Finite Group Databasebeta

← #11878851

Subgroups — #11878851

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#940C211yesmaximal, characteristic
2#10594385C211yesmaximal, characteristic, complemented
3#10592459C211yesmaximal, characteristic, complemented
4C3×#4776C211yesmaximal, characteristic, complemented
5C3×#4762C211yesmaximal, characteristic, complemented
6#10591492C211yesmaximal, characteristic, complemented
7#10591458C211yesmaximal, characteristic, complemented
8#10591438C211yesmaximal, characteristic, complemented
9#10590942C211yesmaximal, characteristic, complemented
10#10590884C211yesmaximal, characteristic, complemented
11#10590799C211yesmaximal, characteristic, complemented
12#10590656C211yesmaximal, characteristic, complemented
13#10590596C211yesmaximal, characteristic, complemented
14#10590552C211yesmaximal, characteristic, complemented
15#10590549C211yesmaximal, characteristic, complemented
16#80387—31nomaximal
17#80138—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22#64149C2211yescharacteristic
23#64097C2211yescharacteristic, complemented
24C3×#940C2211yescharacteristic
25C2×C3×#214C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic, complemented
27C2×C3×#204C2211yescharacteristic, complemented
28C2×C3×#204C2211yescharacteristic, complemented
29C3×#897C2211yescharacteristic
30C3×#887C2211yescharacteristic, complemented
31#63979—21no—
32#63979—21no—
33#63914C2211yescharacteristic
34#63911C2211yescharacteristic
35#63896—21no—
36#63877—21no—
37C4×D3×Dic3C2211yescharacteristic
38#63873C2211yescharacteristic, complemented
39#63856C2211yescharacteristic
40#63847—21no—
41#63844—21no—
42Dic3×Dic6C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic, complemented
44C2×#3717C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, 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#5622—31no—
64#5578—31no—
65C3×#460—31no—
66C3×#450—31no—
67#5218—31no—
68#5175—31no—
69#5175—31no—
70#5175—31no—
71#5175—31no—
72#5169—31no—
73#5169—31no—
74#5163—31no—
75#5163—31no—
76#5075—31no—
77#5046—31no—
78#5027—31no—
79#4848—31no—
80#4833—31no—
81#4776—31no—
82#4776D311yescharacteristic, complemented
83#4762—31no—
84#4762D311yescharacteristic, complemented
85#4760—31no—
86#4760—31no—
87#4760—31no—
88#4760—31no—
89#4760—61no—
90#4731—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×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109D3×#67—44no—
110D3×#67—44no—
111C2×#626—21no—
112C2×#626—21no—
113C2×#626—21no—
114C2×#625—21no—
115C2×#625—21no—
116C2×D3×Dic3D411yescharacteristic
117C2×D3×Dic3D411yescharacteristic
118D3×D12—41no—
119D3×D12—41no—
120C2×C32×C8C2311yescharacteristic
121C32×C4⋊C4C2311yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C3×#214—41no—
127C3×#214—41no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3—21no—
130C3×Dic3⋊C4—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135C3×#204—41no—
136C3×#204—41no—
137#3724—21no—
