Finite Group Databasebeta

← #11878662

Subgroups — #11878662

Order 1152.

1123 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#940C211yesmaximal, characteristic, complemented
2#10594367C211yesmaximal, characteristic, complemented
3#10592459C211yesmaximal, characteristic, complemented
4C3×#4786C211yesmaximal, characteristic, complemented
5C3×#4773C211yesmaximal, characteristic, complemented
6#10591484C211yesmaximal, characteristic, complemented
7#10591447C211yesmaximal, characteristic, complemented
8#10591428C211yesmaximal, characteristic, complemented
9#10590944C211yesmaximal, characteristic, complemented
10#10590886C211yesmaximal, characteristic, complemented
11#10590753C211yesmaximal, characteristic, complemented
12#10590656C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590552C211yesmaximal, characteristic, complemented
15#10590547C211yesmaximal, characteristic, complemented
16#80336—31nomaximal
17#79994—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3795—21no—
23#64149C2211yescharacteristic
24#64097C2211yescharacteristic, complemented
25C3×#940C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic, complemented
28C2×C3×D24C2211yescharacteristic, complemented
29C2×C3×D24C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#893C2211yescharacteristic, complemented
32#63979—21no—
33#63979—21no—
34#63914C2211yescharacteristic
35#63914C2211yescharacteristic, complemented
36#63913—21no—
37#63911C2211yescharacteristic
38#63908C2211yescharacteristic
39Dic3×D12C2211yescharacteristic, complemented
40#63885—21no—
41#63879—21no—
42C4×D3×Dic3C2211yescharacteristic
43C2×#3714C2211yescharacteristic, complemented
44C2×#3714C2211yescharacteristic, complemented
45C2×#3713C2211yescharacteristic, complemented
46C2×#3713C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic, complemented
48#63659C2211yescharacteristic, complemented
49#63648C2211yescharacteristic, complemented
50C8×C3⋊Dic3C2211yescharacteristic, complemented
51#63636C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61C2×#940—31no—
62D3×#127—31no—
63#5596—31no—
64#5548—31no—
65C3×#459—31no—
66C3×#447—31no—
67#5217—31no—
68#5156—31no—
69#5156—31no—
70#5151—31no—
71#5151—31no—
72#5151—31no—
73#5151—31no—
74#5150—31no—
75#5150—31no—
76#5072—31no—
77#5036—31no—
78#5015—31no—
79#4843—31no—
80#4833—31no—
81#4786—31no—
82#4786D311yescharacteristic, complemented
83#4773—31no—
84#4773D311yescharacteristic, complemented
85#4760—31no—
86#4760—31no—
87#4760—31no—
88#4760—31no—
89#4760—61no—
90#4732—31no—
91#4718—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×#634—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×D4—41no—
103C3×D3×D4—41no—
104C2×C3×D12—21no—
105C2×C3×D12C2311yescharacteristic
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3—21no—
110C2×C3×C4×D3C2311yescharacteristic
111D3×#67—44no—
112D3×#67—44no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#625—21no—
117C2×#625—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×#625—21no—
121C2×D3×Dic3—21no—
122C2×D3×Dic3D411yescharacteristic
123C2×D3×Dic3D411yescharacteristic
124D3×D12—41no—
125D3×D12—41no—
126#3795—44no—
127C2×C32×C8C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129C4⋊(C3⋊Dic3)C2311yescharacteristic
130#3750—21no—
131C4×C3⋊Dic3C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133C3×#213—41no—
134C3×#213—41no—
135C3×(C2×D3)⋊C4—21no—
136C3×(C2×D3)⋊C4—21no—
137C3×C4×Dic3C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C3×D24—41no—
141C3×D24—41no—
142(C2×D3)⋊Dic3—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32D411yescharacteristic
145Dic32D411yescharacteristic
146#3714—41no—
