Finite Group Databasebeta

← #11886857

Subgroups — #11886857

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5778C211yesmaximal, characteristic, complemented
2#10595457C211yesmaximal, characteristic, complemented
3#10595446C211yesmaximal, characteristic, complemented
4#10595319C211yesmaximal, characteristic, complemented
5#10592902C211yesmaximal, characteristic, complemented
6C3×#5205C211yesmaximal, characteristic, complemented
7#10591675C211yesmaximal, characteristic, complemented
8#10591666C211yesmaximal, characteristic, complemented
9#10591648C211yesmaximal, characteristic, complemented
10#10591642C211yesmaximal, characteristic, complemented
11#10591618C211yesmaximal, characteristic, complemented
12#10591013C211yesmaximal, characteristic, complemented
13#10590998C211yesmaximal, characteristic, complemented
14#10590980C211yesmaximal, characteristic, complemented
15#10590975C211yesmaximal, characteristic, complemented
16#84014—31nomaximal
17#80302—31nomaximal
18C3×#1010C2211yescharacteristic
19C3×#1009C2211yescharacteristic, complemented
20C3×#1007C2211yescharacteristic
21#64308C2211yescharacteristic, complemented
22C32×#137C2211yescharacteristic, complemented
23#64158C2211yescharacteristic
24#64157C2211yescharacteristic, complemented
25C2×#3755C2211yescharacteristic, complemented
26C3×#950C2211yescharacteristic
27C3×#944C2211yescharacteristic, complemented
28C3×#942C2211yescharacteristic, complemented
29C2×C3×#215C2211yescharacteristic, complemented
30C3×#919—21no—
31C3×#918—21no—
32C3×#914—21no—
33C3×D3×SD16—21no—
34C3×#908C2211yescharacteristic
35C3×#907C2211yescharacteristic, complemented
36#63949—21no—
37#63948—21no—
38#63948—21no—
39#63939—21no—
40D3×#215—21no—
41D3×#215—21no—
42#63935—21no—
43#63925—21no—
44#63911C2211yescharacteristic
45C2×#3717C2211yescharacteristic, complemented
46#63827—21no—
47#63827C2211yescharacteristic, complemented
48#63827C2211yescharacteristic, complemented
49C2×#3715—21no—
50C2×#3715C2211yescharacteristic, complemented
51#63825C2211yescharacteristic
52#63823—21no—
53#63823C2211yescharacteristic
54#63822—21no—
55#63822C2211yescharacteristic
56#63815C2211yescharacteristic, complemented
57#63814C2211yescharacteristic, complemented
58#63663C2211yescharacteristic, complemented
59#63650C2211yescharacteristic, complemented
60#63649C2211yescharacteristic, complemented
61C3×#837C2211yescharacteristic, complemented
62C3×#825C2211yescharacteristic, complemented
63C3×#824C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63569C2211yescharacteristic, complemented
66#63569C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68Dic3×C3⋊C8C2211yescharacteristic, complemented
69C3×#577—31no—
70#5837—31no—
71#5837—31no—
72#5837—31no—
73#5836—31no—
74#5778—31no—
75#5778D311yescharacteristic, complemented
76#5770—31no—
77C3×#456—31no—
78#5246—31no—
79#5241—31no—
80#5205D311yescharacteristic, complemented
81#5203—31no—
82#5203—31no—
83#5203—31no—
84#5203—61no—
