Finite Group Databasebeta

← #11919053

Subgroups — #11919053

Order 1152.

3377 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#10596698C211yesmaximal, characteristic, complemented
3C3×#5836C211yesmaximal, characteristic, complemented
4C3×#5835C211yesmaximal, characteristic, complemented
5#10595473C213yesmaximal, complemented
6#10595471C213yesmaximal, complemented
7#10595461C213yesmaximal, complemented
8#10595460C213yesmaximal, complemented
9#10595449C211yesmaximal, characteristic, complemented
10#10595448C211yesmaximal, characteristic, complemented
11#10595443C211yesmaximal, characteristic, complemented
12#10595115C213yesmaximal, complemented
13C2×#63937C213yesmaximal, complemented
14#10595102C213yesmaximal, complemented
15#10595100C213yesmaximal, complemented
16#87207—31nomaximal
17#87204—31nomaximal
18C32×H(5,𝔽2)C2211yescharacteristic, complemented
19#64366—21no—
20#64366C2213yescomplemented
21#64366C2211yescharacteristic, complemented
22#41×C3⋊D3—21no—
23#41×C3⋊D3C2211yescharacteristic
24#41×C3⋊D3C2213yescomplemented
25#64361—23no—
26#64361C2213yescomplemented
27C2×D4×C3⋊D3—23no—
28C2×D4×C3⋊D3C2213yescomplemented
29C3×#1010C2211yescharacteristic, complemented
30C3×#1009C2211yescharacteristic, complemented
31D3×#239—21no—
32#64315—21no—
33#64314—23no—
34D3×#237—23no—
35#64307C2213yescomplemented
36#64306C2213yescomplemented
37#64297C2213yescomplemented
38C2×#3796C2213yescomplemented
39C3×#951C2213yescomplemented
40C3×#950C2213yescomplemented
41C3×#950C2213yescomplemented
42C3×#949C2213yescomplemented
43C3×#948C2211yescharacteristic, complemented
44C3×#948C2211yescharacteristic, complemented
45C2×C3×#214C2213yescomplemented
46C3×#932C2213yescomplemented
47C3×#932C2213yescomplemented
48C2×C3×#213C2213yescomplemented
49#63951C2211yescharacteristic, complemented
50#63951C2213yescomplemented
51#63950C2216yescomplemented
52#63945C2213yescomplemented
53#63941C2213yescomplemented
54#63937C2213yescomplemented
55#63937C2216yescomplemented
56#63937C2213yescomplemented
57#63937C2216yescomplemented
58#63937C2216yescomplemented
59#63936C2216yescomplemented
60#63931C2213yescomplemented
61#63930C2216yescomplemented
62#63927C2213yescomplemented
63#63926C2216yescomplemented
64#63833C2213yescomplemented
65C2×#3717C2213yescomplemented
66#63830C2213yescomplemented
67#63829C2213yescomplemented
68#63829C2213yescomplemented
69#63825C2213yescomplemented
70#63825C2213yescomplemented
71C2×#3714C2213yescomplemented
72C2×#3712C2213yescomplemented
73#63818C2213yescomplemented
74#63817C2213yescomplemented
75#63817C2213yescomplemented
76#5968—31no—
77#5966—31no—
78D3×H(5,𝔽2)—31no—
79D3×H(5,𝔽2)—31no—
80D3×H(5,𝔽2)—61no—
81C3×#577—31no—
82C3×#576—31no—
83#5837—31no—
84#5836D311yescharacteristic, complemented
85#5835—31no—
86#5835D311yescharacteristic, complemented
87#5778—33no—
88#5777—33no—
89#5775—33no—
90#5774—33no—
91#5774—33no—
92#5773—33no—
93D3×AGL(1,ℤ/8)—33no—
94D3×AGL(1,ℤ/8)—33no—
95#5770—33no—
96#5769—33no—
97#5768—33no—
98#5768—33no—
99#5762—33no—
100C2×#914—33no—
101#5757—33no—
102C2×#911—33no—
103#5752—31no—
104#5751—31no—
105#5750—31no—
106#5750—31no—
107C23×C3⋊D3—23no—
108C32×#41—21no—
