Finite Group Databasebeta

← #11886621

Subgroups — #11886621

Order 1152.

1000 conjugacy classes of subgroups.

The subgroup lattice has 985 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5762C211yesmaximal, characteristic, complemented
2#10595319C211yesmaximal, characteristic, complemented
3#10595097C211yesmaximal, characteristic, complemented
4#10594680C211yesmaximal, characteristic, complemented
5#10592875C211yesmaximal, characteristic, complemented
6C3×#5177C211yesmaximal, characteristic, complemented
7#10591658C211yesmaximal, characteristic, complemented
8#10591646C211yesmaximal, characteristic, complemented
9#10591643C211yesmaximal, characteristic, complemented
10#10591522C211yesmaximal, characteristic, complemented
11#10591510C211yesmaximal, characteristic, complemented
12#10591508C211yesmaximal, characteristic, complemented
13#10590927C211yesmaximal, characteristic, complemented
14#10590922C211yesmaximal, characteristic, complemented
15#10590920C211yesmaximal, characteristic, complemented
16#84015—31nomaximal
17#80932—31nomaximal
18C3×#1007C2211yescharacteristic, complemented
19C3×#1004C2211yescharacteristic, complemented
20#64308C2211yescharacteristic
21#64308C2211yescharacteristic, complemented
22C2×C32×SD16C2211yescharacteristic, complemented
23#64156C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25#64149C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic, complemented
27C2×#3745C2211yescharacteristic, complemented
28C3×#942C2211yescharacteristic, complemented
29C3×#942C2211yescharacteristic, complemented
30C3×#932C2211yescharacteristic
31C3×#932C2211yescharacteristic, complemented
32C3×#916—21no—
33C3×#915—21no—
34C3×#914—21no—
35C3×D3×SD16—21no—
36C3×#904C2211yescharacteristic
37C3×#901C2211yescharacteristic, complemented
38C3×#901C2211yescharacteristic, complemented
39#63949—21no—
40#63948—21no—
41#63939—21no—
42D3×#215—21no—
43#63935—21no—
44#63934—21no—
45#63925—21no—
46D3×#213—21no—
47#63825C2211yescharacteristic
48#63825C2211yescharacteristic, complemented
49#63825C2211yescharacteristic, complemented
50#63825C2211yescharacteristic, complemented
51#63822C2211yescharacteristic
52#63815C2211yescharacteristic, complemented
53#63815C2211yescharacteristic, complemented
54#63808—21no—
55#63794—21no—
56#63794—21no—
57D3×D24—21no—
58#63642C2211yescharacteristic, complemented
59C3×#836C2211yescharacteristic, complemented
60C3×#833C2211yescharacteristic, complemented
61C3×#819C2211yescharacteristic, complemented
62#63578C2211yescharacteristic, complemented
63#63568C2211yescharacteristic, complemented
64#63568C2211yescharacteristic, complemented
65#63568C2211yescharacteristic, complemented
66#63568C2211yescharacteristic, complemented
67#63559C2211yescharacteristic, complemented
68#63559C2211yescharacteristic, complemented
69C3×#577—31no—
70#5837—31no—
71#5835—31no—
72#5778—31no—
73#5774—31no—
74#5769—31no—
75#5762D311yescharacteristic, complemented
76#5752—31no—
77C3×#471—31no—
78#5245—31no—
79#5241—31no—
80#5203—31no—
81#5202—31no—
82#5202—31no—
83#5199—31no—