85#5200—31no—
86#5198—31no—
87#5196—31no—
88#5177—31no—
89#5175—31no—
90#5144—31no—
91#5141—31no—
92#5095—31no—
93#5085—31no—
94#4824—31no—
95#4824—31no—
96#4822—31no—
97#4822—31no—
98#4754—31no—
99#4754—31no—
100C32×#41C2311yescharacteristic
101C2×C32×Q8C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C3×#239—21no—
104C3×#239—21no—
105C3×#239—21no—
106C3×D3×Q8—21no—
107C3×D3×Q8—21no—
108C3×D3×Q8—21no—
109C3×#237—21no—
110C3×#237—41no—
111C3×D3×D4—21no—
112C3×D3×D4—41no—
113C3×#235—21no—
114C3×#235—21no—
115C3×#235—41no—
116C3×#235C2311yescharacteristic
117C3×#235C2311yescharacteristic
118C3×#235C2311yescharacteristic
119C2×C3×D12—21no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×Dic6—21no—
122C2×C3×Dic6C2311yescharacteristic
123#3811—41no—
124C2×#626—41no—
125D3×D12—21no—
126D3×D12—21no—
127#3799—21no—
128#3799—21no—
129C32×Q16—21no—
130C32×SD16—21no—
131C32×M16C2311yescharacteristic
132#3755—21no—
133#3755—21no—
134#3755—21no—
135#3753—21no—
136#3748—21no—
137#3748C2311yescharacteristic
138#3748C2311yescharacteristic
139C2×C3⋊(C3⋊C8)—21no—
140C2×C3⋊(C3⋊C8)C2311yescharacteristic
141C3×#216—21no—
142C3×#216D411yescharacteristic, complemented
143C3×#215—21no—
144C3×#215—21no—
145C3×#215—21no—
146C3×#215D411yescharacteristic, complemented
147C3×#214D411yescharacteristic, complemented
148C3×#213D411yescharacteristic, complemented
149C3×Dic3⋊C4—41no—
150C3×C4×Dic3C2311yescharacteristic
151C3×#208C2311yescharacteristic
152C2×C3×C3⋊C8C2311yescharacteristic
153C3×D24—21no—
154C3×#204—21no—
155C3×ΓL(1,𝔽25)—21no—
156C3×D3×C8—21no—
157#3718—21no—
158#3718—21no—
159#3718D411yescharacteristic, complemented
160#3717—21no—
161#3717—21no—
162#3717—21no—
163#3715—21no—
164#3715—21no—
165#3715—21no—
166#3715—21no—
167#3715—21no—
168#3715D411yescharacteristic, complemented
169#3715D411yescharacteristic, complemented
170#3714—21no—
171#3713—21no—
172#3713D411yescharacteristic, complemented
173#3711—21no—
174#3711—21no—
175D3×C3⋊C8—21no—
176D3×C3⋊C8—21no—
177#3291—91noSylow
178C3×2−1+4—31no—
179C3×2−1+4—31no—
180C3×H(5,𝔽2)—31no—
181#1010C2×D311yescharacteristic
182#1009—31no—
183#1009—31no—
184#1009C2×D311yescharacteristic, complemented
185#1007C2×D311yescharacteristic
186C3×#137—21no—
187C3×#137—31no—
188C3×#137—61no—
189C3×#137C2×D311yescharacteristic, complemented
190C3×#137C2×D311yescharacteristic, complemented
191C3×AGL(1,ℤ/8)—31no—
192C3×AGL(1,ℤ/8)—61no—
193C3×#135—31no—
194C3×#135—61no—
195C2×C3×SD16—31no—
196C2×C3×SD16—61no—
197C3×#131—31no—
198C3×C4⋊Q8—31no—
199#951—31no—
200#951—31no—
201#951—61no—
202#950—31no—
203#950—31no—
204#950—61no—
205#950—61no—
206#950—61no—
207#950—61no—
208#950C2×D311yescharacteristic
209#949—31no—
210#949—31no—
211#949—31no—
212#949—31no—
213#949—61no—
214#949—61no—
215#949—61no—
216#949—61no—
217#948—31no—
218#948—31no—
219#948—31no—
220#948—31no—
221#948—61no—
222#944C2×D311yescharacteristic, complemented
223#942—31no—
224#942—31no—
225#942—61no—