109C32×#41C2313yes—
110C32×#41C2311yescharacteristic
111C2×C32×D4—23no—
112C2×C32×D4C2313yes—
113C2×#638—26no—
114C2×#638—23no—
115#3832—21no—
116#3832D411yescharacteristic
117#3832C2313yes—
118Q8×C3⋊D3D411yescharacteristic
119Q8×C3⋊D3C2311yescharacteristic
120#3830—23no—
121#3830—23no—
122#3830D413yes—
123#3830C2313yes—
124D4×C3⋊D3—23no—
125D4×C3⋊D3—23no—
126D4×C3⋊D3—26no—
127D4×C3⋊D3—23no—
128D4×C3⋊D3—23no—
129D4×C3⋊D3—23no—
130D4×C3⋊D3D413yes—
131D4×C3⋊D3C2313yes—
132D4×C3⋊D3C2316yes—
133#3828—23no—
134#3828—23no—
135#3828C2313yes—
136#3828C2313yes—
137C2×C4⋊(C3⋊D3)—23no—
138C2×C4⋊(C3⋊D3)C2313yes—
139C2×C4×C3⋊D3—23no—
140C2×C4×C3⋊D3C2313yes—
141C3×#239—21no—
142C3×D3×Q8—21no—
143C3×#237—23no—
144C3×D3×D4—23no—
145C3×#235C2313yescomplemented
146C3×#235C2313yescomplemented
147C2×C3×D12C2313yescomplemented
148C2×C3×Dic6C2313yescomplemented
149#3811—23no—
150D3×#67—26no—
151C2×#626—23no—
152#3805—23no—
153#3804—26no—
154C2×D3×Dic3—23no—
155#3802C2313yescomplemented
156D3×D12—23no—
157C4×D32—23no—
158#3799—23no—
159#3798—23no—
160#3797C2313yescomplemented
161#3796—23no—
162#3796—23no—
163#3796C2313yes—
164#3796C2311yescharacteristic
165#3796C2316yescomplemented
166#3795—23no—
167D3×Dic6—23no—
168C3×#216C2311yescharacteristic, complemented
169C3×#216C2313yescomplemented
170C3×#215C2313yescomplemented
171C3×#215C2311yescharacteristic, complemented
172C3×#214C2313yescomplemented
173C3×#214C2316yescomplemented
174C3×#214C2313yescomplemented
175C3×#213C2313yescomplemented
176C3×#213C2316yescomplemented
177C3×#213C2313yescomplemented
178C3×#208C2313yescomplemented
179C3×#208C2313yescomplemented
180C2×C3×C3⋊C8C2313yescomplemented
181C2×C3×C3⋊C8C2313yescomplemented
182#3719C2311yescharacteristic, complemented
183#3719C2313yescomplemented
184#3717C2313yescomplemented
185#3717C2316yescomplemented
186#3717C2313yescomplemented
187#3716C2311yescharacteristic, complemented
188#3716C2313yescomplemented
189#3714C2313yescomplemented
190#3714C2316yescomplemented
191#3714C2313yescomplemented
192#3712C2313yes—
193#3712C2311yescharacteristic
194#3712C2313yescomplemented
195#3712C2313yescomplemented
196#3710C2316yescomplemented
197#3585—91noSylow
198C3×2−1+4—31no—
199C3×H(5,𝔽2)—21no—
200C3×H(5,𝔽2)—31no—
201C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
202C3×H(5,𝔽2)C2×D311yescharacteristic, complemented
203#1010—33no—
204#1010—61no—
205#1010C2×D311yescharacteristic, complemented
206#1009—31no—
207#1009—31no—
208#1009—33no—
209#1009—33no—
210#1009—33no—
211#1009—63no—
212#1009—61no—
213#1009—63no—
214#1009—61no—
215#1009—61no—
216#1009—62no—
217#1009C2×D311yescharacteristic, complemented
218D3×#41—31no—
219D3×#41—31no—
220D3×#41—33no—
221D3×#41—33no—
222D3×#41—33no—
223D3×#41—33no—
224D3×#41—61no—
225D3×#41—63no—
226D3×#41—63no—
227D3×#41—61no—
228D3×#41—61no—
229D3×#41—61no—
230D3×#41—62no—
231#1007—33no—
232#1007—61no—
233C2×#239—33no—
234C2×#239—61no—
235#1004—33no—
236#1004—33no—
237#1004—33no—
238#1004—63no—
239#1004—63no—
240#1004—63no—
241#1004—63no—
242#1004—66no—
243C2×#237—33no—
244C2×#237—63no—
245C2×D3×D4—33no—
246C2×D3×D4—33no—
247C2×D3×D4—63no—
248C2×D3×D4—63no—
249C2×D3×D4—63no—
