Finite Group Databasebeta

← #11886630

Subgroups — #11886630

Order 1152.

982 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5774C211yesmaximal, characteristic, complemented
2#10595457C211yesmaximal, characteristic, complemented
3#10595446C211yesmaximal, characteristic, complemented
4#10595097C211yesmaximal, characteristic, complemented
5#10592898C211yesmaximal, characteristic, complemented
6C3×#5201C211yesmaximal, characteristic, complemented
7#10591676C211yesmaximal, characteristic, complemented
8#10591666C211yesmaximal, characteristic, complemented
9#10591512C211yesmaximal, characteristic, complemented
10#10591505C211yesmaximal, characteristic, complemented
11#10591483C211yesmaximal, characteristic, complemented
12#10591013C211yesmaximal, characteristic, complemented
13#10590998C211yesmaximal, characteristic, complemented
14#10590980C211yesmaximal, characteristic, complemented
15#10590976C211yesmaximal, characteristic, complemented
16#84009—31nomaximal
17#80287—31nomaximal
18C3×#1010C2211yescharacteristic, complemented
19C3×#1009C2211yescharacteristic, complemented
20C3×#1004C2211yescharacteristic
21#64308C2211yescharacteristic, complemented
22C32×AGL(1,ℤ/8)C2211yescharacteristic, complemented
23#64158C2211yescharacteristic, complemented
24#64157C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic, complemented
26C3×#950C2211yescharacteristic
27C3×#936C2211yescharacteristic, complemented
28C3×#932C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#916—21no—
31C3×#914—21no—
32C3×#911—21no—
33C3×D3×D8—21no—
34C3×#908C2211yescharacteristic
35C3×#907C2211yescharacteristic, complemented
36#63948—21no—
37D3×#215—21no—
38#63935—21no—
39#63935—21no—
40#63934—21no—
41#63925—21no—
42#63925—21no—
43D3×#213—21no—
44#63911C2211yescharacteristic, complemented
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, complemented
54#63822—21no—
55#63822C2211yescharacteristic
56#63815C2211yescharacteristic, complemented
57#63814C2211yescharacteristic, complemented
58#63660C2211yescharacteristic, 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
68#63554C2211yescharacteristic, complemented
69C3×#576—31no—
70#5837—31no—
71#5837—31no—
72#5836—31no—
73#5835—31no—
74#5774—31no—
75#5774D311yescharacteristic, complemented
76#5770—31no—
77C3×#454—31no—
78#5242—31no—
79#5241—31no—
80#5201D311yescharacteristic, complemented
81#5200—31no—
82#5199—31no—
83#5199—31no—
84#5199—31no—
85#5199—61no—
86#5198—31no—
87#5197—31no—
88#5160—31no—
89#5154—31no—
90#5145—31no—
91#5141—31no—
92#5061—31no—
93#5058—31no—
94#4823—31no—
95#4823—31no—
96#4822—31no—
97#4822—31no—
98#4754—31no—
99#4754—31no—
100C32×#41C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C2×C4⋊(C3⋊D3)C2311yescharacteristic
103C2×C3×#67—41no—
104C3×#239—21no—
105C3×D3×Q8—21no—
106C3×#237—21no—
107C3×#237—21no—
108C3×#237—21no—
109C3×#237—41no—
110C3×D3×D4—21no—
111C3×D3×D4—21no—
112C3×D3×D4—21no—
113C3×D3×D4—41no—
114C3×#235—21no—
115C3×#235—21no—
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×SD16—21no—
130C32×D8—21no—
131C32×M16C2311yescharacteristic
132#3755—21no—
133#3753—21no—
134#3753—21no—
135#3753—21no—
136#3748—21no—
137#3748C2311yescharacteristic
138#3748C2311yescharacteristic
139C2×C3⋊(C3⋊C8)—21no—
140C2×C3⋊(C3⋊C8)C2311yescharacteristic
141C3×#217—41no—
142C3×#216D411yescharacteristic, complemented
143C3×#215D411yescharacteristic, complemented
144C3×#214—21no—
145C3×#214D411yescharacteristic, complemented
146C3×#213—21no—
147C3×#213—21no—
148C3×#213—21no—
149C3×#213D411yescharacteristic, complemented
