Finite Group Databasebeta

← #11887116

Subgroups — #11887116

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595074C211yesmaximal, characteristic
2#10594993C211yesmaximal, characteristic, complemented
3C2×#63648C211yesmaximal, characteristic, complemented
4C3×#5114C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic, complemented
7#10591092C211yesmaximal, characteristic, complemented
8#10590942C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590878C211yesmaximal, characteristic, complemented
11#10590847C211yesmaximal, characteristic, complemented
12#10590799C211yesmaximal, characteristic, complemented
13#10590792C211yesmaximal, characteristic, complemented
14#10590759C211yesmaximal, characteristic, complemented
15#10590677C211yesmaximal, characteristic, complemented
16#80680—31nomaximal
17#79439—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3811—21no—
20C2×D3×D12C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic, complemented
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
23C3×#930C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#924C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic, complemented
27C2×C3×D3×C8C2211yescharacteristic, complemented
28#63982—21no—
29#63981—21no—
30#67⋊Dic3—21no—
31#63923—21no—
32#63918C2211yescharacteristic, complemented
33#63911C2211yescharacteristic
34#63910—21no—
35#63909C2211yescharacteristic
36#63894C2211yescharacteristic
37#63893—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63856C2211yescharacteristic, complemented
40#63845—21no—
41Dic3×Dic6C2211yescharacteristic, complemented
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic, complemented
47#63648C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic, complemented
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5635—31no—
62#5609—31no—
63D4×D12—31no—
64#5543—31no—
65C3×#465—31no—
66C3×C8×D4—31no—
67#5169—31no—
68#5163—31no—
69#5114—31no—
70#5114D311yescharacteristic, complemented
71C2×#821—31no—
72C2×#821—31no—
73C2×#821—31no—
74C2×#821—61no—
75C8×#67D311yescharacteristic, complemented
76#5046—31no—
77#5034—31no—
78#4870—31no—
79#4863—31no—
80#4848—31no—
81#4842—31no—
82#4807—31no—
83#4788—31no—
84D3×#102—31no—
85#4760—31no—
86#4735—31no—
87#4735—31no—
88#4731—31no—
89#4731—31no—
90#4694—31no—
91C4×#204—31no—
92C23×C3⋊D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)—41no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106#3811—44no—
107C2×#627—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116C2×C32×C8—41no—
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C3×#217—21no—
123C3×#217D411yescharacteristic
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×#204—41no—
134C3×D3×C8—41no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3717—22no—
144#3717—41no—
145#3295—91noSylow
146C2×D3×D4—31no—
147C2×D3×D4—61no—
148C2×D3×D4—61no—
149C22×D12—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×D12—61no—
153C2×C3×SD16—31no—
154C22×C3×C8—21no—
155C22×C3×C8—31no—
156C22×C3×C8C2×D311yescharacteristic, complemented
157C22×C3×C8C2×D311yescharacteristic, complemented
158C3×C22⋊Q8—31no—
159C3×#121—31no—
160C3×C4×D4—31no—
161#946—31no—
162Q8×Dic3—31no—
163C2×#215—31no—
164C2×#215—31no—
165#940—31no—
166#937—61no—
167D4×Dic3—61no—
168#930—31no—
169#930C2×D311yescharacteristic
170C4×#67C2×D311yescharacteristic
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175#924—31no—
176#924C2×D311yescharacteristic, complemented
177C2×#204—31no—
178C2×#204—31no—
179C2×#204C2×D311yescharacteristic, complemented
180C2×D3×C8C2×D311yescharacteristic, complemented
181#897—61no—
182#895—31no—
183#895—61no—
184#893—31no—
185D3×C4⋊C4—31no—
186#890—61no—
187#889—61no—
188#888—31no—
189#884—61no—
190#882—61no—
191#882—61no—
192#882—61no—
193#67⋊C4—61no—
194#878—61no—
195#878—61no—
196#878—61no—
197#874—31no—
198C4×D12—31no—
199#869—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×C4×C8—31no—
208#832—31no—
209#832—31no—
210#830C2×D311yescharacteristic, complemented