250C2×D3×D4—66no—
251C3×#137—33no—
252C3×AGL(1,ℤ/8)—33no—
253C3×AGL(1,ℤ/8)—33no—
254C3×AGL(1,ℤ/8)—33no—
255C3×#135—33no—
256C3×#135—33no—
257C2×C3×SD16—33no—
258C2×C3×D8—33no—
259C3×#131—31no—
260C3×#131—31no—
261#951C2×D313yescomplemented
262#950—33no—
263#950—33no—
264#950C2×D313yescomplemented
265#950C2×D313yescomplemented
266#949—33no—
267#949—33no—
268#949C2×D313yescomplemented
269#948C2×D311yescharacteristic, complemented
270#948C2×D311yescharacteristic, complemented
271#942—33no—
272C2×#215—33no—
273C2×#214C2×D313yescomplemented
274#932—33no—
275#932C2×D313yescomplemented
276#932C2×D313yescomplemented
277C2×#213—33no—
278C2×#213C2×D313yescomplemented
279#919—36no—
280#918—33no—
281#918—33no—
282#918—31no—
283#918—33no—
284#916—36no—
285#916—36no—
286#915—31no—
287#915—33no—
288#915—33no—
289#915—33no—
290#914—33no—
291#914—33no—
292#914—33no—
293#914—36no—
294#914—36no—
295#914—36no—
296#914—33no—
297D3×SD16—36no—
298D3×SD16—36no—
299#912—36no—
300#911—33no—
301#911—36no—
302#911—36no—
303#911—36no—
304#911—33no—
305#911—33no—
306#911—33no—
307D3×D8—36no—
308D3×D8—36no—
309#909—33no—
310#908—33no—
311#908—33no—
312#908—33no—
313#907—33no—
314#907—33no—
315D3×M16—33no—
316D3×M16—33no—
317#904—33no—
318#904—33no—
319C2×D24—33no—
320C2×#204—33no—
321#901—33no—
322#901—33no—
323C2×ΓL(1,𝔽25)—33no—
324C2×ΓL(1,𝔽25)—33no—
325C23×C32—23no—
326C22×C3⋊D3—23no—
327C22×C3⋊D3—23no—
328C22×C3⋊D3—26no—
329C22×C3⋊D3—86no—
330C22×C3⋊D3C2×D413yes—
331C22×C3×D3—23no—
332C2×D32—23no—
333C32×Q8C2×D411yescharacteristic
334C32×Q8C2411yescharacteristic
335C32×D4—23no—
336C32×D4—23no—
337C32×D4C2×D413yes—
338C32×D4C2413yes—
339C2×C32×C4—23no—
340C2×C32×C4C2413yes—
341#638—23no—
342#638—23no—
343#638—23no—
344#638—26no—
345#638C2×D416yes—
346C2×C3⋊Dic3—23no—
347C2×C3⋊Dic3C2×D413yes—
348C4⋊(C3⋊D3)—23no—
349C4⋊(C3⋊D3)—23no—
350C4⋊(C3⋊D3)C2×D413yes—
351C4⋊(C3⋊D3)C2413yes—
352C4×C3⋊D3—21no—
353C4×C3⋊D3—23no—
354C4×C3⋊D3—23no—
355C4×C3⋊D3C2×D413yes—
356C4×C3⋊D3C2×D413yes—
357C4×C3⋊D3C2413yes—
358C4×C3⋊D3C2411yescharacteristic
359#634—21no—
360#634C2×D413yes—
361#634C2411yescharacteristic
362C3×#67—23no—
363C3×#67—23no—
364C2×C3×Dic3—23no—
365C3×D12—23no—
366C3×D12C2413yes—
367C3×D12C2411yescharacteristic
368C3×C4×D3—23no—
369C3×C4×D3—23no—
370C3×Dic6—23no—
371C3×Dic6C2413yes—
372C3×Dic6C2411yescharacteristic
373#627—23no—
374#626—23no—
375#626—26no—
376#626—21no—
377#625—23no—
378#624—23no—
379D3×Dic3—26no—
380D3×Dic3—23no—
381D3×Dic3—21no—
382C3×C3⋊C8C2413yes—
383C3×C3⋊C8C2413yes—
384C3×C3⋊C8C2411yescharacteristic
385C3×C3⋊C8C2411yescharacteristic
386#585—91no—
387C2×H(5,𝔽2)—91no—
388#577—31no—
389#577—91no—
390#577—93no—
391#577—93no—
392#576—31no—
393#576—91no—
394#576—93no—
395#576—93no—
396#575—93no—
397#575—93no—
398C2×AGL(1,ℤ/8)—93no—
399C2×AGL(1,ℤ/8)—93no—
400#568—91no—
401C23×D3—63no—
402C23×D3—63no—
403C23×D3—66no—
404C3×#41—22no—
405C3×#41—21no—
406C3×#41—21no—
407C3×#41—23no—
408C3×#41—21no—
409C3×#41—33no—
410C3×#41—33no—
411C3×#41—61no—
412C3×#41—63no—
413C3×#41C22×D313yes—
414C3×#41C22×D313yes—
415C3×#41C22×D311yescharacteristic
416C3×#41C22×D311yescharacteristic
417C2×C3×Q8—33no—
