Finite Group Databasebeta

← #11878658

Subgroups — #11878658

Order 1152.

1134 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#940C211yesmaximal, characteristic, complemented
2#10595133C211yesmaximal, characteristic, complemented
3#10592849C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic, complemented
5C3×#5151C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591487C211yesmaximal, characteristic, complemented
8#10591486C211yesmaximal, characteristic, complemented
9#10591482C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11#10591433C211yesmaximal, characteristic, complemented
12#10590944C211yesmaximal, characteristic, complemented
13#10590878C211yesmaximal, characteristic, complemented
14#10590749C211yesmaximal, characteristic, complemented
15#10590655C211yesmaximal, characteristic, complemented
16#81785—31nomaximal
17#79994—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×#3805—21no—
22C2×D3×D12C2211yescharacteristic
23C2×C32×D8C2211yescharacteristic, complemented
24#64149C2211yescharacteristic
25D4×C3⋊Dic3C2211yescharacteristic, complemented
26C2×#3753C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic
28C3×#940C2211yescharacteristic, complemented
29C3×#938C2211yescharacteristic
30C2×C3×#213C2211yescharacteristic, complemented
31C2×C3×#213C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic, complemented
33C2×C3×D24C2211yescharacteristic, complemented
34#63979—21no—
35#63979—21no—
36#67⋊Dic3—21no—
37#63970—21no—
38#63959—21no—
39#63918C2211yescharacteristic, complemented
40#63914C2211yescharacteristic
41#63911C2211yescharacteristic
42#63908C2211yescharacteristic
43#63898C2211yescharacteristic, complemented
44C4×D3×Dic3C2211yescharacteristic
45C2×#3714C2211yescharacteristic, complemented
46C2×#3713C2211yescharacteristic, complemented
47#63659C2211yescharacteristic, complemented
48#63648C2211yescharacteristic, complemented
49#63641C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C2×#940—31no—
62#5716—31no—
63D3×#127—31no—
64#5596—31no—
65C3×#493—31no—
66C3×#447—31no—
67#5217—31no—
68#5156—31no—
69#5156—31no—
70#5156—31no—
71#5156D311yescharacteristic, complemented
72#5151—31no—
73#5151D311yescharacteristic, complemented
74#5150—31no—
75#5150—31no—
76#5150—31no—
77#5150—31no—
78#5150—31no—
79#5150—31no—
80#5150—61no—
81#5073—31no—
82#5070—31no—
83#5036—31no—
84#4786—31no—
85#4786—31no—
86#4760—31no—
87#4760—31no—
88#4732—31no—
89#4718—31no—
90#4694—31no—
91#4685—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×C32×D4C2311yescharacteristic
96C2×#638—21no—
97C2×#638—21no—
98C22×C3⋊Dic3—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C3×D3×D4—41no—
107C3×D3×D4—41no—
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3C2311yescharacteristic
112D3×#67—44no—
113D3×#67—44no—
114C2×#627—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×#625—21no—
121#3805—44no—
122C2×D3×Dic3—21no—
123C2×D3×Dic3D411yescharacteristic
124C2×D3×Dic3D411yescharacteristic
125D3×D12—41no—
126D3×D12—41no—
127C32×D8—41no—
128C2×C32×C8C2311yescharacteristic
129#3757—21no—
130#3753—41no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C3×#217—21no—
135C3×#213—41no—
136C3×#213—41no—
137C3×#213—41no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4×Dic3C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C3×D24—41no—
143Dic3⋊Dic3—21no—
144(C2×D3)⋊Dic3—21no—
145(C2×D3)⋊Dic3—21no—
146Dic32D411yescharacteristic