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—31no—
221#821—31no—
222#821—31no—
223#821—61no—
224#821—61no—
225#821—61no—
226#821—61no—
227#821C2×D311yescharacteristic, complemented
228(C2×D3)⋊C8C2×D311yescharacteristic, complemented
229#817—31no—
230#817—31no—
231#817C2×D311yescharacteristic, complemented
232#816C2×D311yescharacteristic, complemented
233Dic3⋊C8C2×D311yescharacteristic, complemented
234C8×Dic3C2×D311yescharacteristic, complemented
235#809—31no—
236#809—31no—
237#808—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—42no—
244C22×C3⋊D3—81no—
245C22×C3×D3—21no—
246C22×C3×D3C2×D411yescharacteristic
247C2×D32—42no—
248C2×D32—42no—
249C2×D32—81no—
250C2×C32×C4—21no—
251C2×C32×C4—21no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—81no—
257C4⋊(C3⋊D3)—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—42no—
261C4⋊(C3⋊D3)#4112yes—
262C3×#67—42no—
263C3×#67SD1614yescomplemented
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C2×C3×Dic3C2×D411yescharacteristic
270C3×D12—21no—
271C3×D12—21no—
272C3×C4×D3—21no—
273C3×C4×D3—21no—
274C3×Dic6—21no—
275C3×Dic6—21no—
276#627—81no—
277#626—42no—
278#626—42no—
279#626—42no—
280#626—81no—
281#624—42no—
282D3×Dic3—81no—
283C32×C8—21no—
284C32×C8—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—91no—
289#486—91no—
290#481—91no—
291#481—91no—
292#476—91no—
293#465—31no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—31no—
300C2×#102—91no—
301C2×#102—91no—
302C23×D3—61no—
303C23×D3—61no—
304C23×D3—61no—
305C23×D3—61no—
306C23×D3—121no—
307C2×C3×Q8—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—61no—
311C22×C3×C4—21no—
312C22×C3×C4—31no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—21no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67D1211yescharacteristic
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325D3×D4—62no—
326D3×D4—121no—
327D3×D4—124no—
328D3×D4—124no—
329C2×D12—31no—
330C2×D12—31no—
331C2×D12—31no—
332C2×D12—31no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—62no—
336C2×D12—62no—
337C2×D12—62no—
338C2×D12—64no—
339C2×D12—61no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—121no—
346C2×D12—121no—
347C2×D12—121no—
348C2×D12—121no—
349C2×D12—122no—
350C2×D12C22×D311yescharacteristic
351C2×C4×D3—61no—
352C2×C4×D3—61no—
353C2×C4×D3—61no—
354C2×C4×D3C22×D311yescharacteristic
355C2×Dic6—61no—
356C2×Dic6—61no—
357C2×Dic6C22×D311yescharacteristic
358C3×SD16—121no—
359C2×C3×C8—21no—
360C2×C3×C8—21no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—41no—
364C2×C3×C8—41no—
365C2×C3×C8—42no—
366C2×C3×C8—121no—
367C2×C3×C8C22×D311yescharacteristic
368C2×C3×C8C22×D311yescharacteristic
369C2×C3×C8C22×D311yescharacteristic
370C2×C3×C8C22×D311yescharacteristic
371C3×C4⋊C4—31no—
372C3×C4⋊C4—31no—
373C3×C4⋊C4—31no—
374C3×C4⋊C4—61no—
375C3×C22⋊C4—31no—
376C3×C22⋊C4—31no—
377C3×C22⋊C4—61no—
378C3×C22⋊C4—61no—
379C3×C42—31no—
380#217—21no—
381#217—61no—
382#217D1211yescharacteristic
383#215—62no—
384#215—121no—
385(C2×D3)⋊C4—21no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4D1211yescharacteristic
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—31no—
395C4⋊Dic3—31no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3—61no—
401C4⋊Dic3—61no—
402C4⋊Dic3—61no—
403C4⋊Dic3—121no—
404C4⋊Dic3C22×D311yescharacteristic
405C4⋊Dic3C22×D311yescharacteristic
406Dic3⋊C4—21no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4D1211yescharacteristic
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3C22×D311yescharacteristic
416C2×C3⋊C8C22×D311yescharacteristic
417C2×C3⋊C8C22×D311yescharacteristic
418#204—41no—
419#204—62no—
420#204—121no—
421D3×C8—41no—
422C22×C32—21no—
423C22×C32—21no—
424C22×C32C2×SD1612yes—
425C22×C32C22×D411yescharacteristic
426C2×C3⋊D3—22no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—41no—
430C2×C3⋊D3—41no—
431C2×C3⋊D3—41no—
432C2×C3⋊D3—84no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—41no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3C2×SD1612yes—