418C2×C3×Q8—61no—
419C2×C3×D4—26no—
420C2×C3×D4—23no—
421C2×C3×D4—23no—
422C2×C3×D4—23no—
423C2×C3×D4—33no—
424C2×C3×D4—63no—
425C2×C3×D4C22×D313yes—
426C2×C3×D4C22×D313yes—
427C2×#67—63no—
428C2×#67—63no—
429C2×#67—63no—
430C2×#67—66no—
431C2×#67—66no—
432C2×#67—66no—
433C2×#67—66no—
434C2×#67—612no—
435C22×Dic3—63no—
436#239—21no—
437#239—31no—
438#239—31no—
439#239—33no—
440#239—33no—
441#239—33no—
442#239—31no—
443#239—36no—
444#239—61no—
445#239—63no—
446#239—63no—
447#239—63no—
448#239—63no—
449#239—62no—
450#239—61no—
451#239—61no—
452D3×Q8—21no—
453D3×Q8—31no—
454D3×Q8—31no—
455D3×Q8—31no—
456D3×Q8—31no—
457D3×Q8—33no—
458D3×Q8—33no—
459D3×Q8—61no—
460D3×Q8—61no—
461D3×Q8—63no—
462#237—23no—
463#237—33no—
464#237—33no—
465#237—33no—
466#237—33no—
467#237—33no—
468#237—31no—
469#237—36no—
470#237—63no—
471#237—63no—
472#237—63no—
473#237—63no—
474#237—63no—
475#237—63no—
476#237—63no—
477#237—66no—
478#237—63no—
479#237—63no—
480#237—63no—
481#237—63no—
482#237—66no—
483#237—66no—
484D3×D4—23no—
485D3×D4—33no—
486D3×D4—33no—
487D3×D4—36no—
488D3×D4—36no—
489D3×D4—33no—
490D3×D4—33no—
491D3×D4—33no—
492D3×D4—33no—
493D3×D4—63no—
494D3×D4—63no—
495D3×D4—66no—
496D3×D4—63no—
497D3×D4—63no—
498D3×D4—63no—
499D3×D4—63no—
500D3×D4—63no—
501D3×D4—63no—
502D3×D4—63no—
503D3×D4—63no—
504D3×D4—63no—
505D3×D4—66no—
506D3×D4—66no—
507D3×D4—66no—
508D3×D4—63no—
509D3×D4—63no—
510D3×D4—66no—
511D3×D4—66no—
512D3×D4—66no—
513D3×D4—66no—
514D3×D4—612no—
515D3×D4—66no—
516D3×D4—63no—
517D3×D4—63no—
518#235—33no—
519#235—33no—
520#235—33no—
521#235—33no—
522#235—63no—
523#235—63no—
524#235—63no—
525#235—63no—
526#235—63no—
527#235—63no—
528#235—63no—
529#235—63no—
530#235—63no—
531#235—63no—
532#235—66no—
533#235—66no—
534#235—66no—
535#235C22×D313yescomplemented
536#235C22×D313yescomplemented
537C2×D12—33no—
538C2×D12—33no—
539C2×D12—63no—
540C2×D12—63no—
541C2×D12—63no—
542C2×D12—63no—
543C2×D12—66no—
544C2×D12—63no—
545C2×D12C22×D313yescomplemented
546C2×C4×D3—33no—
547C2×C4×D3—33no—
548C2×C4×D3—63no—
549C2×C4×D3—63no—
550C2×C4×D3—63no—
551C2×C4×D3—63no—
552C2×C4×D3—63no—
553C2×C4×D3—63no—
554C2×C4×D3—66no—
555C2×Dic6—63no—
556C2×Dic6C22×D313yescomplemented
557C3×Q16—31no—
558C3×Q16—33no—
559C3×SD16—31no—
560C3×SD16—33no—
561C3×SD16—33no—
562C3×SD16—36no—
563C3×SD16—33no—
564C3×D8—33no—
565C3×D8—36no—
566C3×D8—33no—
567C3×M16—33no—
568C3×M16—33no—
569C2×C3×C8—33no—
570C2×C3×C8—33no—
571#216—31no—
572#216—33no—
573#216C22×D313yescomplemented
574#216C22×D311yescharacteristic, complemented
575#215—33no—
576#215—36no—
577#215—33no—
578#215C22×D311yescharacteristic, complemented
579#215C22×D313yescomplemented
580#214—31no—
581#214—33no—
582#214C22×D313yescomplemented
583#214C22×D316yescomplemented
584#214C22×D313yescomplemented
585#213—33no—
586#213—36no—
587#213—33no—
588#213C22×D313yescomplemented
589#213C22×D316yescomplemented
590#213C22×D313yescomplemented
591#208C22×D313yescomplemented
592#208C22×D313yescomplemented
593C2×C3⋊C8C22×D313yescomplemented
594C2×C3⋊C8C22×D313yescomplemented
595Dic12—31no—
596Dic12—33no—
597D24—33no—
598D24—36no—
599D24—33no—
600#204—31no—
601#204—33no—
602#204—33no—
