Finite Group Databasebeta

← #11878664

Subgroups — #11878664

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#10594369C211yesmaximal, characteristic, complemented
3#10592485C211yesmaximal, characteristic, complemented
4C3×#4773C211yesmaximal, characteristic, complemented
5C3×#4760C211yesmaximal, characteristic, complemented
6#10591482C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic, complemented
8#10591433C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590880C211yesmaximal, characteristic, complemented
11#10590749C211yesmaximal, characteristic, complemented
12#10590655C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590551C211yesmaximal, characteristic, complemented
15#10590548C211yesmaximal, characteristic, complemented
16#81566—31nomaximal
17#79994—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×#3796—21no—
23#64149C2211yescharacteristic
24C2×#3753C2211yescharacteristic, complemented
25C2×#3745C2211yescharacteristic, complemented
26#64102C2211yescharacteristic, complemented
27C3×#940C2211yescharacteristic
28C2×C3×#213C2211yescharacteristic, complemented
29C2×C3×D24C2211yescharacteristic, complemented
30C3×#895C2211yescharacteristic
31C3×#888C2211yescharacteristic, complemented
32#63979—21no—
33#63979—21no—
34#63914C2211yescharacteristic
35#63911C2211yescharacteristic
36#63911C2211yescharacteristic, complemented
37#63909C2211yescharacteristic
38#63907—21no—
39#63898C2211yescharacteristic, complemented
40#63886—21no—
41#63881—21no—
42C4×D3×Dic3C2211yescharacteristic
43C2×#3714C2211yescharacteristic, complemented
44C2×#3714C2211yescharacteristic, complemented
45C2×#3714C2211yescharacteristic, complemented
46C2×#3713C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic, complemented
48#63641C2211yescharacteristic, complemented
49#63636C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C2×#940—31no—
62#5725—31no—
63D3×#127—31no—
64#5596—31no—
65C3×#486—31no—
66C3×#447—31no—
67#5217—31no—
68#5151—31no—
69#5151—31no—
70#5150—31no—
71#5150—31no—
72#5088—31no—
73#5073—31no—
74#5036—31no—
75#4786—31no—
76#4786—31no—
77#4786—31no—
78#4786—31no—
79#4786—31no—
80#4786—31no—
81#4786—61no—
82#4773—31no—
83#4773—31no—
84#4773—31no—
85#4773D311yescharacteristic, complemented
86#4760—31no—
87#4760D311yescharacteristic, complemented
88#4732—31no—
89#4718—31no—
90#4695—31no—
91#4685—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C2×C32×D4C2311yescharacteristic
95C2×#638—21no—
96C2×#638—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3—21no—
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C3×D3×D4—41no—
104C3×D3×D4—41no—
105C2×C3×D12—21no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×C4×D3C2311yescharacteristic
110C2×C3×Dic6—21no—
111D3×#67—44no—
112D3×#67—44no—
113C2×#626—21no—
114C2×#626—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×#625—21no—
121C2×D3×Dic3—21no—
122C2×D3×Dic3D411yescharacteristic
123C2×D3×Dic3D411yescharacteristic
124D3×D12—41no—
125D3×D12—41no—
126#3796—44no—
127C2×C32×C8C2311yescharacteristic
128C32×C4⋊C4C2311yescharacteristic
129#3753—41no—
130#3752—21no—
131C4×C3⋊Dic3C2311yescharacteristic
132C2×C3⋊(C3⋊C8)C2311yescharacteristic
133#3745—41no—
134C3×#213—41no—
135C3×(C2×D3)⋊C4—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—41no—
142#3722—21no—
143(C2×D3)⋊Dic3—21no—
144Dic32D411yescharacteristic
145Dic32D411yescharacteristic
146#3714—41no—
147#3714—41no—
148#3714—41no—
149#3713—41no—
150#3205—91noSylow
151C22×C3×D4—31no—
152C22×#67—61no—
153C22×#67—61no—
154C2×#239—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—31no—
162C2×C3×D8—31no—
163C3×C4⋊Q8—31no—
164C3×#127—31no—
165C3×#121—31no—
166#947—61no—
167#940—31no—
168#940—31no—
169#940—31no—
170#940—31no—
171#940—31no—
172#940—31no—
173#940—61no—
174#940—61no—
175#940—61no—
176#940—61no—
177#940—61no—
178#940C2×D311yescharacteristic
179#939—61no—
180D4×Dic3—31no—
181C2×#213—31no—
182C2×#213—31no—
