Finite Group Databasebeta

← #30617106

Subgroups — #30617106

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462592C211yesmaximal, characteristic, complemented
2#21462591C211yesmaximal, characteristic, complemented
3C2×#16840807C211yesmaximal, characteristic, complemented
4#21462389C211yesmaximal, characteristic, complemented
5#21461977C211yesmaximal, characteristic, complemented
6#21461939C211yesmaximal, characteristic, complemented
7#21461907C211yesmaximal, characteristic, complemented
8#21461906C211yesmaximal, characteristic, complemented
9#21461857C211yesmaximal, characteristic, complemented
10#21461856C211yesmaximal, characteristic, complemented
11#21461706C211yesmaximal, characteristic, complemented
12#21461628C211yesmaximal, characteristic, complemented
13#21461578C211yesmaximal, characteristic, complemented
14#21461576C211yesmaximal, characteristic, complemented
15#21455534C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic
17D61⋊#131C2211yescharacteristic
18C2×#14519864C2211yescharacteristic
19#41×#6923C2211yescharacteristic
20#16840809—21no—
21#16840808—21no—
22#16840807—21no—
23#16840807—21no—
24#16840807—21no—
25#16840807—21no—
26#16840807—21no—
27#16840807—21no—
28#16840806—21no—
29#16840805—21no—
30#16840805—21no—
31#16840804—21no—
32#16840777C2211yescharacteristic
33#16840777C2211yescharacteristic
34C2×#14519848C2211yescharacteristic
35#16840772C2211yescharacteristic
36#16840761C2211yescharacteristic
37#16840760C2211yescharacteristic
38#16840759C2211yescharacteristic
39#16840759C2211yescharacteristic
40C2×#14519842C2211yescharacteristic
41C2×#14519841C2211yescharacteristic
42#16840743C2211yescharacteristic
43#16840742C2211yescharacteristic
44#16840728—21no—
45#16840728C2211yescharacteristic
46#16840728C2211yescharacteristic
47#16840728C2211yescharacteristic
48#16840725—21no—
49#16840725C2211yescharacteristic
50M16×#6923—21no—
51M16×#6923C2211yescharacteristic
52C2×#14519831—21no—
53C2×#14519831C2211yescharacteristic
54#16840645C2211yescharacteristic
55#16840645C2211yescharacteristic
56#16840645C2211yescharacteristic
57#16840645C2211yescharacteristic
58#16840634C2211yescharacteristic
59#16840634C2211yescharacteristic
60#16840561C2211yescharacteristic
61#16840558C2211yescharacteristic
62C2×#14519798C2211yescharacteristic
63#131×D61C2211yescharacteristic
64#16840036C411yescharacteristic, complemented
65#16840035C411yescharacteristic, complemented
66#16840031C411yescharacteristic, complemented
67#16840030C411yescharacteristic, complemented
68#16840026C411yescharacteristic, complemented
69#16840025C411yescharacteristic, complemented
70#16840022C411yescharacteristic, complemented
71#108×D61C2211yescharacteristic
72#16839745C2211yescharacteristic
73#16839743C2211yescharacteristic
74C61×#471C411yescharacteristic, complemented
75#14519865—21no—
76#14519865—21no—
77#14519865—21no—
78#14519865—21no—
79#14519865D411yescharacteristic
80#14519865D411yescharacteristic
81#14519864—21no—
82#14519864—21no—
83#14519864—21no—
84#14519864—21no—
85#14519864—21no—
86#14519864—21no—
87#14519864D411yescharacteristic
88#14519864D411yescharacteristic
89C2×#11758213—21no—
90C2×#11758213C2311yescharacteristic
91C2×#11758213C2311yescharacteristic
92D61⋊M16—21no—
93D61⋊M16C2311yescharacteristic
94C2×#11758217—21no—
