Finite Group Databasebeta

← #29727330

Subgroups — #29727330

Order 15616.

1114 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840023C211yesmaximal, characteristic, complemented
2#21455451C211yesmaximal, characteristic, complemented
3C2×#16839913C211yesmaximal, characteristic, complemented
4#21454546C211yesmaximal, characteristic, complemented
5C22×#14519694C211yesmaximal, characteristic, complemented
6#21447179C211yesmaximal, characteristic, complemented
7#21447108C211yesmaximal, characteristic, complemented
8#21447081C211yesmaximal, characteristic, complemented
9#21446933C211yesmaximal, characteristic, complemented
10#21446725C211yesmaximal, characteristic, complemented
11#21446484C211yesmaximal, characteristic, complemented
12#21446329C211yesmaximal, characteristic, complemented
13#21446285C211yesmaximal, characteristic, complemented
14#21446023C211yesmaximal, characteristic, complemented
15C61×#3003C211yesmaximal, characteristic
16C2×#14519807C2211yescharacteristic, complemented
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C2×#14519784C2211yescharacteristic, complemented
20C22×#11758194C2211yescharacteristic
21C22×#11758194C2211yescharacteristic
22C2×#14519756C2211yescharacteristic
23#16840023—24no—
24#16840018—21no—
25#16840006—21no—
26#16840001—21no—
27#16839989—21no—
28#16839913—21no—
29#16839913—21no—
30#16839913—21no—
31#16839913—21no—
32#16839840—21no—
33#16839834—21no—
34#16839834—21no—
35D4×#92418—21no—
36C2×#14519712C2211yescharacteristic, complemented
37C2×#14519712C2211yescharacteristic, complemented
38#16839805C2211yescharacteristic, complemented
39#16839789C2211yescharacteristic, complemented
40#16839770C2211yescharacteristic, complemented
41#16839763C2211yescharacteristic, complemented
42C2×#14519698C2211yescharacteristic
43C2×#14519698C2211yescharacteristic
44C2×#14519695C2211yescharacteristic, complemented
45C2×#14519695C2211yescharacteristic, complemented
46C2×#14519694—24no—
47C2×#14519694C2211yescharacteristic
48C2×#14519694C2211yescharacteristic
49C2×#14519694C2211yescharacteristic
50C2×#14519694C2211yescharacteristic
51#16839729C2211yescharacteristic, complemented
52C2×C22⋊#92418C2211yescharacteristic
53#16839718C2211yescharacteristic, complemented
54#16839530C2211yescharacteristic, complemented
55#16839530C2211yescharacteristic, complemented
56#16839526C2211yescharacteristic, complemented
57#16839526C2211yescharacteristic, complemented
58C23×D4×C61C2211yescharacteristic
59C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
60C2×AGL(1,ℤ/8)×C61C2211yescharacteristic
61C61×#525C2211yescharacteristic
62C61×#450—21no—
63C61×#450—21no—
64C61×#447—21no—
65C61×#447—21no—
66C61×#418C2211yescharacteristic
67C61×#418C2211yescharacteristic
68C61×#407C2211yescharacteristic
69C22×Dic122C2311yescharacteristic
70#14519807—22no—
71#14519807—41no—
72C2×#11758202—21no—
73C2×#11758200—21no—
74C2×#11758200—22no—
75C2×#11758200—22no—
76C2×#11758200—21no—
77C2×#11758200—21no—
78C2×#11758200—21no—
79C2×#11758200—21no—
80C2×#11758200—41no—
81C2×#11758200—41no—
82#14519784—22no—
83#14519784—41no—
84C2×#11758194—21no—
85C2×#11758194—21no—
86C2×#11758194—21no—
87C2×#11758194—22no—
88C2×#11758194—22no—
89C2×#11758194—41no—
90C2×#11758194—41no—
91C2×#11758194C2311yescharacteristic
92C2×#11758194C2311yescharacteristic
93C2×#11758194C2311yescharacteristic
94C2×#11758194C2311yescharacteristic
95C22×#92418—21no—
96C22×#92418—21no—
97C22×#92418—21no—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100#14519756—21no—
101#14519756—21no—
102#14519756—21no—
103#14519756—21no—
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×C22⋊Dic61—21no—
107#14519712—22no—
108#14519712—41no—
109#14519710—21no—
110#14519708—21no—
111C4⋊#92418—21no—
112C4⋊#92418—21no—
113#14519701—21no—
114#14519700—21no—
115#14519700—21no—
116#14519698—21no—
117#14519698—21no—
118#14519698—21no—
119#14519698—21no—
120#14519698—21no—
121#14519695—22no—
122#14519695—41no—
123#14519694—22no—
124#14519694—22no—
125#14519694—22no—
126#14519694D414yescomplemented
127C22⋊#92418—21no—
128C22⋊#92418—21no—