603#204—36no—
604#204—33no—
605ΓL(1,𝔽25)—31no—
606ΓL(1,𝔽25)—31no—
607ΓL(1,𝔽25)—33no—
608ΓL(1,𝔽25)—33no—
609ΓL(1,𝔽25)—33no—
610ΓL(1,𝔽25)—33no—
611ΓL(1,𝔽25)—33no—
612ΓL(1,𝔽25)—33no—
613D3×C8—36no—
614D3×C8—36no—
615C22×C32—23no—
616C22×C32—83no—
617C22×C32C22×D413yes—
618C2×C3⋊D3—23no—
619C2×C3⋊D3—43no—
620C2×C3⋊D3—46no—
621C2×C3⋊D3—86no—
622C2×C3⋊D3—83no—
623C2×C3⋊D3C22×D413yes—
624C2×C3⋊D3C22×D411yescharacteristic
625C2×C3×D3—23no—
626C2×C3×D3—21no—
627C2×C3×D3—83no—
628D32—83no—
629C32×C4—21no—
630C32×C4C22×D413yes—
631C32×C4C2511yescharacteristic
632C3⋊Dic3—21no—
633C3⋊Dic3C22×D411yescharacteristic
634C3⋊Dic3C22×D413yes—
635C3×Dic3—23no—
636C3×Dic3—21no—
6372−1+4—31no—
6382−1+4—93no—
6392−1+4—181no—
640H(5,𝔽2)—31no—
641H(5,𝔽2)—93no—
642H(5,𝔽2)—93no—
643H(5,𝔽2)—91no—
644H(5,𝔽2)—93no—
645H(5,𝔽2)—183no—
646H(5,𝔽2)—183no—
647H(5,𝔽2)—181no—
648H(5,𝔽2)D3211yescharacteristic, complemented
649C2×#41—91no—
650C2×#41—93no—
651C2×#41—93no—
652C2×#41—93no—
653C2×#41—183no—
654C2×#41—181no—
655C2×#41—181no—
656C22×D4—93no—
657C22×D4—183no—
658#137—33no—
659#137—93no—
660#137—93no—
661#137—91no—
662#137—93no—
663#137—93no—
664AGL(1,ℤ/8)—33no—
665AGL(1,ℤ/8)—33no—
666AGL(1,ℤ/8)—33no—
667AGL(1,ℤ/8)—93no—
668AGL(1,ℤ/8)—93no—
669AGL(1,ℤ/8)—93no—
670AGL(1,ℤ/8)—93no—
671AGL(1,ℤ/8)—93no—
672AGL(1,ℤ/8)—96no—
673AGL(1,ℤ/8)—93no—
674AGL(1,ℤ/8)—96no—
675AGL(1,ℤ/8)—96no—
676AGL(1,ℤ/8)—93no—
677#135—33no—
678#135—33no—
679#135—93no—
680#135—93no—
681#135—96no—
682#135—96no—
683C2×SD16—33no—
684C2×SD16—93no—
685C2×SD16—96no—
686C2×D8—33no—
687C2×D8—93no—
688C2×D8—96no—
689#131—31no—
690#131—31no—
691#131—93no—
692#131—93no—
693C2×M16—93no—
694C2×M16—93no—
695C23×C3—26no—
696C23×C3—23no—
697C23×C3—23no—
698C23×C3—63no—
699C22×D3—23no—
700C22×D3—33no—
701C22×D3—33no—
702C22×D3—63no—
703C22×D3—63no—
704C22×D3—63no—
705C22×D3—63no—
706C22×D3—63no—
707C22×D3—66no—
708C22×D3—66no—
709C22×D3—66no—
710C22×D3—612no—
711C22×D3—66no—
712C22×D3—63no—
713C22×D3—63no—
714C22×D3—246no—
715C22×D3—246no—
716C22×D3—2412no—
717C3×Q8—21no—
718C3×Q8—21no—
719C3×Q8—31no—
720C3×Q8—33no—
721C3×Q8—63no—
722C3×Q8D3×D411yescharacteristic
723C3×Q8D3×D411yescharacteristic
724C3×Q8C23×D311yescharacteristic
725C3×Q8C23×D311yescharacteristic
726C3×D4—26no—
727C3×D4—26no—
728C3×D4—23no—
729C3×D4—23no—
730C3×D4—23no—
731C3×D4—23no—
732C3×D4—23no—
733C3×D4—23no—
734C3×D4—31no—
735C3×D4—33no—
736C3×D4—63no—
737C3×D4—63no—
738C3×D4—63no—
739C3×D4D3×D413yes—
740C3×D4D3×D413yes—
741C3×D4C23×D313yes—
742C3×D4C23×D313yes—
743C2×C3×C4—26no—
744C2×C3×C4—23no—
745C2×C3×C4—23no—
746C2×C3×C4—23no—
747C2×C3×C4—63no—
748C2×C3×C4—63no—
749C2×C3×C4—63no—
750C2×C3×C4C23×D313yes—
751C2×C3×C4C23×D313yes—
752#67—23no—
753#67—23no—
754#67—36no—
755#67—36no—
756#67—66no—
757#67—61no—
758#67—63no—
759#67—66no—
760#67—63no—
761#67—63no—
762#67—66no—
763#67—66no—
764#67—63no—
765#67—63no—
766#67—63no—
767#67—63no—
768#67—66no—
769#67—612no—
770#67—66no—
771#67—66no—
772#67—63no—
773#67—63no—
774C2×Dic3—23no—
775C2×Dic3—33no—
776C2×Dic3—33no—
777C2×Dic3—63no—
778C2×Dic3—66no—
779C2×Dic3—61no—
780C2×Dic3—63no—
781C2×Dic3—63no—
782C2×Dic3—63no—
783C2×Dic3—66no—