439D32—84no—
440C32×C4—21no—
441C32×C4C2×#4111yescharacteristic
442C32×C4H(5,𝔽2)11yescharacteristic
443C3⋊Dic3—41no—
444C3⋊Dic3—41no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3C2×SD1612yes—
451C22×D4—91no—
452C22×D4—91no—
453C22×D4—181no—
454C2×SD16—31no—
455C2×SD16—91no—
456C2×SD16—91no—
457C22×C8—31no—
458C22×C8D3211yescharacteristic, complemented
459C4⋊Q8—91no—
460#127—91no—
461#125—181no—
462C22⋊Q8—31no—
463C22⋊Q8—91no—
464C22⋊Q8—181no—
465C22⋊Q8—181no—
466#121—31no—
467#121—91no—
468#121—181no—
469#120—181no—
470#120—181no—
471C4×Q8—91no—
472C4×D4—31no—
473C4×D4—91no—
474C4×D4—181no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477#106—31no—
478#106—91no—
479#106—91no—
480C4⋊C8—31no—
481#103—31no—
482#102—31no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490#102—91no—
491C22⋊C8—31no—
492C22⋊C8—31no—
493C4×C8—31no—
494C23×C3—21no—
495C23×C3—31no—
496C23×C3—61no—
497C23×C3C2×D1211yescharacteristic
498C23×C3D3×D411yescharacteristic
499C22×D3—21no—
500C22×D3—61no—
501C22×D3—61no—
502C22×D3—61no—
503C22×D3—61no—
504C22×D3—121no—
505C22×D3—121no—
506C22×D3—122no—
507C22×D3—122no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—124no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—242no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—241no—
519C22×D3—241no—
520C22×D3—242no—
521C22×D3C2×D1211yescharacteristic
522C3×Q8—61no—
523C3×Q8—61no—
524C3×D4—34no—
525C3×D4—61no—
526C3×D4—61no—
527C3×D4—122no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—31no—
537C2×C3×C4—31no—
538C2×C3×C4—31no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4C2×D1211yescharacteristic
545C2×C3×C4D3×D411yescharacteristic
546C2×C3×C4C23×D311yescharacteristic
547C2×C3×C4C23×D311yescharacteristic
548#67—42no—
549#67—122no—
550#67—122no—
551#67—122no—
552#67—241no—
553#67#20414yescomplemented
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—241no—
564C2×Dic3—241no—
565C2×Dic3—241no—
566C2×Dic3—242no—
567C2×Dic3C2×D1211yescharacteristic
568C2×Dic3C2×D1211yescharacteristic
569C2×Dic3C2×D1211yescharacteristic
570D12—21no—
571D12—21no—
572D12—32no—
573D12—32no—
574D12—62no—
575D12—62no—
576D12—61no—
577D12—61no—
578D12—61no—
579D12—61no—
580D12—61no—
581D12—61no—
582D12—121no—
583D12—121no—
584D12—122no—
585D12—122no—
586D12—124no—
587D12—122no—
588D12—122no—
589D12—122no—
590D12—241no—
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—122no—
594C4×D3—122no—
595C4×D3—241no—
596Dic6—21no—
597Dic6—21no—
598Dic6—241no—
599Dic6—241no—
600C3×C8—21no—
601C3×C8—21no—
602C3×C8—21no—
603C3×C8—21no—
604C3×C8—41no—
605C3×C8—41no—
606C3×C8—61no—
607C3×C8—61no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C2×C32—22no—
611C2×C32#54611yescharacteristic
612C2×C32C22×SD1611yescharacteristic
613C2×C32#57611yescharacteristic
614C3⋊D3—42no—
615C3⋊D3—81no—
616C3×D3—22no—
617C3×D3—81no—
618C24—181no—
619C24—181no—
620C2×Q8—31no—
621C2×Q8—181no—
622C2×D4—31no—
623C2×D4—31no—
624C2×D4—61no—
625C2×D4—91no—
626C2×D4—91no—
627C2×D4—182no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4—181no—
631C2×D4—182no—
632C2×D4—181no—
633C2×D4—181no—
634C2×D4—361no—
635C2×D4—361no—
636C2×D4—364no—
637C22×C4—31no—
638C22×C4—181no—
639C22×C4—181no—
640C22×C4—181no—
641C22×C4C2×D3211yescharacteristic
642SD16—121no—
643SD16—182no—
644SD16—361no—
645C2×C8—31no—
646C2×C8—31no—
647C2×C8—41no—
648C2×C8—121no—
649C2×C8C2×D3211yescharacteristic
650C2×C8C2×D3211yescharacteristic
651C4⋊C4—31no—
652C4⋊C4—31no—
653C4⋊C4—31no—
654C4⋊C4—61no—
655C4⋊C4—91no—
656C4⋊C4—91no—
657C4⋊C4—181no—
658C4⋊C4—181no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C22⋊C4—31no—
663C22⋊C4—31no—
664C22⋊C4—61no—
665C22⋊C4—61no—
666C22⋊C4—181no—
667C22⋊C4—181no—
668C22⋊C4—181no—
669C42—31no—
670C42—181no—
671C22×C3—22no—
672C22×C3—22no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—22no—
679C22×C3—32no—
680C22×C3—61no—
681C22×C3—61no—
682C22×C3—121no—
683C22×C3—121no—
684C22×C3—121no—
685C22×C3C2×#20412yes—