129C22⋊#92418D411yescharacteristic
130C22⋊#92418D411yescharacteristic
131C22⋊#92418D411yescharacteristic
132C22⋊#92418D411yescharacteristic
133#14519688—21no—
134C4×#92418—21no—
135C25×C61—21no—
136C2×#41×C61C2311yescharacteristic
137C22×D4×C61—22no—
138C22×D4×C61—22no—
139C22×D4×C61—21no—
140C22×D4×C61—21no—
141C22×D4×C61—21no—
142C22×D4×C61—21no—
143C22×D4×C61—21no—
144C22×D4×C61—41no—
145C22×D4×C61—41no—
146C22×D4×C61C2311yescharacteristic
147C22×D4×C61C2311yescharacteristic
148C23×C4×C61C2311yescharacteristic
149AGL(1,ℤ/8)×C61—22no—
150AGL(1,ℤ/8)×C61—22no—
151AGL(1,ℤ/8)×C61—41no—
152AGL(1,ℤ/8)×C61—41no—
153C2×SD16×C61—21no—
154C2×SD16×C61—21no—
155C2×D8×C61—21no—
156C2×D8×C61—21no—
157C2×M16×C61C2311yescharacteristic
158C2×M16×C61C2311yescharacteristic
159#123×C61—21no—
160C22⋊Q8×C61D411yescharacteristic
161C22⋊Q8×C61D411yescharacteristic
162#121×C61D411yescharacteristic
163#121×C61D411yescharacteristic
164#120×C61—21no—
165C4×D4×C61—21no—
166C4×D4×C61—21no—
167#117×C61C2311yescharacteristic
168#102×C61—21no—
169#102×C61—21no—
170#102×C61—21no—
171#102×C61—21no—
172C22⋊C8×C61—21no—
173C22⋊C8×C61—21no—
174C24×C61—24no—
175C24×C61—21no—
176C24×C61—21no—
177C24×C61—42no—
178C24×C61—41no—
179C24×C61—41no—
180C24×C61—82no—
181C24×C61—82no—
182C24×C61#4111yescharacteristic
183#41×C61—21no—
184#41×C61—21no—
185#41×C61—21no—
186#41×C61—21no—
187C2×Q8×C61C2×D411yescharacteristic
188C2×D4×C61—24no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—21no—
201C2×D4×C61—21no—
202C2×D4×C61—42no—
203C2×D4×C61—42no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
209C2×D4×C61—42no—
210C2×D4×C61—42no—
211C2×D4×C61—41no—
212C2×D4×C61—41no—
213C2×D4×C61C2×D412yes—
214C2×D4×C61C2×D411yescharacteristic
215C2×D4×C61#4112yes—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61#4111yescharacteristic
226C22×C4×C61C2411yescharacteristic
227C22×Dic61—21no—
228C22×Dic61—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235SD16×C61—42no—
236SD16×C61—42no—
237D8×C61—42no—
238D8×C61—42no—
239M16×C61—21no—
240M16×C61—21no—
241M16×C61—21no—
242M16×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61C2×D411yescharacteristic
248C4⋊C4×C61C2×D411yescharacteristic
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C22⋊C4×C61—21no—
254C42×C61—21no—
255C22⋊Dic61—41no—
256C22⋊Dic61—41no—
257#11758202—42no—
258#11758200—42no—
259#11758200—42no—
260#11758200—42no—
261#11758200—42no—
262#11758200—42no—
263C4⋊Dic61—21no—
264C4⋊Dic61—21no—
265#11758196—41no—
266#11758196—41no—
267#11758194—21no—
268#11758194—21no—
269#11758194—21no—
270#11758194—21no—
271#11758194—21no—
272#11758194—21no—
273#11758194—42no—
274#11758194—42no—
275#11758194—42no—
276#11758194C2×D412yes—
277#11758194C2×D412yes—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—42no—
287C2×#92418—42no—
288C2×#92418—42no—
289C2×#92418C2×D411yescharacteristic
290C2×#92418C2×D411yescharacteristic
291C2×#92418C2×D411yescharacteristic
292C2×#92418C2×D411yescharacteristic
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—22no—
296C23×C61—21no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—41no—
300C23×C61—44no—
301C23×C61—44no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—82no—
307C23×C61—82no—
308C23×C61—82no—
309C23×C61—81no—
310C23×C61—81no—
311C23×C61—81no—
312C23×C61—81no—
313C23×C61—88no—
314C23×C61—88no—
315C23×C61—82no—
316C23×C61#12111yescharacteristic
317C23×C61#12111yescharacteristic
318C23×C61C2×#4111yescharacteristic
319Q8×C61—21no—
320Q8×C61—21no—
321D4×C61—21no—
322D4×C61—22no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—21no—
326D4×C61—22no—
327D4×C61—44no—
328D4×C61—44no—
329D4×C61—41no—
330D4×C61—41no—
331D4×C61—42no—
332D4×C61—41no—
333D4×C61—41no—
334D4×C61—41no—
335D4×C61—41no—
336D4×C61—81no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61#12111yescharacteristic
353C2×C4×C61#12111yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C2×#4111yescharacteristic
358C2×C4×C61H(5,𝔽2)11yescharacteristic
359C2×C4×C61H(5,𝔽2)11yescharacteristic
360C2×Dic61—41no—
361C2×Dic61—41no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—81no—