84#5198—31no—
85#5198—31no—
86#5197—31no—
87#5177D311yescharacteristic, complemented
88#5176—31no—
89#5176—31no—
90#5176—61no—
91#5145—31no—
92#5145—31no—
93#5142—31no—
94#4897—31no—
95#4894—31no—
96#4754—31no—
97#4753—31no—
98#4749—31no—
99#4747—31no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C2×#638—41no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C3×#67—41no—
106C3×#239—21no—
107C3×#239—21no—
108C3×D3×Q8—21no—
109C3×D3×Q8—21no—
110C3×#237—21no—
111C3×#237—21no—
112C3×D3×D4—21no—
113C3×D3×D4—21no—
114C3×#235—41no—
115C3×#235C2311yescharacteristic
116C3×#235C2311yescharacteristic
117C3×#235C2311yescharacteristic
118C3×#235C2311yescharacteristic
119#3811—41no—
120#3811—41no—
121D3×D12—21no—
122D3×D12—21no—
123D3×D12—21no—
124D3×D12—21no—
125#3799—21no—
126#3799—21no—
127#3799—21no—
128#3799—21no—
129C32×SD16—21no—
130C32×SD16—21no—
131C2×C32×C8C2311yescharacteristic
132#3755—21no—
133#3755—21no—
134#3753—21no—
135#3753—21no—
136#3752—41no—
137C4×C3⋊Dic3C2311yescharacteristic
138C2×C3⋊(C3⋊C8)C2311yescharacteristic
139#3745—21no—
140#3745—21no—
141C3×#216—21no—
142C3×#216—21no—
143C3×#215—21no—
144C3×#215—21no—
145C3×#214—21no—
146C3×#214—21no—
147C3×#213—21no—
148C3×#213—21no—
149C3×#208C2311yescharacteristic
150C3×#208C2311yescharacteristic
151C3×#208C2311yescharacteristic
152C3×#208C2311yescharacteristic
153C3×Dic12D411yescharacteristic, complemented
154C3×D24D411yescharacteristic, complemented
155C3×#204D411yescharacteristic, complemented
156C3×#204D411yescharacteristic, complemented
157C3×ΓL(1,𝔽25)—21no—
158C3×ΓL(1,𝔽25)—21no—
159C3×D3×C8—21no—
160C3×D3×C8—21no—
161#3718D411yescharacteristic, complemented
162#3717—21no—
163#3717—21no—
164#3717—21no—
165#3717—21no—
166#3715D411yescharacteristic, complemented
167#3715D411yescharacteristic, complemented
168#3714—21no—
169#3714—21no—
170#3714—21no—
171#3714—21no—
172#3713D411yescharacteristic, complemented
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3288—91noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—31no—
180#1009—31no—
181#1009—31no—
182#1009—31no—
183#1009—31no—
184#1007C2×D311yescharacteristic, complemented
185#1004C2×D311yescharacteristic, complemented
186C3×#137—31no—
187C3×#137—31no—
188C3×#137—61no—
189C3×AGL(1,ℤ/8)—31no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—61no—
192C3×#135—31no—
193C3×#135—61no—
194C2×C3×SD16—21no—
195C2×C3×SD16—61no—
196C2×C3×SD16C2×D311yescharacteristic, complemented
197C2×C3×SD16C2×D311yescharacteristic, complemented
198C3×#131—31no—
199C3×#131—31no—
200#950—31no—
201#950—31no—
202#950—61no—
203#950—61no—
204#949—31no—
205#949—31no—
206#949—31no—
207#949—31no—
208#949—61no—
209#949—61no—
210#948—31no—
211#948—31no—
212#947—31no—
213#947—31no—
214#947—61no—
215#942—61no—
216#942C2×D311yescharacteristic, complemented
217#942C2×D311yescharacteristic, complemented
218C2×#215—31no—
219C2×#215—31no—
220C2×#215—61no—
221C2×#215—61no—
222#940—31no—
223#940—31no—
224#940—61no—
225#932—61no—
226#932C2×D311yescharacteristic
227#932C2×D311yescharacteristic, complemented