147Dic32D411yescharacteristic
148#3714—41no—
149#3713—41no—
150#3205—91noSylow
151C22×C3×D4—31no—
152C22×#67—61no—
153C22×#67—61no—
154C2×#237—61no—
155C2×#237—61no—
156C2×D3×D4—31no—
157C2×D3×D4—61no—
158C2×D3×D4—61no—
159C2×D3×D4C2×D311yescharacteristic
160C22×D12—31no—
161C2×C3×D8—21no—
162C2×C3×D8—31no—
163C2×C3×D8—31no—
164C2×C3×D8—31no—
165C2×C3×D8—31no—
166C2×C3×D8C2×D311yescharacteristic, complemented
167C2×C3×D8C2×D311yescharacteristic, complemented
168C3×#127—31no—
169C3×#127—31no—
170C3×#121—31no—
171#940—31no—
172#940—31no—
173#940—31no—
174#940—31no—
175#940—31no—
176#940—61no—
177#940—61no—
178#940—61no—
179#940—61no—
180#940—61no—
181#940C2×D311yescharacteristic
182#940C2×D311yescharacteristic, complemented
183#939—61no—
184#938—31no—
185#938—61no—
186#938C2×D311yescharacteristic
187#936—61no—
188D4×Dic3—31no—
189D4×Dic3—31no—
190D4×Dic3—31no—
191D4×Dic3—61no—
192D4×Dic3—61no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—61no—
199C2×#213C2×D311yescharacteristic, complemented
200C2×#213C2×D311yescharacteristic, complemented
201C2×#213C2×D311yescharacteristic, complemented
202#930—31no—
203C2×C4×Dic3—31no—
204C2×D24—31no—
205C2×D24C2×D311yescharacteristic, complemented
206#893—31no—
207#888—31no—
208#885—61no—
209#67⋊C4—61no—
210#874—31no—
211C42×D3—31no—
212#869—31no—
213C3×#102—31no—
214C3×#102—31no—
215C3×C22⋊C8—31no—
216C3×C4×C8—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—31no—
222#832—61no—
223#832C2×D311yescharacteristic, complemented
224#830—31no—
225#821—31no—
226#821—31no—
227#821—31no—
228#821—31no—
229#821—31no—
230#821—61no—
231#821C2×D311yescharacteristic, complemented
232(C2×D3)⋊C8—31no—
233(C2×D3)⋊C8C2×D311yescharacteristic
234Dic3⋊C8—31no—
235Dic3⋊C8—31no—
236Dic3⋊C8—31no—
237Dic3⋊C8—31no—
238Dic3⋊C8—61no—
239C8×Dic3—31no—
240C8×Dic3C2×D311yescharacteristic, complemented
241#809—31no—
242#809—31no—
243C4×C3⋊C8—31no—
244C23×C32—21no—
245C23×C32—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—
259C32×D4—21no—
260C32×D4—21no—
261C2×C32×C4C2411yescharacteristic
262#638—42no—
263#638—42no—
264C2×C3⋊Dic3—21no—
265C2×C3⋊Dic3—42no—
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C3×#67—42no—
271C3×#67—42no—
272C3×#67—42no—
273C3×#67—42no—
274C3×#67—42no—
275C3×#67—42no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3C2×D411yescharacteristic
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C3×D12—21no—
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×C4×D3—21no—
287C3×C4×D3—21no—
288#627—42no—
289#626—42no—
290#626—42no—
291#626—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—31no—
305#493—91no—
306#486—91no—
307#486—91no—
308#459—91no—
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—21no—
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—61no—
331C2×C3×D4—61no—
332C2×C3×D4—121no—
333C2×C3×D4—121no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C2×C3×D4C22×D311yescharacteristic
337C2×C3×D4C22×D311yescharacteristic
338C22×C3×C4—31no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—21no—
344C2×#67—21no—
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—61no—
357C2×#67—61no—
358C2×#67—121no—
359C2×#67—121no—
360C2×#67—124no—
361C2×#67—124no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—121no—
368#237—124no—
369#237—124no—
370D3×D4—41no—
371D3×D4—41no—
372D3×D4—121no—
373D3×D4—121no—
374D3×D4—124no—
375D3×D4—124no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—121no—