365Dic122—41no—
366Dic122—41no—
367Dic122—41no—
368Dic122—41no—
369C8×C61—41no—
370C8×C61—41no—
371#92418—21no—
372#92418—21no—
373#92418—22no—
374#92418—22no—
375#92418—21no—
376#92418—21no—
377#92418—41no—
378#92418—41no—
379#25144—611nomaximal, Sylow
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—42no—
388C22×C61—42no—
389C22×C61—41no—
390C22×C61—42no—
391C22×C61—42no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—82no—
395C22×C61—82no—
396C22×C61—88no—
397C22×C61—82no—
398C22×C61—82no—
399C22×C61—88no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61#47112yescomplemented
405C22×C61C2×#12111yescharacteristic
406C22×C61#52511yescharacteristic
407C22×C61#53811yescharacteristic
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61D4211yescharacteristic
414C4×C61D4211yescharacteristic
415C4×C61#54611yescharacteristic
416C4×C61#54611yescharacteristic
417Dic61—81no—
418Dic61—81no—
419C2×#471—611no—
420#3056—611no—
421#3003D6111yescharacteristic
422C2×#450—611no—
423#2933—611no—
424C22×#100—611no—
425#2063—611no—
426#2051—611no—
427#2046—611no—
428#2019—611no—
429#1977—611no—
430#1931—611no—
431#1907—611no—
432#1901—611no—
433#1855—611no—
434C2×C61—21no—
435C2×C61—21no—
436C2×C61—22no—
437C2×C61—41no—
438C2×C61—81no—
439C2×C61—82no—
440C2×C61—82no—
441C2×C61#242411yescharacteristic
442C2×C61C2×#47111yescharacteristic
443C2×C61#306811yescharacteristic
444C23×D4C2×D6111yescharacteristic
445C2×#137—611no—
446C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
447C2×AGL(1,ℤ/8)C2×D6111yescharacteristic
448C22×SD16—611no—
449C22×SD16—611no—
450C2×#131—611no—
451C22×M16—611no—
452C22×M16—611no—
453#525C2×D6111yescharacteristic
454C2×C22⋊Q8—611no—
455#471—1224no—
456#470—1221no—
457#468—1221no—
458#467—1221no—
459#465—1221no—
460#450—21no—
461#450—21no—
462#450—1221no—
463#450—1221no—
464#450—1221no—
465#450—1221no—
466#447—21no—
467#447—21no—
468#436—1221no—
469#435—1221no—
470#435—1221no—
471C8×D4—1221no—
472C2×#108—611no—
473C2×#108—611no—
474#428—611no—
475#424—611no—
476#419—611no—
477#418C2×D6111yescharacteristic
478#418C2×D6111yescharacteristic
479#417—611no—
480C2×#102—611no—
481C2×#102—611no—
482C2×#101—611no—
483C2×#101—611no—
484C2×#100—611no—
485C2×#100—611no—
486C2×#100—611no—
487C2×#100—611no—
488C2×#100—1224no—
489#408—611no—
490#407C2×D6111yescharacteristic
491C2×C22⋊C8—611no—
492#405—611no—
493#343—611no—
494#343—611no—
495#341—611no—
496#341—611no—
497C61#2514411yescharacteristic, complemented, Sylow
498C25—21no—
499C2×#41C22×D6111yescharacteristic
500C22×Q8—611no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C22×D6111yescharacteristic
511C22×D4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513#137—1222no—
514#137—2441no—
515AGL(1,ℤ/8)—22no—
516AGL(1,ℤ/8)—22no—
517AGL(1,ℤ/8)—41no—
518AGL(1,ℤ/8)—41no—
519C2×Q16—1221no—
520C2×SD16—21no—
521C2×SD16—21no—
522C2×SD16—1221no—
523C2×SD16—1221no—
524C2×SD16—1221no—
525C2×SD16—1221no—
526C2×SD16—1222no—
527C2×SD16—1222no—
528C2×SD16—1221no—
529C2×SD16—2441no—
530C2×SD16—2441no—
531C2×D8—21no—
532C2×D8—21no—
533#131—1222no—
534#131—2441no—
535C2×M16—611no—
536C2×M16—611no—
537C2×M16—611no—
538C2×M16—611no—
539C2×M16—1221no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1222no—
543C2×M16—1222no—
544C2×M16—2441no—
545C2×M16—2441no—
546C2×M16C22×D6111yescharacteristic
547C2×M16C22×D6111yescharacteristic
548C22×C8—611no—
549C22×C8—611no—
550C22×C8—1221no—
551C22×C8—1221no—
552C22×C8—1221no—
553#123—21no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8C22⋊D6111yescharacteristic
559C22⋊Q8C22⋊D6111yescharacteristic
560#121C22⋊D6111yescharacteristic
561#121C22⋊D6111yescharacteristic
562#120—21no—
563C4×D4—21no—
564C4×D4—21no—
565#117C22×D6111yescharacteristic
566C2×C4⋊C4—611no—
567C2×C4⋊C4—1221no—
568C2×C22⋊C4—1221no—
569#108—1222no—
570#108—2441no—
571#107—1221no—
572#106—1221no—
573C4⋊C8—1221no—
574C4⋊C8—1221no—
575#103—1221no—
576#103—1221no—
577#103—1221no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102—1221no—
583#102—1221no—
584#102—1221no—