228C2×#213—31no—
229C2×#213—31no—
230C2×#213—61no—
231C2×#213—61no—
232#919—61no—
233#919—61no—
234#918—61no—
235#916—21no—
236#916—61no—
237#915—21no—
238#914—21no—
239#914—61no—
240#914—61no—
241#914—61no—
242#914—61no—
243D3×SD16—21no—
244D3×SD16—61no—
245#911—61no—
246D3×D8—61no—
247D3×D8—61no—
248#908—31no—
249#908—31no—
250#908—31no—
251#908—31no—
252#908—61no—
253#908—61no—
254#907—31no—
255#907—31no—
256#904—61no—
257#904C2×D311yescharacteristic
258C2×D24—31no—
259C2×D24—31no—
260C2×D24—61no—
261C2×D24—61no—
262#901C2×D311yescharacteristic, complemented
263#901C2×D311yescharacteristic, complemented
264C3×#108—31no—
265C3×#101—31no—
266C3×#100—31no—
267#837—31no—
268#837—31no—
269#837—31no—
270#837—31no—
271#836C2×D311yescharacteristic, complemented
272#833C2×D311yescharacteristic, complemented
273#825—31no—
274#825—31no—
275#825—31no—
276#825—31no—
277#823—31no—
278#823—31no—
279#823—31no—
280#823—31no—
281#822—31no—
282#822—31no—
283#819C2×D311yescharacteristic, complemented
284#815—31no—
285#815—31no—
286#815—61no—
287C23×C32—21no—
288C22×C3⋊D3—21no—
289C22×C3⋊D3—21no—
290C22×C3×D3—41no—
291C2×D32—41no—
292C2×D32—41no—
293C32×Q8—21no—
294C32×Q8—21no—
295C32×D4—21no—
296C32×D4—21no—
297C2×C32×C4—21no—
298C2×C32×C4C2411yescharacteristic
299#638—82no—
300C2×C3⋊Dic3—21no—
301C4⋊(C3⋊D3)—21no—
302C4⋊(C3⋊D3)—21no—
303C4⋊(C3⋊D3)—21no—
304C4⋊(C3⋊D3)—21no—
305C3×#67—21no—
306C3×#67—21no—
307C3×#67—21no—
308C3×#67—21no—
309C3×#67—41no—
310C3×#67—41no—
311C2×C3×Dic3—41no—
312C3×D12—41no—
313C3×D12C2×D411yescharacteristic
314C3×D12C2×D411yescharacteristic
315C3×D12C2×D411yescharacteristic
316C3×D12C2×D411yescharacteristic
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3—41no—
322C3×C4×D3—41no—
323C3×Dic6—41no—
324C3×Dic6C2×D411yescharacteristic
325C3×Dic6C2×D411yescharacteristic
326C3×Dic6C2×D411yescharacteristic
327C3×Dic6C2×D411yescharacteristic
328#626—41no—
329#626—41no—
330#626—41no—
331#626—41no—
332#624—41no—
333#624—41no—
334C32×C8C2×D411yescharacteristic
335C32×C8C2×D411yescharacteristic
336C3⋊(C3⋊C8)C2×D411yescharacteristic
337C3⋊(C3⋊C8)C2×D411yescharacteristic
338C3×C3⋊C8—21no—
339C3×C3⋊C8—21no—
340C3×C3⋊C8—21no—
341C3×C3⋊C8—21no—
342#577—31no—
343#577—91no—
344#576—91no—
345#576—91no—
346#496—91no—
347#472—91no—
348#472—91no—
349#471—31no—
350#471—91no—
351#455—91no—
352#454—91no—
353#453—91no—
354#453—91no—
355#444—91no—
356#444—91no—
357C3×#41—31no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41—121no—
366C2×C3×Q8—21no—
367C2×C3×Q8—61no—
368C2×C3×Q8—61no—
369C2×C3×Q8C22×D311yescharacteristic
370C2×C3×Q8C22×D311yescharacteristic
371C2×C3×D4—21no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—121no—
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C2×#67—41no—
378C2×#67—121no—
379C2×#67—121no—
380C2×#67—122no—
381#239—21no—
382#239—21no—
383#239—61no—
384#239—61no—
385#239—61no—
386#239—61no—
387D3×Q8—21no—
388D3×Q8—21no—
389#237—21no—
390#237—21no—
391D3×D4—21no—
392D3×D4—21no—
393D3×D4—61no—
394D3×D4—61no—
395D3×D4—61no—
396D3×D4—61no—
