Finite Group Databasebeta

← #11886605

Subgroups — #11886605

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×#5770C211yesmaximal, characteristic, complemented
2C3×#5769C211yesmaximal, characteristic, complemented
3#10595446C211yesmaximal, characteristic, complemented
4#10595444C211yesmaximal, characteristic, complemented
5#10592896C211yesmaximal, characteristic, complemented
6#10591684C211yesmaximal, characteristic, complemented
7#10591681C211yesmaximal, characteristic, complemented
8#10591678C211yesmaximal, characteristic, complemented
9#10591665C211yesmaximal, characteristic, complemented
10#10591665C211yesmaximal, characteristic, complemented
11#10591664C211yesmaximal, characteristic, complemented
12#10590926C211yesmaximal, characteristic, complemented
13#10590925C211yesmaximal, characteristic, complemented
14#10590922C211yesmaximal, characteristic, complemented
15#10590887C211yesmaximal, characteristic, complemented
16#84015—31nomaximal
17#84009—31nomaximal
18C3×#1010C2211yescharacteristic, complemented
19C3×#1009C2211yescharacteristic
20C3×#1009C2211yescharacteristic, complemented
21C3×#1009C2211yescharacteristic, complemented
22C32×#135C2211yescharacteristic
23#64157C2211yescharacteristic, complemented
24#64157C2211yescharacteristic, complemented
25C3×#951C2211yescharacteristic, complemented
26C3×#949C2211yescharacteristic
27C3×#949C2211yescharacteristic, complemented
28C3×#949C2211yescharacteristic, complemented
29C3×#919—21no—
30C3×#918—21no—
31C3×#916—21no—
32C3×#914—21no—
33C3×#914—21no—
34C3×D3×SD16—21no—
35C3×#911—21no—
36C3×D3×D8—21no—
37C2×C3×D24C2211yescharacteristic, complemented
38C2×C3×#204C2211yescharacteristic, complemented
39C3×#901C2211yescharacteristic, complemented
40C3×#901C2211yescharacteristic, complemented
41#63914C2211yescharacteristic, complemented
42#63863C2211yescharacteristic, complemented
43#63827—21no—
44#63827C2211yescharacteristic, complemented
45C2×#3715—21no—
46C2×#3715C2211yescharacteristic, complemented
47#63823—21no—
48#63823—21no—
49#63823—21no—
50#63823C2211yescharacteristic
51#63823C2211yescharacteristic, complemented
52#63823C2211yescharacteristic, complemented
53#63822—21no—
54#63822—21no—
55#63822C2211yescharacteristic
56C2×#3713—21no—
57C2×#3713C2211yescharacteristic, complemented
58#63664C2211yescharacteristic, complemented
59#63664C2211yescharacteristic, complemented
60#63646C2211yescharacteristic, complemented
61#63642C2211yescharacteristic, complemented
62#63578C2211yescharacteristic, complemented
63#63568C2211yescharacteristic, complemented
64#63568C2211yescharacteristic, complemented
65#63560C2211yescharacteristic, complemented
66#63558C2211yescharacteristic, complemented
67#63558C2211yescharacteristic, complemented
68#63558C2211yescharacteristic, complemented
69C3×#577—31no—
70C3×#576—31no—
71#5837—31no—
72#5836—31no—
73#5835—31no—
74#5835—31no—
75#5770D311yescharacteristic, complemented
76#5769D311yescharacteristic, complemented
77#5245—31no—
78#5242—31no—
79#5241—31no—
80#5241—31no—
