Finite Group Databasebeta

← #11886596

Subgroups — #11886596

Order 1152.

980 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5774C211yesmaximal, characteristic, complemented
2#10595466C211yesmaximal, characteristic, complemented
3#10595444C211yesmaximal, characteristic, complemented
4#10595106C211yesmaximal, characteristic, complemented
5#10592899C211yesmaximal, characteristic, complemented
6C3×#5198C211yesmaximal, characteristic, complemented
7#10591688C211yesmaximal, characteristic, complemented
8#10591676C211yesmaximal, characteristic, complemented
9#10591509C211yesmaximal, characteristic, complemented
10#10591505C211yesmaximal, characteristic, complemented
11#10591469C211yesmaximal, characteristic, complemented
12#10591019C211yesmaximal, characteristic, complemented
13#10590996C211yesmaximal, characteristic, complemented
14#10590982C211yesmaximal, characteristic, complemented
15#10590976C211yesmaximal, characteristic, complemented
16#84009—31nomaximal
17#80280—31nomaximal
18C3×#1009C2211yescharacteristic
19C3×#1009C2211yescharacteristic, complemented
20C3×#1004C2211yescharacteristic, complemented
21#64298C2211yescharacteristic, complemented
22C32×AGL(1,ℤ/8)C2211yescharacteristic
23#64160C2211yescharacteristic, complemented
24#64157C2211yescharacteristic, complemented
25C2×#3754C2211yescharacteristic, complemented
26C3×#950C2211yescharacteristic
27C3×#940C2211yescharacteristic, complemented
28C3×#932C2211yescharacteristic, complemented
29C2×C3×#213C2211yescharacteristic, complemented
30C3×#916—21no—
31C3×#914—21no—
32C3×#911—21no—
33C3×D3×D8—21no—
34C3×#908C2211yescharacteristic, complemented
35C3×#907C2211yescharacteristic, complemented
36#63947—21no—
37#63943—21no—
38#63933—21no—
39#63932—21no—
40#63932—21no—
41#63929—21no—
42D3×#214—21no—
43D3×#214—21no—
44#63860C2211yescharacteristic, complemented
45#63831C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47#63823—21no—
48#63823—21no—
49#63823C2211yescharacteristic
50#63823C2211yescharacteristic, complemented
51#63823C2211yescharacteristic, complemented
52#63822—21no—
53#63822C2211yescharacteristic
54C2×#3713—21no—
55C2×#3713C2211yescharacteristic, complemented
56#63815C2211yescharacteristic, complemented
57#63814C2211yescharacteristic, complemented
58#63660C2211yescharacteristic, complemented
59#63651C2211yescharacteristic, complemented
60#63649C2211yescharacteristic, complemented
61C3×#837C2211yescharacteristic, complemented
62C3×#825C2211yescharacteristic, complemented
63C3×#823C2211yescharacteristic, complemented
64#63577C2211yescharacteristic, complemented
65#63569C2211yescharacteristic, complemented
66#63569C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63554C2211yescharacteristic, complemented
69C3×#576—31no—
70#5836—31no—
71#5836—31no—
72#5835—31no—
73#5835—31no—
74#5775—31no—
75#5774D311yescharacteristic, complemented
76#5770—31no—
77C3×#453—31no—
78#5242—31no—
79#5241—31no—
80#5201—31no—
81#5200—31no—
82#5200—31no—
83#5200—61no—
84#5199—31no—
85#5199—31no—
86#5198D311yescharacteristic, complemented
87#5197—31no—
88#5160—31no—
89#5154—31no—
90#5145—31no—
91#5141—31no—
92#5077—31no—
93#5074—31no—
94#4827—31no—
95#4825—31no—
96#4823—31no—
97#4823—31no—
98#4749—31no—
99#4748—31no—
100C32×#41C2311yescharacteristic
101C2×C32×D4C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×#67—41no—