784D12—23no—
785D12—33no—
786D12—33no—
787D12—33no—
788D12—33no—
789D12—63no—
790D12—63no—
791D12—63no—
792D12—63no—
793D12—66no—
794D12—66no—
795D12—63no—
796D12—66no—
797D12—61no—
798D12—63no—
799D12—63no—
800D12C23×D313yes—
801D12C23×D311yescharacteristic
802C4×D3—23no—
803C4×D3—23no—
804C4×D3—33no—
805C4×D3—33no—
806C4×D3—33no—
807C4×D3—33no—
808C4×D3—33no—
809C4×D3—33no—
810C4×D3—31no—
811C4×D3—31no—
812C4×D3—63no—
813C4×D3—63no—
814C4×D3—61no—
815C4×D3—63no—
816C4×D3—63no—
817C4×D3—63no—
818C4×D3—63no—
819C4×D3—63no—
820C4×D3—61no—
821C4×D3—63no—
822C4×D3—66no—
823C4×D3—61no—
824C4×D3—61no—
825C4×D3—62no—
826C4×D3—66no—
827C4×D3—66no—
828C4×D3—63no—
829C4×D3—63no—
830Dic6—23no—
831Dic6—33no—
832Dic6—33no—
833Dic6—31no—
834Dic6—31no—
835Dic6—63no—
836Dic6—61no—
837Dic6—63no—
838Dic6—63no—
839Dic6—61no—
840Dic6—61no—
841Dic6—62no—
842Dic6C23×D313yes—
843Dic6C23×D311yescharacteristic
844C3×C8—33no—
845C3×C8—33no—
846C3×C8—31no—
847C3×C8—31no—
848C3⋊C8C23×D313yes—
849C3⋊C8C23×D313yes—
850C3⋊C8C23×D311yescharacteristic
851C3⋊C8C23×D311yescharacteristic
852C2×C32—23no—
853C2×C32—43no—
854C2×C32C23×D411yescharacteristic
855C3⋊D3—21no—
856C3⋊D3—23no—
857C3⋊D3—43no—
858C3×D3—41no—
859C3×D3—43no—
860C24—183no—
861#41—21no—
862#41—33no—
863#41—33no—
864#41—61no—
865#41—63no—
866#41—91no—
867#41—93no—
868#41—93no—
869#41—96no—
870#41—93no—
871#41—91no—
872#41—93no—
873#41—93no—
874#41—93no—
875#41—183no—
876#41—183no—
877#41—183no—
878#41—186no—
879#41—183no—
880#41—183no—
881#41—183no—
882#41—183no—
883#41—183no—
884#41—183no—
885#41—183no—
886#41—181no—
887#41C2×D3213yes—
888#41C2×D3211yescharacteristic
889C2×Q8—33no—
890C2×Q8—61no—
891C2×Q8—91no—
892C2×Q8—93no—
893C2×Q8—91no—
894C2×Q8—183no—
895C2×D4—23no—
896C2×D4—33no—
897C2×D4—63no—
898C2×D4—93no—
899C2×D4—93no—
900C2×D4—96no—
901C2×D4—93no—
902C2×D4—93no—
903C2×D4—183no—
904C2×D4—183no—
905C2×D4—183no—
906C2×D4—183no—
907C2×D4—183no—
908C2×D4—183no—
909C2×D4—186no—
910C2×D4—183no—
911C2×D4—183no—
912C2×D4—183no—
913C2×D4—186no—
914C2×D4—186no—
915C2×D4—183no—
916C2×D4C2×D3213yes—
917C22×C4—93no—
918C22×C4—183no—
919C22×C4—183no—
920C22×C4—183no—
921Q16—31no—
922Q16—33no—
923Q16—91no—
924Q16—93no—
925SD16—31no—
926SD16—33no—
927SD16—33no—
928SD16—36no—
929SD16—33no—
930SD16—91no—
931SD16—93no—
932SD16—93no—
933SD16—96no—
934SD16—93no—
935D8—33no—
936D8—36no—
937D8—33no—
938D8—93no—
939D8—93no—
940D8—96no—
941M16—33no—
942M16—33no—
943M16—91no—
944M16—93no—
945M16—93no—
946M16—93no—
947C2×C8—33no—
948C2×C8—33no—
949C2×C8—96no—
950C22×C3—26no—
951C22×C3—23no—
952C22×C3—23no—
953C22×C3—23no—
954C22×C3—63no—
955C22×C3—61no—
956C22×C3—83no—
957C22×C3—83no—
958C22×C3—86no—
959C22×C3—243no—
960C22×C3C2×D3×D413yes—
961C22×C3C2×D3×D413yes—
962C2×D3—21no—
963C2×D3—23no—
964C2×D3—31no—
965C2×D3—31no—
966C2×D3—33no—
967C2×D3—33no—
968C2×D3—61no—
969C2×D3—63no—
970C2×D3—66no—
971C2×D3—63no—
972C2×D3—63no—
973C2×D3—83no—
974C2×D3—123no—
975C2×D3—123no—
976C2×D3—126no—
977C2×D3—1212no—
978C2×D3—126no—
979C2×D3—126no—
980C2×D3—243no—
981C2×D3—243no—
982C2×D3—246no—
983C2×D3—246no—
984C2×D3—243no—
985C2×D3—243no—
986C2×D3—246no—
987C2×D3—2412no—