183C2×#213—31no—
184C2×#213—31no—
185C2×#213—31no—
186C2×#213—31no—
187C2×#213—31no—
188C2×#213—61no—
189C2×#213C2×D311yescharacteristic, complemented
190#930—31no—
191C2×C4×Dic3—31no—
192C2×D24—31no—
193C2×D24—31no—
194C2×D24—31no—
195C2×D24—31no—
196C2×D24—31no—
197C2×D24—61no—
198C2×D24C2×D311yescharacteristic, complemented
199#895—31no—
200#895—61no—
201#895C2×D311yescharacteristic
202#893—31no—
203#893—31no—
204#893—31no—
205#893—61no—
206#893—61no—
207#888C2×D311yescharacteristic, complemented
208#885—61no—
209#67⋊C4—61no—
210#874—31no—
211#874—31no—
212C42×D3—31no—
213C3×#102—21no—
214C3×#102—31no—
215C3×#102—31no—
216C3×#102—31no—
217C3×#102—31no—
218C3×#102C2×D311yescharacteristic, complemented
219C3×#102C2×D311yescharacteristic, complemented
220C3×C22⋊C8—31no—
221C3×C4×C8—31no—
222#832—31no—
223#832C2×D311yescharacteristic, complemented
224#830—31no—
225#821—31no—
226#821C2×D311yescharacteristic, complemented
227(C2×D3)⋊C8—31no—
228(C2×D3)⋊C8C2×D311yescharacteristic
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—31no—
232Dic3⋊C8—31no—
233Dic3⋊C8—61no—
234C8×Dic3—31no—
235C8×Dic3C2×D311yescharacteristic, complemented
236#809—31no—
237#809—31no—
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⋊Dic3C2×D411yescharacteristic
264C2×C3⋊Dic3C2×D411yescharacteristic
265C4⋊(C3⋊D3)—21no—
266C4⋊(C3⋊D3)—21no—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4×C3⋊D3—42no—
270C3×#67—42no—
271C3×#67—42no—
272C3×#67—42no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
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×Dic6—42no—
287#626—42no—
288#626—42no—
289#626—42no—
290#626—42no—
291#626—42no—
292#626—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—31no—
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×Q8—61no—
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—121no—
331C2×C3×D4—121no—
332C2×C3×D4C22×D311yescharacteristic
333C2×C3×D4C22×D311yescharacteristic
334C22×C3×C4—31no—
335C2×#67—21no—
336C2×#67—21no—
337C2×#67—21no—
338C2×#67—61no—
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—121no—
353C2×#67—121no—
354C2×#67—124no—
355C2×#67—124no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—61no—
359#239—124no—
360#237—124no—
361D3×D4—41no—
362D3×D4—41no—
363D3×D4—121no—
364D3×D4—121no—
365D3×D4—124no—
366D3×D4—124no—
367C2×D12—21no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—61no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—61no—
377C2×D12—61no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—121no—
381C2×D12—121no—
382C2×D12C22×D311yescharacteristic
383C2×D12C22×D311yescharacteristic
384C2×D12C22×D311yescharacteristic
385C2×C4×D3—31no—
386C2×C4×D3—31no—
387C2×C4×D3—61no—
388C2×C4×D3—61no—
389C2×C4×D3—61no—
390C2×C4×D3—121no—
391C2×C4×D3C22×D311yescharacteristic
392C2×Dic6—21no—
393C3×D8—121no—
394C3×D8—121no—
395C2×C3×C8—21no—
396C2×C3×C8—31no—
397C2×C3×C8—31no—
398C2×C3×C8C22×D311yescharacteristic
399C2×C3×C8C22×D311yescharacteristic
400C3×C4⋊C4—21no—
401C3×C4⋊C4—31no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C4⋊C4C22×D311yescharacteristic
405C3×C22⋊C4—61no—
406C3×C42—31no—
407#217—61no—
408#213—41no—
409#213—121no—
410#213—121no—
411#213—121no—
412#213—121no—
413#213—121no—
414#213—121no—
415#213—121no—
416#213—122no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—61no—
421(C2×D3)⋊C4—61no—
422(C2×D3)⋊C4—61no—
423(C2×D3)⋊C4—121no—
424C4⋊Dic3C22×D311yescharacteristic
425Dic3⋊C4—21no—
426C4×Dic3—31no—
427C4×Dic3—31no—
428C4×Dic3—31no—
429C4×Dic3—31no—
430C4×Dic3—31no—
431C4×Dic3—31no—
432C4×Dic3—61no—
433C4×Dic3C22×D311yescharacteristic
434C2×C3⋊C8—31no—
435C2×C3⋊C8—31no—
436C2×C3⋊C8—61no—
437C2×C3⋊C8C22×D311yescharacteristic
438C2×C3⋊C8C22×D311yescharacteristic
439D24—41no—
440D24—121no—
441D24—121no—
442D24—122no—
443D24—121no—
444D24—121no—
445D24—121no—
446C22×C32—41no—
447C22×C32—41no—
448C22×C32—41no—
449C22×C32C22×D411yescharacteristic