104C2×C3×#67—41no—
105C3×#239—21no—
106C3×#239—21no—
107C3×#237—21no—
108C3×#237—21no—
109C3×D3×D4—21no—
110C3×D3×D4—21no—
111C3×D3×D4—21no—
112C3×D3×D4—21no—
113C3×D3×D4—41no—
114C3×D3×D4—41no—
115C3×#235—21no—
116C3×#235—21no—
117C3×#235C2311yescharacteristic
118C3×#235C2311yescharacteristic
119C3×#235C2311yescharacteristic
120C2×C3×D12—21no—
121C2×C3×D12—21no—
122C2×C3×D12C2311yescharacteristic
123C2×C3×D12C2311yescharacteristic
124#3805—41no—
125#3795—21no—
126#3795—21no—
127D3×Dic6—21no—
128D3×Dic6—21no—
129C32×SD16—21no—
130C32×D8—21no—
131C32×M16C2311yescharacteristic
132#3756—21no—
133#3754—21no—
134#3754—21no—
135#3754—21no—
136#3748—21no—
137#3748C2311yescharacteristic
138#3748C2311yescharacteristic
139C2×C3⋊(C3⋊C8)—21no—
140C2×C3⋊(C3⋊C8)C2311yescharacteristic
141C3×#216D411yescharacteristic, complemented
142C3×#215D411yescharacteristic, complemented
143C3×#214—21no—
144C3×#214D411yescharacteristic, complemented
145C3×#213—21no—
146C3×#213—21no—
147C3×#213—21no—
148C3×#213D411yescharacteristic, complemented
149C3×C4×Dic3C2311yescharacteristic
150C3×#208C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152C3×D24—21no—
153C3×#204—21no—
154C3×ΓL(1,𝔽25)—21no—
155C3×D3×C8—21no—
156(C2×D3)⋊Dic3—41no—
157#3719—21no—
158#3718D411yescharacteristic, complemented
159#3716—21no—
160#3716—21no—
161#3716—21no—
162#3715—21no—
163#3715—21no—
164#3715—21no—
165#3715D411yescharacteristic, complemented
166#3715D411yescharacteristic, complemented
167#3713—21no—
168#3713—21no—
169#3713—21no—
170#3713—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×H(5,𝔽2)—31no—
179C3×H(5,𝔽2)—31no—
180C3×H(5,𝔽2)—31no—
181#1010—31no—
182#1010—31no—
183#1009C2×D311yescharacteristic
184#1009C2×D311yescharacteristic, complemented
185#1004C2×D311yescharacteristic, complemented
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
192C3×AGL(1,ℤ/8)C2×D311yescharacteristic
193C3×#135—31no—
194C3×#135—61no—
195C2×C3×D8—31no—
196C2×C3×D8—61no—
197C3×#131—31no—
198C3×#127—31no—
199#951—31no—
200#951—31no—
201#951—31no—
202#951—61no—
203#951—61no—
204#951—61no—
205#950—31no—
206#950—31no—
207#950—61no—
208#950—61no—
209#950—61no—
210#950—61no—
211#950C2×D311yescharacteristic
212#949—31no—
213#949—31no—
214#949—31no—
215#949—61no—
216#949—61no—
217#948—31no—
218#948—31no—
219#948—31no—
220#948—31no—
221#948—61no—
222#940C2×D311yescharacteristic, complemented
223#936—31no—
224C2×#214—31no—
225C2×#214—31no—
226C2×#214—31no—
227C2×#214—61no—
228C2×#214—61no—
229C2×#214—61no—
230#932—31no—
231#932—31no—
232#932—31no—
233#932—61no—
234#932—61no—
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#915—61no—
247#914—21no—
248D3×SD16—61no—
249D3×SD16—61no—
250#912—61no—
251#911—21no—
252#911—61no—
253#911—61no—
254D3×D8—21no—
255#909—31no—
256#908C2×D311yescharacteristic, complemented
257#907—31no—
258#907C2×D311yescharacteristic, complemented
259C2×#204—31no—
260#901—31no—
261#875—31no—
262C3×#104—31no—
263C3×#104—31no—
264C3×#100—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#824—31no—
274#824—31no—
275#824—61no—
276#823—31no—
277#823C2×D311yescharacteristic, complemented
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—
292C22×C3×D3—41no—
293C32×Q8C2×D411yescharacteristic
294C32×D4—21no—
295C32×D4—21no—
296C32×D4—21no—
297C32×D4C2×D411yescharacteristic