226#942—61no—
227#942—61no—
228#942C2×D311yescharacteristic, complemented
229C2×#215—31no—
230C2×#215—31no—
231C2×#215—31no—
232C2×#215—31no—
233C2×#215—61no—
234C2×#215—61no—
235C2×#215—61no—
236C2×#215—61no—
237C2×#215C2×D311yescharacteristic, complemented
238#940—31no—
239C2×#214—31no—
240C2×#214—61no—
241#932—31no—
242#932—61no—
243#919—21no—
244#919—61no—
245#918—21no—
246#918—61no—
247#918—61no—
248#916—61no—
249#914—21no—
250#914—61no—
251D3×SD16—21no—
252D3×SD16—61no—
253D3×SD16—61no—
254#911—61no—
255#908—31no—
256#908C2×D311yescharacteristic
257#907—31no—
258#907C2×D311yescharacteristic, complemented
259C2×#204—31no—
260#901—31no—
261#874—31no—
262C3×#104—31no—
263C3×#104—31no—
264C3×#101—31no—
265#837—31no—
266#837—31no—
267#837C2×D311yescharacteristic, complemented
268#836—31no—
269#836—31no—
270#836—61no—
271#833—31no—
272#825C2×D311yescharacteristic, complemented
273#824C2×D311yescharacteristic, complemented
274#823—31no—
275#823—31no—
276#823—31no—
277#823—61no—
278#822—31no—
279#822—31no—
280#822—31no—
281#822—61no—
282#819—31no—
283C8×Dic3—31no—
284#805—31no—
285#805—31no—
286C4×C3⋊C8—31no—
287C22×C3⋊D3—21no—
288C22×C3×D3—21no—
289C22×C3×D3—41no—
290C2×D32—41no—
291C32×Q8—21no—
292C32×Q8—21no—
293C32×Q8C2×D411yescharacteristic
294C32×D4—21no—
295C32×D4C2×D411yescharacteristic
296C2×C32×C4—21no—
297C2×C32×C4—21no—
298C2×C32×C4C2411yescharacteristic
299C4⋊(C3⋊D3)—21no—
300C4⋊(C3⋊D3)—21no—
301C3×#67—21no—
302C3×#67—21no—
303C3×#67—21no—
304C3×#67—41no—
305C3×#67—41no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—41no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—41no—
312C3×D12—41no—
313C3×D12C2×D411yescharacteristic
314C3×D12C2×D411yescharacteristic
315C3×D12C2×D411yescharacteristic
316C3×C4×D3—21no—
317C3×C4×D3—21no—
318C3×C4×D3—21no—
319C3×C4×D3—41no—
320C3×C4×D3—41no—
321C3×C4×D3—41no—
322C3×C4×D3—41no—
323C3×Dic6—21no—
324C3×Dic6—21no—
325C3×Dic6—41no—
326C3×Dic6—41no—
327C3×Dic6C2×D411yescharacteristic
328C3×Dic6C2×D411yescharacteristic
329C3×Dic6C2×D411yescharacteristic
330#626—41no—
331#626—41no—
332#626—82no—
333#624—41no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3⋊(C3⋊C8)—21no—
337C3⋊(C3⋊C8)C2×D411yescharacteristic
338C3⋊(C3⋊C8)C2×D411yescharacteristic
339C3×C3⋊C8—21no—
340C3×C3⋊C8C2×D411yescharacteristic
341C3×C3⋊C8C2×D411yescharacteristic
342#577—31no—
343#577—91no—
344#577—91no—
345#577—91no—
346#492—91no—
347#471—91no—
348#471—91no—
349#471—91no—
350#471—91no—
351#456—31no—
352#456—91no—
353#453—91no—
354#453—91no—
355#443—91no—
356#443—91no—
357C3×#41—21no—
358C3×#41—31no—
359C3×#41—31no—
360C3×#41—31no—
361C3×#41—61no—
362C3×#41—61no—
363C3×#41—61no—
364C3×#41—61no—
365C3×#41—61no—
366C3×#41—61no—
367C3×#41—121no—
368C3×#41—121no—
369C3×#41C22×D311yescharacteristic
370C3×#41C22×D311yescharacteristic
371C2×C3×Q8—21no—
372C2×C3×Q8—31no—
373C2×C3×Q8—61no—
374C2×C3×Q8—61no—
375C2×C3×Q8—61no—
376C2×C3×Q8—61no—
377C2×C3×Q8C22×D311yescharacteristic