95C2×D61⋊C8—21no—
96C2×D61⋊C8—21no—
97C2×D61⋊C8C2311yescharacteristic
98C22×#92420—21no—
99Q8×#6923—21no—
100D4×#6923—21no—
101D4×#6923—22no—
102#14519856—21no—
103#14519856C2311yescharacteristic
104#14519856C2311yescharacteristic
105#14519856C2311yescharacteristic
106C2×C4×#6923—21no—
107C2×C4×#6923C2311yescharacteristic
108#14519848—21no—
109#14519848—21no—
110#14519848—21no—
111#14519848—21no—
112#14519847—21no—
113#14519847—21no—
114#14519846—21no—
115#14519845—21no—
116#14519842—21no—
117#14519842—21no—
118#14519842—21no—
119#14519842—21no—
120#14519842—21no—
121#14519842—21no—
122#14519841—21no—
123#14519841—21no—
124#14519841—21no—
125#14519841—21no—
126#14519841—21no—
127#14519841—21no—
128#14519836—22no—
129#14519835—22no—
130#14519831—21no—
131#14519831—21no—
132#14519831—21no—
133#14519831—21no—
134#14519831—21no—
135#14519831D411yescharacteristic
136#14519831D411yescharacteristic
137#14519831D411yescharacteristic
138#14519831D411yescharacteristic
139C8×#6923—21no—
140C8×#6923—21no—
141C8×#6923—21no—
142C8×#6923—21no—
143C8×#6923—21no—
144C2×#11758226C2311yescharacteristic
145C2×#11758224C2311yescharacteristic
146#41×D61C2311yescharacteristic
147#14519810C2×C411yescharacteristic
148#14519809—21no—
149#14519808C2×C411yescharacteristic
150#14519807C2×C411yescharacteristic
151#14519806—21no—
152#14519805C2×C411yescharacteristic
153#14519804—21no—
154#14519803C2×C411yescharacteristic
155#14519802C2×C411yescharacteristic
156#14519801—21no—
157#14519800—21no—
158#14519798—21no—
159#14519798—21no—
160#14519798—21no—
161#14519798—21no—
162#14519798—21no—
163#14519798—21no—
164#14519796—21no—
165C2×#11758202C2×C411yescharacteristic, complemented
166C2×#11758190C2×C411yescharacteristic, complemented
167C2×#11758199C2×C411yescharacteristic, complemented
168#14519785—21no—
169#14519785C2×C411yescharacteristic
170#14519784C2×C411yescharacteristic
171#14519783—21no—
172#14519783C2×C411yescharacteristic
173M16×D61—21no—
174M16×D61C2311yescharacteristic
175M16×D61C2311yescharacteristic
176M16×D61C2311yescharacteristic
177C2×C8×D61—21no—
178C2×C8×D61C2311yescharacteristic
179#14519713C2×C411yescharacteristic, complemented
180#14519712C2×C411yescharacteristic, complemented
181#14519712C2×C411yescharacteristic, complemented
182#14519696C2×C411yescharacteristic, complemented
183#14519695C2×C411yescharacteristic, complemented
184#14519695C2×C411yescharacteristic, complemented
185#14519694C2×C411yescharacteristic, complemented
186#14519693C2×C411yescharacteristic, complemented
187#14519693C2×C411yescharacteristic, complemented
188#137×C61C2×C411yescharacteristic
189AGL(1,ℤ/8)×C61C2×C411yescharacteristic
190C2×SD16×C61C2×C411yescharacteristic, complemented
191#131×C61C2×C411yescharacteristic
192#108×C61C2×C411yescharacteristic, complemented
193#101×C61C2×C411yescharacteristic, complemented
194#100×C61C2×C411yescharacteristic, complemented
195C22×#6923—22no—
196C22×#6923—21no—
197#41×C61C22×C411yescharacteristic
198C2×Q8×C61C22×C411yescharacteristic
199C2×D4×C61C22×C411yescharacteristic
200C2×C22⋊D61—21no—
201C22×Dic61—21no—
202#11758226—21no—
203#11758226—21no—
204#11758226—21no—
205#11758226—21no—
206#11758226C2×D411yescharacteristic
207Q8×D61#4111yescharacteristic
208#11758224—21no—
209#11758224—21no—
210#11758224—21no—