298C2×C32×C4—21no—
299C2×C32×C4C2411yescharacteristic
300C2×C3⋊Dic3—21no—
301#634—21no—
302#634—21no—
303C3×#67—21no—
304C3×#67—21no—
305C3×#67—21no—
306C3×#67—41no—
307C3×#67—41no—
308C3×#67—41no—
309C3×#67—41no—
310C3×#67—82no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—41no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—41no—
318C3×D12—41no—
319C3×D12C2×D411yescharacteristic
320C3×D12C2×D411yescharacteristic
321C3×D12C2×D411yescharacteristic
322C3×C4×D3—21no—
323C3×C4×D3—21no—
324C3×C4×D3—21no—
325C3×C4×D3—41no—
326C3×C4×D3—41no—
327C3×Dic6C2×D411yescharacteristic
328C3×Dic6C2×D411yescharacteristic
329C3×Dic6C2×D411yescharacteristic
330#627—41no—
331#625—41no—
332D3×Dic3—41no—
333D3×Dic3—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—91no—
353#453—31no—
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×#41C22×D311yescharacteristic
368C3×#41C22×D311yescharacteristic
369C2×C3×D4—21no—
370C2×C3×D4—31no—
371C2×C3×D4—31no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4—61no—
376C2×C3×D4—61no—
377C2×C3×D4—61no—
378C2×C3×D4—121no—
379C2×C3×D4—121no—
380C2×C3×D4—121no—
381C2×C3×D4—121no—
382C2×C3×D4C22×D311yescharacteristic
383C2×C3×D4C22×D311yescharacteristic
384C2×#67—41no—
385C2×#67—41no—
386#239—21no—
387#239—21no—
388D3×Q8—61no—
389D3×Q8—61no—
390#237—21no—
391#237—21no—
392#237—61no—
393#237—61no—
394#237—121no—
395#237—121no—
396D3×D4—21no—
397D3×D4—21no—
398D3×D4—21no—
399D3×D4—21no—
400D3×D4—41no—
401D3×D4—41no—
402#235—21no—
403#235—21no—
404#235—61no—
405#235—61no—
406#235C22×D311yescharacteristic
407#235C22×D311yescharacteristic
408#235C22×D311yescharacteristic
409C2×D12—21no—
410C2×D12—21no—
411C2×D12C22×D311yescharacteristic
412C2×D12C22×D311yescharacteristic
413C2×Dic6—31no—
414C2×Dic6—31no—
415C2×Dic6—61no—
416C2×Dic6—61no—
417C2×Dic6—61no—
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×C42—31no—
442#217—121no—
443#216—31no—
444#216—31no—
445#216—61no—
446#216—61no—
447#216—61no—
448#216—121no—
449#216#6711yescharacteristic, complemented
450#215—31no—
451#215—31no—
452#215—61no—
453#215—61no—
454#215—61no—
455#215#6711yescharacteristic, complemented
456#214—21no—
457#214—31no—
458#214—31no—
459#214—61no—
460#214—61no—
461#214—61no—
462#214—61no—
463#214—61no—
464#214—61no—
465#214—61no—
466#214—61no—
467#214—61no—
468#214—61no—
469#214—61no—
470#214—61no—
471#214—121no—
472#214—121no—
473#214—121no—
474#214#6711yescharacteristic, complemented
475#213—21no—
476#213—21no—
477#213—21no—
478#213—31no—
479#213—31no—
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—61no—
489#213—61no—
490#213#6711yescharacteristic, complemented
491(C2×D3)⋊C4—121no—
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
514Dic12—61no—
515D24—21no—
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—21no—
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—81no—
536C2×C3×D3—81no—
537C2×C3×D3—161no—
538C2×C3×D3—161no—
539C2×C3×D3—161no—
540C32×C4—21no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3⋊Dic3—41no—
544C3×Dic3—21no—
545C3×Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3—41no—
5482−1+4—91no—
549H(5,𝔽2)—31no—
550H(5,𝔽2)—31no—
551H(5,𝔽2)—31no—
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
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—31no—
587#124—91no—
588#108—91no—
589#108—91no—