383C2×D12—121no—
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×D12C22×D311yescharacteristic
387C2×C4×D3—31no—
388C2×C4×D3—31no—
389C2×C4×D3—61no—
390C2×C4×D3C22×D311yescharacteristic
391C2×Dic6—61no—
392C2×Dic6—61no—
393C3×D8—41no—
394C3×D8—41no—
395C3×D8—42no—
396C3×D8—121no—
397C3×D8—121no—
398C3×D8—121no—
399C3×D8—121no—
400C2×C3×C8—21no—
401C2×C3×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—31no—
406C3×C22⋊C4—61no—
407C3×C42—31no—
408#217—21no—
409#217—61no—
410#217—61no—
411#217—61no—
412#217—61no—
413#217—121no—
414#213—41no—
415#213—41no—
416#213—41no—
417#213—121no—
418#213—121no—
419#213—121no—
420#213—121no—
421#213—121no—
422#213—122no—
423(C2×D3)⋊C4—61no—
424(C2×D3)⋊C4—61no—
425C4⋊Dic3—31no—
426C4⋊Dic3—31no—
427C4⋊Dic3—61no—
428C4⋊Dic3—61no—
429C4⋊Dic3C22×D311yescharacteristic
430Dic3⋊C4—61no—
431C4×Dic3—31no—
432C4×Dic3—31no—
433C4×Dic3—31no—
434C4×Dic3—31no—
435C4×Dic3—31no—
436C4×Dic3—31no—
437C4×Dic3—61no—
438C4×Dic3C22×D311yescharacteristic
439C2×C3⋊C8—31no—
440C2×C3⋊C8—31no—
441C2×C3⋊C8—61no—
442C2×C3⋊C8C22×D311yescharacteristic
443C2×C3⋊C8C22×D311yescharacteristic
444D24—41no—
445D24—121no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32—41no—
450C22×C32—41no—
451C22×C32—41no—
452C22×C32C22×D411yescharacteristic
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3×D3—21no—
457C2×C3×D3—21no—
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—41no—
466C2×C3×D3—41no—
467C2×C3×D3—84no—
468C2×C3×D3C2×D812yes—
469D32—84no—
470C32×C4H(5,𝔽2)11yescharacteristic
471C32×C4H(5,𝔽2)11yescharacteristic
472C3⋊Dic3—21no—
473C3⋊Dic3—41no—
474C3⋊Dic3C2×D812yes—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3C2×D812yes—
478C3×Dic3AGL(1,ℤ/8)12yes—
479C2×#41—181no—
480C22×D4—31no—
481C22×D4—91no—
482C22×D4—181no—
483C22×D4—181no—
484C2×D8—31no—
485C2×D8—31no—
486C2×D8—31no—
487C2×D8—31no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8D3211yescharacteristic, complemented
492C4⋊Q8—91no—
493#127—31no—
494#127—31no—
495#127—91no—
496#127—91no—
497#127—91no—
498#127—181no—
499#127—181no—
500#124—181no—
501#121—31no—
502#121—91no—
503#121—181no—
504C4×D4—91no—
505C4×D4—91no—
506C4×D4—181no—
507C2×C42—91no—
508C4⋊C8—91no—
509C4⋊C8—91no—
510#102—31no—
511#102—31no—
512#102—91no—
513#102—91no—
514#102—91no—
515#102—91no—
516#102—91no—
517#102—91no—
518C22⋊C8—31no—
519C22⋊C8—91no—
520C4×C8—31no—
521C4×C8—91no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—31no—
527C23×C3—41no—
528C23×C3—41no—
529C23×C3—61no—
530C23×C3—61no—
531C23×C3—61no—
532C23×C3—122no—
533C23×C3—122no—
534C23×C3—122no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—42no—
539C22×D3—42no—
540C22×D3—42no—
541C22×D3—61no—
542C22×D3—61no—
543C22×D3—121no—
544C22×D3—122no—
545C22×D3—122no—
546C22×D3—122no—
547C22×D3—122no—
548C22×D3—122no—
549C22×D3—122no—
550C22×D3D3×D411yescharacteristic
551C3×D4—22no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—21no—
557C3×D4—21no—
558C3×D4—21no—
559C3×D4—21no—
560C3×D4—41no—
561C3×D4—41no—
562C3×D4—41no—
563C3×D4—61no—
564C3×D4—61no—
565C3×D4—61no—
566C3×D4—61no—
567C3×D4—61no—
568C3×D4—61no—
569C3×D4—122no—
570C3×D4—122no—
571C3×D4—122no—
572C3×D4—122no—
573C3×D4—122no—
574C3×D4—122no—
575C2×C3×C4—21no—
576C2×C3×C4—31no—
577C2×C3×C4—31no—
578C2×C3×C4—31no—
579C2×C3×C4—61no—
580C2×C3×C4—61no—
581C2×C3×C4—61no—
582C2×C3×C4C23×D311yescharacteristic
583C2×C3×C4C23×D311yescharacteristic