138#3724—21no—
139#3724—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143Dic32D411yescharacteristic
144Dic32D411yescharacteristic
145#3717—41no—
146#3717—41no—
147#3715—41no—
148#3715—41no—
149#3208—91noSylow
150C22×C3×D4—31no—
151C22×#67—61no—
152C22×#67—61no—
153C2×D3×D4—31no—
154C2×D3×D4—61no—
155C2×D3×D4—61no—
156C2×D3×D4C2×D311yescharacteristic
157C22×D12—31no—
158C2×C3×SD16—31no—
159C2×C3×SD16—31no—
160C2×C3×SD16—31no—
161C2×C3×SD16—31no—
162C3×#127—31no—
163C3×C22⋊Q8—31no—
164C3×C4×Q8—31no—
165#946—31no—
166Q8×Dic3—31no—
167#944—31no—
168#944—31no—
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—31no—
173#940—31no—
174#940—31no—
175#940—31no—
176#940—31no—
177#940—31no—
178#940—61no—
179#940—61no—
180#940—61no—
181#940—61no—
182#940—61no—
183#940C2×D311yescharacteristic
184C2×#214—31no—
185C2×#214—31no—
186C2×#214C2×D311yescharacteristic, complemented
187C2×#214C2×D311yescharacteristic, complemented
188#924—31no—
189C2×C4×Dic3—31no—
190C2×#204—31no—
191C2×#204—31no—
192C2×#204C2×D311yescharacteristic, complemented
193C2×#204C2×D311yescharacteristic, complemented
194#897C2×D311yescharacteristic
195#896—61no—
196#889—61no—
197#889—61no—
198#888—31no—
199#888—31no—
200#888—61no—
201#887—61no—
202#887C2×D311yescharacteristic, complemented
203#878—61no—
204#877—61no—
205#874—31no—
206#872—61no—
207C42×D3—31no—
208C4×Dic6—31no—
209C4×Dic6—61no—
210C3×C4⋊C8—31no—
211C3×#102—21no—
212C3×#102—31no—
213C3×#102—31no—
214C3×#102C2×D311yescharacteristic, complemented
215C3×#102C2×D311yescharacteristic, complemented
216C3×C22⋊C8—31no—
217#832—31no—
218#832—31no—
219#832—31no—
220#832—31no—
221#832—61no—
222#830—31no—
223#821—31no—
224#821—31no—
225#821—31no—
226#821—31no—
227#821—61no—
228(C2×D3)⋊C8—31no—
229(C2×D3)⋊C8C2×D311yescharacteristic
230Dic3⋊C8—31no—
231Dic3⋊C8C2×D311yescharacteristic, complemented
232C8×Dic3—31no—
233C8×Dic3—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236C8×Dic3—61no—
237#809—31no—
238#809—31no—
239#809—61no—
240#809C2×D311yescharacteristic, complemented
241#809C2×D311yescharacteristic, complemented
242C4⋊(C3⋊C8)—31no—
243C23×C32—21no—
244C22×C3⋊D3—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—42no—
248C22×C3×D3—42no—
249C22×C3×D3—42no—
250C22×C3×D3C2×D411yescharacteristic
251C2×D32—42no—
252C2×D32—42no—
253C2×D32—42no—
254C32×D4—21no—
255C32×D4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2411yescharacteristic
258#638—42no—
259#638—42no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C4⋊(C3⋊D3)—21no—
264C4⋊(C3⋊D3)—21no—
265#634—42no—
266C3×#67—42no—
267C3×#67—42no—
268C3×#67—42no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3C2×D411yescharacteristic
272C2×C3×Dic3C2×D411yescharacteristic
273C2×C3×Dic3C2×D411yescharacteristic
274C3×D12—21no—
275C3×D12—21no—
276C3×D12—21no—
277C3×D12—21no—
278C3×C4×D3—21no—
279C3×C4×D3—21no—
280C3×Dic6—21no—
281C3×Dic6—21no—
282C3×Dic6—21no—
283C3×Dic6—21no—