81#5203—31no—
82#5202—31no—
83#5201—31no—
84#5200—31no—
85#5199—31no—
86#5199—31no—
87#5198—31no—
88#5198—31no—
89#5197—31no—
90#5197—31no—
91#5197—61no—
92#5177—31no—
93#5176—31no—
94#5160—31no—
95#5154—31no—
96#5145—31no—
97#5145—31no—
98#5142—31no—
99#5141—31no—
100C32×#41C2311yescharacteristic
101C32×#41C2311yescharacteristic
102C3×#239—21no—
103C3×#239—21no—
104C3×#239—21no—
105C3×D3×Q8—21no—
106C3×#237—21no—
107C3×#237—41no—
108C3×D3×D4—21no—
109C3×D3×D4—21no—
110C3×D3×D4—21no—
111C3×D3×D4—41no—
112C3×D3×D4—41no—
113C3×D3×D4—41no—
114C3×#235—21no—
115C3×#235—21no—
116C3×#235—21no—
117C3×#235—21no—
118C3×#235C2311yescharacteristic
119C3×#235C2311yescharacteristic
120C2×C3×D12—21no—
121C2×C3×D12—21no—
122C2×C3×D12—21no—
123C2×C3×D12C2311yescharacteristic
124C2×C3×D12C2311yescharacteristic
125C2×C3×D12C2311yescharacteristic
126C2×C3×Dic6—21no—
127C2×C3×Dic6C2311yescharacteristic
128C2×#625—41no—
129C32×Q16D411yescharacteristic, complemented
130C32×SD16D411yescharacteristic, complemented
131C32×SD16D411yescharacteristic, complemented
132C32×D8D411yescharacteristic, complemented
133C2×C32×C8C2311yescharacteristic
134C4×C3⋊Dic3C2311yescharacteristic
135#3748—21no—
136#3748—21no—
137#3748C2311yescharacteristic
138#3748C2311yescharacteristic
139C2×C3⋊(C3⋊C8)—21no—
140C2×C3⋊(C3⋊C8)—21no—
141C2×C3⋊(C3⋊C8)C2311yescharacteristic
142C3×#216—21no—
143C3×#215—21no—
144C3×#215—21no—
145C3×#215—21no—
146C3×#214—21no—
147C3×#213—21no—
148C3×#213—21no—
149C3×#213—21no—
150C3×#208C2311yescharacteristic
151C3×#208C2311yescharacteristic
152C3×D24—21no—
153C3×D24—21no—
154C3×#204—21no—
155C3×#204—21no—
156C3×ΓL(1,𝔽25)—21no—
157C3×ΓL(1,𝔽25)—21no—
158C3×D3×C8—21no—
159C3×D3×C8—21no—
160(C2×D3)⋊Dic3—41no—
161#3718—21no—
162#3718D411yescharacteristic, complemented
163#3715—21no—
164#3715—21no—
165#3715—21no—
166#3715—21no—
167#3715—21no—
168#3715—21no—
169#3715D411yescharacteristic, complemented
170#3715D411yescharacteristic, complemented
171#3713—21no—
172#3713—21no—
173#3713—21no—
174#3713—21no—
175#3713—21no—
176#3713D411yescharacteristic, complemented
177#3288—91noSylow
178C3×2−1+4—31no—
179C3×H(5,𝔽2)—31no—
180C3×H(5,𝔽2)—31no—
181C3×H(5,𝔽2)—31no—
182#1010C2×D311yescharacteristic, complemented
183#1009C2×D311yescharacteristic
184#1009C2×D311yescharacteristic, complemented
185#1009C2×D311yescharacteristic, complemented
186C3×#137—31no—
187C3×#137—61no—
188C3×AGL(1,ℤ/8)—31no—
189C3×AGL(1,ℤ/8)—31no—
190C3×AGL(1,ℤ/8)—31no—
191C3×AGL(1,ℤ/8)—61no—
192C3×AGL(1,ℤ/8)—61no—
193C3×AGL(1,ℤ/8)—61no—
194C3×#135—21no—
195C3×#135—61no—
196C3×#135—61no—
197C3×#135C2×D311yescharacteristic
198C3×#135C2×D311yescharacteristic
199C2×C3×SD16—31no—
200C2×C3×SD16—61no—
201C2×C3×D8—31no—
202C2×C3×D8—61no—
203C3×#131—31no—
204C3×#131—31no—
205#951—31no—
206#951—61no—
207#951C2×D311yescharacteristic, complemented
208#950—31no—
209#950—31no—
210#950—61no—
211#950—61no—
212#950—61no—
213#950—61no—
214#949—31no—
215#949—31no—
216#949—31no—
217#949—61no—
218#949—61no—
219#949—61no—