147#3714—41no—
148#3713—41no—
149#3713—41no—
150#3205—91noSylow
151C22×C3×D4—31no—
152C22×#67—61no—
153C22×#67—61no—
154C2×#237—61no—
155C2×D3×D4—31no—
156C2×D3×D4—61no—
157C2×D3×D4—61no—
158C2×D3×D4C2×D311yescharacteristic
159C2×#235—61no—
160C22×D12—31no—
161C2×C3×D8—31no—
162C2×C3×D8—31no—
163C2×C3×D8—31no—
164C2×C3×D8—31no—
165C3×#127—31no—
166C3×#121—31no—
167C3×C4×D4—31no—
168#940—31no—
169#940—31no—
170#940—31no—
171#940—31no—
172#940—31no—
173#940—31no—
174#940—31no—
175#940—61no—
176#940—61no—
177#940—61no—
178#940—61no—
179#940—61no—
180#940C2×D311yescharacteristic
181#939—61no—
182#938—31no—
183D4×Dic3—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—31no—
189C2×#213—31no—
190C2×#213C2×D311yescharacteristic, complemented
191C2×#213C2×D311yescharacteristic, complemented
192#930—31no—
193C4×#67—61no—
194C2×C4×Dic3—31no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24C2×D311yescharacteristic, complemented
198C2×D24C2×D311yescharacteristic, complemented
199#895C2×D311yescharacteristic
200#893C2×D311yescharacteristic, complemented
201#888—31no—
202#888—31no—
203#888—61no—
204#885—61no—
205#885—61no—
206#884—61no—
207#67⋊C4—61no—
208#874—31no—
209C4×D12—31no—
210C42×D3—31no—
211C3×C4⋊C8—31no—
212C3×#102—21no—
213C3×#102—31no—
214C3×#102—31no—
215C3×#102C2×D311yescharacteristic, complemented
216C3×#102C2×D311yescharacteristic, complemented
217C3×C22⋊C8—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—31no—
222#832—61no—
223#830—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—61no—
229(C2×D3)⋊C8—31no—
230(C2×D3)⋊C8C2×D311yescharacteristic
231Dic3⋊C8—31no—
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236C8×Dic3—31no—
237C8×Dic3—61no—
238#809—31no—
239#809—31no—
240#809—61no—
241#809C2×D311yescharacteristic, complemented
242#809C2×D311yescharacteristic, complemented
243C4⋊(C3⋊C8)—31no—
244C23×C32—21no—
245C22×C3⋊D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3—42no—
251C22×C3×D3—42no—
252C22×C3×D3—42no—
253C22×C3×D3C2×D411yescharacteristic
254C2×D32—42no—
255C2×D32—42no—
256C2×D32—42no—
257C32×D4—21no—
258C32×D4—21no—
259C2×C32×C4—21no—
260C2×C32×C4C2411yescharacteristic
261#638—42no—
262#638—42no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3C2×D411yescharacteristic
265C2×C3⋊Dic3C2×D411yescharacteristic
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—21no—
268#634—42no—
269C3×#67—42no—
270C3×#67—42no—
271C3×#67—42no—
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C2×C3×Dic3C2×D411yescharacteristic
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×D12—21no—
279C3×D12—21no—
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—42no—
284C3×C4×D3—21no—
285C3×C4×D3—21no—
286C3×C4×D3—42no—
287#626—42no—
288#626—42no—
289#626—42no—
290#625—42no—
291#625—42no—
292#625—42no—
293#625—42no—
294#625—42no—
295D3×Dic3—22no—
296D3×Dic3—42no—
297D3×Dic3D814yescomplemented
298C32×C8—21no—
299C3⋊(C3⋊C8)—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302#532—91no—
303C2×#127—91no—
304#493—91no—
305#493—91no—
306#486—91no—
307#486—91no—
308#459—31no—
309#459—91no—
310#459—91no—
311#459—91no—
312#447—31no—
313#447—91no—
314#447—91no—
315#447—91no—
316#431—91no—
317C24×C3—61no—
318C23×D3—21no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×D4—21no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C2×C3×D4—31no—
325C2×C3×D4—31no—
326C2×C3×D4—61no—
327C2×C3×D4—61no—
328C2×C3×D4—61no—
329C2×C3×D4—61no—
330C2×C3×D4—121no—
331C2×C3×D4—121no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—31no—
335C22×C3×C4—61no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—21no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—121no—