284#626—42no—
285#626—42no—
286#626—42no—
287#625—42no—
288#625—42no—
289D3×Dic3—22no—
290D3×Dic3SD1614yescomplemented
291C32×C8—21no—
292C3⋊(C3⋊C8)—21no—
293C3×C3⋊C8—21no—
294C3×C3⋊C8—21no—
295#533—91no—
296C2×#127—91no—
297#492—91no—
298#492—91no—
299#486—91no—
300#486—91no—
301#460—31no—
302#460—91no—
303#460—91no—
304#460—91no—
305#450—31no—
306#450—91no—
307#450—91no—
308#450—91no—
309#431—91no—
310C24×C3—61no—
311C23×D3—21no—
312C23×D3—61no—
313C23×D3—61no—
314C2×C3×Q8—31no—
315C2×C3×Q8—31no—
316C2×C3×D4—21no—
317C2×C3×D4—31no—
318C2×C3×D4—31no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—121no—
323C2×C3×D4—121no—
324C2×C3×D4C22×D311yescharacteristic
325C2×C3×D4C22×D311yescharacteristic
326C22×C3×C4—31no—
327C2×#67—21no—
328C2×#67—21no—
329C2×#67—21no—
330C2×#67—61no—
331C2×#67—61no—
332C2×#67—61no—
333C2×#67—61no—
334C2×#67—61no—
335C2×#67—61no—
336C2×#67—61no—
337C2×#67—61no—
338C2×#67—61no—
339C2×#67—61no—
340C2×#67—61no—
341C2×#67—121no—
342C2×#67—121no—
343C2×#67—124no—
344C2×#67—124no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347D3×D4—41no—
348D3×D4—41no—
349D3×D4—121no—
350D3×D4—121no—
351D3×D4—124no—
352D3×D4—124no—
353C2×D12—31no—
354C2×D12—31no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—121no—
360C2×D12—121no—
361C2×D12C22×D311yescharacteristic
362C2×D12C22×D311yescharacteristic
363C2×C4×D3—31no—
364C2×C4×D3—31no—
365C2×C4×D3C22×D311yescharacteristic
366C2×Dic6—61no—
367C2×Dic6—61no—
368C2×Dic6—121no—
369C2×Dic6C22×D311yescharacteristic
370C2×Dic6C22×D311yescharacteristic
371C3×SD16—121no—
372C3×SD16—121no—
373C3×SD16—121no—
374C3×SD16—121no—
375C2×C3×C8—21no—
376C2×C3×C8—31no—
377C2×C3×C8—31no—
378C2×C3×C8C22×D311yescharacteristic
379C2×C3×C8C22×D311yescharacteristic
380C3×C4⋊C4—21no—
381C3×C4⋊C4—61no—
382C3×C4⋊C4—61no—
383C3×C4⋊C4C22×D311yescharacteristic
384C3×C4⋊C4C22×D311yescharacteristic
385C3×C22⋊C4—61no—
386C3×C42—31no—
387C3×C42—61no—
388#217—61no—
389#215—121no—
390#215—121no—
391#215—121no—
392#215—121no—
393#214—41no—
394#214—41no—
395#214—121no—
396#214—121no—
397(C2×D3)⋊C4—21no—
398(C2×D3)⋊C4—61no—
399C4⋊Dic3—21no—
400C4⋊Dic3—31no—
401C4⋊Dic3—31no—
402C4⋊Dic3—61no—
403C4⋊Dic3—61no—
404Dic3⋊C4—21no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—121no—
415C4×Dic3—21no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—31no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—31no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—61no—
425C4×Dic3C22×D311yescharacteristic
426C2×C3⋊C8—31no—
427C2×C3⋊C8—31no—
428C2×C3⋊C8—61no—
429C2×C3⋊C8C22×D311yescharacteristic
430C2×C3⋊C8C22×D311yescharacteristic
431#204—41no—
432#204—41no—
433#204—121no—
434#204—121no—
435C22×C32—41no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32C22×D411yescharacteristic
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—41no—
442C2×C3×D3—21no—
443C2×C3×D3—21no—
444C2×C3×D3—41no—
445C2×C3×D3—41no—
446C2×C3×D3—41no—