220#949C2×D311yescharacteristic
221#949C2×D311yescharacteristic, complemented
222#949C2×D311yescharacteristic, complemented
223#948—31no—
224#948—31no—
225#948—31no—
226#948—31no—
227#948—61no—
228#948—61no—
229#947—31no—
230#942—31no—
231#942—61no—
232C2×#215—31no—
233C2×#215—61no—
234#940—31no—
235#940—31no—
236#936—31no—
237C2×#214—31no—
238C2×#214—61no—
239#932—31no—
240#932—31no—
241#932—31no—
242#932—61no—
243#932—61no—
244#932—61no—
245C2×#213—31no—
246C2×#213—31no—
247C2×#213—61no—
248C2×#213—61no—
249#919—21no—
250#918—21no—
251#916—21no—
252#914—21no—
253#914—21no—
254D3×SD16—21no—
255#911—21no—
256D3×D8—21no—
257C2×D24C2×D311yescharacteristic, complemented
258C2×#204C2×D311yescharacteristic, complemented
259#901C2×D311yescharacteristic, complemented
260#901C2×D311yescharacteristic, complemented
261#837—31no—
262#837—31no—
263#837—31no—
264#837—31no—
265#837—31no—
266#837—31no—
267#837—61no—
268#837—61no—
269#836—31no—
270#833—31no—
271#833—31no—
272#833—31no—
273#825—31no—
274#825—31no—
275#824—31no—
276#823—31no—
277#823—31no—
278#823—31no—
279#822—31no—
280#822—31no—
281#819—31no—
282#819—31no—
283#819—61no—
284#815—31no—
285#815—31no—
286#815—61no—
287C22×C3×D3—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×Q8C2×D411yescharacteristic
295C32×D4—21no—
296C32×D4—21no—
297C32×D4C2×D411yescharacteristic
298C32×D4C2×D411yescharacteristic
299C2×C32×C4—21no—
300C2×C32×C4—21no—
301C2×C32×C4C2411yescharacteristic
302C2×C3⋊Dic3—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—41no—
311C3×D12—21no—
312C3×D12—21no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—41no—
318C3×D12—41no—
319C3×D12—41no—
320C3×D12C2×D411yescharacteristic
321C3×D12C2×D411yescharacteristic
322C3×C4×D3—21no—
323C3×C4×D3—21no—
324C3×C4×D3—41no—
325C3×C4×D3—41no—
326C3×C4×D3—41no—
327C3×C4×D3—41no—
328C3×Dic6—21no—
329C3×Dic6—21no—
330C3×Dic6—41no—
331C3×Dic6C2×D411yescharacteristic
332C3×Dic6C2×D411yescharacteristic
333#625—82no—
334C32×C8C2×D411yescharacteristic
335C32×C8C2×D411yescharacteristic
336C3⋊(C3⋊C8)—21no—
337C3⋊(C3⋊C8)—21no—
338C3⋊(C3⋊C8)C2×D411yescharacteristic
339C3⋊(C3⋊C8)C2×D411yescharacteristic
340C3×C3⋊C8—21no—
341C3×C3⋊C8—21no—
342#577—31no—
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—91no—
354#453—91no—
355#444—91no—
356#444—91no—
357C3×#41—21no—
358C3×#41—21no—
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—61no—
368C3×#41—61no—
369C3×#41—121no—
370C3×#41C22×D311yescharacteristic
371C3×#41C22×D311yescharacteristic
372C3×#41C22×D311yescharacteristic
373C3×#41C22×D311yescharacteristic
374C2×C3×Q8—31no—
375C2×C3×Q8—61no—
376C2×C3×Q8—61no—
377C2×C3×D4—31no—
378C2×C3×D4—31no—
379C2×C3×D4—31no—
380C2×C3×D4—61no—
381C2×C3×D4—61no—
382C2×C3×D4—61no—
383C2×C3×D4—61no—
384C2×C3×D4—61no—
385C2×C3×D4—61no—
386C2×C3×D4—121no—
387C2×C3×D4—121no—
388C2×C3×D4—121no—
389C2×#67—121no—
390C2×#67—121no—
391#239—21no—
392#239—21no—
393#239—21no—
394D3×Q8—21no—
395#237—21no—
396#237—41no—
397D3×D4—21no—
398D3×D4—21no—
399D3×D4—21no—
400D3×D4—41no—