378C2×C3×Q8C22×D311yescharacteristic
379C2×C3×D4—31no—
380C2×C3×D4—61no—
381C2×C3×D4—61no—
382C2×C3×D4—121no—
383C2×#67—121no—
384#239—21no—
385#239—21no—
386#239—21no—
387#239—61no—
388#239—61no—
389D3×Q8—21no—
390D3×Q8—21no—
391D3×Q8—21no—
392#237—21no—
393#237—41no—
394D3×D4—21no—
395D3×D4—41no—
396D3×D4—61no—
397D3×D4—61no—
398D3×D4—121no—
399D3×D4—121no—
400#235—21no—
401#235—21no—
402#235—41no—
403#235—61no—
404#235—61no—
405#235C22×D311yescharacteristic
406#235C22×D311yescharacteristic
407#235C22×D311yescharacteristic
408C2×D12—21no—
409C2×D12—31no—
410C2×D12—31no—
411C2×D12—61no—
412C2×D12—61no—
413C2×D12—61no—
414C2×D12—121no—
415C2×D12C22×D311yescharacteristic
416C2×Dic6—21no—
417C2×Dic6C22×D311yescharacteristic
418C3×Q16—21no—
419C3×Q16—21no—
420C3×Q16—31no—
421C3×Q16—41no—
422C3×Q16—61no—
423C3×SD16—21no—
424C3×SD16—21no—
425C3×SD16—31no—
426C3×SD16—31no—
427C3×SD16—41no—
428C3×SD16—61no—
429C3×SD16—61no—
430C3×SD16—61no—
431C3×SD16—61no—
432C3×D8—31no—
433C3×D8—61no—
434C3×M16—21no—
435C3×M16—31no—
436C3×M16—61no—
437C3×M16C22×D311yescharacteristic
438C3×M16C22×D311yescharacteristic
439C2×C3×C8—31no—
440C2×C3×C8—61no—
441C3×C4⋊C4—121no—
442C3×C42—31no—
443#216—21no—
444#216—31no—
445#216—31no—
446#216—61no—
447#216—61no—
448#216—61no—
449#216—61no—
450#216#6711yescharacteristic, complemented
451#215—21no—
452#215—21no—
453#215—21no—
454#215—31no—
455#215—31no—
456#215—61no—
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—61no—
466#215—61no—
467#215—61no—
468#215—61no—
469#215—61no—
470#215—121no—
471#215—121no—
472#215—121no—
473#215#6711yescharacteristic, complemented
474#214—31no—
475#214—31no—
476#214—61no—
477#214—61no—
478#214—61no—
479#214—61no—
480#214—61no—
481#214#6711yescharacteristic, complemented
482#213—31no—
483#213—31no—
484#213—61no—
485#213—61no—
486#213—61no—
487#213—61no—
488#213—61no—
489#213—121no—
490#213#6711yescharacteristic, complemented
491Dic3⋊C4—41no—
492C4×Dic3C22×D311yescharacteristic
493#208—31no—
494#208—31no—
495#208—31no—
496#208—31no—
497#208—61no—
498#208—61no—
499#208—61no—
500#208—61no—
501#208—61no—
502#208—61no—
503#208—121no—
504#208C22×D311yescharacteristic
505C2×C3⋊C8—31no—
506C2×C3⋊C8—31no—
507C2×C3⋊C8—61no—
508C2×C3⋊C8—61no—
509C2×C3⋊C8—61no—
510C2×C3⋊C8—61no—
511C2×C3⋊C8—61no—
512C2×C3⋊C8—121no—
513C2×C3⋊C8C22×D311yescharacteristic
514D24—21no—
515D24—61no—
516#204—21no—
517#204—61no—
518#204—61no—
519#204—61no—
520ΓL(1,𝔽25)—21no—
521ΓL(1,𝔽25)—61no—
522ΓL(1,𝔽25)—61no—
523D3×C8—21no—
524D3×C8—61no—
525D3×C8—61no—
526C22×C32—21no—
527C22×C32H(5,𝔽2)11yescharacteristic
528C2×C3⋊D3—41no—
529C2×C3⋊D3—81no—
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D3—41no—
534C2×C3×D3—81no—
535C2×C3×D3—161no—
536D32—161no—
537C32×C4—21no—
538C32×C4—41no—
539C32×C4C22×D411yescharacteristic
540C32×C4C22×D411yescharacteristic
541C3×Dic3—22no—
542C3×Dic3—21no—
543C3×Dic3—21no—
544C3×Dic3—21no—
545C3×Dic3—41no—
5462−1+4—31no—