357C2×#67—121no—
358C2×#67—124no—
359C2×#67—124no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—61no—
363#237—124no—
364D3×D4—41no—
365D3×D4—41no—
366D3×D4—121no—
367D3×D4—121no—
368D3×D4—124no—
369D3×D4—124no—
370#235—124no—
371C2×D12—21no—
372C2×D12—31no—
373C2×D12—31no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—121no—
379C2×D12—121no—
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×C4×D3—21no—
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—61no—
388C2×C4×D3C22×D311yescharacteristic
389C2×Dic6—61no—
390C2×Dic6—61no—
391C2×Dic6—121no—
392C3×D8—121no—
393C3×D8—121no—
394C3×D8—121no—
395C3×D8—121no—
396C2×C3×C8—21no—
397C2×C3×C8—31no—
398C2×C3×C8—31no—
399C2×C3×C8C22×D311yescharacteristic
400C2×C3×C8C22×D311yescharacteristic
401C3×C4⋊C4—21no—
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C42—31no—
407#217—61no—
408#217—61no—
409#213—41no—
410#213—41no—
411#213—121no—
412#213—121no—
413#213—121no—
414#213—121no—
415#213—121no—
416#213—121no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—21no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421C4⋊Dic3—31no—
422C4⋊Dic3—31no—
423C4⋊Dic3—61no—
424Dic3⋊C4—61no—
425Dic3⋊C4—61no—
426Dic3⋊C4—121no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—61no—
434C4×Dic3C22×D311yescharacteristic
435C2×C3⋊C8—31no—
436C2×C3⋊C8—31no—
437C2×C3⋊C8—61no—
438C2×C3⋊C8C22×D311yescharacteristic
439C2×C3⋊C8C22×D311yescharacteristic
440D24—41no—
441D24—41no—
442D24—121no—
443D24—121no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32—41no—
447C22×C32C22×D411yescharacteristic
448C2×C3⋊D3—41no—
449C2×C3⋊D3—41no—
450C2×C3⋊D3—41no—
451C2×C3×D3—21no—
452C2×C3×D3—21no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—84no—
466C2×C3×D3C2×D812yes—
467D32—84no—
468C32×C4—41no—
469C32×C4H(5,𝔽2)11yescharacteristic
470C32×C4H(5,𝔽2)11yescharacteristic
471C3⋊Dic3—41no—
472C3⋊Dic3C2×D812yes—
473C3⋊Dic3AGL(1,ℤ/8)12yes—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3C2×D812yes—
477C2×#41—181no—
478C22×D4—31no—
479C22×D4—91no—
480C22×D4—181no—
481C22×D4—181no—
482C2×D8—31no—
483C2×D8—31no—
484C2×D8—31no—
485C2×D8—31no—
486C2×D8—91no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C4⋊Q8—91no—
491#127—31no—
492#127—91no—
493#127—91no—
494#127—91no—
495#127—91no—
496#127—181no—
497#127—181no—
498#124—181no—
499#121—31no—
500#121—91no—
501#121—181no—
502C4×D4—31no—
503C4×D4—91no—
504C4×D4—181no—
505C2×C42—91no—
506C4⋊C8—31no—
507C4⋊C8—91no—
508#102—31no—
509#102—31no—
510#102—91no—
511#102—91no—
512#102—91no—
513#102—91no—
514#102—91no—
515#102D3211yescharacteristic, complemented
516C22⋊C8—31no—
517C22⋊C8—91no—
518C4×C8—91no—
519C4×C8—91no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—31no—
523C23×C3—41no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—122no—
529C23×C3—122no—
530C23×C3—122no—
531C22×D3—21no—
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—42no—
536C22×D3—42no—
537C22×D3—42no—
538C22×D3—61no—
539C22×D3—61no—
540C22×D3—121no—
541C22×D3—122no—
542C22×D3—122no—
543C22×D3—122no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3D3×D411yescharacteristic
548C3×D4—21no—
549C3×D4—21no—
550C3×D4—21no—
551C3×D4—21no—
552C3×D4—41no—
553C3×D4—41no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C3×D4—61no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—122no—
563C3×D4—122no—
564C3×D4—122no—
565C3×D4—122no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—31no—
570C2×C3×C4—31no—
571C2×C3×C4—31no—
572C2×C3×C4—41no—
573C2×C3×C4—61no—
574C2×C3×C4—61no—
575C2×C3×C4—122no—
576C2×C3×C4C23×D311yescharacteristic
577C2×C3×C4C23×D311yescharacteristic