211#11758224—21no—
212#11758224—21no—
213#11758224C2×D411yescharacteristic
214D4×D61—21no—
215D4×D61#4111yescharacteristic
216#11758222—21no—
217#11758222C22×C411yescharacteristic
218C2×D244—21no—
219C2×D244C22×C411yescharacteristic
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61C2411yescharacteristic
223C2×Dic122C22×C411yescharacteristic
224C22⋊#6923—22no—
225C22⋊#6923—21no—
226C22⋊#6923—21no—
227C22⋊#6923#4112yes—
228#11758217—21no—
229#11758217—21no—
230#11758217—21no—
231#11758217—41no—
232#11758217—41no—
233C2×#92420—21no—
234C2×#92420—21no—
235C2×#92420—21no—
236C2×#92420—21no—
237C2×#92420—41no—
238C2×#92420—41no—
239C2×#92420#4111yescharacteristic
240C2×#92420#4111yescharacteristic
241C4⋊#6923—22no—
242C4⋊#6923—21no—
243C4⋊#6923—21no—
244C4⋊#6923—21no—
245C4×#6923—22no—
246C4×#6923—21no—
247C4×#6923—21no—
248C4×#6923—21no—
249C4×#6923—21no—
250C4×#6923C2×D411yescharacteristic
251C4×#6923C2×D411yescharacteristic
252#11758213—21no—
253#11758213—21no—
254#11758213—21no—
255#11758213—21no—
256#11758213—21no—
257#11758213—21no—
258#11758213—41no—
259#11758213—41no—
260#11758213C2×D411yescharacteristic
261#11758213C2×D411yescharacteristic
262D61⋊C8—21no—
263D61⋊C8—21no—
264D61⋊C8—21no—
265D61⋊C8—41no—
266D61⋊C8—41no—
267D61⋊C8C2×D411yescharacteristic
268D61⋊C8C2×D411yescharacteristic
269D61⋊C8C2×D411yescharacteristic
270D61⋊C8C2×D411yescharacteristic
271Q16×C61—21no—
272SD16×C61—21no—
273SD16×C61—21no—
274SD16×C61—21no—
275SD16×C61—21no—
276D8×C61—21no—
277M16×C61—21no—
278M16×C61C22×C411yescharacteristic
279M16×C61C22×C411yescharacteristic
280M16×C61C22×C411yescharacteristic
281C2×C8×C61—21no—
282C2×C8×C61C22×C411yescharacteristic
283#11758202—21no—
284#11758202—21no—
285#11758202—21no—
286#11758202—21no—
287#11758201—21no—
288#11758201—21no—
289#11758200—21no—
290#11758200—21no—
291#11758199—21no—
292#11758199—21no—
293#11758199—21no—
294#11758199—21no—
295#11758194—21no—
296#11758194C22×C411yescharacteristic
297#11758194C22×C411yescharacteristic
298#11758194C22×C411yescharacteristic
299C2×#92418—21no—
300C2×#92418C22×C411yescharacteristic
301Dic244—21no—
302D488—21no—
303#11758190—21no—
304#11758190—21no—
305#11758190—21no—
306#11758190—21no—
307#11758189—21no—
308#11758189—21no—
309#11758189—21no—
310#11758189—21no—
311#11758189—21no—
312C8×D61—21no—
313C8×D61—21no—
314C8×D61—21no—
315C8×D61—21no—
316C8×D61—21no—
317C8×D61C2×D411yescharacteristic
318C8×D61C2×D411yescharacteristic
319C8×D61#4111yescharacteristic
320C8×D61#4111yescharacteristic
321C23×C61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61C2×#4111yescharacteristic
325C2×#6923—21no—
326C2×#6923—22no—
327C2×#6923—21no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—81no—
331C2×#6923—82no—
332Q8×C61—21no—
333Q8×C61—21no—
334Q8×C61C4×D411yescharacteristic
335D4×C61—21no—
336D4×C61—21no—
337D4×C61—21no—
338D4×C61C4×D411yescharacteristic
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61C23×C411yescharacteristic
342C22⋊D61—21no—
343C22⋊D61—21no—
344C22⋊D61—21no—
345C22⋊D61—41no—
346C22⋊D61—41no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—41no—
350C2×Dic61—41no—
351C2×Dic61C2×#4111yescharacteristic
352D244—21no—
353D244—21no—
354D244—21no—
355D244—41no—
356D244—41no—
357D244C4×D411yescharacteristic
358C4×D61—21no—