401D3×D4—41no—
402D3×D4—41no—
403#235—21no—
404#235—21no—
405#235—21no—
406#235—21no—
407#235C22×D311yescharacteristic
408#235C22×D311yescharacteristic
409C2×D12—21no—
410C2×D12—21no—
411C2×D12—21no—
412C2×D12C22×D311yescharacteristic
413C2×D12C22×D311yescharacteristic
414C2×D12C22×D311yescharacteristic
415C2×Dic6—21no—
416C2×Dic6C22×D311yescharacteristic
417C3×Q16—21no—
418C3×Q16—61no—
419C3×Q16#6711yescharacteristic, complemented
420C3×Q16#6711yescharacteristic, complemented
421C3×SD16—21no—
422C3×SD16—21no—
423C3×SD16—61no—
424C3×SD16—61no—
425C3×SD16—61no—
426C3×SD16—61no—
427C3×SD16—61no—
428C3×SD16—61no—
429C3×SD16#6711yescharacteristic, complemented
430C3×SD16#6711yescharacteristic, complemented
431C3×SD16#6711yescharacteristic, complemented
432C3×SD16#6711yescharacteristic, complemented
433C3×D8—21no—
434C3×D8—61no—
435C3×D8—61no—
436C3×D8—61no—
437C3×D8—61no—
438C3×D8—61no—
439C3×D8#6711yescharacteristic, complemented
440C3×D8#6711yescharacteristic, complemented
441C3×M16—31no—
442C3×M16—31no—
443C3×M16—61no—
444C3×M16—61no—
445C2×C3×C8—21no—
446C2×C3×C8—61no—
447C2×C3×C8—61no—
448C2×C3×C8C22×D311yescharacteristic
449C2×C3×C8C22×D311yescharacteristic
450#217—121no—
451#216—21no—
452#216—31no—
453#216—31no—
454#216—61no—
455#216—61no—
456#215—21no—
457#215—21no—
458#215—21no—
459#215—31no—
460#215—31no—
461#215—61no—
462#215—61no—
463#215—61no—
464#215—61no—
465#215—61no—
466#215—61no—
467#214—21no—
468#214—31no—
469#214—31no—
470#214—61no—
471#214—61no—
472#214—61no—
473#214—61no—
474#214—61no—
475#214—61no—
476#213—21no—
477#213—21no—
478#213—21no—
479#213—31no—
480#213—31no—
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—61no—
491(C2×D3)⋊C4—121no—
492C4×Dic3—31no—
493C4×Dic3—31no—
494C4×Dic3—61no—
495#208—31no—
496#208—31no—
497#208—31no—
498#208—31no—
499#208—61no—
500#208—61no—
501#208—61no—
502#208—61no—
503#208—61no—
504#208—61no—
505#208—121no—
506#208—121no—
507#208C22×D311yescharacteristic
508#208C22×D311yescharacteristic
509C2×C3⋊C8—31no—
510C2×C3⋊C8—31no—
511C2×C3⋊C8—61no—
512C2×C3⋊C8—61no—
513C2×C3⋊C8—61no—
514C2×C3⋊C8—61no—
515C2×C3⋊C8—61no—
516C2×C3⋊C8—121no—
517C2×C3⋊C8—121no—
518D24—21no—
519D24—21no—
520#204—21no—
521#204—21no—
522ΓL(1,𝔽25)—21no—
523ΓL(1,𝔽25)—21no—
524D3×C8—21no—
525D3×C8—21no—
526C22×C32—21no—
527C22×C32—21no—
528C22×C32H(5,𝔽2)11yescharacteristic
529C2×C3×D3—21no—
530C2×C3×D3—21no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—41no—
534C2×C3×D3—81no—
535C2×C3×D3—81no—
536C2×C3×D3—81no—
537C2×C3×D3—161no—
538C2×C3×D3—161no—
539C2×C3×D3—161no—
540C32×C4—21no—
541C32×C4—21no—
542C32×C4C22×D411yescharacteristic
543C32×C4C22×D411yescharacteristic
544C3⋊Dic3—41no—
545C3×Dic3—21no—
546C3×Dic3—21no—
547C3×Dic3—41no—
5482−1+4—31no—
549H(5,𝔽2)—31no—
550H(5,𝔽2)—31no—
551H(5,𝔽2)—31no—
552#137—31no—
553#137—61no—
554#137—91no—
555#137—181no—
556AGL(1,ℤ/8)—31no—
557AGL(1,ℤ/8)—31no—
558AGL(1,ℤ/8)—31no—
559AGL(1,ℤ/8)—61no—
560AGL(1,ℤ/8)—61no—
561AGL(1,ℤ/8)—61no—
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—