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#3288—91noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—31no—
180C3×H(5,𝔽2)—31no—
181#1010C2×D311yescharacteristic, complemented
182#1009—31no—
183#1009—31no—
184#1009C2×D311yescharacteristic, complemented
185#1004C2×D311yescharacteristic
186C3×AGL(1,ℤ/8)—21no—
187C3×AGL(1,ℤ/8)—31no—
188C3×AGL(1,ℤ/8)—31no—
189C3×AGL(1,ℤ/8)—61no—
190C3×AGL(1,ℤ/8)—61no—
191C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
192C3×AGL(1,ℤ/8)C2×D311yescharacteristic, complemented
193C3×#135—31no—
194C3×#135—61no—
195C2×C3×D8—31no—
196C2×C3×D8—61no—
197C3×#131—31no—
198C3×#124—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#942—31no—
223#942—31no—
224#942—61no—
225#942—61no—
226C2×#215—31no—
227C2×#215—31no—
228C2×#215—61no—
229C2×#215—61no—
230#940—31no—
231#936C2×D311yescharacteristic, complemented
232C2×#214—31no—
233C2×#214—61no—
234#932—31no—
235#932—61no—
236#932—61no—
237#932C2×D311yescharacteristic, complemented
238C2×#213—31no—
239C2×#213—31no—
240C2×#213—61no—
241C2×#213—61no—
242C2×#213C2×D311yescharacteristic, complemented
243#918—61no—
244#916—21no—
245#916—61no—
246#916—61no—
247#914—21no—
248#914—61no—
249D3×SD16—61no—
250#911—21no—
251#911—61no—
252#911—61no—
253D3×D8—21no—
254D3×D8—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#833—31no—
269#833—31no—
270#833—31no—
271#833—61no—
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—
283#815—31no—
284#805—31no—
285#805—31no—
286#803—31no—
287C23×C32—21no—
288C22×C3⋊D3—21no—
289C22×C3×D3—21no—
290C22×C3×D3—41no—
291C22×C3×D3—41no—
292C2×D32—41no—
293C32×Q8C2×D411yescharacteristic
294C32×D4—21no—
295C32×D4—21no—
296C32×D4—21no—
297C32×D4C2×D411yescharacteristic
298C2×C32×C4—21no—
299C2×C32×C4C2411yescharacteristic
300C4⋊(C3⋊D3)—21no—
301C4⋊(C3⋊D3)—21no—
302C3×#67—21no—
303C3×#67—21no—
304C3×#67—21no—
305C3×#67—41no—
306C3×#67—41no—
307C3×#67—41no—
308C3×#67—41no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—41no—
312C2×C3×Dic3—41no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—41no—
316C3×D12C2×D411yescharacteristic
317C3×D12C2×D411yescharacteristic
318C3×D12C2×D411yescharacteristic
319C3×C4×D3—21no—
320C3×C4×D3—21no—
321C3×C4×D3—21no—
322C3×C4×D3—41no—
323C3×C4×D3—41no—
324C3×Dic6—21no—
325C3×Dic6—21no—
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—91no—
343#577—91no—
344#576—31no—
345#576—91no—
346#496—91no—
347#472—91no—
348#472—91no—
349#471—91no—
350#471—91no—
351#455—91no—
352#454—31no—
353#453—91no—
354#453—91no—
355#444—91no—
356#444—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×#41C22×D311yescharacteristic
369C3×#41C22×D311yescharacteristic
370C2×C3×Q8—31no—
371C2×C3×Q8—61no—
372C2×C3×Q8—61no—
373C2×C3×D4—21no—
374C2×C3×D4—31no—
375C2×C3×D4—61no—
376C2×C3×D4—61no—
377C2×C3×D4—61no—
378C2×C3×D4—61no—
379C2×C3×D4—121no—
380C2×C3×D4—121no—
381C2×C3×D4C22×D311yescharacteristic
382C2×C3×D4C22×D311yescharacteristic
383C2×#67—41no—
384C2×#67—121no—
385#239—21no—
386#239—61no—
387#239—61no—
388D3×Q8—21no—
389#237—21no—
390#237—21no—
391#237—21no—
392#237—41no—
393D3×D4—21no—
394D3×D4—21no—
395D3×D4—21no—
396D3×D4—41no—
397D3×D4—61no—
398D3×D4—61no—
399D3×D4—121no—
400D3×D4—121no—
401#235—21no—
402#235—21no—
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—31no—
419C3×SD16—21no—
420C3×SD16—21no—
421C3×SD16—31no—
422C3×SD16—31no—
423C3×SD16—41no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×D8—21no—
427C3×D8—21no—
428C3×D8—31no—
429C3×D8—41no—
430C3×D8—61no—
431C3×D8—61no—