359C4×D61—21no—
360C4×D61—21no—
361C4×D61—41no—
362C4×D61—41no—
363C4×D61C22×D411yescharacteristic
364C4×D61C22×D411yescharacteristic
365C4×D61C2×#4111yescharacteristic
366C4×D61C2×#4111yescharacteristic
367Dic122—21no—
368Dic122—21no—
369Dic122—21no—
370Dic122C4×D411yescharacteristic
371#92420—21no—
372#92420—21no—
373#92420—41no—
374#92420—41no—
375#92420#12111yescharacteristic
376#92420#12111yescharacteristic
377#92420#12111yescharacteristic
378#92420#12111yescharacteristic
379C8×C61—21no—
380C8×C61—21no—
381C8×C61—21no—
382C8×C61C4×D411yescharacteristic
383C8×C61C4×D411yescharacteristic
384#92418—21no—
385#92418—21no—
386#92418—21no—
387#92418C4×D411yescharacteristic
388#92418C4×D411yescharacteristic
389#21559—611nomaximal, Sylow
390C22×C61—21no—
391C22×C61—41no—
392C22×C61—81no—
393C22×C61C4×#4111yescharacteristic
394C2×D61—21no—
395C2×D61—41no—
396C2×D61—42no—
397C2×D61—41no—
398C2×D61—81no—
399C2×D61#52511yescharacteristic
400C2×D61#53211yescharacteristic
401#6923—42no—
402#6923—41no—
403#6923—41no—
404#6923—81no—
405#6923—81no—
406C4×C61—21no—
407C4×C61—41no—
408C4×C61C2×C4×D411yescharacteristic
409C4×C61C2×C4×D411yescharacteristic
410Dic61—21no—
411Dic61—41no—
412Dic61C2×#12111yescharacteristic
413Dic61#52911yescharacteristic
414#3067—611no—
415#2955—611no—
416#2955—611no—
417C2×#444—611no—
418#2875—611no—
419#1976—611no—
420#1953—611no—
421#1932—611no—
422#1932—611no—
423#1906—611no—
424#1906—611no—
425#1814—611no—
426#1773—611no—
427#1757—611no—
428#1757—611no—
429C2×C61—21no—
430C2×C61—41no—
431C2×C61—81no—
432C2×C61C4×#12111yescharacteristic
433D61—21no—
434D61—21no—
435D61—41no—
436D61—81no—
437#575—611no—
438#575—611no—
439C2×#135—611no—
440C2×#131—611no—
441C2×#131—611no—
442C2×#131—611no—
443C2×#131—611no—
444C4×#41—611no—
445#473—611no—
446#473—611no—
447#472—611no—
448#472—611no—
449#471—611no—
450#471—611no—
451#471—611no—
452#471#692311yescharacteristic, complemented
453#444—1221no—
454#444—1221no—
455#444—1221no—
456#444—1221no—
457#444—1221no—
458#444—1221no—
459#444—1221no—
460#444—1221no—
461#443—1221no—
462#443—1221no—
463#443—1221no—
464#443—1221no—
465#430—611no—
466#430—611no—
467C2×#108—611no—
468C2×#108—611no—
469#427—611no—
470#421—611no—
471#421—611no—
472#421—611no—
473#421—611no—
474C2×#104—611no—
475C2×#104—611no—
476#413—611no—
477#413—611no—
478#410—611no—
479#410—611no—
480#405—611no—
481#405—611no—
482#405—611no—
483#405—611no—
484#405—1221no—
485#405—1221no—
486C4×M16—611no—
487C4×M16—1221no—
488C2×#97—611no—
489C2×#97—1221no—
490#344—611no—
491#344—611no—
492#344—611no—
493#344—611no—
494#339—611no—
495#339—611no—
496C61#2155911yescharacteristic, complemented, Sylow
497C2×#41—611no—
498C2×#41—611no—
499C2×#41—611no—
500#137—611no—
501#137—611no—
502#137—611no—
503#137—1221no—
504#137—1221no—
505#137C2×#692311yescharacteristic
506AGL(1,ℤ/8)—611no—
507AGL(1,ℤ/8)—611no—
508AGL(1,ℤ/8)—611no—
509AGL(1,ℤ/8)—1221no—
510AGL(1,ℤ/8)—1221no—
511AGL(1,ℤ/8)C2×#692311yescharacteristic
512#135—1221no—
513#135—1221no—
514#135—1221no—
515#135—1221no—
516#135—1221no—
517#135—1221no—
518#135—1221no—
519#135—1221no—
520C2×Q16—611no—
521C2×SD16—611no—
522C2×SD16C2×#692311yescharacteristic, complemented
523C2×D8—611no—
524#131—611no—
525#131—611no—
526#131—611no—
527#131—611no—