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
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×C4—41no—
471C32×C4H(5,𝔽2)11yescharacteristic
472C32×C4H(5,𝔽2)11yescharacteristic
473C3⋊Dic3—21no—
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—91no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—91no—
492C4⋊Q8—31no—
493#127—31no—
494#127—91no—
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—31no—
513#102—31no—
514#102—91no—
515#102—91no—
516#102—91no—
517#102D3211yescharacteristic, complemented
518C22⋊C8—31no—
519C22⋊C8—91no—
520C4×C8—31no—
521C4×C8—91no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—31no—
525C23×C3—41no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—122no—
530C23×C3—122no—
531C23×C3—122no—
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—61no—
541C22×D3—61no—
542C22×D3—121no—
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×Q8—122no—
552C3×D4—21no—
553C3×D4—21no—
554C3×D4—21no—
555C3×D4—21no—
556C3×D4—41no—
557C3×D4—41no—
558C3×D4—61no—
559C3×D4—61no—
560C3×D4—61no—
561C3×D4—61no—
562C3×D4—61no—
563C3×D4—61no—
564C3×D4—122no—
565C3×D4—122no—
566C3×D4—122no—
567C3×D4—122no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—31no—
572C2×C3×C4—31no—
573C2×C3×C4—31no—
574C2×C3×C4—41no—
575C2×C3×C4—61no—
576C2×C3×C4—61no—
577C2×C3×C4—61no—
578C2×C3×C4C23×D311yescharacteristic
579C2×C3×C4C23×D311yescharacteristic
580#67—42no—
581#67—42no—
582#67—42no—
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—242no—
598#67—242no—
599C2×Dic3—21no—
600C2×Dic3—31no—
601C2×Dic3—31no—
602C2×Dic3—34no—
603C2×Dic3—31no—
604C2×Dic3—31no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—62no—
608C2×Dic3—122no—
609C2×Dic3D3×D411yescharacteristic
610C2×Dic3D3×D411yescharacteristic
611C2×Dic3D3×D411yescharacteristic
612D12—21no—
613D12—21no—
614D12—21no—
615D12—21no—
616D12—21no—
617D12—21no—
618D12—42no—
619D12—62no—
620D12—61no—
621D12—61no—
622D12—61no—
623D12—61no—
624D12—61no—
625D12—61no—
626D12—61no—
627D12—61no—
628D12—121no—
629D12—121no—
630D12—121no—
631D12—122no—
632D12—122no—
633D12—122no—
634D12—122no—
635D12—122no—
636D12—122no—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—34no—
640C4×D3—62no—
641C4×D3—122no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—242no—
645Dic6—42no—
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#53511yescharacteristic
658C2×C32C22×D811yescharacteristic
659C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
660C3⋊D3—81no—
661C3⋊D3—81no—
662C3×D3—22no—
663C3×D3—81no—
664C3×D3—81no—
665C3×D3—81no—
666C24—61no—
667C24—181no—
668#41—364no—
669C2×Q8—61no—
670C2×D4—31no—
671C2×D4—31no—
672C2×D4—31no—
673C2×D4—61no—
674C2×D4—61no—
675C2×D4—61no—
676C2×D4—61no—
677C2×D4—91no—
678C2×D4—91no—
679C2×D4—121no—
680C2×D4—121no—
681C2×D4—181no—
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—181no—
691C2×D4—361no—
692C2×D4—361no—
693C2×D4—364no—
694C2×D4—364no—
695C2×D4C2×D3211yescharacteristic
696C22×C4—31no—
697C22×C4—91no—
698C22×C4—91no—
699C22×C4—181no—
700C22×C4—181no—
701D8—121no—
702D8—121no—
703D8—361no—
704D8—361no—
705D8—361no—
706D8—361no—
707D8—361no—
708D8—361no—
709C2×C8—31no—
710C2×C8—31no—
711C2×C8—91no—
712C2×C8C2×D3211yescharacteristic
713C4⋊C4—31no—
714C4⋊C4—61no—
715C4⋊C4C2×D3211yescharacteristic
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—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—61no—
733C22×C3—61no—
734C22×C3—81no—
735C22×C3—81no—
736C22×C3—81no—
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—121no—
746C22×C3—244no—
747C22×C3C2×D3×D411yescharacteristic
748C22×C3C2×D3×D411yescharacteristic
749C2×D3—21no—
750C2×D3—21no—
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—84no—
761C2×D3—122no—
762C2×D3—121no—
763C2×D3—121no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—241no—
775C2×D3—241no—
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—41no—