397D3×D4—121no—
398D3×D4—121no—
399D3×D4—121no—
400D3×D4—121no—
401#235—41no—
402#235—61no—
403#235—61no—
404#235—61no—
405#235—61no—
406#235C22×D311yescharacteristic
407#235C22×D311yescharacteristic
408#235C22×D311yescharacteristic
409#235C22×D311yescharacteristic
410C2×D12—31no—
411C2×D12—31no—
412C2×D12—31no—
413C2×D12—31no—
414C2×D12—61no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—61no—
418C2×D12—61no—
419C2×D12—61no—
420C3×Q16—31no—
421C3×Q16—61no—
422C3×Q16—61no—
423C3×SD16—21no—
424C3×SD16—21no—
425C3×SD16—21no—
426C3×SD16—21no—
427C3×SD16—31no—
428C3×SD16—31no—
429C3×SD16—41no—
430C3×SD16—41no—
431C3×SD16—61no—
432C3×SD16—61no—
433C3×SD16—61no—
434C3×SD16—61no—
435C3×D8—31no—
436C3×D8—61no—
437C3×D8—61no—
438C3×M16—31no—
439C3×M16—31no—
440C3×M16—31no—
441C3×M16—31no—
442C3×M16—61no—
443C3×M16—61no—
444C2×C3×C8—21no—
445C2×C3×C8—61no—
446C2×C3×C8—61no—
447C2×C3×C8C22×D311yescharacteristic
448C2×C3×C8C22×D311yescharacteristic
449#216—21no—
450#216—21no—
451#216—31no—
452#216—31no—
453#215—21no—
454#215—21no—
455#215—31no—
456#215—31no—
457#215—61no—
458#215—61no—
459#215—61no—
460#215—61no—
461#215—61no—
462#215—61no—
463#215—61no—
464#215—61no—
465#215—121no—
466#215—121no—
467#214—21no—
468#214—21no—
469#214—31no—
470#214—31no—
471#213—21no—
472#213—21no—
473#213—31no—
474#213—31no—
475#213—61no—
476#213—61no—
477#213—61no—
478#213—61no—
479#213—61no—
480#213—61no—
481#213—61no—
482#213—61no—
483#213—121no—
484#213—121no—
485(C2×D3)⋊C4—121no—
486(C2×D3)⋊C4—121no—
487(C2×D3)⋊C4—122no—
488C4×Dic3—31no—
489C4×Dic3—31no—
490C4×Dic3—61no—
491#208—61no—
492#208—61no—
493#208C22×D311yescharacteristic
494#208C22×D311yescharacteristic
495#208C22×D311yescharacteristic
496#208C22×D311yescharacteristic
497C2×C3⋊C8—31no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8—61no—
502Dic12#6711yescharacteristic, complemented
503D24—61no—
504D24—61no—
505D24—61no—
506D24—61no—
507D24—61no—
508D24—61no—
509D24—61no—
510D24—61no—
511D24—121no—
512D24—121no—
513D24#6711yescharacteristic, complemented
514#204—61no—
515#204—61no—
516#204—61no—
517#204—61no—
518#204#6711yescharacteristic, complemented
519#204#6711yescharacteristic, complemented
520ΓL(1,𝔽25)—21no—
521ΓL(1,𝔽25)—21no—
522ΓL(1,𝔽25)—61no—
523ΓL(1,𝔽25)—61no—
524D3×C8—21no—
525D3×C8—21no—
526D3×C8—61no—
527D3×C8—61no—
528C22×C32—41no—
529C22×C32—81no—
530C22×C32H(5,𝔽2)11yescharacteristic
531C2×C3⋊D3—41no—
532C2×C3⋊D3—41no—
533C2×C3⋊D3—81no—
534C2×C3⋊D3—81no—
535C2×C3×D3—21no—
536C2×C3×D3—21no—
537C2×C3×D3—21no—
538C2×C3×D3—21no—
539C2×C3×D3—161no—
540D32—161no—
541D32—161no—
542C32×C4—41no—
543C32×C4C22×D411yescharacteristic
544C32×C4C22×D411yescharacteristic
545C3⋊Dic3—41no—
546C3×Dic3—21no—
547C3×Dic3—21no—
548C3×Dic3—21no—
549C3×Dic3—21no—
5502−1+4—31no—
551H(5,𝔽2)—31no—
552H(5,𝔽2)—91no—
553H(5,𝔽2)—91no—
554#137—31no—
555#137—31no—
556#137—61no—
557#137—181no—
558AGL(1,ℤ/8)—31no—
559AGL(1,ℤ/8)—31no—
560AGL(1,ℤ/8)—61no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—91no—
563AGL(1,ℤ/8)—91no—
564AGL(1,ℤ/8)—91no—
565AGL(1,ℤ/8)—181no—
