Finite Group Databasebeta

← #30555925

Subgroups — #30555925

Order 15616.

2658 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840577C212yesmaximal, complemented
2#21459585C211yesmaximal, characteristic, complemented
3#21457405C214yesmaximal, complemented
4#21457400C214yesmaximal, complemented
5#21457390C214yesmaximal, complemented
6#21457385C214yesmaximal, complemented
7#21456264C211yesmaximal, characteristic, complemented
8#21455478C212yesmaximal, complemented
9#21455291C211yesmaximal, characteristic, complemented
10#21455287C211yesmaximal, characteristic, complemented
11#21455134C212yesmaximal, complemented
12#21455131C212yesmaximal, complemented
13C2×#16839867C211yesmaximal, characteristic, complemented
14#21454537C211yesmaximal, characteristic, complemented
15C61×#3497C211yesmaximal, characteristic, complemented
16C2×#14519824C2212yes—
17#16840577—216no—
18C2×#14519808C2212yes—
19C2×#14519808C2214yes—
20C2×#14519807C2212yes—
21C2×#14519807C2214yes—
22C2×#14519797C2212yes—
23C2×#14519797C2214yes—
24C2×#14519797C2212yes—
25C22×#11758202C2214yes—
26C22×#11758202C2211yescharacteristic
27C2×#14519784C2212yes—
28#16840433C2212yes—
29#16840432—21no—
30D4×Dic122C2212yes—
31#16840427—21no—
32#16840421C2214yes—
33#16840420—22no—
34#16840340C2212yes—
35#16840339—22no—
36#16840312C2211yescharacteristic
37#16840307—22no—
38C2×C4×Dic122C2211yescharacteristic
39#16840157C2212yes—
40#16840154C2212yes—
41#16840152C2212yes—
42#16840149C2212yes—
43#16840018C2214yes—
44#16840013C2214yes—
45#16839993C2214yes—
46#16839989C2214yes—
47#16839984C2214yes—
48#16839981C2214yes—
49#16839972C2212yes—
50#16839969C2212yes—
51#16839962C2212yes—
52#16839959C2212yes—
53#16839924C2214yes—
54#16839922C2214yes—
55#16839918C2214yes—
56#16839917C2214yes—
57#16839907C2214yes—
58#16839905C2214yes—
59#16839901C2214yes—
60#16839900C2214yes—
61#16839867C2214yes—
62#16839867C2214yes—
63#16839834C2214yes—
64#16839834C2214yes—
65C2×#14519708C2211yescharacteristic
66#16839786C2211yescharacteristic
67#16839763C2212yes—
68#16839761C2212yes—
69C2×#14519701C2211yescharacteristic
70C2×#14519700C2211yescharacteristic
71#16839729C2212yes—
72C2×#14519688C2211yescharacteristic
73C2×2−1+4×C61C2212yes—
74C61×#550—21no—
75C61×#550C2212yes—
76D4×Q8×C61—21no—
77D4×Q8×C61C2212yes—
78C61×#548—22no—
79C61×#548C2214yes—
80C61×#537—22no—
81C61×#537C2212yes—
82C61×#532—22no—
83C61×#532C2211yescharacteristic
84C61×#532C2211yescharacteristic
85C2×C4×Q8×C61C2211yescharacteristic
86#14519824—28no—
87#14519824—44no—
88C2×#11758222C2312yes—
89C2×#11758222C2314yes—
90C2×#11758224—24no—
91C2×#11758224—22no—
92C22×Dic122C2314yes—
93C22×Dic122C2311yescharacteristic
94C2×Q8×D61—22no—
95#14519808—28no—
96#14519808—216no—
97#14519807—28no—
98#14519807—216no—
99#14519797—216no—
100#14519797—28no—
101#14519797—44no—
102C2×#11758202—216no—
103C2×#11758202D418yescomplemented
104C2×#11758202C2314yes—
105C2×#11758202C2314yes—
106C2×#11758202C2312yes—
107C2×#11758202C2312yes—
108C2×#11758202C2314yes—
109C2×#11758200C2314yes—
110C2×#11758200C2312yes—
111C2×#11758200C2312yes—