568#135—61no—
569#135—61no—
570#135—91no—
571#135—181no—
572#135—181no—
573#135D3211yescharacteristic
574C2×SD16—31no—
575C2×SD16—61no—
576C2×SD16—91no—
577C2×SD16—181no—
578C2×D8—31no—
579C2×D8—61no—
580C2×D8—91no—
581C2×D8—181no—
582#131—31no—
583#131—31no—
584#131—91no—
585#131—91no—
586#127—91no—
587#124—91no—
588#108—91no—
589#108—91no—
590#104—91no—
591#104—91no—
592#104—91no—
593#104—91no—
594#101—91no—
595#100—91no—
596#100—91no—
597#100—91no—
598#97—91no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—121no—
603C23×C3—121no—
604C23×C3—121no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C3×Q8—21no—
612C3×Q8—21no—
613C3×Q8—31no—
614C3×Q8—31no—
615C3×Q8—61no—
616C3×Q8—61no—
617C3×Q8—121no—
618C3×Q8C2×#6711yescharacteristic
619C3×Q8C2×#6711yescharacteristic
620C3×Q8C2×#6711yescharacteristic
621C3×Q8C2×#6711yescharacteristic
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—21no—
625C3×D4—21no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—31no—
629C3×D4—31no—
630C3×D4—41no—
631C3×D4—41no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
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×D4—121no—
646C3×D4—121no—
647C3×D4C2×#6711yescharacteristic
648C3×D4C2×#6711yescharacteristic
649C3×D4C2×#6711yescharacteristic
650C3×D4C2×#6711yescharacteristic
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—41no—
657C2×C3×C4—41no—
658C2×C3×C4—61no—
659C2×C3×C4—61no—
660C2×C3×C4—61no—
661C2×C3×C4—121no—
662C2×C3×C4—121no—
663C2×C3×C4—121no—
664C2×C3×C4—121no—
665C2×C3×C4—121no—
666C2×C3×C4C23×D311yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668#67—21no—
669#67—21no—
670#67—41no—
671#67—41no—
672#67—41no—
673#67—41no—
674#67—242no—
675#67—242no—
676C2×Dic3—21no—
677C2×Dic3—41no—
678C2×Dic3—61no—
679C2×Dic3—61no—
680C2×Dic3—121no—
681D12—21no—
682D12—21no—
683D12—21no—
684D12—21no—
685D12—21no—
686D12—21no—
687D12—41no—
688D12—41no—
689D12—41no—
690D12D3×D411yescharacteristic
691D12D3×D411yescharacteristic
692C4×D3—21no—
693C4×D3—21no—
694C4×D3—41no—
695C4×D3—41no—
696C4×D3—41no—
697C4×D3—41no—
698Dic6—21no—
699Dic6—21no—
700Dic6—41no—
701Dic6D3×D411yescharacteristic
702Dic6D3×D411yescharacteristic
703C3×C8—21no—
704C3×C8—21no—
705C3×C8—61no—
706C3×C8—61no—
707C3×C8C2×#6711yescharacteristic
708C3×C8C2×#6711yescharacteristic
709C3×C8C2×#6711yescharacteristic
710C3×C8C2×#6711yescharacteristic
711C3⋊C8—21no—
712C3⋊C8—21no—
713C3⋊C8—31no—
714C3⋊C8—31no—
715C3⋊C8—31no—
716C3⋊C8—31no—
717C3⋊C8—61no—
718C3⋊C8—61no—
719C3⋊C8—61no—
720C3⋊C8—61no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—121no—
724C3⋊C8—121no—
725C2×C32—21no—
726C2×C32—41no—
727C2×C32—41no—
728C2×C32D4211yescharacteristic
729C3×D3—41no—
730C3×D3—41no—
731C3×D3—81no—
732C3×D3—81no—
733C3×D3—81no—
734#41—31no—
735#41—31no—
736#41—61no—
737#41—61no—
738#41—61no—
739#41—61no—
740#41—61no—
741#41—61no—
742#41—61no—
743#41—61no—
744#41—121no—
745#41C2×D3211yescharacteristic
746#41C2×D3211yescharacteristic
747C2×Q8—31no—
748C2×Q8—61no—
