#1171994712yes—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—1061no—
554C22×C4—1061no—
555C22×C4—1061no—
556C22×C4—1061no—
557C22×C4C2×C22⋊D5311yescharacteristic
558C22×C4C2×C22⋊D5311yescharacteristic
559C22×C4C2×C22⋊D5311yescharacteristic
560C22×C4C2×C22⋊D5311yescharacteristic
561C22×C4C23×D5311yescharacteristic
562M16—2124no—
563C2×C8—1061no—
564C2×C8—1061no—
565C2×C8—1061no—
566C2×C8—1061no—
567C2×C8—1061no—
568C2×C8—1061no—
569C2×C8—1061no—
570C2×C8—1061no—
571C2×C8—1061no—
572C2×C8—1061no—
573C2×C8—1061no—
574C2×C8—1061no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—41no—
580C4⋊C4—42no—
581C4⋊C4—1061no—
582C4⋊C4—1061no—
583C4⋊C4—1061no—
584C4⋊C4—1061no—
585C4⋊C4—1061no—
586C4⋊C4—1061no—
587C4⋊C4—1061no—
588C4⋊C4—1061no—
589C4⋊C4—2122no—
590C22⋊C4—41no—
591C22⋊C4—41no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—4241no—
598C22⋊C4—4241no—
599C22⋊C4—4241no—
600C22⋊C4—4241no—
601C42—21no—
602C42—21no—
603C42—2122no—
604C23—21no—
605C23—22no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23C22×C22⋊D5311yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—41no—
629Q8—41no—
630Q8—4244no—
631D4—22no—
632D4—22no—
633D4—44no—
634D4—48no—
635D4—41no—
636D4—41no—
637D4—84no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—48no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—2121no—
668C2×C4—2121no—
669C2×C4—2121no—
670C2×C4—2121no—
671C2×C4—2121no—
672C2×C4—2121no—
673C2×C4—2121no—
674C2×C4—2121no—
675C2×C4—2121no—
676C2×C4—2121no—
677C2×C4—2121no—
678C2×C4—2121no—
679C2×C4#1313324712yes—
680C2×C4C2×#1171994711yescharacteristic
681C2×C4C2×#1171994711yescharacteristic
682C2×C4#1313326211yescharacteristic
683C2×C4#1313326211yescharacteristic
684C2×C4#1313326211yescharacteristic
685C2×C4#1313326211yescharacteristic
686C8—2121no—
687C8—2121no—
688C8—2121no—
689C8—2121no—
690C22—42no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—42no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22#1681118211yescharacteristic
712C22#1681126711yescharacteristic
713C22#1681126711yescharacteristic
714C22C2×#1313324711yescharacteristic
715C22#1681142111yescharacteristic
716C22#1681142611yescharacteristic
717C22#1681143111yescharacteristic
718C4—22no—
719C4—41no—
720C4—41no—
721C4—42no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—4241no—
726C4—4241no—
727C4—4241no—
728C4—4241no—
729C4#1681120811yescharacteristic
730C4#1681120811yescharacteristic
731C4#1681130411yescharacteristic
732C4#1681136611yescharacteristic
733C2—81no—
734C2—81no—
735C2—82no—
736C2#2028109311yescharacteristic
737C2#2028554111yescharacteristic
738C2#2028556111yescharacteristic
739C2#2028687111yescharacteristic
740C2#2028690111yescharacteristic
741C2#2028703111yescharacteristic
742C2#2028705311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC22×C4×C53C24
FrattiniC22×C4C23×D53
Fitting, prime radicalC53×#2407C2
socleC23×C53C22×D4
hypercenter#2407D53
hypocenterC53#31279
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. #20279888C2semidirect
2. #20276152C2semidirect
3. #20276141C2semidirect
4. #20275908C2semidirect
5. #20275894C2semidirect
6. #20275856C2semidirect
7. #20275851C2semidirect
8. #20275353C2semidirect
9. #20275339C2semidirect
10. #20275154C2semidirect
11. #20275149C2semidirect
12. #20275013C2semidirect
13. #20274655C2semidirect
14. #20274655C2semidirect
430. C53#31279semidirect

Maximal subgroups

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

subgroupindex
#202798882
#202761522
#202761412
#202759082
#202758942
#202758562
#202758512
#202753532
#202753392
#202751542
#202751492
#202750132
#202746552
C53×#24072
#3127953