528#131—611no—
529#131—611no—
530#131—611no—
531#131—1221no—
532#131—1221no—
533#131—1221no—
534#131—1221no—
535#131—1221no—
536#131—1221no—
537#131—1221no—
538#131—1221no—
539#131—1221no—
540#131—1221no—
541#131—1221no—
542#131—1221no—
543#131C2×#692311yescharacteristic
544C2×M16—611no—
545C2×M16—611no—
546C2×M16—611no—
547C2×M16—611no—
548C2×M16—611no—
549C2×M16—611no—
550C2×M16—1221no—
551C2×M16—1221no—
552C2×M16—1221no—
553C2×M16—1221no—
554C22×C8—611no—
555C22×C8—611no—
556C22×C8—1221no—
557C22×C8—1221no—
558C22×C8—1221no—
559C22×C8—1221no—
560C4×Q8—1221no—
561C4×D4—1222no—
562C4×D4—1221no—
563#117—611no—
564#117—611no—
565#117—611no—
566#117—1221no—
567C2×C42—611no—
568C2×C42—1221no—
569#108—611no—
570#108—611no—
571#108—611no—
572#108—1221no—
573#108—1221no—
574#108—1221no—
575#108—1221no—
576#108—1221no—
577#108—1221no—
578#108C2×#692311yescharacteristic, complemented
579#107—1221no—
580#106—1221no—
581#104—1221no—
582#104—1221no—
583#104—1221no—
584#104—1221no—
585#104—1221no—
586#104—1221no—
587#104—1221no—
588#104—1221no—
589#104—1221no—
590#104—1221no—
591#104—1221no—
592#104—1221no—
593#101—611no—
594#101—611no—
595#101—611no—
596#101C2×#692311yescharacteristic, complemented
597#100—611no—
598#100—611no—
599#100—611no—
600#100C2×#692311yescharacteristic, complemented
601#99—1222no—
602#99—1222no—
603#97—611no—
604#97—611no—
605#97—611no—
606#97—611no—
607#97—1221no—
608#97—1221no—
609#97—1221no—
610#97—1221no—
611#97—1221no—
612C4×C8—1221no—
613C4×C8—1221no—
614C4×C8—1221no—
615C4×C8—1221no—
616C4×C8—1221no—
617#41—611no—
618#41—611no—
619#41—611no—
620#41—1221no—
621#41—1221no—
622#41—1221no—
623#41—1221no—
624#41—1221no—
625#41—1221no—
626#41—1221no—
627#41—1221no—
628#41—1221no—
629#41—1221no—
630#41C22×#692311yescharacteristic
631C2×Q8—611no—
632C2×Q8—611no—
633C2×Q8C22×#692311yescharacteristic
634C2×D4—611no—
635C2×D4—611no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4C22×#692311yescharacteristic
640C22×C4—611no—
641C22×C4—1221no—
642C22×C4—1221no—
643C22×C4—1221no—
644C22×C4—1221no—
645C22×C4—1222no—
646Q16—21no—
647Q16—1221no—
648Q16—1221no—
649Q16—1221no—
650Q16—1221no—
651Q16—1221no—
652SD16—21no—
653SD16—21no—
654SD16—21no—
655SD16—21no—
656SD16—1221no—
657SD16—1221no—
658SD16—1221no—
659SD16—1221no—
660SD16—1221no—
661SD16—1221no—
662SD16—1221no—
663SD16—1221no—
664D8—21no—
665D8—1221no—
666D8—1221no—
667D8—1221no—
668D8—1221no—
669D8—1221no—
670M16—21no—
671M16—611no—
672M16—611no—
673M16—611no—
674M16—611no—
675M16—611no—
676M16—1221no—
677M16—1221no—
678M16—1221no—
679M16—1221no—
680M16—1221no—
681M16—1221no—
682M16—1221no—
683M16—1221no—
684M16—1221no—
685M16—1221no—
686M16—1221no—
687M16—1221no—
688M16—1221no—
689M16—1221no—
690M16—1221no—
691M16—2441no—
692M16—2441no—
693M16—2441no—
694M16—2441no—
695M16C22×#692311yescharacteristic
696M16C22×#692311yescharacteristic
697M16C22×#692311yescharacteristic
698C2×C8—21no—
699C2×C8—611no—
700C2×C8—611no—
701C2×C8—611no—
702C2×C8—611no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—611no—
706C2×C8—611no—
707C2×C8—611no—
708C2×C8—611no—
709C2×C8—611no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—2441no—
724C2×C8—2441no—
725C2×C8—2441no—
726C2×C8—2441no—
727C2×C8C22×#692311yescharacteristic
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1222no—