585#102—1221no—
586#102—1221no—
587#101—1222no—
588#101—2441no—
589#100—614no—
590#100—1222no—
591#100—1222no—
592#100—1222no—
593C22⋊C8—21no—
594C22⋊C8—21no—
595C22⋊C8—611no—
596C22⋊C8—611no—
597C22⋊C8—611no—
598C22⋊C8—611no—
599C22⋊C8—1221no—
600C22⋊C8—1221no—
601#97—1221no—
602C4×C8—1221no—
603C24—24no—
604C24—21no—
605C24—21no—
606C24—42no—
607C24—41no—
608C24—41no—
609C24—82no—
610C24—82no—
611C24#1175822411yescharacteristic
612#41—21no—
613#41—21no—
614#41—21no—
615#41—21no—
616C2×Q8—1221no—
617C2×Q8—1221no—
618C2×Q8—1221no—
619C2×Q8—1221no—
620C2×Q8—1221no—
621C2×Q8—1221no—
622C2×Q8C2×C22⋊D6111yescharacteristic
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—41no—
647C2×D4—41no—
648C2×D4D4×D6112yes—
649C2×D4#1175822412yes—
650C2×D4C2×C22⋊D6111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4D4×D6111yescharacteristic
659C22×C4D4×D6111yescharacteristic
660C22×C4#1175822411yescharacteristic
661C22×C4C2×C22⋊D6111yescharacteristic
662C22×C4C2×C22⋊D6111yescharacteristic
663C22×C4C23×D6111yescharacteristic
664Q16—2442no—
665SD16—42no—
666SD16—42no—
667SD16—2442no—
668SD16—2442no—
669SD16—2442no—
670SD16—2442no—
671SD16—2442no—
672D8—42no—
673D8—42no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—612no—
679M16—612no—
680M16—1221no—
681M16—1221no—
682M16—1221no—
683M16—1221no—
684M16—1221no—
685M16—1221no—
686M16—2442no—
687M16—2442no—
688M16—2442no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—611no—
692C2×C8—611no—
693C2×C8—611no—
694C2×C8—611no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—1221no—
701C2×C8—1221no—
702C2×C8—1221no—
703C2×C8—2442no—
704C2×C8—2442no—
705C2×C8—2442no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—2441no—
711C4⋊C4—2441no—
712C4⋊C4C2×C22⋊D6111yescharacteristic
713C4⋊C4C2×C22⋊D6111yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—2441no—
720C22⋊C4—2441no—
721C42—21no—
722C23—21no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—41no—
729C23—44no—
730C23—44no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—81no—
736C23—81no—
737C23—81no—
738C23—81no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—88no—
743C23—88no—
744C23—82no—
745C23#1451974911yescharacteristic
746C23#1451974911yescharacteristic
747C23C2×#1175822411yescharacteristic
748Q8—21no—
749Q8—21no—
750Q8—2441no—
751Q8—2441no—
752Q8—2441no—
753Q8—2441no—
754D4—22no—
755D4—21no—
756D4—22no—
757D4—22no—
758D4—21no—
759D4—22no—
760D4—44no—
761D4—44no—
762D4—41no—
763D4—42no—
764D4—41no—
765D4—41no—
766D4—41no—
767D4—41no—
768D4—41no—
769D4—81no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—4881no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4#1451974911yescharacteristic
791C2×C4#1451974911yescharacteristic
792C2×C4C2×D4×D6111yescharacteristic
793C2×C4C2×D4×D6111yescharacteristic
794C2×C4C22×C22⋊D6111yescharacteristic
795C2×C4C2×#1175822411yescharacteristic
796C2×C4#1451982211yescharacteristic
797C2×C4#1451982211yescharacteristic
798C8—41no—
799C8—41no—
800C8—1221no—
801C8—1221no—
802C8—1222no—
803C8—1222no—
804C8—1221no—
805C8—1221no—
806C8—2441no—
807C8—2441no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—42no—
816C22—42no—
817C22—41no—
818C22—42no—
819C22—42no—
820C22—41no—
821C22—41no—
822C22—82no—
823C22—82no—
824C22—88no—
825C22—82no—
826C22—82no—
827C22—88no—
828C22—81no—
829C22—81no—
830C22—81no—
831C22—81no—
832C22#1684002312yescomplemented
833C22C2×#1451974911yescharacteristic
834C22#1684026811yescharacteristic
835C22#1684034711yescharacteristic
836C4—21no—
837C4—21no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—4881no—
842C4—4881no—
843C4#1684039411yescharacteristic
844C4D4×C22⋊D6111yescharacteristic
845C4#1684039911yescharacteristic
846C4#1684040611yescharacteristic
847C2—21no—
848C2—22no—
849C2—21no—
850C2—41no—
851C2—81no—
852C2—82no—
853C2—82no—
854C2#2144935911yescharacteristic
855C2C2×#1684002311yescharacteristic
856C2#2145554411yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3003C2
socleC22×C61C2×#121
hypercenter#3003D61
hypocenterC61#25144
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3003