447C2×C3×D3—41no—
448C2×C3×D3—41no—
449C2×C3×D3—41no—
450C2×C3×D3—84no—
451C2×C3×D3C2×SD1612yes—
452D32—84no—
453C32×C4—41no—
454C32×C4H(5,𝔽2)11yescharacteristic
455C32×C4H(5,𝔽2)11yescharacteristic
456C3⋊Dic3—41no—
457C3⋊Dic3C2×SD1612yes—
458C3⋊Dic3AGL(1,ℤ/8)12yes—
459C3×Dic3—21no—
460C3×Dic3—21no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3C2×SD1612yes—
464C22×D4—31no—
465C22×D4—91no—
466C22×D4—181no—
467C22×D4—181no—
468C2×SD16—31no—
469C2×SD16—31no—
470C2×SD16—31no—
471C2×SD16—31no—
472C2×SD16—91no—
473C2×SD16—91no—
474C2×SD16—91no—
475C2×SD16—91no—
476C4⋊Q8—91no—
477C4⋊Q8—91no—
478#127—31no—
479#127—91no—
480#127—91no—
481#127—91no—
482#127—181no—
483#127—181no—
484#125—181no—
485C22⋊Q8—31no—
486C22⋊Q8—91no—
487C22⋊Q8—181no—
488C4×Q8—31no—
489C4×Q8—91no—
490C4×Q8—181no—
491#117—181no—
492C2×C42—91no—
493C4⋊C8—31no—
494C4⋊C8—91no—
495#102—31no—
496#102—31no—
497#102—91no—
498#102—91no—
499#102—91no—
500#102—91no—
501#102—91no—
502#102D3211yescharacteristic, complemented
503C22⋊C8—31no—
504C22⋊C8—91no—
505C4×C8—91no—
506C4×C8—91no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—31no—
510C23×C3—41no—
511C23×C3—61no—
512C23×C3—61no—
513C23×C3—122no—
514C23×C3—122no—
515C23×C3—122no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—42no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—61no—
522C22×D3—61no—
523C22×D3—121no—
524C22×D3—122no—
525C22×D3—122no—
526C22×D3—122no—
527C22×D3—122no—
528C22×D3—122no—
529C22×D3—122no—
530C22×D3D3×D411yescharacteristic
531C3×Q8—61no—
532C3×Q8—61no—
533C3×Q8—61no—
534C3×Q8—61no—
535C3×D4—21no—
536C3×D4—21no—
537C3×D4—21no—
538C3×D4—21no—
539C3×D4—41no—
540C3×D4—41no—
541C3×D4—61no—
542C3×D4—61no—
543C3×D4—61no—
544C3×D4—61no—
545C3×D4—122no—
546C3×D4—122no—
547C3×D4—122no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—31no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—41no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4C23×D311yescharacteristic
560C2×C3×C4C23×D311yescharacteristic
561#67—42no—
562#67—42no—
563#67—42no—
564#67—122no—
565#67—122no—
566#67—122no—
567#67—122no—
568#67—122no—
569#67—122no—
570#67—122no—
571#67—122no—
572#67—122no—
573#67—122no—
574#67—122no—
575#67—242no—
576#67—242no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—31no—
580C2×Dic3—31no—
581C2×Dic3—31no—
582C2×Dic3—31no—
583C2×Dic3—34no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—62no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—121no—
590C2×Dic3D3×D411yescharacteristic
591C2×Dic3D3×D411yescharacteristic
592C2×Dic3D3×D411yescharacteristic
593D12—21no—
594D12—21no—
595D12—21no—
596D12—21no—
597D12—61no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—121no—
602D12—121no—
603D12—122no—
604D12—122no—
605D12—122no—
606C4×D3—21no—
607C4×D3—21no—
608C4×D3—34no—
609C4×D3—62no—
610Dic6—21no—
611Dic6—21no—
612Dic6—21no—
613Dic6—21no—
614Dic6—122no—
615Dic6—122no—
616Dic6—242no—
617C3×C8—21no—
618C3×C8—21no—