787C3×C4—41no—
788C3×C4—61no—
789C3×C4—81no—
790C3×C4—121no—
791C3×C4#100411yescharacteristic
792C3×C4#100411yescharacteristic
793C3×C4#100911yescharacteristic
794C3×C4#100911yescharacteristic
795Dic3—21no—
796Dic3—32no—
797Dic3—32no—
798Dic3—41no—
799Dic3—62no—
800Dic3—61no—
801Dic3—61no—
802Dic3—121no—
803Dic3D3×D812yes—
804Dic3#91412yes—
805C32#320511yescharacteristic, complemented, Sylow
806C23—21no—
807C23—31no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—122no—
812C23—122no—
813C23—122no—
814C23—181no—
815C23—181no—
816C23—362no—
817C23—362no—
818C23—362no—
819Q8—122no—
820D4—21no—
821D4—21no—
822D4—61no—
823D4—61no—
824D4—61no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—122no—
829D4—122no—
830D4—122no—
831D4—122no—
832D4—181no—
833D4—181no—
834D4—181no—
835D4—181no—
836D4—362no—
837D4—362no—
838D4—362no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—362no—
845D4—362no—
846C2×C4—21no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—94no—
854C2×C4—91no—
855C2×C4—91no—
856C2×C4—182no—
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—81no—
869C2×C3—81no—
870C2×C3—161no—
871C2×C3—241no—
872C2×C3—241no—
873C2×C3—241no—
874C2×C3#559211yescharacteristic
875C2×C3#567411yescharacteristic
876C2×C3C2×D3×D811yescharacteristic
877C2×C3C2×D3×D811yescharacteristic
878C2×C3C2×#91411yescharacteristic
879C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
880D3—22no—
881D3—81no—
882D3—81no—
883D3—81no—
884D3—242no—
885D3—241no—
886D3—241no—
887D3—241no—
888D3—241no—
889D3—481no—
890C22—32no—
891C22—41no—
892C22—41no—
893C22—41no—
894C22—61no—
895C22—61no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—121no—
905C22—244no—
906C22—361no—
907C22—361no—
908C22—361no—
909C22—361no—
910C22—361no—
911C22—361no—
912C22—724no—
913C22D32×D411yescharacteristic
914C4—32no—
915C4—32no—
916C4—41no—
917C4—61no—
918C4—92no—
919C4—121no—
920C4—181no—
921C4#6430711yescharacteristic
922C4#6431411yescharacteristic
923C3—21no—
924C3#7999411yescharacteristic, complemented
925C3#8156611yescharacteristic, complemented
926C2—62no—
927C2—81no—
928C2—241no—
929C2—241no—
930C2—241no—
931C2—721no—
932C2—721no—
933C2#1059427011yescharacteristic
934C2D32×D811yescharacteristic
935C2D3×#91411yescharacteristic
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. #10594369C2semidirect
3. #10592485C2semidirect
4. C3×#4773C2semidirect
5. C3×#4760C2semidirect
6. #10591482C2semidirect
7. #10591448C2semidirect
8. #10591433C2semidirect
9. #10590947C2semidirect
10. #10590880C2semidirect
11. #10590749C2semidirect
12. #10590655C2semidirect
13. #10590595C2semidirect
14. #10590551C2semidirect
15. #10590548C2semidirect
24. C2×#3753C22semidirect
25. C2×#3745C22semidirect
26. #64102C22semidirect
28. C2×C3×#213C22semidirect
29. C2×C3×D24C22semidirect
31. C3×#888C22semidirect
36. #63911C22semidirect
39. #63898C22semidirect
43. C2×#3714C22semidirect
44. C2×#3714C22semidirect
45. C2×#3714C22semidirect
46. C2×#3713C22semidirect
47. C32×#102C22semidirect
48. #63641C22semidirect
49. #63636C22semidirect
50. C3×#832C22semidirect
51. C3×#821C22semidirect
53. C3×C8×Dic3C22semidirect
54. C3×#809C22semidirect
55. C3×#809C22semidirect
56. #63572C22semidirect
57. #63564C22semidirect
58. #63562C22semidirect
60. Dic3×C3⋊C8C22semidirect
85. #4773D3semidirect
87. #4760D3semidirect
189. C2×#213C2×D3semidirect
198. C2×D24C2×D3semidirect
207. #888C2×D3semidirect
218. C3×#102C2×D3semidirect
219. C3×#102C2×D3semidirect
223. #832C2×D3semidirect
226. #821C2×D3semidirect
235. C8×Dic3C2×D3semidirect
241. #809C2×D3semidirect
242. #809C2×D3semidirect
297. D3×Dic3D8semidirect
517. #102D32semidirect
805. C32#3205semidirect
924. C3#79994semidirect
925. C3#81566semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
#105943692
#105924852
C3×#47732
C3×#47602
#105914822
#105914482
#105914332
#105909472
#105908802
#105907492
#105906552
#105905952
#105905512
#105905482
#815663
#799943