578#67—42no—
579#67—42no—
580#67—42no—
581#67—122no—
582#67—122no—
583#67—122no—
584#67—122no—
585#67—122no—
586#67—122no—
587#67—122no—
588#67—122no—
589#67—122no—
590#67—122no—
591#67—122no—
592#67—122no—
593#67—122no—
594#67—122no—
595#67—122no—
596#67—122no—
597#67—122no—
598#67—242no—
599#67—242no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—31no—
603C2×Dic3—31no—
604C2×Dic3—34no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—62no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—121no—
611C2×Dic3—122no—
612C2×Dic3D3×D411yescharacteristic
613C2×Dic3D3×D411yescharacteristic
614C2×Dic3D3×D411yescharacteristic
615D12—21no—
616D12—21no—
617D12—21no—
618D12—21no—
619D12—21no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—42no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—121no—
629D12—121no—
630D12—122no—
631D12—122no—
632D12—122no—
633C4×D3—21no—
634C4×D3—21no—
635C4×D3—34no—
636C4×D3—42no—
637C4×D3—62no—
638C4×D3—122no—
639Dic6—122no—
640Dic6—122no—
641Dic6—242no—
642C3×C8—21no—
643C3×C8—21no—
644C3×C8—41no—
645C3×C8—61no—
646C3×C8—61no—
647C3⋊C8—21no—
648C3⋊C8—21no—
649C3⋊C8—61no—
650C3⋊C8—61no—
651C3⋊C8—121no—
652C2×C32—81no—
653C2×C32#53511yescharacteristic
654C2×C32C22×D811yescharacteristic
655C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
656C3⋊D3—81no—
657C3×D3—22no—
658C3×D3—81no—
659C3×D3—81no—
660C3×D3—81no—
661C3×D3—81no—
662C24—61no—
663C24—181no—
664#41—364no—
665C2×Q8—181no—
666C2×D4—31no—
667C2×D4—31no—
668C2×D4—31no—
669C2×D4—31no—
670C2×D4—61no—
671C2×D4—61no—
672C2×D4—61no—
673C2×D4—61no—
674C2×D4—91no—
675C2×D4—121no—
676C2×D4—121no—
677C2×D4—181no—
678C2×D4—181no—
679C2×D4—181no—
680C2×D4—181no—
681C2×D4—181no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—361no—
688C2×D4—361no—
689C2×D4—364no—
690C2×D4—364no—
691C2×D4C2×D3211yescharacteristic
692C22×C4—31no—
693C22×C4—61no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—181no—
697D8—121no—
698D8—121no—
699D8—121no—
700D8—121no—
701D8—361no—
702D8—361no—
703D8—361no—
704D8—361no—
705C2×C8—31no—
706C2×C8—31no—
707C2×C8—91no—
708C2×C8C2×D3211yescharacteristic
709C4⋊C4—91no—
710C4⋊C4—181no—
711C4⋊C4C2×D3211yescharacteristic
712C22⋊C4—61no—
713C22⋊C4—61no—
714C22⋊C4—181no—
715C22⋊C4—181no—
716C42—31no—
717C42—91no—
718C42—91no—
719C42—91no—
720C22×C3—21no—
721C22×C3—32no—
722C22×C3—41no—
723C22×C3—41no—
724C22×C3—41no—
725C22×C3—41no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—81no—
731C22×C3—81no—
732C22×C3—81no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3—121no—
738C22×C3—121no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—244no—
746C22×C3C2×D3×D411yescharacteristic
747C22×C3C2×D3×D411yescharacteristic
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—41no—
751C2×D3—41no—
752C2×D3—41no—
753C2×D3—41no—
754C2×D3—41no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—84no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—241no—
770C2×D3—241no—
771C2×D3—241no—
772C2×D3—244no—
773C2×D3—244no—
774C2×D3D3×D812yes—
775C3×C4—21no—
776C3×C4—21no—
777C3×C4—32no—
778C3×C4—41no—
779C3×C4—41no—
780C3×C4—61no—
781C3×C4—61no—
782C3×C4—81no—
783C3×C4#100411yescharacteristic
784C3×C4#100411yescharacteristic
785C3×C4#100411yescharacteristic
786C3×C4#100911yescharacteristic
787Dic3—21no—
788Dic3—21no—
789Dic3—32no—
790Dic3—32no—
791Dic3—32no—
792Dic3—32no—
793Dic3—62no—
794Dic3—62no—
795Dic3—121no—
796Dic3—121no—
797Dic3—241no—
798Dic3D3×D812yes—
799C32#320511yescharacteristic, complemented, Sylow
800C23—21no—
801C23—31no—
802C23—61no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—122no—
807C23—122no—