619C3×C8—41no—
620C3×C8—61no—
621C3×C8—61no—
622C3⋊C8—21no—
623C3⋊C8—21no—
624C3⋊C8—61no—
625C3⋊C8—61no—
626C3⋊C8—121no—
627C2×C32—81no—
628C2×C32#53511yescharacteristic
629C2×C32C22×SD1611yescharacteristic
630C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
631C3⋊D3—81no—
632C3×D3—22no—
633C3×D3—81no—
634C3×D3—81no—
635C24—61no—
636C24—181no—
637C2×Q8—31no—
638C2×Q8—31no—
639C2×Q8—181no—
640C2×D4—31no—
641C2×D4—31no—
642C2×D4—61no—
643C2×D4—61no—
644C2×D4—61no—
645C2×D4—91no—
646C2×D4—121no—
647C2×D4—121no—
648C2×D4—181no—
649C2×D4—181no—
650C2×D4—181no—
651C2×D4—181no—
652C2×D4—181no—
653C2×D4—181no—
654C2×D4—181no—
655C2×D4—361no—
656C2×D4—361no—
657C2×D4—364no—
658C2×D4—364no—
659C2×D4C2×D3211yescharacteristic
660C22×C4—31no—
661C22×C4—91no—
662C22×C4—91no—
663SD16—121no—
664SD16—121no—
665SD16—121no—
666SD16—121no—
667SD16—361no—
668SD16—361no—
669SD16—361no—
670SD16—361no—
671C2×C8—31no—
672C2×C8—31no—
673C2×C8—91no—
674C2×C8C2×D3211yescharacteristic
675C4⋊C4—61no—
676C4⋊C4—61no—
677C4⋊C4—91no—
678C4⋊C4—181no—
679C4⋊C4—181no—
680C4⋊C4—181no—
681C4⋊C4—181no—
682C4⋊C4—181no—
683C4⋊C4C2×D3211yescharacteristic
684C22⋊C4—61no—
685C22⋊C4—181no—
686C42—31no—
687C42—61no—
688C42—91no—
689C42—91no—
690C42—91no—
691C42—181no—
692C22×C3—21no—
693C22×C3—32no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—61no—
701C22×C3—61no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3—81no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—121no—
709C22×C3—121no—
710C22×C3—121no—
711C22×C3—244no—
712C22×C3C2×D3×D411yescharacteristic
713C22×C3C2×D3×D411yescharacteristic
714C2×D3—21no—
715C2×D3—21no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—41no—
722C2×D3—84no—
723C2×D3—121no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—121no—
729C2×D3—241no—
730C2×D3—241no—
731C2×D3—241no—
732C2×D3—244no—
733C2×D3—244no—
734C2×D3D3×SD1612yes—
735C3×C4—21no—
736C3×C4—21no—
737C3×C4—32no—
738C3×C4—41no—
739C3×C4—41no—
740C3×C4—61no—
741C3×C4—61no—
742C3×C4—81no—
743C3×C4—121no—
744C3×C4—121no—
745C3×C4#100411yescharacteristic
746C3×C4#100411yescharacteristic
747C3×C4#100411yescharacteristic
748C3×C4#100911yescharacteristic
749Dic3—21no—
750Dic3—21no—
751Dic3—32no—
752Dic3—32no—
753Dic3—32no—
754Dic3—32no—
755Dic3—41no—
756Dic3—41no—
757Dic3—62no—
758Dic3—62no—
759Dic3—121no—
760Dic3—121no—
761Dic3—241no—
762Dic3D3×SD1612yes—
763C32#320811yescharacteristic, complemented, Sylow
764C23—21no—
765C23—31no—
766C23—61no—
767C23—61no—
768C23—122no—
769C23—122no—
770C23—122no—
771C23—181no—
772C23—362no—
773C23—362no—
774C23—362no—
775Q8—61no—
776Q8—61no—
777Q8—61no—
778Q8—61no—
779Q8—362no—
780D4—21no—
781D4—21no—
782D4—61no—
783D4—61no—
784D4—61no—
785D4—61no—
786D4—122no—
787D4—122no—
788D4—122no—
789D4—181no—
790D4—181no—
791D4—362no—
792D4—362no—
793D4—362no—
794D4—362no—
795D4—362no—
796D4—362no—
797D4—362no—
798C2×C4—21no—
799C2×C4—31no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—94no—