112C2×#11758201C2314yes—
113C2×#11758201C2312yes—
114C2×#11758201C2312yes—
115C2×#11758199C2312yes—
116C2×#11758199C2312yes—
117#14519784—28no—
118C2×#11758194C2312yes—
119C2×#11758194C2314yes—
120C22×#92418C2311yescharacteristic
121C22×#92418C2314yes—
122C22×#92418C2311yescharacteristic
123#14519777C2311yescharacteristic
124#14519776—22no—
125#14519774C2311yescharacteristic
126#14519773—22no—
127#14519765C2312yes—
128#14519763—24no—
129#14519756C2314yes—
130#14519755—24no—
131#14519754—24no—
132#14519753—22no—
133#14519751—21no—
134#14519751—21no—
135#14519751C2314yes—
136#14519750—24no—
137#14519749—24no—
138#14519749—24no—
139#14519748—22no—
140C4×Dic122—21no—
141C4×Dic122—21no—
142C4×Dic122C2312yes—
143C4×Dic122C2312yes—
144C4×D244—21no—
145C4×D244—21no—
146D4×Dic61—22no—
147#14519739—22no—
148#14519737—24no—
149C2×C4⋊Dic61C2311yescharacteristic
150C2×#11758196—21no—
151C2×C4×Dic61—21no—
152#14519708C2314yes—
153C4⋊#92418C2312yes—
154C4⋊#92418C2312yes—
155#14519701C2314yes—
156#14519701C2314yes—
157#14519700C2314yes—
158#14519700C2314yes—
159#14519698C2314yes—
160#14519697C2314yes—
161C22⋊#92418C2314yes—
162C22⋊#92418C2314yes—
163#14519688C2312yes—
164#14519688C2312yes—
1652−1+4×C61—28no—
1662−1+4×C61—44no—
167C2×#41×C61—24no—
168C2×#41×C61—22no—
169C2×#41×C61C2312yes—
170C2×#41×C61C2314yes—
171C2×#41×C61C2312yes—
172C22×Q8×C61—22no—
173C22×Q8×C61C2314yes—
174C22×Q8×C61C2311yescharacteristic
175C4⋊Q8×C61—22no—
176C4⋊Q8×C61D411yescharacteristic
177C4⋊Q8×C61C2311yescharacteristic
178#127×C61—22no—
179#127×C61D411yescharacteristic
180#127×C61C2311yescharacteristic
181#124×C61—24no—
182#124×C61D412yes—
183#124×C61C2312yes—
184C22⋊Q8×C61—22no—
185C22⋊Q8×C61—24no—
186C22⋊Q8×C61—24no—
187C22⋊Q8×C61C2314yes—
188#121×C61—24no—
189#121×C61—24no—
190#121×C61—22no—
191#121×C61—21no—
192#121×C61—21no—
193#121×C61—24no—
194#121×C61D412yes—
195#121×C61D412yes—
196#121×C61C2314yes—
197C4×Q8×C61—21no—
198C4×Q8×C61—21no—
199C4×Q8×C61C2312yes—
200C4×Q8×C61C2312yes—
201C4×D4×C61—22no—
202C4×D4×C61—22no—
203C4×D4×C61—24no—
204C4×D4×C61—21no—
205C4×D4×C61—21no—
206C4×D4×C61C2312yes—
207C4×D4×C61C2312yes—
208C2×C4⋊C4×C61—21no—
209C2×C4⋊C4×C61C2311yescharacteristic
210C2×C42×C61—21no—
211C2×C42×C61C2311yescharacteristic
212#41×C61—24no—
213#41×C61—24no—
214#41×C61—28no—
215#41×C61—24no—
216#41×C61—24no—
217#41×C61—44no—
218#41×C61—416no—
219#41×C61—48no—
220C2×Q8×C61—21no—
221C2×Q8×C61—24no—
222C2×Q8×C61—22no—
223C2×Q8×C61—28no—
224C2×Q8×C61—44no—
225C2×Q8×C61—48no—
226C2×Q8×C61C2×D414yes—
227C2×Q8×C61C2×D412yes—
228C2×Q8×C61C2412yes—
229C2×Q8×C61C2412yes—
230C2×D4×C61—22no—
231C2×D4×C61—24no—
232C2×D4×C61—24no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61C2×D414yes—
236C2×D4×C61C2×D412yes—
237C2×D4×C61C2×D412yes—
238C2×D4×C61C2×D412yes—
239C2×D4×C61C2412yes—
240C22×C4×C61—21no—
241C22×C4×C61—24no—
242C22×C4×C61—21no—
243C22×C4×C61—24no—
244C22×C4×C61—22no—
245C22×C4×C61C2×D411yescharacteristic
246C22×C4×C61C2×D411yescharacteristic
247C22×C4×C61C2414yes—
248C22×C4×C61C2411yescharacteristic