432C3×D8—61no—
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×C22⋊C4—121no—
442C3×C42—31no—
443#217—41no—
444#216—31no—
445#216—31no—
446#216—61no—
447#216—61no—
448#216—61no—
449#216—61no—
450#216#6711yescharacteristic, complemented
451#215—31no—
452#215—31no—
453#215—61no—
454#215—61no—
455#215—61no—
456#215—61no—
457#215—61no—
458#215—61no—
459#215—61no—
460#215—61no—
461#215—61no—
462#215—61no—
463#215—121no—
464#215#6711yescharacteristic, complemented
465#214—21no—
466#214—31no—
467#214—31no—
468#214—61no—
469#214—61no—
470#214—61no—
471#214—61no—
472#214—61no—
473#214#6711yescharacteristic, complemented
474#213—21no—
475#213—21no—
476#213—21no—
477#213—31no—
478#213—31no—
479#213—61no—
480#213—61no—
481#213—61no—
482#213—61no—
483#213—61no—
484#213—61no—
485#213—61no—
486#213—61no—
487#213—61no—
488#213—121no—
489#213—121no—
490#213—121no—
491#213#6711yescharacteristic, complemented
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×C32—41no—
528C22×C32—81no—
529C22×C32H(5,𝔽2)11yescharacteristic
530C2×C3⋊D3—41no—
531C2×C3⋊D3—81no—
532C2×C3×D3—21no—
533C2×C3×D3—21no—
534C2×C3×D3—21no—
535C2×C3×D3—41no—
536C2×C3×D3—81no—
537C2×C3×D3—161no—
538C2×C3×D3—161no—
539D32—161no—
540C32×C4—21no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3×Dic3—21no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—41no—
547C3×Dic3—41no—
5482−1+4—31no—
549H(5,𝔽2)—31no—
550H(5,𝔽2)—31no—
551H(5,𝔽2)—91no—
552#137—91no—
553#137—91no—
554#137—181no—
555#137—181no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—31no—
558AGL(1,ℤ/8)—61no—
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—
566AGL(1,ℤ/8)—181no—
567AGL(1,ℤ/8)D3211yescharacteristic, complemented
568#135—31no—
569#135—61no—
570#135—91no—
571#135—181no—
572#135—181no—
573#135—181no—
574C2×SD16—91no—
575C2×SD16—91no—
576C2×SD16—181no—
577C2×SD16—181no—
578C2×D8—31no—
579C2×D8—61no—
580C2×D8—91no—
581C2×D8—181no—
582#131—31no—
583#131—91no—
584#131—91no—
585#131—91no—
586#127—91no—
587#124—31no—
588#108—91no—
589#108—91no—
590#104—31no—
591#104—31no—
592#104—91no—
593#104—91no—
594#101—31no—
595#100—91no—
596#100—91no—
597#100—91no—
598#97—91no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—41no—
602C23×C3—61no—
603C23×C3—121no—
604C23×C3—121no—
605C22×D3—21no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—121no—
611C22×D3—121no—
612C22×D3—121no—
613C3×Q8—21no—
614C3×Q8—31no—
615C3×Q8—31no—
616C3×Q8—31no—
617C3×Q8—61no—
618C3×Q8—61no—
619C3×Q8—121no—
620C3×Q8D3×D411yescharacteristic
621C3×Q8C2×#6711yescharacteristic
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—31no—
630C3×D4—31no—
631C3×D4—31no—
632C3×D4—41no—
633C3×D4—41no—
634C3×D4—41no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—121no—
641C3×D4—121no—
642C3×D4—121no—
643C3×D4—121no—
644C3×D4—121no—
645C3×D4D3×D411yescharacteristic
646C3×D4C2×#6711yescharacteristic
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—41no—
651C2×C3×C4—61no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—121no—
657C2×C3×C4—121no—
658C2×C3×C4—121no—
659C2×C3×C4—121no—
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662#67—21no—
663#67—21no—
664#67—21no—
665#67—41no—
666#67—41no—
667#67—41no—
668#67—41no—
669#67—121no—
670#67—121no—
671#67—242no—
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—41no—
675C2×Dic3—41no—
676D12—21no—
677D12—21no—
678D12—41no—
679D12—61no—
680D12—61no—
681D12—61no—
682D12—61no—
683D12—121no—
684D12—121no—
685D12—121no—
686D12—121no—
687D12—242no—
688D12D3×D411yescharacteristic