749C2×Q8—61no—
750C2×D4—31no—
751C2×D4—31no—
752C2×D4—31no—
753C2×D4—61no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—61no—
759C2×D4—121no—
760C2×D4—121no—
761C2×D4—121no—
762C2×D4—361no—
763Q16—61no—
764Q16—91no—
765Q16—181no—
766Q16#62511yescharacteristic, complemented
767SD16—61no—
768SD16—61no—
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#62511yescharacteristic, complemented
782SD16#62511yescharacteristic, complemented
783D8—61no—
784D8—61no—
785D8—61no—
786D8—61no—
787D8—61no—
788D8—91no—
789D8—181no—
790D8—181no—
791D8—181no—
792D8—181no—
793D8—181no—
794D8#62511yescharacteristic, complemented
795M16—31no—
796M16—31no—
797M16—61no—
798M16—61no—
799M16—91no—
800M16—91no—
801M16—181no—
802M16—181no—
803C2×C8—61no—
804C2×C8—61no—
805C2×C8—91no—
806C2×C8—181no—
807C2×C8—181no—
808C2×C8C2×D3211yescharacteristic
809C22⋊C4—361no—
810C42—91no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—41no—
817C22×C3—41no—
818C22×C3—61no—
819C22×C3—61no—
820C22×C3—121no—
821C22×C3—121no—
822C22×C3—121no—
823C22×C3—241no—
824C22×C3—241no—
825C22×C3—241no—
826C22×C3—481no—
827C22×C3—481no—
828C22×C3—481no—
829C22×C3#100411yescharacteristic
830C22×C3#100411yescharacteristic
831C2×D3—21no—
832C2×D3—21no—
833C2×D3—41no—
834C2×D3—41no—
835C2×D3—41no—
836C2×D3—81no—
837C2×D3—81no—
838C2×D3—81no—
839C2×D3—161no—
840C2×D3—161no—
841C2×D3—161no—
842C3×C4—21no—
843C3×C4—21no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—41no—
849C3×C4—41no—
850C3×C4—61no—
851C3×C4—61no—
852C3×C4—121no—
853C3×C4C2×D3×D411yescharacteristic
854C3×C4C2×D3×D411yescharacteristic
855C3×C4C22×#6711yescharacteristic
856C3×C4C22×#6711yescharacteristic
857Dic3—21no—
858Dic3—21no—
859Dic3—41no—
860Dic3—121no—
861Dic3—121no—
862Dic3—241no—
863C32#328811yescharacteristic, complemented, Sylow
864C23—61no—
865C23—61no—
866C23—61no—
867C23—121no—
868C23—121no—
869C23—121no—
870Q8—31no—
871Q8—31no—
872Q8—61no—
873Q8—61no—
874Q8—121no—
875Q8C2×#62511yescharacteristic
876Q8C2×#62511yescharacteristic
877D4—21no—
878D4—21no—
879D4—31no—
880D4—31no—
881D4—61no—
882D4—61no—
883D4—61no—
884D4—61no—
885D4—61no—
886D4—61no—
887D4—61no—
888D4—61no—
889D4—121no—
890D4—121no—
891D4—121no—
892D4—121no—
893D4—121no—
894D4—121no—
895D4—121no—
896D4—722no—
897D4C2×#62511yescharacteristic
898D4C2×#62511yescharacteristic
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—121no—
905C2×C4—121no—
906C2×C4—121no—
907C2×C4—121no—
908C2×C4—121no—
909C2×C4—181no—
910C2×C4C22×D3211yescharacteristic
911C8—61no—
912C8—61no—
913C8—91no—
914C8—91no—
915C8—181no—
916C8—181no—
917C8C2×#62511yescharacteristic
918C8C2×#62511yescharacteristic
919C2×C3—21no—
920C2×C3—21no—
921C2×C3—21no—
922C2×C3—41no—
923C2×C3—41no—
924C2×C3—41no—
925C2×C3—41no—
926C2×C3—41no—
927C2×C3—81no—
928C2×C3—81no—
929C2×C3—121no—
930C2×C3—121no—
931C2×C3—241no—
932C2×C3—241no—
933C2×C3—241no—
934C2×C3D4×#6711yescharacteristic
935C2×C3D4×#6711yescharacteristic
936D3—41no—
937D3—41no—
938D3—81no—
939D3—81no—
940D3—81no—
941C22—21no—