249C2×C22⋊D61—22no—
250C2×C22⋊D61—24no—
251C2×C22⋊D61—24no—
252C22×Dic61—21no—
253C22×Dic61—24no—
254C22×Dic61—21no—
255Q8×D61—48no—
256#11758224—48no—
257#11758224—416no—
258#11758222—24no—
259#11758222—24no—
260#11758222—28no—
261#11758222—44no—
262C2×D244—21no—
263C2×D244—21no—
264C2×D244C2412yes—
265C2×C4×D61—24no—
266C2×C4×D61—22no—
267C2×Dic122—21no—
268C2×Dic122—22no—
269C2×Dic122—28no—
270C2×Dic122—24no—
271C2×Dic122—44no—
272C2×Dic122C2×D414yes—
273C2×Dic122C2412yes—
274C2×Dic122C2412yes—
275C4⋊C4×C61—22no—
276C4⋊C4×C61—22no—
277C4⋊C4×C61—21no—
278C4⋊C4×C61—21no—
279C4⋊C4×C61—21no—
280C4⋊C4×C61—24no—
281C4⋊C4×C61C2×D412yes—
282C4⋊C4×C61C2×D412yes—
283C4⋊C4×C61C2412yes—
284C22⋊C4×C61—24no—
285C22⋊C4×C61—22no—
286C22⋊C4×C61—22no—
287C22⋊C4×C61—24no—
288C22⋊C4×C61C2×D414yes—
289C22⋊C4×C61C2×D414yes—
290C42×C61—22no—
291C42×C61—22no—
292C42×C61C2×D411yescharacteristic
293C42×C61C2×D411yescharacteristic
294C42×C61C2411yescharacteristic
295C42×C61C2411yescharacteristic
296C22⋊Dic61—24no—
297#11758202—28no—
298#11758202—28no—
299#11758202—24no—
300#11758202—42no—
301#11758202C2×D4116yes—
302#11758201—28no—
303#11758201—24no—
304#11758201—42no—
305#11758200—28no—
306#11758200—24no—
307#11758200—42no—
308#11758199—24no—
309#11758199—42no—
310#11758198—22no—
311#11758198—24no—
312#11758198—22no—
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61—21no—
316C4⋊Dic61C2412yes—
317#11758196—22no—
318#11758196—22no—
319#11758196—24no—
320C4×Dic61—22no—
321C4×Dic61—22no—
322#11758194—24no—
323#11758194—28no—
324C2×#92418—22no—
325C2×#92418—28no—
326C2×#92418C2×D414yes—
327C2×#92418C2412yes—
328C2×#92418C2414yes—
329C2×#92418C2412yes—
330C23×C61—22no—
331C23×C61C22×D414yes—
332C23×C61C22×D411yescharacteristic
333C22×D61—22no—
334Q8×C61—24no—
335Q8×C61—24no—
336Q8×C61—22no—
337Q8×C61—22no—
338Q8×C61—22no—
339Q8×C61—48no—
340Q8×C61C22×D414yes—
341D4×C61—28no—
342D4×C61—24no—
343D4×C61—22no—
344D4×C61—22no—
345D4×C61—42no—
346D4×C61—42no—
347D4×C61—48no—
348D4×C61—42no—
349D4×C61—44no—
350D4×C61—81no—
351D4×C61—84no—
352C2×C4×C61—24no—
353C2×C4×C61—22no—
354C2×C4×C61—24no—
355C2×C4×C61—24no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—48no—
361C2×C4×C61—48no—
362C2×C4×C61—44no—
363C2×C4×C61—81no—
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61C22×D411yescharacteristic
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D414yes—
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D412yes—
371C2×C4×C61H(5,𝔽2)12yes—
372C2×C4×C61C2511yescharacteristic
373C22⋊D61—48no—
374C22⋊D61—44no—
375C22⋊D61—84no—
376C2×Dic61—24no—
377C2×Dic61—22no—
378C2×Dic61—22no—
379C2×Dic61—22no—
380C2×Dic61—48no—
381C2×Dic61—81no—
382D244—22no—
383D244—22no—
384D244—42no—
385D244—81no—
386C4×D61—48no—
387C4×D61—44no—
388Dic122—24no—
389Dic122—22no—
390Dic122—22no—
391Dic122—22no—
392Dic122—48no—
393Dic122C22×D414yes—
394#92418—24no—
395#92418—22no—
396#92418C22×D414yes—
397#61081—611nomaximal, Sylow
398C22×C61—21no—
399C22×C61—21no—
400C22×C61—24no—
401C22×C61—24no—
402C22×C61—24no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—42no—