689D12D3×D411yescharacteristic
690D12C2×#6711yescharacteristic
691C4×D3—21no—
692C4×D3—21no—
693C4×D3—21no—
694C4×D3—41no—
695C4×D3—41no—
696C4×D3—121no—
697C4×D3—121no—
698Dic6—21no—
699Dic6—21no—
700Dic6—41no—
701Dic6D3×D411yescharacteristic
702Dic6D3×D411yescharacteristic
703Dic6C2×#6711yescharacteristic
704C3×C8—21no—
705C3×C8—21no—
706C3×C8—31no—
707C3×C8—31no—
708C3×C8—41no—
709C3×C8—61no—
710C3⋊C8—21no—
711C3⋊C8—31no—
712C3⋊C8—31no—
713C3⋊C8—31no—
714C3⋊C8—31no—
715C3⋊C8—61no—
716C3⋊C8—61no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—61no—
720C3⋊C8—61no—
721C3⋊C8—121no—
722C3⋊C8—121no—
723C3⋊C8C2×#6711yescharacteristic
724C3⋊C8C2×#6711yescharacteristic
725C2×C32—21no—
726C2×C32—41no—
727C2×C32—81no—
728C2×C32D4211yescharacteristic
729C3⋊D3—81no—
730C3×D3—41no—
731C3×D3—41no—
732C3×D3—41no—
733C3×D3—81no—
734#41—31no—
735#41—31no—
736#41—31no—
737#41—61no—
738#41—61no—
739#41—61no—
740#41—61no—
741#41—61no—
742#41—61no—
743#41—121no—
744#41—181no—
745#41—181no—
746#41C2×D3211yescharacteristic
747C2×Q8—31no—
748C2×Q8—61no—
749C2×Q8—61no—
750C2×D4—31no—
751C2×D4—61no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—61no—
755C2×D4—91no—
756C2×D4—121no—
757C2×D4—121no—
758C2×D4—181no—
759C2×D4—181no—
760C2×D4—361no—
761C2×D4—361no—
762C2×D4C2×D3211yescharacteristic
763Q16—31no—
764Q16—91no—
765Q16—181no—
766Q16—181no—
767SD16—21no—
768SD16—31no—
769SD16—31no—
770SD16—61no—
771SD16—61no—
772SD16—91no—
773SD16—91no—
774SD16—181no—
775SD16—181no—
776SD16—181no—
777SD16—181no—
778SD16—181no—
779SD16—181no—
780SD16—181no—
781SD16—181no—
782SD16—181no—
783D8—21no—
784D8—31no—
785D8—61no—
786D8—61no—
787D8—61no—
788D8—61no—
789D8—91no—
790D8—181no—
791D8—181no—
792D8—181no—
793D8—181no—
794D8—181no—
795M16—31no—
796M16—61no—
797M16—91no—
798M16—91no—
799M16—181no—
800M16—181no—
801M16—181no—
802M16C2×D3211yescharacteristic
803C2×C8—31no—
804C2×C8—61no—
805C2×C8—91no—
806C2×C8—181no—
807C2×C8—181no—
808C2×C8—181no—
809C22⋊C4—121no—
810C42—31no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—41no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—61no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—81no—
821C22×C3—81no—
822C22×C3—81no—
823C22×C3—121no—
824C22×C3—161no—
825C22×C3—241no—
826C22×C3—481no—
827C22×C3—481no—
828C22×C3#100411yescharacteristic
829C22×C3#100411yescharacteristic
830C2×D3—21no—
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—41no—
834C2×D3—81no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—161no—
838C2×D3—161no—
839C2×D3—241no—
840C2×D3—241no—
841C2×D3—241no—
842C2×D3—481no—
843C2×D3—481no—
844C2×D3—481no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—21no—
849C3×C4—41no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—61no—
853C3×C4—121no—
854C3×C4—121no—
855C3×C4C2×D3×D411yescharacteristic
856C3×C4C2×D3×D411yescharacteristic
857C3×C4C2×D3×D411yescharacteristic
858C3×C4C22×#6711yescharacteristic
859Dic3—21no—
860Dic3—21no—
861Dic3—21no—
862Dic3—41no—
863Dic3—41no—
864C32#328811yescharacteristic, complemented, Sylow
865C23—21no—
866C23—61no—
867C23—121no—
868C23—121no—
869C23—181no—
870C23—361no—
871Q8—31no—
872Q8—31no—
873Q8—31no—
874Q8—61no—
875Q8—61no—
876Q8—121no—
877Q8D3×#6711yescharacteristic
878D4—21no—
879D4—21no—
880D4—21no—
881D4—31no—
882D4—31no—
883D4—31no—
884D4—61no—
885D4—61no—
886D4—61no—
887D4—61no—
888D4—61no—
889D4—121no—
890D4—121no—
891D4—121no—
892D4—121no—
893D4—121no—
894D4—181no—
895D4—181no—
896D4—361no—
897D4—361no—
898D4—722no—
899D4D3×#6711yescharacteristic