807C2×C4—91no—
808C2×C4—91no—
809C2×C4—182no—
810C2×C4—181no—
811C2×C4C22×D3211yescharacteristic
812C8—21no—
813C8—61no—
814C8—61no—
815C8—181no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—62no—
820C2×C3—81no—
821C2×C3—81no—
822C2×C3—161no—
823C2×C3—241no—
824C2×C3—241no—
825C2×C3#559211yescharacteristic
826C2×C3#560711yescharacteristic
827C2×C3C2×D3×SD1611yescharacteristic
828C2×C3C2×D3×SD1611yescharacteristic
829C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
830C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
831D3—22no—
832D3—81no—
833D3—81no—
834D3—241no—
835D3—241no—
836D3—481no—
837C22—32no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—61no—
842C22—61no—
843C22—121no—
844C22—121no—
845C22—121no—
846C22—121no—
847C22—121no—
848C22—121no—
849C22—244no—
850C22—361no—
851C22—361no—
852C22—361no—
853C22—724no—
854C22D32×D411yescharacteristic
855C4—32no—
856C4—41no—
857C4—61no—
858C4—61no—
859C4—92no—
860C4—92no—
861C4—121no—
862C4—121no—
863C4—361no—
864C4#6430711yescharacteristic
865C4#6431311yescharacteristic
866C3—21no—
867C3#8013811yescharacteristic, complemented
868C3#8038711yescharacteristic, complemented
869C2—62no—
870C2—81no—
871C2—241no—
872C2—241no—
873C2—721no—
874C2#1059426911yescharacteristic
875C2#1059472611yescharacteristic
876C2D32×SD1611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalD3×#940C2
hypercenter#102D32
hypocenterC32#3208
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
2. #10594385C2semidirect
3. #10592459C2semidirect
4. C3×#4776C2semidirect
5. C3×#4762C2semidirect
6. #10591492C2semidirect
7. #10591458C2semidirect
8. #10591438C2semidirect
9. #10590942C2semidirect
10. #10590884C2semidirect
11. #10590799C2semidirect
12. #10590656C2semidirect
13. #10590596C2semidirect
14. #10590552C2semidirect
15. #10590549C2semidirect
23. #64097C22semidirect
25. C2×C3×#214C22semidirect
26. C2×C3×#214C22semidirect
27. C2×C3×#204C22semidirect
28. C2×C3×#204C22semidirect
30. C3×#887C22semidirect
38. #63873C22semidirect
42. Dic3×Dic6C22semidirect
43. C2×#3717C22semidirect
44. C2×#3717C22semidirect
45. C2×#3715C22semidirect
46. C2×#3715C22semidirect
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. #4776D3semidirect
84. #4762D3semidirect
186. C2×#214C2×D3semidirect
187. C2×#214C2×D3semidirect
192. C2×#204C2×D3semidirect
193. C2×#204C2×D3semidirect
202. #887C2×D3semidirect
214. C3×#102C2×D3semidirect
215. C3×#102C2×D3semidirect
231. Dic3⋊C8C2×D3semidirect
240. #809C2×D3semidirect
241. #809C2×D3semidirect
290. D3×Dic3SD16semidirect
502. #102D32semidirect
763. C32#3208semidirect
867. C3#80138semidirect
868. C3#80387semidirect

Maximal subgroups

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

subgroupindex
D3×#9402
#105943852
#105924592
C3×#47762
C3×#47622
#105914922
#105914582
#105914382
#105909422
#105908842
#105907992
#105906562
#105905962
#105905522
#105905492
#803873
#801383