5472−1+4—31no—
548H(5,𝔽2)—31no—
549H(5,𝔽2)—91no—
550#137—31no—
551#137—61no—
552#137—91no—
553#137—91no—
554#137—181no—
555#137—181no—
556#137—181no—
557#137D3211yescharacteristic, complemented
558AGL(1,ℤ/8)—31no—
559AGL(1,ℤ/8)—61no—
560AGL(1,ℤ/8)—91no—
561AGL(1,ℤ/8)—91no—
562AGL(1,ℤ/8)—91no—
563AGL(1,ℤ/8)—181no—
564AGL(1,ℤ/8)—181no—
565AGL(1,ℤ/8)—181no—
566#135—31no—
567#135—61no—
568#135—91no—
569#135—181no—
570#135—181no—
571#135—181no—
572C2×SD16—31no—
573C2×SD16—61no—
574C2×SD16—91no—
575C2×SD16—91no—
576C2×SD16—91no—
577C2×SD16—181no—
578C2×SD16—181no—
579C2×SD16—181no—
580#131—31no—
581#131—91no—
582#131—91no—
583#131—91no—
584C4⋊Q8—31no—
585#127—91no—
586#108—91no—
587#108—91no—
588#104—31no—
589#104—31no—
590#104—91no—
591#104—91no—
592#101—31no—
593#101—91no—
594#100—91no—
595#100—91no—
596C4×C8—91no—
597C23×C3—61no—
598C23×C3—121no—
599C22×D3—21no—
600C22×D3—41no—
601C22×D3—61no—
602C22×D3—61no—
603C22×D3—121no—
604C22×D3—121no—
605C22×D3—121no—
606C3×Q8—21no—
607C3×Q8—21no—
608C3×Q8—21no—
609C3×Q8—21no—
610C3×Q8—21no—
611C3×Q8—31no—
612C3×Q8—31no—
613C3×Q8—31no—
614C3×Q8—41no—
615C3×Q8—41no—
616C3×Q8—61no—
617C3×Q8—61no—
618C3×Q8—121no—
619C3×Q8—121no—
620C3×Q8D3×D411yescharacteristic
621C3×Q8C2×#6711yescharacteristic
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—31no—
626C3×D4—31no—
627C3×D4—31no—
628C3×D4—41no—
629C3×D4—61no—
630C3×D4—61no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—121no—
635C3×D4—121no—
636C3×D4—121no—
637C3×D4—121no—
638C3×D4D3×D411yescharacteristic
639C3×D4C2×#6711yescharacteristic
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—41no—
646C2×C3×C4—41no—
647C2×C3×C4—61no—
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×C4—121no—
656C2×C3×C4—121no—
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659#67—21no—
660#67—21no—
661#67—21no—
662#67—41no—
663#67—41no—
664#67—121no—
665#67—121no—
666#67—242no—
667C2×Dic3—21no—
668C2×Dic3—21no—
669C2×Dic3—41no—
670D12—21no—
671D12—21no—
672D12—41no—
673D12—41no—
674D12—61no—
675D12—61no—
676D12—61no—
677D12—61no—
678D12—121no—
679D12—121no—
680D12—121no—
681D12—121no—
682D12—242no—
683D12D3×D411yescharacteristic
684D12D3×D411yescharacteristic
685D12C2×#6711yescharacteristic
686C4×D3—21no—
687C4×D3—21no—
688C4×D3—21no—
689C4×D3—41no—
690C4×D3—41no—
691C4×D3—41no—
692C4×D3—41no—
693C4×D3—121no—
694C4×D3—121no—
695Dic6—21no—
696Dic6—21no—
697Dic6—41no—
698Dic6—41no—
699Dic6D3×D411yescharacteristic
700Dic6D3×D411yescharacteristic
701Dic6C2×#6711yescharacteristic
702C3×C8—21no—
703C3×C8—21no—
704C3×C8—31no—
705C3×C8—31no—
706C3×C8—41no—
707C3×C8—61no—
708C3⋊C8—21no—
709C3⋊C8—31no—
710C3⋊C8—31no—
711C3⋊C8—31no—
712C3⋊C8—31no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—121no—
720C3⋊C8—121no—
721C3⋊C8C2×#6711yescharacteristic
722C3⋊C8C2×#6711yescharacteristic
723C2×C32—21no—
724C2×C32—41no—
725C2×C32D4211yescharacteristic
726C3⋊D3—81no—
727C3×D3—41no—
728C3×D3—41no—
729C3×D3—41no—