900C2×C4—21no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—121no—
910C2×C4—361no—
911C2×C4C22×D3211yescharacteristic
912C8—21no—
913C8—31no—
914C8—31no—
915C8—61no—
916C8—91no—
917C8—91no—
918C8—181no—
919C8—181no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—21no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—81no—
927C2×C3—81no—
928C2×C3—81no—
929C2×C3—121no—
930C2×C3—121no—
931C2×C3—121no—
932C2×C3—161no—
933C2×C3—241no—
934C2×C3#559011yescharacteristic
935C2×C3D4×#6711yescharacteristic
936D3—41no—
937D3—41no—
938D3—41no—
939D3—81no—
940D3—241no—
941D3—241no—
942D3—481no—
943C22—21no—
944C22—41no—
945C22—61no—
946C22—61no—
947C22—61no—
948C22—81no—
949C22—121no—
950C22—241no—
951C22—361no—
952C22—481no—
953C22—481no—
954C22—721no—
955C22—1441no—
956C22#6431311yescharacteristic
957C4—21no—
958C4—61no—
959C4—61no—
960C4—61no—
961C4—121no—
962C4—121no—
963C4D32×D411yescharacteristic
964C4C2×D3×#6711yescharacteristic
965C3—21no—
966C3#8028711yescharacteristic, complemented
967C3#8400911yescharacteristic, complemented
968C2—21no—
969C2—41no—
970C2—81no—
971C2—121no—
972C2—121no—
973C2—121no—
974C2—241no—
975C2—721no—
976C2#1059528711yescharacteristic
subgroupG/H
centerC2#10595287
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×AGL(1,ℤ/8)C22
socleC2×C32D42
hypercenterAGL(1,ℤ/8)D32
hypocenterC32#3288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C3×#5774C2semidirect
2. #10595457C2semidirect
3. #10595446C2semidirect
4. #10595097C2semidirect
5. #10592898C2semidirect
6. C3×#5201C2semidirect
7. #10591676C2semidirect
8. #10591666C2semidirect
9. #10591512C2semidirect
10. #10591505C2semidirect
11. #10591483C2semidirect
12. #10591013C2semidirect
13. #10590998C2semidirect
14. #10590980C2semidirect
15. #10590976C2semidirect
18. C3×#1010C22semidirect
19. C3×#1009C22semidirect
21. #64308C22semidirect
22. C32×AGL(1,ℤ/8)C22semidirect
23. #64158C22semidirect
24. #64157C22semidirect
25. C2×#3753C22semidirect
27. C3×#936C22semidirect
28. C3×#932C22semidirect
29. C2×C3×#213C22semidirect
35. C3×#907C22semidirect
44. #63911C22semidirect
45. C2×#3717C22semidirect
47. #63827C22semidirect
48. #63827C22semidirect
50. C2×#3715C22semidirect
53. #63823C22semidirect
56. #63815C22semidirect
57. #63814C22semidirect
58. #63660C22semidirect
59. #63650C22semidirect
60. #63649C22semidirect
61. C3×#837C22semidirect
62. C3×#825C22semidirect
63. C3×#824C22semidirect
64. #63577C22semidirect
65. #63569C22semidirect
66. #63569C22semidirect
67. #63558C22semidirect
68. #63554C22semidirect
75. #5774D3semidirect
80. #5201D3semidirect
142. C3×#216D4semidirect
143. C3×#215D4semidirect
145. C3×#214D4semidirect
149. C3×#213D4semidirect
159. #3718D4semidirect
168. #3715D4semidirect
169. #3715D4semidirect
172. #3713D4semidirect
181. #1010C2×D3semidirect
184. #1009C2×D3semidirect
191. C3×AGL(1,ℤ/8)C2×D3semidirect
192. C3×AGL(1,ℤ/8)C2×D3semidirect
231. #936C2×D3semidirect
237. #932C2×D3semidirect
242. C2×#213C2×D3semidirect
258. #907C2×D3semidirect
267. #837C2×D3semidirect
272. #825C2×D3semidirect
273. #824C2×D3semidirect
450. #216#67semidirect
464. #215#67semidirect
473. #214#67semidirect
491. #213#67semidirect
567. AGL(1,ℤ/8)D32semidirect
864. C32#3288semidirect
966. C3#80287semidirect
967. C3#84009semidirect

Maximal subgroups

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

subgroupindex
C3×#57742
#105954572
#105954462
#105950972
#105928982
C3×#52012
#105916762
#105916662
#105915122
#105915052
#105914832
#105910132
#105909982
#105909802
#105909762
#840093
#802873