566AGL(1,ℤ/8)—181no—
567AGL(1,ℤ/8)—181no—
568AGL(1,ℤ/8)—181no—
569AGL(1,ℤ/8)—181no—
570#135—31no—
571#135—61no—
572#135—91no—
573#135—181no—
574#135—181no—
575#135—181no—
576C2×SD16—61no—
577C2×SD16—91no—
578C2×SD16—181no—
579C2×SD16D3211yescharacteristic, complemented
580C2×D8—91no—
581C2×D8—91no—
582C2×D8—181no—
583C2×D8—181no—
584#131—31no—
585#131—31no—
586#131—91no—
587#131—91no—
588#127—91no—
589#124—91no—
590#108—31no—
591#108—91no—
592#104—91no—
593#104—91no—
594#104—91no—
595#104—91no—
596#101—31no—
597#100—31no—
598#100—91no—
599#100—91no—
600#97—91no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—41no—
604C23×C3—121no—
605C22×D3—41no—
606C22×D3—61no—
607C22×D3—61no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C22×D3—121no—
614C22×D3—121no—
615C22×D3—121no—
616C3×Q8—21no—
617C3×Q8—21no—
618C3×Q8—21no—
619C3×Q8—21no—
620C3×Q8—31no—
621C3×Q8—31no—
622C3×Q8—31no—
623C3×Q8—31no—
624C3×Q8—41no—
625C3×Q8—41no—
626C3×Q8—121no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—21no—
631C3×D4—31no—
632C3×D4—31no—
633C3×D4—31no—
634C3×D4—31no—
635C3×D4—41no—
636C3×D4—41no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—121no—
642C3×D4—121no—
643C3×D4—121no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—41no—
648C2×C3×C4—61no—
649C2×C3×C4—61no—
650C2×C3×C4—61no—
651C2×C3×C4—61no—
652C2×C3×C4—121no—
653C2×C3×C4—121no—
654C2×C3×C4—121no—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657#67—21no—
658#67—21no—
659#67—21no—
660#67—21no—
661#67—41no—
662#67—41no—
663#67—121no—
664#67—121no—
665#67—121no—
666#67—121no—
667#67—242no—
668#67—242no—
669#67—244no—
670C2×Dic3—41no—
671C2×Dic3—62no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674D12—41no—
675D12—61no—
676D12—61no—
677D12—61no—
678D12—61no—
679D12—61no—
680D12—61no—
681D12—61no—
682D12—61no—
683D12—121no—
684D12—121no—
685D12—121no—
686D12—121no—
687D12—121no—
688D12—121no—
689D12—121no—
690D12—121no—
691D12D3×D411yescharacteristic
692D12D3×D411yescharacteristic
693D12C2×#6711yescharacteristic
694D12C2×#6711yescharacteristic
695C4×D3—21no—
696C4×D3—21no—
697C4×D3—21no—
698C4×D3—21no—
699C4×D3—41no—
700C4×D3—41no—
701C4×D3—121no—
702C4×D3—121no—
703C4×D3—121no—
704C4×D3—121no—
705Dic6—41no—
706Dic6D3×D411yescharacteristic
707Dic6D3×D411yescharacteristic
708Dic6C2×#6711yescharacteristic
709Dic6C2×#6711yescharacteristic
710C3×C8—21no—
711C3×C8—21no—
712C3×C8—61no—
713C3×C8—61no—
714C3×C8—61no—
715C3×C8—61no—
716C3×C8D3×D411yescharacteristic
717C3×C8D3×D411yescharacteristic
718C3×C8C2×#6711yescharacteristic
719C3×C8C2×#6711yescharacteristic
720C3⋊C8—21no—
721C3⋊C8—21no—
722C3⋊C8—21no—
723C3⋊C8—21no—
724C3⋊C8—31no—
725C3⋊C8—31no—
726C3⋊C8—31no—
727C3⋊C8—31no—
728C3⋊C8—61no—
729C3⋊C8—61no—
730C2×C32—21no—
731C2×C32—81no—
732C2×C32D4211yescharacteristic
733C3⋊D3—81no—
734C3⋊D3—81no—
735C3×D3—41no—
736C3×D3—41no—
737C3×D3—41no—
738C3×D3—41no—
739#41—31no—
740#41—31no—
741#41—31no—
742#41—31no—
743#41—61no—
744#41—61no—
745#41—61no—
746#41—61no—
747#41—121no—
748#41—181no—
749#41—181no—
750#41—181no—