988C3×C4—22no—
989C3×C4—21no—
990C3×C4—21no—
991C3×C4—23no—
992C3×C4—21no—
993C3×C4—61no—
994C3×C4—63no—
995C3×C4C2×D3×D413yes—
996C3×C4C2×D3×D413yes—
997C3×C4C24×D311yescharacteristic
998C3×C4C24×D311yescharacteristic
999Dic3—23no—
1000Dic3—21no—
1001Dic3—33no—
1002Dic3—33no—
1003Dic3—31no—
1004Dic3—31no—
1005Dic3—61no—
1006Dic3—63no—
1007Dic3—62no—
1008Dic3—61no—
1009Dic3—61no—
1010C32#358511yescharacteristic, complemented, Sylow
1011C23—23no—
1012C23—63no—
1013C23—93no—
1014C23—183no—
1015C23—186no—
1016C23—183no—
1017C23—183no—
1018C23—726no—
1019Q8—33no—
1020Q8—31no—
1021Q8—63no—
1022Q8—93no—
1023Q8—91no—
1024Q8—181no—
1025Q8—183no—
1026Q8#381111yescharacteristic
1027Q8C22×D3211yescharacteristic
1028D4—23no—
1029D4—23no—
1030D4—33no—
1031D4—31no—
1032D4—63no—
1033D4—63no—
1034D4—63no—
1035D4—96no—
1036D4—93no—
1037D4—93no—
1038D4—183no—
1039D4—181no—
1040D4—183no—
1041D4—186no—
1042D4—183no—
1043D4—186no—
1044D4—183no—
1045D4—183no—
1046D4—183no—
1047D4—183no—
1048D4#381113yes—
1049D4C22×D3213yes—
1050C2×C4—23no—
1051C2×C4—63no—
1052C2×C4—63no—
1053C2×C4—63no—
1054C2×C4—93no—
1055C2×C4—93no—
1056C2×C4—93no—
1057C2×C4—93no—
1058C2×C4—91no—
1059C2×C4—183no—
1060C2×C4—181no—
1061C2×C4—183no—
1062C2×C4—181no—
1063C2×C4—183no—
1064C2×C4—186no—
1065C2×C4—183no—
1066C2×C4—183no—
1067C2×C4C22×D3213yes—
1068C8—31no—
1069C8—31no—
1070C8—33no—
1071C8—33no—
1072C2×C3—23no—
1073C2×C3—23no—
1074C2×C3—21no—
1075C2×C3—43no—
1076C2×C3—46no—
1077C2×C3—43no—
1078C2×C3—43no—
1079C2×C3—121no—
1080C2×C3—123no—
1081C2×C3C22×D3×D411yescharacteristic
1082C2×C3C22×D3×D411yescharacteristic
1083D3—43no—
1084D3—41no—
1085D3—62no—
1086D3—61no—
1087D3—63no—
1088D3—61no—
1089D3—63no—
1090D3—123no—
1091D3—126no—
1092D3—123no—
1093D3—123no—
1094C22—23no—
1095C22—61no—
1096C22—63no—
1097C22—83no—
1098C22—91no—
1099C22—93no—
1100C22—183no—
1101C22—243no—
1102C22—363no—
1103C22—366no—
1104C22—723no—
1105C22—726no—
1106C22—723no—
1107C22C2×#381113yes—
1108C4—21no—
1109C4—61no—
1110C4—63no—
1111C4—91no—
1112C4—93no—
1113C4—181no—
1114C4C2×#381113yes—
1115C4C23×D3211yescharacteristic
1116C3—21no—
1117C3#8720411yescharacteristic, complemented
1118C3#8720711yescharacteristic, complemented
1119C2—23no—
1120C2—43no—
1121C2—123no—
1122C2—121no—
1123C2—181no—
1124C2—183no—
1125C2—363no—
1126C2C22×#381111yescharacteristic
subgroupG/H
centerC2C22×#3811
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC32×H(5,𝔽2)C22
socleC2×C32C23×D4
hypercenterH(5,𝔽2)D32
hypocenterC32#3585
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ #41 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×H(5,𝔽2)C2semidirect
2. #10596698C2semidirect
3. C3×#5836C2semidirect
4. C3×#5835C2semidirect
5. #10595473C2semidirect
6. #10595471C2semidirect
7. #10595461C2semidirect
8. #10595460C2semidirect
9. #10595449C2semidirect
10. #10595448C2semidirect
11. #10595443C2semidirect
12. #10595115C2semidirect
13. C2×#63937C2semidirect
14. #10595102C2semidirect
15. #10595100C2semidirect
18. C32×H(5,𝔽2)C22semidirect
20. #64366C22semidirect
21. #64366C22semidirect
24. #41×C3⋊D3C22semidirect
26. #64361C22semidirect
28. C2×D4×C3⋊D3C22semidirect