Complements

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

NH ≅ G/Ntype
1. C2×#16840023C2semidirect
2. #21455451C2semidirect
3. C2×#16839913C2semidirect
4. #21454546C2semidirect
5. C22×#14519694C2semidirect
6. #21447179C2semidirect
7. #21447108C2semidirect
8. #21447081C2semidirect
9. #21446933C2semidirect
10. #21446725C2semidirect
11. #21446484C2semidirect
12. #21446329C2semidirect
13. #21446285C2semidirect
14. #21446023C2semidirect
16. C2×#14519807C22semidirect
19. C2×#14519784C22semidirect
36. C2×#14519712C22semidirect
37. C2×#14519712C22semidirect
38. #16839805C22semidirect
39. #16839789C22semidirect
40. #16839770C22semidirect
41. #16839763C22semidirect
44. C2×#14519695C22semidirect
45. C2×#14519695C22semidirect
51. #16839729C22semidirect
53. #16839718C22semidirect
54. #16839530C22semidirect
55. #16839530C22semidirect
56. #16839526C22semidirect
57. #16839526C22semidirect
126. #14519694D4semidirect
404. C22×C61#471semidirect
497. C61#25144semidirect
832. C22#16840023semidirect

Maximal subgroups

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

subgroupindex
C2×#168400232
#214554512
C2×#168399132
#214545462
C22×#145196942
#214471792
#214471082
#214470812
#214469332
#214467252
#214464842
#214463292
#214462852
#214460232
C61×#30032
#2514461