942C22—21no—
943C22—61no—
944C22—61no—
945C22—121no—
946C22—121no—
947C22—121no—
948C22—241no—
949C22—241no—
950C22—241no—
951C22—481no—
952C22—481no—
953C22—481no—
954C22#6431311yescharacteristic
955C4—21no—
956C4—21no—
957C4—61no—
958C4—61no—
959C4—121no—
960C4—361no—
961C4D32×D411yescharacteristic
962C4C22×#62511yescharacteristic
963C3—21no—
964C3#8400911yescharacteristic, complemented
965C3#8401511yescharacteristic, complemented
966C2—21no—
967C2—41no—
968C2—41no—
969C2—121no—
970C2—121no—
971C2—241no—
972C2—241no—
973C2—241no—
974C2D4×#62511yescharacteristic
subgroupG/H
centerC2D4×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#135C22
socleC2×C32D42
hypercenter#135D32
hypocenterC32#3288
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. C3×#5770C2semidirect
2. C3×#5769C2semidirect
3. #10595446C2semidirect
4. #10595444C2semidirect
5. #10592896C2semidirect
6. #10591684C2semidirect
7. #10591681C2semidirect
8. #10591678C2semidirect
9. #10591665C2semidirect
10. #10591665C2semidirect
11. #10591664C2semidirect
12. #10590926C2semidirect
13. #10590925C2semidirect
14. #10590922C2semidirect
15. #10590887C2semidirect
18. C3×#1010C22semidirect
20. C3×#1009C22semidirect
21. C3×#1009C22semidirect
23. #64157C22semidirect
24. #64157C22semidirect
25. C3×#951C22semidirect
27. C3×#949C22semidirect
28. C3×#949C22semidirect
37. C2×C3×D24C22semidirect
38. C2×C3×#204C22semidirect
39. C3×#901C22semidirect
40. C3×#901C22semidirect
41. #63914C22semidirect
42. #63863C22semidirect
44. #63827C22semidirect
46. C2×#3715C22semidirect
51. #63823C22semidirect
52. #63823C22semidirect
57. C2×#3713C22semidirect
58. #63664C22semidirect
59. #63664C22semidirect
60. #63646C22semidirect
61. #63642C22semidirect
62. #63578C22semidirect
63. #63568C22semidirect
64. #63568C22semidirect
65. #63560C22semidirect
66. #63558C22semidirect
67. #63558C22semidirect
68. #63558C22semidirect
75. #5770D3semidirect
76. #5769D3semidirect
129. C32×Q16D4semidirect
130. C32×SD16D4semidirect
131. C32×SD16D4semidirect
132. C32×D8D4semidirect
162. #3718D4semidirect
169. #3715D4semidirect
170. #3715D4semidirect
176. #3713D4semidirect
182. #1010C2×D3semidirect
184. #1009C2×D3semidirect
185. #1009C2×D3semidirect
207. #951C2×D3semidirect
221. #949C2×D3semidirect
222. #949C2×D3semidirect
257. C2×D24C2×D3semidirect
258. C2×#204C2×D3semidirect
259. #901C2×D3semidirect
260. #901C2×D3semidirect
419. C3×Q16#67semidirect
420. C3×Q16#67semidirect
429. C3×SD16#67semidirect
430. C3×SD16#67semidirect
431. C3×SD16#67semidirect
432. C3×SD16#67semidirect
439. C3×D8#67semidirect
440. C3×D8#67semidirect
766. Q16#625semidirect
781. SD16#625semidirect
782. SD16#625semidirect
794. D8#625semidirect
863. C32#3288semidirect
964. C3#84009semidirect
965. C3#84015semidirect

Maximal subgroups

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

subgroupindex
C3×#57702
C3×#57692
#105954462
#105954442
#105928962
#105916842
#105916812
#105916782
#105916652
#105916642
#105909262
#105909252
#105909222
#105908872
#840153
#840093