590#104—31no—
591#104—31no—
592#104—91no—
593#104—91no—
594#101—91no—
595#100—31no—
596#100—91no—
597#100—91no—
598#97—91no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—41no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—121no—
605C23×C3—121no—
606C23×C3—121no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3—41no—
612C3×Q8—21no—
613C3×Q8—31no—
614C3×Q8—31no—
615C3×Q8—31no—
616C3×Q8D3×D411yescharacteristic
617C3×Q8C2×#6711yescharacteristic
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—31no—
626C3×D4—31no—
627C3×D4—31no—
628C3×D4—41no—
629C3×D4—41no—
630C3×D4—41no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—61no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—121no—
639C3×D4—121no—
640C3×D4—121no—
641C3×D4—121no—
642C3×D4—121no—
643C3×D4—121no—
644C3×D4—242no—
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—121no—
656C2×C3×C4—121no—
657C2×C3×C4—121no—
658C2×C3×C4C23×D311yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660#67—21no—
661#67—21no—
662#67—21no—
663#67—41no—
664#67—41no—
665#67—41no—
666#67—41no—
667#67—82no—
668#67—121no—
669#67—121no—
670C2×Dic3—21no—
671C2×Dic3—41no—
672C2×Dic3—61no—
673C2×Dic3—61no—
674C2×Dic3—121no—
675C2×Dic3—121no—
676C2×Dic3—121no—
677D12—21no—
678D12—21no—
679D12—21no—
680D12—21no—
681D12—41no—
682D12—41no—
683D12D3×D411yescharacteristic
684D12D3×D411yescharacteristic
685D12C2×#6711yescharacteristic
686C4×D3—21no—
687C4×D3—21no—
688C4×D3—21no—
689C4×D3—41no—
690C4×D3—41no—
691C4×D3—121no—
692C4×D3—121no—
693Dic6—61no—
694Dic6—61no—
695Dic6—61no—
696Dic6—61no—
697Dic6—121no—
698Dic6—121no—
699Dic6—121no—
700Dic6—121no—
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—41no—
730C3×D3—41no—
731C3×D3—41no—
732C3×D3—81no—
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—181no—
744#41—181no—
745#41—361no—
746#41C2×D3211yescharacteristic
747C2×Q8—91no—
748C2×Q8—181no—
749C2×Q8—181no—
750C2×D4—31no—
751C2×D4—31no—
752C2×D4—61no—
753C2×D4—61no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—121no—
759C2×D4—121no—
760C2×D4—121no—
761C2×D4—121no—
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—361no—
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—121no—
825C22×C3—161no—
826C22×C3—241no—
827C22×C3—241no—
828C22×C3—481no—
829C22×C3—481no—
830C22×C3—481no—
831C22×C3#100411yescharacteristic
832C22×C3#100411yescharacteristic
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—81no—
839C2×D3—81no—
840C2×D3—161no—
841C2×D3—161no—
842C2×D3—161no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—41no—
848C3×C4—61no—
849C3×C4—61no—
850C3×C4—61no—
851C3×C4—121no—
852C3×C4C2×D3×D411yescharacteristic
853C3×C4C2×D3×D411yescharacteristic
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C22×#6711yescharacteristic
856Dic3—21no—
857Dic3—21no—
858Dic3—21no—
859Dic3—41no—
860Dic3—121no—
861Dic3—121no—
862Dic3—241no—
863C32#328811yescharacteristic, complemented, Sylow
864C23—21no—
865C23—61no—
866C23—61no—
867C23—121no—
868C23—121no—
869C23—121no—
870Q8—31no—
871Q8—31no—
872Q8—31no—
873Q8—181no—
874Q8—181no—
875Q8—361no—
876Q8D3×#6711yescharacteristic
877D4—21no—
878D4—21no—
879D4—21no—
880D4—31no—
881D4—31no—
882D4—31no—
883D4—61no—
884D4—61no—
885D4—61no—
886D4—61no—
887D4—61no—
888D4—61no—
889D4—61no—
890D4—121no—
891D4—121no—
892D4—121no—
893D4—121no—
894D4—121no—