730C3×D3—81no—
731#41—31no—
732#41—31no—
733#41—31no—
734#41—61no—
735#41—61no—
736#41—61no—
737#41—61no—
738#41—61no—
739#41—61no—
740#41—121no—
741#41—121no—
742#41—181no—
743#41—181no—
744#41C2×D3211yescharacteristic
745C2×Q8—31no—
746C2×Q8—61no—
747C2×Q8—61no—
748C2×Q8—61no—
749C2×Q8—61no—
750C2×Q8C2×D3211yescharacteristic
751C2×D4—31no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—91no—
755C2×D4—121no—
756C2×D4—181no—
757C2×D4—181no—
758C2×D4—361no—
759C2×D4—361no—
760Q16—21no—
761Q16—31no—
762Q16—61no—
763Q16—91no—
764Q16—181no—
765Q16—181no—
766SD16—21no—
767SD16—31no—
768SD16—31no—
769SD16—61no—
770SD16—61no—
771SD16—61no—
772SD16—61no—
773SD16—91no—
774SD16—91no—
775SD16—181no—
776SD16—181no—
777SD16—181no—
778SD16—181no—
779SD16—181no—
780SD16—181no—
781SD16—181no—
782SD16—181no—
783SD16—181no—
784SD16—181no—
785SD16—181no—
786D8—31no—
787D8—61no—
788D8—91no—
789D8—181no—
790D8—181no—
791D8—181no—
792M16—31no—
793M16—61no—
794M16—91no—
795M16—91no—
796M16—181no—
797M16—181no—
798M16—181no—
799M16C2×D3211yescharacteristic
800C2×C8—31no—
801C2×C8—61no—
802C2×C8—91no—
803C2×C8—181no—
804C2×C8—181no—
805C2×C8—181no—
806C4⋊C4—121no—
807C42—31no—
808C22×C3—21no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—41no—
812C22×C3—61no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—121no—
816C22×C3—241no—
817C22×C3—481no—
818C22×C3#100411yescharacteristic
819C22×C3#100411yescharacteristic
820C2×D3—21no—
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—41no—
824C2×D3—81no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—161no—
828C2×D3—241no—
829C2×D3—241no—
830C2×D3—241no—
831C2×D3—481no—
832C2×D3—481no—
833C2×D3—481no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—41no—
839C3×C4—41no—
840C3×C4—41no—
841C3×C4—62no—
842C3×C4—61no—
843C3×C4—61no—
844C3×C4—61no—
845C3×C4—81no—
846C3×C4—121no—
847C3×C4C2×D3×D411yescharacteristic
848C3×C4C2×D3×D411yescharacteristic
849C3×C4C2×D3×D411yescharacteristic
850C3×C4C22×#6711yescharacteristic
851Dic3—22no—
852Dic3—21no—
853Dic3—21no—
854Dic3—21no—
855Dic3—41no—
856C32#329111yescharacteristic, complemented, Sylow
857C23—61no—
858C23—121no—
859C23—181no—
860C23—361no—
861Q8—21no—
862Q8—21no—
863Q8—31no—
864Q8—31no—
865Q8—31no—
866Q8—61no—
867Q8—61no—
868Q8—121no—
869Q8—121no—
870Q8D3×#6711yescharacteristic
871D4—21no—
872D4—31no—
873D4—31no—
874D4—31no—
875D4—61no—
876D4—61no—
877D4—61no—
878D4—61no—
879D4—61no—
880D4—121no—
881D4—121no—
882D4—121no—
883D4—121no—
884D4—181no—
885D4—181no—
886D4—361no—
887D4—361no—
888D4—722no—
889D4D3×#6711yescharacteristic
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—121no—
898C2×C4—121no—
899C2×C4—121no—
900C2×C4—121no—
901C2×C4—121no—
902C2×C4—361no—
903C2×C4C22×D3211yescharacteristic
904C8—21no—
905C8—31no—
906C8—31no—
907C8—61no—
908C8—91no—
909C8—91no—
910C8—181no—
911C8—181no—
912C2×C3—21no—
913C2×C3—21no—
914C2×C3—21no—
915C2×C3—41no—
916C2×C3—41no—
917C2×C3—41no—
918C2×C3—81no—