584#67—42no—
585#67—42no—
586#67—42no—
587#67—42no—
588#67—42no—
589#67—42no—
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—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—242no—
604#67—242no—
605C2×Dic3—21no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—34no—
609C2×Dic3—31no—
610C2×Dic3—31no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—62no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—121no—
617C2×Dic3—122no—
618C2×Dic3—122no—
619C2×Dic3—122no—
620C2×Dic3—242no—
621C2×Dic3D3×D411yescharacteristic
622C2×Dic3D3×D411yescharacteristic
623C2×Dic3D3×D411yescharacteristic
624D12—21no—
625D12—21no—
626D12—21no—
627D12—21no—
628D12—21no—
629D12—21no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—121no—
635D12—121no—
636D12—122no—
637D12—122no—
638D12—122no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—34no—
642C4×D3—62no—
643C4×D3—122no—
644Dic6—122no—
645Dic6—122no—
646C3×C8—21no—
647C3×C8—21no—
648C3×C8—41no—
649C3×C8—61no—
650C3×C8—61no—
651C3⋊C8—21no—
652C3⋊C8—21no—
653C3⋊C8—61no—
654C3⋊C8—61no—
655C3⋊C8—121no—
656C2×C32—81no—
657C2×C32—81no—
658C2×C32#53511yescharacteristic
659C2×C32C22×D811yescharacteristic
660C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
661C3⋊D3—81no—
662C3×D3—22no—
663C3×D3—81no—
664C3×D3—81no—
665C3×D3—81no—
666C24—61no—
667C24—181no—
668#41—364no—
669C2×Q8—181no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—61no—
678C2×D4—61no—
679C2×D4—91no—
680C2×D4—121no—
681C2×D4—121no—
682C2×D4—181no—
683C2×D4—181no—
684C2×D4—181no—
685C2×D4—181no—
686C2×D4—181no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—181no—
690C2×D4—361no—
691C2×D4—361no—
692C2×D4—364no—
693C2×D4—364no—
694C2×D4C2×D3211yescharacteristic
695C2×D4C2×D3211yescharacteristic
696C22×C4—31no—
697C22×C4—91no—
698C22×C4—91no—
699C22×C4—181no—
700C22×C4—181no—
701D8—41no—
702D8—121no—
703D8—121no—
704D8—121no—
705D8—121no—
706D8—361no—
707D8—361no—
708D8—361no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—91no—
712C2×C8C2×D3211yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—91no—
715C4⋊C4—181no—
716C22⋊C4—61no—
717C22⋊C4—181no—
718C22⋊C4—181no—
719C22⋊C4—181no—
720C42—31no—
721C42—91no—
722C42—91no—
723C42—91no—
724C22×C3—21no—
725C22×C3—32no—
726C22×C3—42no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—61no—
740C22×C3—61no—
741C22×C3—81no—
742C22×C3—81no—
743C22×C3—81no—
744C22×C3—81no—
745C22×C3—81no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—244no—
756C22×C3C2×D3×D411yescharacteristic
757C22×C3C2×D3×D411yescharacteristic
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—84no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—241no—
777C2×D3—241no—
778C2×D3—241no—
779C2×D3—244no—
780C2×D3—244no—
781C2×D3D3×D812yes—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—32no—
785C3×C4—32no—
786C3×C4—61no—
787C3×C4—121no—
788C3×C4#100411yescharacteristic
789C3×C4#100411yescharacteristic
790C3×C4#100411yescharacteristic
791C3×C4#100411yescharacteristic
792Dic3—21no—
793Dic3—32no—
794Dic3—32no—
795Dic3—41no—
796Dic3—62no—
797Dic3—61no—
798Dic3—61no—
799Dic3—121no—
800Dic3—121no—
801Dic3—121no—
802Dic3—241no—
803Dic3D3×D812yes—
804Dic3#91112yes—
805C32#320511yescharacteristic, complemented, Sylow
806C23—21no—
807C23—21no—
808C23—31no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—122no—
813C23—122no—
814C23—122no—
815C23—181no—
816C23—362no—
817C23—362no—
818C23—362no—