751#41—181no—
752C2×Q8—61no—
753C2×Q8—61no—
754C2×Q8C2×D3211yescharacteristic
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—91no—
758C2×D4—91no—
759C2×D4—121no—
760C2×D4—181no—
761C2×D4—181no—
762C2×D4—181no—
763C2×D4—181no—
764C2×D4—361no—
765C2×D4—361no—
766C2×D4—361no—
767C2×D4C2×D3211yescharacteristic
768Q16—31no—
769Q16—61no—
770Q16—61no—
771Q16—91no—
772SD16—21no—
773SD16—21no—
774SD16—31no—
775SD16—31no—
776SD16—61no—
777SD16—61no—
778SD16—61no—
779SD16—61no—
780SD16—91no—
781SD16—91no—
782SD16—181no—
783SD16—181no—
784SD16—181no—
785SD16—181no—
786SD16—181no—
787SD16—181no—
788D8—31no—
789D8—61no—
790D8—61no—
791D8—91no—
792D8—181no—
793D8—181no—
794D8—181no—
795D8—181no—
796D8—181no—
797D8—181no—
798D8—181no—
799D8—181no—
800M16—31no—
801M16—31no—
802M16—31no—
803M16—31no—
804M16—61no—
805M16—61no—
806M16—181no—
807M16—181no—
808C2×C8—61no—
809C2×C8—61no—
810C2×C8—91no—
811C2×C8—181no—
812C2×C8—181no—
813C2×C8C2×D3211yescharacteristic
814C22⋊C4—361no—
815C42—91no—
816C22×C3—21no—
817C22×C3—41no—
818C22×C3—41no—
819C22×C3—61no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—81no—
824C22×C3—81no—
825C22×C3—81no—
826C22×C3—82no—
827C22×C3—481no—
828C22×C3#100411yescharacteristic
829C22×C3#100911yescharacteristic
830C2×D3—21no—
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—21no—
834C2×D3—121no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—161no—
839C2×D3—241no—
840C2×D3—241no—
841C2×D3—241no—
842C2×D3—241no—
843C2×D3—241no—
844C2×D3—241no—
845C2×D3—242no—
846C2×D3—242no—
847C2×D3—481no—
848C2×D3—481no—
849C2×D3—481no—
850C2×D3—481no—
851C3×C4—21no—
852C3×C4—21no—
853C3×C4—41no—
854C3×C4—41no—
855C3×C4—61no—
856C3×C4—61no—
857C3×C4—61no—
858C3×C4—61no—
859C3×C4—81no—
860C3×C4C2×D3×D411yescharacteristic
861C3×C4C2×D3×D411yescharacteristic
862C3×C4C2×D3×D411yescharacteristic
863C3×C4C22×#6711yescharacteristic
864Dic3—21no—
865Dic3—21no—
866Dic3—21no—
867Dic3—21no—
868Dic3—122no—
869Dic3—121no—
870Dic3—121no—
871C32#328811yescharacteristic, complemented, Sylow
872C23—21no—
873C23—121no—
874C23—181no—
875C23—181no—
876C23—361no—
877C23—361no—
878Q8—21no—
879Q8—21no—
880Q8—31no—
881Q8—31no—
882Q8—31no—
883Q8—31no—
884Q8—121no—
885D4—21no—
886D4—21no—
887D4—31no—
888D4—31no—
889D4—31no—
890D4—31no—
891D4—61no—
892D4—61no—
893D4—61no—
894D4—61no—
895D4—121no—
896D4—121no—
897D4—121no—
898D4—181no—
899D4—181no—
900D4—181no—
901D4—181no—
902D4—361no—
903D4—361no—
904D4—361no—
905D4—361no—
906D4—722no—
907C2×C4—21no—
908C2×C4—61no—
909C2×C4—61no—
910C2×C4—61no—
911C2×C4—61no—
912C2×C4—121no—
913C2×C4—121no—
914C2×C4—121no—
915C2×C4—181no—
916C2×C4—361no—
917C2×C4—361no—
918C2×C4C22×D3211yescharacteristic
919C8—61no—
920C8—61no—
921C8—61no—
922C8—61no—
923C8—91no—
924C8—91no—
925C8D3×#6711yescharacteristic
926C8D3×#6711yescharacteristic
927C2×C3—22no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—81no—
932C2×C3—81no—
933C2×C3—121no—
934C2×C3—121no—
935C2×C3—121no—
936C2×C3—121no—
937C2×C3—161no—
938C2×C3#560911yescharacteristic
939C2×C3D4×#6711yescharacteristic