406C22×C61D4212yes—
407C22×C61C23×D411yescharacteristic
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—42no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—24no—
416C4×C61—24no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61D4212yes—
420C4×C61C23×D411yescharacteristic
421C4×C61C2×H(5,𝔽2)11yescharacteristic
422Dic61—24no—
423Dic61—42no—
424Dic61—42no—
425C2×#578—612no—
426#3497—611no—
427#3497D6111yescharacteristic, complemented
428#3271—614no—
429#3271—614no—
430#3270—614no—
431#3270—614no—
432#3150—611no—
433#3060—612no—
434#3037—611no—
435#3037—611no—
436#3013—612no—
437#3013—612no—
438C2×#441—611no—
439#2932—611no—
440C2×C61—22no—
441C2×C61—44no—
442C2×C61—82no—
443C2×C61C2×D4211yescharacteristic
444C2×C61#358611yescharacteristic
445C2×C61#358611yescharacteristic
446D61—82no—
447C2×2−1+4—612no—
448C2×2−1+4C2×D6112yes—
449#578—12216no—
450C2×#137—612no—
451C2×#137—614no—
452C2×#137—612no—
453C2×#137—614no—
454C2×#135—612no—
455C2×#135—614no—
456C2×#135—612no—
457C22×Q16—611no—
458C22×Q16—614no—
459C2×#131—612no—
460#550—21no—
461#550—612no—
462#550—1221no—
463#550C2×D6112yes—
464D4×Q8—21no—
465D4×Q8—612no—
466D4×Q8—1221no—
467D4×Q8C2×D6112yes—
468#548—22no—
469#548—614no—
470#548—1222no—
471#548C2×D6114yes—
472#537—22no—
473#537—612no—
474#537—1222no—
475#537C2×D6112yes—
476#532—22no—
477#532—611no—
478#532—1222no—
479#532C2×D6111yescharacteristic
480#532C2×D6111yescharacteristic
481C2×C4×Q8—611no—
482C2×C4×Q8C2×D6111yescharacteristic
483#497—612no—
484#497—612no—
485#496—612no—
486#496—612no—
487#470—614no—
488#469—614no—
489#465—614no—
490#465—614no—
491#464—614no—
492#464—614no—
493#462—612no—
494#462—612no—
495#460—612no—
496#460—612no—
497#452—614no—
498#452—614no—
499#451—614no—
500#451—614no—
501#449—614no—
502#449—614no—
503#448—614no—
504#448—614no—
505#441—614no—
506#441—614no—
507#435—614no—
508#435—614no—
509C2×#106—611no—
510#423—611no—
511#417—612no—
512#417—612no—
513C2×#103—611no—
514C2×#103—611no—
515#408—612no—
516C2×#97—611no—
517C61#6108111yescharacteristic, complemented, Sylow
5182−1+4—28no—
5192−1+4—44no—
5202−1+4—1228no—
5212−1+4—2444no—
522C2×#41—24no—
523C2×#41—22no—
524C2×#41—612no—
525C2×#41—614no—
526C2×#41—1224no—
527C2×#41—1222no—
528C2×#41C22×D6112yes—
529C2×#41C22×D6114yes—
530C2×#41C22×D6112yes—
531C22×Q8—22no—
532C22×Q8—611no—
533C22×Q8—614no—
534C22×Q8—1222no—
535C22×Q8C22×D6114yes—
536C22×Q8C22×D6111yescharacteristic
537#137—12216no—
538#137—12216no—
539#137—1228no—
540#137—1228no—
541#135—1228no—
542#135—12216no—
543#135—2444no—
544C2×Q16—618no—
545C2×Q16—614no—
546C2×Q16—612no—
547C2×Q16—614no—
548C2×Q16—614no—
549C2×Q16—612no—
550C2×Q16—12216no—
551C2×SD16—614no—
552C2×SD16—612no—
553C2×SD16—614no—
554C2×SD16—612no—
555C2×SD16—612no—
556C2×SD16—612no—
557C2×D8—612no—
558C2×D8—612no—
559#131—1228no—
560C2×M16—612no—
561C2×M16—614no—
562C22×C8—611no—
563C22×C8—614no—
564C22×C8—611no—
565C4⋊Q8—22no—
566C4⋊Q8—611no—
567C4⋊Q8—1222no—
568C4⋊Q8C22⋊D6111yescharacteristic
569C4⋊Q8C22×D6111yescharacteristic