29. C3×#1010C22semidirect
30. C3×#1009C22semidirect
35. #64307C22semidirect
36. #64306C22semidirect
37. #64297C22semidirect
38. C2×#3796C22semidirect
39. C3×#951C22semidirect
40. C3×#950C22semidirect
41. C3×#950C22semidirect
42. C3×#949C22semidirect
43. C3×#948C22semidirect
44. C3×#948C22semidirect
45. C2×C3×#214C22semidirect
46. C3×#932C22semidirect
47. C3×#932C22semidirect
48. C2×C3×#213C22semidirect
49. #63951C22semidirect
50. #63951C22semidirect
51. #63950C22semidirect
52. #63945C22semidirect
53. #63941C22semidirect
54. #63937C22semidirect
55. #63937C22semidirect
56. #63937C22semidirect
57. #63937C22semidirect
58. #63937C22semidirect
59. #63936C22semidirect
60. #63931C22semidirect
61. #63930C22semidirect
62. #63927C22semidirect
63. #63926C22semidirect
64. #63833C22semidirect
65. C2×#3717C22semidirect
66. #63830C22semidirect
67. #63829C22semidirect
68. #63829C22semidirect
69. #63825C22semidirect
70. #63825C22semidirect
71. C2×#3714C22semidirect
72. C2×#3712C22semidirect
73. #63818C22semidirect
74. #63817C22semidirect
75. #63817C22semidirect
84. #5836D3semidirect
86. #5835D3semidirect
145. C3×#235C23semidirect
146. C3×#235C23semidirect
147. C2×C3×D12C23semidirect
148. C2×C3×Dic6C23semidirect
155. #3802C23semidirect
160. #3797C23semidirect
165. #3796C23semidirect
168. C3×#216C23semidirect
169. C3×#216C23semidirect
170. C3×#215C23semidirect
171. C3×#215C23semidirect
172. C3×#214C23semidirect
173. C3×#214C23semidirect
174. C3×#214C23semidirect
175. C3×#213C23semidirect
176. C3×#213C23semidirect
177. C3×#213C23semidirect
178. C3×#208C23semidirect
179. C3×#208C23semidirect
180. C2×C3×C3⋊C8C23semidirect
181. C2×C3×C3⋊C8C23semidirect
182. #3719C23semidirect
183. #3719C23semidirect
184. #3717C23semidirect
185. #3717C23semidirect
186. #3717C23semidirect
187. #3716C23semidirect
188. #3716C23semidirect
189. #3714C23semidirect
190. #3714C23semidirect
191. #3714C23semidirect
194. #3712C23semidirect
195. #3712C23semidirect
196. #3710C23semidirect
201. C3×H(5,𝔽2)C2×D3semidirect
202. C3×H(5,𝔽2)C2×D3semidirect
205. #1010C2×D3semidirect
217. #1009C2×D3semidirect
261. #951C2×D3semidirect
264. #950C2×D3semidirect
265. #950C2×D3semidirect
268. #949C2×D3semidirect
269. #948C2×D3semidirect
270. #948C2×D3semidirect
273. C2×#214C2×D3semidirect
275. #932C2×D3semidirect
276. #932C2×D3semidirect
278. C2×#213C2×D3semidirect
535. #235C22×D3semidirect
536. #235C22×D3semidirect
545. C2×D12C22×D3semidirect
556. C2×Dic6C22×D3semidirect
573. #216C22×D3semidirect
574. #216C22×D3semidirect
578. #215C22×D3semidirect
579. #215C22×D3semidirect
582. #214C22×D3semidirect
583. #214C22×D3semidirect
584. #214C22×D3semidirect
588. #213C22×D3semidirect
589. #213C22×D3semidirect
590. #213C22×D3semidirect
591. #208C22×D3semidirect
592. #208C22×D3semidirect
593. C2×C3⋊C8C22×D3semidirect
594. C2×C3⋊C8C22×D3semidirect
648. H(5,𝔽2)D32semidirect
1010. C32#3585semidirect
1117. C3#87204semidirect
1118. C3#87207semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×H(5,𝔽2)2
#105966982
C3×#58362
C3×#58352
#105954732
#105954712
#105954612
#105954602
#105954492
#105954482
#105954432
#105951152
C2×#639372
#105951022
#105951002
#872073
#872043