895D4—121no—
896D4—242no—
897D4—361no—
898D4D3×#6711yescharacteristic
899C2×C4—21no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—181no—
908C2×C4—361no—
909C2×C4—361no—
910C2×C4C22×D3211yescharacteristic
911C8—21no—
912C8—31no—
913C8—31no—
914C8—61no—
915C8—91no—
916C8—91no—
917C8—181no—
918C8—181no—
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—41no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—81no—
926C2×C3—81no—
927C2×C3—81no—
928C2×C3—121no—
929C2×C3—121no—
930C2×C3—121no—
931C2×C3—161no—
932C2×C3—241no—
933C2×C3—241no—
934C2×C3#559011yescharacteristic
935C2×C3D4×#6711yescharacteristic
936D3—41no—
937D3—41no—
938D3—41no—
939D3—81no—
940D3—81no—
941C22—21no—
942C22—41no—
943C22—61no—
944C22—61no—
945C22—61no—
946C22—81no—
947C22—121no—
948C22—121no—
949C22—241no—
950C22—241no—
951C22—481no—
952C22—481no—
953C22—481no—
954C22#6431311yescharacteristic
955C4—21no—
956C4—61no—
957C4—61no—
958C4—61no—
959C4—121no—
960C4—361no—
961C4D32×D411yescharacteristic
962C4C2×D3×#6711yescharacteristic
963C3—21no—
964C3#8028011yescharacteristic, complemented
965C3#8400911yescharacteristic, complemented
966C2—21no—
967C2—41no—
968C2—81no—
969C2—121no—
970C2—121no—
971C2—121no—
972C2—241no—
973C2—241no—
974C2#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. #10595466C2semidirect
3. #10595444C2semidirect
4. #10595106C2semidirect
5. #10592899C2semidirect
6. C3×#5198C2semidirect
7. #10591688C2semidirect
8. #10591676C2semidirect
9. #10591509C2semidirect
10. #10591505C2semidirect
11. #10591469C2semidirect
12. #10591019C2semidirect
13. #10590996C2semidirect
14. #10590982C2semidirect
15. #10590976C2semidirect
19. C3×#1009C22semidirect
20. C3×#1004C22semidirect
21. #64298C22semidirect
23. #64160C22semidirect
24. #64157C22semidirect
25. C2×#3754C22semidirect
27. C3×#940C22semidirect
28. C3×#932C22semidirect
29. C2×C3×#213C22semidirect
34. C3×#908C22semidirect
35. C3×#907C22semidirect
44. #63860C22semidirect
45. #63831C22semidirect
46. C2×#3716C22semidirect
50. #63823C22semidirect
51. #63823C22semidirect
55. C2×#3713C22semidirect
56. #63815C22semidirect
57. #63814C22semidirect
58. #63660C22semidirect
59. #63651C22semidirect
60. #63649C22semidirect
61. C3×#837C22semidirect
62. C3×#825C22semidirect
63. C3×#823C22semidirect
64. #63577C22semidirect
65. #63569C22semidirect
66. #63569C22semidirect
67. #63558C22semidirect
68. #63554C22semidirect
75. #5774D3semidirect
86. #5198D3semidirect
141. C3×#216D4semidirect
142. C3×#215D4semidirect
144. C3×#214D4semidirect
148. C3×#213D4semidirect
158. #3718D4semidirect
165. #3715D4semidirect
166. #3715D4semidirect
172. #3713D4semidirect
184. #1009C2×D3semidirect
185. #1004C2×D3semidirect
222. #940C2×D3semidirect
237. #932C2×D3semidirect
242. C2×#213C2×D3semidirect
256. #908C2×D3semidirect
258. #907C2×D3semidirect
267. #837C2×D3semidirect
272. #825C2×D3semidirect
277. #823C2×D3semidirect
449. #216#67semidirect
455. #215#67semidirect
474. #214#67semidirect
490. #213#67semidirect
863. C32#3288semidirect
964. C3#80280semidirect
965. C3#84009semidirect

Maximal subgroups

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

subgroupindex
C3×#57742
#105954662
#105954442
#105951062
#105928992
C3×#51982
#105916882
#105916762
#105915092
#105915052
#105914692
#105910192
#105909962
#105909822
#105909762
#840093
#802803