570#127—22no—
571#127—611no—
572#127—1222no—
573#127C22⋊D6111yescharacteristic
574#127C22×D6111yescharacteristic
575#124—24no—
576#124—612no—
577#124—1224no—
578#124C22⋊D6112yes—
579#124C22×D6112yes—
580C22⋊Q8—22no—
581C22⋊Q8—24no—
582C22⋊Q8—24no—
583C22⋊Q8—614no—
584C22⋊Q8—1222no—
585C22⋊Q8—1224no—
586C22⋊Q8—1224no—
587C22⋊Q8C22×D6114yes—
588#121—24no—
589#121—24no—
590#121—22no—
591#121—21no—
592#121—21no—
593#121—24no—
594#121—614no—
595#121—1224no—
596#121—1222no—
597#121—1224no—
598#121—1221no—
599#121—1221no—
600#121—1224no—
601#121C22⋊D6112yes—
602#121C22⋊D6112yes—
603#121C22×D6114yes—
604C4×Q8—21no—
605C4×Q8—21no—
606C4×Q8—612no—
607C4×Q8—612no—
608C4×Q8—1221no—
609C4×Q8—1221no—
610C4×Q8C22×D6112yes—
611C4×Q8C22×D6112yes—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—24no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—1222no—
618C4×D4—1222no—
619C4×D4—1224no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4C22×D6112yes—
623C4×D4C22×D6112yes—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4C22×D6111yescharacteristic
628C2×C42—21no—
629C2×C42—1221no—
630C2×C42C22×D6111yescharacteristic
631#106—614no—
632C4⋊C8—612no—
633C4⋊C8—612no—
634#103—614no—
635#103—614no—
636#103—614no—
637#103—614no—
638#102—614no—
639#102—614no—
640C22⋊C8—614no—
641C22⋊C8—614no—
642#97—612no—
643#97—612no—
644#41—24no—
645#41—24no—
646#41—28no—
647#41—24no—
648#41—24no—
649#41—44no—
650#41—416no—
651#41—48no—
652#41—1228no—
653#41—1224no—
654#41—1224no—
655#41—2444no—
656#41—24416no—
657#41—2448no—
658C2×Q8—21no—
659C2×Q8—24no—
660C2×Q8—22no—
661C2×Q8—28no—
662C2×Q8—44no—
663C2×Q8—48no—
664C2×Q8—614no—
665C2×Q8—612no—
666C2×Q8—612no—
667C2×Q8—1228no—
668C2×Q8—1221no—
669C2×Q8—1224no—
670C2×Q8—1222no—
671C2×Q8—2444no—
672C2×Q8—2448no—
673C2×Q8D4×D6114yes—
674C2×Q8C2×C22⋊D6112yes—
675C2×Q8C23×D6112yes—
676C2×Q8C23×D6112yes—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—612no—
683C2×D4—1224no—
684C2×D4—1222no—
685C2×D4—1224no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4C2×C22⋊D6114yes—
689C2×D4C2×C22⋊D6112yes—
690C2×D4C2×C22⋊D6112yes—
691C2×D4C2×C22⋊D6112yes—
692C2×D4C23×D6112yes—
693C22×C4—21no—
694C22×C4—24no—
695C22×C4—21no—
696C22×C4—24no—
697C22×C4—22no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1224no—
701C22×C4—1224no—
702C22×C4—1222no—
703C22×C4C2×C22⋊D6111yescharacteristic
704C22×C4C2×C22⋊D6111yescharacteristic
705C22×C4C23×D6114yes—
706C22×C4C23×D6111yescharacteristic
707Q16—6116no—
708Q16—1224no—
709Q16—1228no—
710Q16—1228no—
711Q16—2442no—
712SD16—1224no—
713SD16—1224no—
714SD16—1228no—
715SD16—1228no—
716SD16—2442no—
717SD16—2442no—
718D8—1224no—
719D8—2442no—
720M16—1228no—
721M16—1224no—
722C2×C8—614no—
723C2×C8—612no—
724C2×C8—612no—
725C2×C8—614no—
726C2×C8—1228no—
727C2×C8—1222no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—24no—
734C4⋊C4—612no—
735C4⋊C4—1221no—
736C4⋊C4—1222no—
737C4⋊C4—1222no—
738C4⋊C4—1224no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4C2×C22⋊D6112yes—
742C4⋊C4C2×C22⋊D6112yes—
743C4⋊C4C23×D6112yes—