819Q8—362no—
820D4—21no—
821D4—21no—
822D4—21no—
823D4—21no—
824D4—61no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—61no—
829D4—61no—
830D4—122no—
831D4—122no—
832D4—122no—
833D4—122no—
834D4—122no—
835D4—122no—
836D4—181no—
837D4—181no—
838D4—362no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845D4—362no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—94no—
853C2×C4—91no—
854C2×C4—91no—
855C2×C4—182no—
856C2×C4—181no—
857C2×C4—362no—
858C2×C4—362no—
859C2×C4C22×D3211yescharacteristic
860C8—21no—
861C8—61no—
862C8—61no—
863C8—181no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—62no—
868C2×C3—82no—
869C2×C3—81no—
870C2×C3—81no—
871C2×C3—81no—
872C2×C3—81no—
873C2×C3—161no—
874C2×C3—241no—
875C2×C3—241no—
876C2×C3—241no—
877C2×C3#559211yescharacteristic
878C2×C3#571511yescharacteristic
879C2×C3C2×D3×D811yescharacteristic
880C2×C3C2×D3×D811yescharacteristic
881C2×C3C2×#91111yescharacteristic
882C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
883D3—22no—
884D3—81no—
885D3—81no—
886D3—81no—
887D3—241no—
888D3—241no—
889D3—481no—
890C22—32no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—61no—
898C22—61no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—121no—
906C22—121no—
907C22—121no—
908C22—244no—
909C22—361no—
910C22—361no—
911C22—361no—
912C22—724no—
913C22D32×D411yescharacteristic
914C4—32no—
915C4—32no—
916C4—61no—
917C4—92no—
918C4—121no—
919C4—181no—
920C4—361no—
921C4#6431311yescharacteristic
922C4#6433011yescharacteristic
923C3—21no—
924C3#7999411yescharacteristic, complemented
925C3#8178511yescharacteristic, complemented
926C2—62no—
927C2—81no—
928C2—81no—
929C2—241no—
930C2—241no—
931C2—241no—
932C2—721no—
933C2D32×D811yescharacteristic
934C2D3×#91111yescharacteristic
935C2#1059528611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. D3×#940C2semidirect
2. #10595133C2semidirect
3. #10592849C2semidirect
4. C3×#5156C2semidirect
5. C3×#5151C2semidirect
6. #10591515C2semidirect
7. #10591487C2semidirect
8. #10591486C2semidirect
9. #10591482C2semidirect
10. #10591447C2semidirect
11. #10591433C2semidirect
12. #10590944C2semidirect
13. #10590878C2semidirect
14. #10590749C2semidirect
15. #10590655C2semidirect
23. C2×C32×D8C22semidirect
25. D4×C3⋊Dic3C22semidirect
26. C2×#3753C22semidirect
28. C3×#940C22semidirect
30. C2×C3×#213C22semidirect
31. C2×C3×#213C22semidirect
32. C2×C3×#213C22semidirect
33. C2×C3×D24C22semidirect
39. #63918C22semidirect
43. #63898C22semidirect
45. C2×#3714C22semidirect
46. C2×#3713C22semidirect
47. #63659C22semidirect
48. #63648C22semidirect
49. #63641C22semidirect
50. C3×#832C22semidirect
51. C3×#821C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63572C22semidirect
55. #63564C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
71. #5156D3semidirect
73. #5151D3semidirect
166. C2×C3×D8C2×D3semidirect
167. C2×C3×D8C2×D3semidirect
182. #940C2×D3semidirect
199. C2×#213C2×D3semidirect
200. C2×#213C2×D3semidirect
201. C2×#213C2×D3semidirect
205. C2×D24C2×D3semidirect
223. #832C2×D3semidirect
231. #821C2×D3semidirect
240. C8×Dic3C2×D3semidirect
297. D3×Dic3D8semidirect
491. C2×D8D32semidirect
805. C32#3205semidirect
924. C3#79994semidirect
925. C3#81785semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
#105951332
#105928492
C3×#51562
C3×#51512
#105915152
#105914872
#105914862
#105914822
#105914472
#105914332
#105909442
#105908782
#105907492
#105906552
#817853
#799943