732C22⋊C4—612no—
733C22⋊C4—1222no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C42—611no—
737C42—611no—
738C42—1221no—
739C42—1221no—
740C42—1221no—
741C42—1221no—
742C42—1222no—
743C23—21no—
744C23—611no—
745C23—1221no—
746C23—1221no—
747Q8—21no—
748Q8—21no—
749Q8—611no—
750Q8—1221no—
751Q8—1221no—
752Q8—1221no—
753Q8D4×#692311yescharacteristic
754D4—21no—
755D4—21no—
756D4—21no—
757D4—611no—
758D4—1221no—
759D4—1221no—
760D4—1221no—
761D4—1221no—
762D4—1221no—
763D4—1221no—
764D4—2441no—
765D4—2441no—
766D4—2441no—
767D4—2441no—
768D4D4×#692311yescharacteristic
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1222no—
783C2×C4—1221no—
784C2×C4—4881no—
785C2×C4—4882no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4C23×#692311yescharacteristic
793C8—21no—
794C8—21no—
795C8—21no—
796C8—611no—
797C8—611no—
798C8—611no—
799C8—611no—
800C8—611no—
801C8—611no—
802C8—1221no—
803C8—1221no—
804C8—1221no—
805C8—1221no—
806C8—1221no—
807C8—2441no—
808C8—2441no—
809C8D4×#692311yescharacteristic
810C8D4×#692311yescharacteristic
811C22—21no—
812C22—41no—
813C22—81no—
814C22—611no—
815C22—611no—
816C22—1221no—
817C22—4881no—
818C22—2441no—
819C22—2442no—
820C22—2441no—
821C22#41×#692311yescharacteristic
822C4—21no—
823C4—41no—
824C4—611no—
825C4—611no—
826C4—1221no—
827C4—4881no—
828C4—4881no—
829C4—2441no—
830C4—2441no—
831C4—2442no—
832C4—2441no—
833C4C2×D4×#692311yescharacteristic
834C4C2×D4×#692311yescharacteristic
835C2—21no—
836C2—41no—
837C2—81no—
838C2—1221no—
839C2—1221no—
840C2—4881no—
841C2—2441no—
842C2#121×#692311yescharacteristic
subgroupG/H
centerC2#121×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#471C4
socleC2×C61C4×#121
prime radical#21455534C2
cosocleC2×C4×D61C24
hypercenter#471#6923
hypocenterC61#21559
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #21462592C2semidirect
2. #21462591C2semidirect
3. C2×#16840807C2semidirect
4. #21462389C2semidirect
5. #21461977C2semidirect
6. #21461939C2semidirect
7. #21461907C2semidirect
8. #21461906C2semidirect
9. #21461857C2semidirect
10. #21461856C2semidirect
11. #21461706C2semidirect
12. #21461628C2semidirect
13. #21461578C2semidirect
14. #21461576C2semidirect
64. #16840036C4semidirect
65. #16840035C4semidirect
66. #16840031C4semidirect
67. #16840030C4semidirect
68. #16840026C4semidirect
69. #16840025C4semidirect
70. #16840022C4semidirect
74. C61×#471C4semidirect
165. C2×#11758202C2×C4semidirect
166. C2×#11758190C2×C4semidirect
167. C2×#11758199C2×C4semidirect
179. #14519713C2×C4semidirect
180. #14519712C2×C4semidirect
181. #14519712C2×C4semidirect
182. #14519696C2×C4semidirect
183. #14519695C2×C4semidirect
184. #14519695C2×C4semidirect
185. #14519694C2×C4semidirect
186. #14519693C2×C4semidirect
187. #14519693C2×C4semidirect
190. C2×SD16×C61C2×C4semidirect
192. #108×C61C2×C4semidirect
193. #101×C61C2×C4semidirect
194. #100×C61C2×C4semidirect
452. #471#6923semidirect
496. C61#21559semidirect
522. C2×SD16C2×#6923semidirect
578. #108C2×#6923semidirect
596. #101C2×#6923semidirect
600. #100C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625922
#214625912
C2×#168408072
#214623892
#214619772
#214619392
#214619072
#214619062
#214618572
#214618562
#214617062
#214616282
#214615782
#214615762
#214555342
#2155961