808C23—122no—
809C23—181no—
810C23—362no—
811C23—362no—
812C23—362no—
813Q8—362no—
814D4—21no—
815D4—21no—
816D4—61no—
817D4—61no—
818D4—61no—
819D4—61no—
820D4—61no—
821D4—61no—
822D4—61no—
823D4—61no—
824D4—122no—
825D4—122no—
826D4—122no—
827D4—122no—
828D4—181no—
829D4—181no—
830D4—362no—
831D4—362no—
832D4—362no—
833D4—362no—
834D4—362no—
835D4—362no—
836D4—362no—
837D4—362no—
838D4—362no—
839D4—362no—
840C2×C4—21no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—31no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—94no—
847C2×C4—91no—
848C2×C4—91no—
849C2×C4—122no—
850C2×C4—182no—
851C2×C4—181no—
852C2×C4—362no—
853C2×C4C22×D3211yescharacteristic
854C8—21no—
855C8—61no—
856C8—61no—
857C8—181no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—21no—
861C2×C3—62no—
862C2×C3—81no—
863C2×C3—81no—
864C2×C3—161no—
865C2×C3—241no—
866C2×C3—241no—
867C2×C3—241no—
868C2×C3—241no—
869C2×C3#559211yescharacteristic
870C2×C3#560711yescharacteristic
871C2×C3C2×D3×D811yescharacteristic
872C2×C3C2×D3×D811yescharacteristic
873C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
874C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
875D3—22no—
876D3—81no—
877D3—81no—
878D3—81no—
879D3—81no—
880D3—241no—
881D3—241no—
882D3—481no—
883C22—32no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—61no—
888C22—61no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—244no—
902C22—361no—
903C22—361no—
904C22—361no—
905C22—724no—
906C22D32×D411yescharacteristic
907C4—32no—
908C4—41no—
909C4—61no—
910C4—61no—
911C4—92no—
912C4—92no—
913C4—361no—
914C4#6430711yescharacteristic
915C4#6431311yescharacteristic
916C3—21no—
917C3#7999411yescharacteristic, complemented
918C3#8033611yescharacteristic, complemented
919C2—62no—
920C2—81no—
921C2—241no—
922C2—241no—
923C2—241no—
924C2—241no—
925C2—721no—
926C2#1059426911yescharacteristic
927C2D32×D811yescharacteristic
928C2#1059474011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. D3×#940C2semidirect
2. #10594367C2semidirect
3. #10592459C2semidirect
4. C3×#4786C2semidirect
5. C3×#4773C2semidirect
6. #10591484C2semidirect
7. #10591447C2semidirect
8. #10591428C2semidirect
9. #10590944C2semidirect
10. #10590886C2semidirect
11. #10590753C2semidirect
12. #10590656C2semidirect
13. #10590595C2semidirect
14. #10590552C2semidirect
15. #10590547C2semidirect
24. #64097C22semidirect
26. C2×C3×#213C22semidirect
27. C2×C3×#213C22semidirect
28. C2×C3×D24C22semidirect
29. C2×C3×D24C22semidirect
31. C3×#893C22semidirect
35. #63914C22semidirect
39. Dic3×D12C22semidirect
43. C2×#3714C22semidirect
44. C2×#3714C22semidirect
45. C2×#3713C22semidirect
46. C2×#3713C22semidirect
47. C32×#102C22semidirect
48. #63659C22semidirect
49. #63648C22semidirect
50. C8×C3⋊Dic3C22semidirect
51. #63636C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×#809C22semidirect
55. C3×#809C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63563C22semidirect
58. #63563C22semidirect
60. #63553C22semidirect
82. #4786D3semidirect
84. #4773D3semidirect
190. C2×#213C2×D3semidirect
191. C2×#213C2×D3semidirect
197. C2×D24C2×D3semidirect
198. C2×D24C2×D3semidirect
200. #893C2×D3semidirect
215. C3×#102C2×D3semidirect
216. C3×#102C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
241. #809C2×D3semidirect
242. #809C2×D3semidirect
297. D3×Dic3D8semidirect
515. #102D32semidirect
799. C32#3205semidirect
917. C3#79994semidirect
918. C3#80336semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
#105943672
#105924592
C3×#47862
C3×#47732
#105914842
#105914472
#105914282
#105909442
#105908862
#105907532
#105906562
#105905952
#105905522
#105905472
#803363
#799943