940D3—41no—
941D3—41no—
942D3—41no—
943D3—41no—
944D3—241no—
945D3—241no—
946D3—241no—
947D3—241no—
948D3—481no—
949D3—481no—
950C22—41no—
951C22—61no—
952C22—61no—
953C22—61no—
954C22—61no—
955C22—81no—
956C22—361no—
957C22—361no—
958C22—481no—
959C22—721no—
960C22—721no—
961C22—1441no—
962C22—1441no—
963C22#6431411yescharacteristic
964C4—41no—
965C4—61no—
966C4—61no—
967C4—61no—
968C4—61no—
969C4—361no—
970C4D32×D411yescharacteristic
971C4C2×D3×#6711yescharacteristic
972C3—21no—
973C3#8093211yescharacteristic, complemented
974C3#8401511yescharacteristic, complemented
975C2—21no—
976C2—81no—
977C2—121no—
978C2—121no—
979C2—121no—
980C2—121no—
981C2—721no—
982C2—721no—
983C2#1059528811yescharacteristic
subgroupG/H
centerC2#10595288
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC2×C32D42
hypercenterC2×SD16D32
hypocenterC32#3288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. C3×#5762C2semidirect
2. #10595319C2semidirect
3. #10595097C2semidirect
4. #10594680C2semidirect
5. #10592875C2semidirect
6. C3×#5177C2semidirect
7. #10591658C2semidirect
8. #10591646C2semidirect
9. #10591643C2semidirect
10. #10591522C2semidirect
11. #10591510C2semidirect
12. #10591508C2semidirect
13. #10590927C2semidirect
14. #10590922C2semidirect
15. #10590920C2semidirect
18. C3×#1007C22semidirect
19. C3×#1004C22semidirect
21. #64308C22semidirect
22. C2×C32×SD16C22semidirect
23. #64156C22semidirect
24. C2×#3755C22semidirect
25. #64149C22semidirect
26. C2×#3753C22semidirect
27. C2×#3745C22semidirect
28. C3×#942C22semidirect
29. C3×#942C22semidirect
31. C3×#932C22semidirect
37. C3×#901C22semidirect
38. C3×#901C22semidirect
48. #63825C22semidirect
49. #63825C22semidirect
50. #63825C22semidirect
52. #63815C22semidirect
53. #63815C22semidirect
58. #63642C22semidirect
59. C3×#836C22semidirect
60. C3×#833C22semidirect
61. C3×#819C22semidirect
62. #63578C22semidirect
63. #63568C22semidirect
64. #63568C22semidirect
65. #63568C22semidirect
66. #63568C22semidirect
67. #63559C22semidirect
68. #63559C22semidirect
75. #5762D3semidirect
87. #5177D3semidirect
153. C3×Dic12D4semidirect
154. C3×D24D4semidirect
155. C3×#204D4semidirect
156. C3×#204D4semidirect
161. #3718D4semidirect
166. #3715D4semidirect
167. #3715D4semidirect
172. #3713D4semidirect
184. #1007C2×D3semidirect
185. #1004C2×D3semidirect
196. C2×C3×SD16C2×D3semidirect
197. C2×C3×SD16C2×D3semidirect
216. #942C2×D3semidirect
217. #942C2×D3semidirect
227. #932C2×D3semidirect
262. #901C2×D3semidirect
263. #901C2×D3semidirect
271. #836C2×D3semidirect
272. #833C2×D3semidirect
283. #819C2×D3semidirect
502. Dic12#67semidirect
513. D24#67semidirect
518. #204#67semidirect
519. #204#67semidirect
579. C2×SD16D32semidirect
871. C32#3288semidirect
973. C3#80932semidirect
974. C3#84015semidirect

Maximal subgroups

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

subgroupindex
C3×#57622
#105953192
#105950972
#105946802
#105928752
C3×#51772
#105916582
#105916462
#105916432
#105915222
#105915102
#105915082
#105909272
#105909222
#105909202
#840153
#809323