919C2×C3—121no—
920C2×C3—121no—
921C2×C3—121no—
922C2×C3—241no—
923C2×C3#559011yescharacteristic
924C2×C3D4×#6711yescharacteristic
925D3—41no—
926D3—41no—
927D3—41no—
928D3—81no—
929D3—241no—
930D3—241no—
931D3—481no—
932C22—21no—
933C22—61no—
934C22—61no—
935C22—61no—
936C22—121no—
937C22—241no—
938C22—361no—
939C22—481no—
940C22—721no—
941C22—1441no—
942C22#6431311yescharacteristic
943C4—21no—
944C4—41no—
945C4—62no—
946C4—61no—
947C4—61no—
948C4—61no—
949C4—121no—
950C4D32×D411yescharacteristic
951C4C2×D3×#6711yescharacteristic
952C3—21no—
953C3#8030211yescharacteristic, complemented
954C3#8401411yescharacteristic, complemented
955C2—21no—
956C2—41no—
957C2—121no—
958C2—121no—
959C2—121no—
960C2—241no—
961C2—721no—
962C2#1059528711yescharacteristic
subgroupG/H
centerC2#10595287
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#137C22
socleC2×C32D42
hypercenter#137D32
hypocenterC32#3291
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. C3×#5778C2semidirect
2. #10595457C2semidirect
3. #10595446C2semidirect
4. #10595319C2semidirect
5. #10592902C2semidirect
6. C3×#5205C2semidirect
7. #10591675C2semidirect
8. #10591666C2semidirect
9. #10591648C2semidirect
10. #10591642C2semidirect
11. #10591618C2semidirect
12. #10591013C2semidirect
13. #10590998C2semidirect
14. #10590980C2semidirect
15. #10590975C2semidirect
19. C3×#1009C22semidirect
21. #64308C22semidirect
22. C32×#137C22semidirect
24. #64157C22semidirect
25. C2×#3755C22semidirect
27. C3×#944C22semidirect
28. C3×#942C22semidirect
29. C2×C3×#215C22semidirect
35. C3×#907C22semidirect
45. C2×#3717C22semidirect
47. #63827C22semidirect
48. #63827C22semidirect
50. C2×#3715C22semidirect
56. #63815C22semidirect
57. #63814C22semidirect
58. #63663C22semidirect
59. #63650C22semidirect
60. #63649C22semidirect
61. C3×#837C22semidirect
62. C3×#825C22semidirect
63. C3×#824C22semidirect
64. #63577C22semidirect
65. #63569C22semidirect
66. #63569C22semidirect
67. #63558C22semidirect
68. Dic3×C3⋊C8C22semidirect
75. #5778D3semidirect
80. #5205D3semidirect
142. C3×#216D4semidirect
146. C3×#215D4semidirect
147. C3×#214D4semidirect
148. C3×#213D4semidirect
159. #3718D4semidirect
168. #3715D4semidirect
169. #3715D4semidirect
172. #3713D4semidirect
184. #1009C2×D3semidirect
189. C3×#137C2×D3semidirect
190. C3×#137C2×D3semidirect
222. #944C2×D3semidirect
228. #942C2×D3semidirect
237. C2×#215C2×D3semidirect
258. #907C2×D3semidirect
267. #837C2×D3semidirect
272. #825C2×D3semidirect
273. #824C2×D3semidirect
450. #216#67semidirect
473. #215#67semidirect
481. #214#67semidirect
490. #213#67semidirect
557. #137D32semidirect
856. C32#3291semidirect
953. C3#80302semidirect
954. C3#84014semidirect

Maximal subgroups

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

subgroupindex
C3×#57782
#105954572
#105954462
#105953192
#105929022
C3×#52052
#105916752
#105916662
#105916482
#105916422
#105916182
#105910132
#105909982
#105909802
#105909752
#840143
#803023