744C22⋊C4—24no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—24no—
748C22⋊C4—1224no—
749C22⋊C4—1222no—
750C22⋊C4—1224no—
751C22⋊C4—1222no—
752C22⋊C4C2×C22⋊D6114yes—
753C22⋊C4C2×C22⋊D6114yes—
754C42—22no—
755C42—22no—
756C42—1222no—
757C42—1222no—
758C42C2×C22⋊D6111yescharacteristic
759C42C2×C22⋊D6111yescharacteristic
760C42C23×D6111yescharacteristic
761C42C23×D6111yescharacteristic
762C23—22no—
763C23—1222no—
764C23C22×C22⋊D6114yes—
765C23C22×C22⋊D6111yescharacteristic
766Q8—22no—
767Q8—24no—
768Q8—24no—
769Q8—22no—
770Q8—22no—
771Q8—48no—
772Q8—614no—
773Q8—1222no—
774Q8—1224no—
775Q8—1222no—
776Q8—1222no—
777Q8—2448no—
778Q8C2×D4×D6114yes—
779D4—28no—
780D4—22no—
781D4—22no—
782D4—24no—
783D4—42no—
784D4—42no—
785D4—48no—
786D4—42no—
787D4—44no—
788D4—81no—
789D4—84no—
790D4—1222no—
791D4—1222no—
792D4—4881no—
793D4—4884no—
794D4—2442no—
795D4—2448no—
796D4—2444no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—48no—
806C2×C4—48no—
807C2×C4—44no—
808C2×C4—81no—
809C2×C4—1222no—
810C2×C4—1224no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—4881no—
814C2×C4—2448no—
815C2×C4—2448no—
816C2×C4—2444no—
817C2×C4C2×D4×D6112yes—
818C2×C4C22×C22⋊D6111yescharacteristic
819C2×C4C22×C22⋊D6111yescharacteristic
820C2×C4C22×C22⋊D6111yescharacteristic
821C2×C4C22×C22⋊D6111yescharacteristic
822C2×C4C22×C22⋊D6114yes—
823C2×C4C22×C22⋊D6111yescharacteristic
824C2×C4#1451982212yes—
825C2×C4C24×D6111yescharacteristic
826C8—614no—
827C8—1224no—
828C8—1222no—
829C22—21no—
830C22—21no—
831C22—24no—
832C22—24no—
833C22—24no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—2442no—
838C22—2442no—
839C22—2442no—
840C22D4×C22⋊D6112yes—
841C22C23×C22⋊D6111yescharacteristic
842C4—24no—
843C4—24no—
844C4—21no—
845C4—21no—
846C4—21no—
847C4—21no—
848C4—42no—
849C4—42no—
850C4—1224no—
851C4—2442no—
852C4—2442no—
853C4D4×C22⋊D6112yes—
854C4C22×D4×D6111yescharacteristic
855C4C2×#1451982211yescharacteristic
856C2—22no—
857C2—44no—
858C2—82no—
859C2—4882no—
860C2C2×D4×C22⋊D6111yescharacteristic
861C2#2146060511yescharacteristic
862C2#2146060611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3497C2
socleC22×C61C23×D4
hypercenter#3497D61
hypocenterC61#61081
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ #532 ◁ #3497

Complements

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

NH ≅ G/Ntype
1. C2×#16840577C2semidirect
2. #21459585C2semidirect
3. #21457405C2semidirect
4. #21457400C2semidirect
5. #21457390C2semidirect
6. #21457385C2semidirect
7. #21456264C2semidirect
8. #21455478C2semidirect
9. #21455291C2semidirect
10. #21455287C2semidirect
11. #21455134C2semidirect
12. #21455131C2semidirect
13. C2×#16839867C2semidirect
14. #21454537C2semidirect
15. C61×#3497C2semidirect
103. C2×#11758202D4semidirect
427. #3497D61semidirect
517. C61#61081semidirect

Maximal subgroups

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

subgroupindex
C2×#168405772
#214595852
#214574052
#214574002
#214573902
#214573852
#214562642
#214554782
#214552912
#214552872
#214551342
#214551312
C2×#168398672
#214545372
C61×#34972
#6108161