686C22×C3D3×SD1612yes—
687C22×C3C22×D1211yescharacteristic
688C22×C3C2×D3×D411yescharacteristic
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—62no—
695C2×D3—62no—
696C2×D3—122no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—122no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—241no—
709C2×D3—241no—
710C2×D3—241no—
711C2×D3—241no—
712C2×D3—244no—
713C2×D3—244no—
714C2×D3—244no—
715C2×D3—244no—
716C2×D3—248no—
717C2×D3C2×#20412yes—
718C3×C4—22no—
719C3×C4—21no—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—32no—
724C3×C4—61no—
725C3×C4—61no—
726C3×C4—121no—
727C3×C4—121no—
728C3×C4—121no—
729C3×C4#100411yescharacteristic
730C3×C4#100411yescharacteristic
731C3×C4D3×#4111yescharacteristic
732C3×C4D3×#4111yescharacteristic
733Dic3—21no—
734Dic3—21no—
735Dic3—41no—
736Dic3—41no—
737Dic3—41no—
738Dic3—121no—
739Dic3—121no—
740Dic3—121no—
741Dic3—121no—
742Dic3—241no—
743Dic3—241no—
744Dic3C2×#20412yes—
745C32#329511yescharacteristic, complemented, Sylow
746C23—31no—
747C23—61no—
748C23—181no—
749C23—181no—
750C23—362no—
751C23—362no—
752C23—362no—
753C23—362no—
754C23—721no—
755C23—721no—
756C23D3×D1211yescharacteristic
757Q8—61no—
758Q8—61no—
759Q8—721no—
760D4—34no—
761D4—61no—
762D4—61no—
763D4—92no—
764D4—122no—
765D4—181no—
766D4—181no—
767D4—181no—
768D4—362no—
769D4—362no—
770D4—362no—
771D4—362no—
772D4—721no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—31no—
776C2×C4—31no—
777C2×C4—31no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—181no—
784C2×C4—181no—
785C2×C4—362no—
786C2×C4—721no—
787C2×C4—721no—
788C2×C4D3×D1211yescharacteristic
789C2×C4C22×D3211yescharacteristic
790C8—21no—
791C8—21no—
792C8—61no—
793C8—61no—
794C2×C3—24no—
795C2×C3—22no—
796C2×C3—22no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—62no—
801C2×C3—241no—
802C2×C3#555411yescharacteristic
803C2×C3#561011yescharacteristic
804C2×C3C22×#20411yescharacteristic
805C2×C3#575211yescharacteristic
806C2×C3C2×D3×SD1611yescharacteristic
807C2×C3#576911yescharacteristic
808D3—22no—
809D3—81no—
810D3—122no—
811D3—122no—
812D3—242no—
813D3—242no—
814D3—241no—
815D3—241no—
816C22—21no—
817C22—21no—
818C22—32no—
819C22—61no—
820C22—61no—
821C22—121no—
822C22—121no—
823C22—121no—
824C22—182no—
825C22—361no—
826C22—361no—
827C22—361no—
828C22—361no—
829C22—361no—
830C22—724no—
831C22—724no—
832C22D3×#20412yes—
833C22C2×D3×D1211yescharacteristic
834C4—21no—
835C4—32no—
836C4—61no—
837C4—61no—
838C4—121no—
839C4—121no—
840C4—121no—
841C4—361no—
842C4—361no—
843C4#6430611yescharacteristic
844C4#6433011yescharacteristic
845C3—21no—
846C3#7943911yescharacteristic, complemented
847C3#8068011yescharacteristic, complemented
848C2—22no—
849C2—62no—
850C2—241no—
851C2—362no—
852C2—721no—
853C2C2×D3×#20411yescharacteristic
854C2#1059468011yescharacteristic
855C2#1059507511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595074C2
hypercenterC22×C8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594993C2semidirect
3. C2×#63648C2semidirect
4. C3×#5114C2semidirect
5. C3×C8×#67C2semidirect
6. #10591183C2semidirect
7. #10591092C2semidirect
8. #10590942C2semidirect
9. D3×#821C2semidirect
10. #10590878C2semidirect
11. #10590847C2semidirect
12. #10590799C2semidirect
13. #10590792C2semidirect
14. #10590759C2semidirect
15. #10590677C2semidirect
21. C22×C32×C8C22semidirect
22. C2×C4⋊(C3⋊Dic3)C22semidirect
25. C3×#924C22semidirect
26. C2×C3×#204C22semidirect
27. C2×C3×D3×C8C22semidirect
32. #63918C22semidirect
38. D3×C4⋊Dic3C22semidirect
39. #63856C22semidirect
41. Dic3×Dic6C22semidirect
43. C2×#3717C22semidirect
46. #63648C22semidirect
47. #63648C22semidirect
48. C3×#830C22semidirect
49. C3×#821C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#817C22semidirect
52. C3×#816C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
58. #63564C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
70. #5114D3semidirect
75. C8×#67D3semidirect
156. C22×C3×C8C2×D3semidirect
157. C22×C3×C8C2×D3semidirect
176. #924C2×D3semidirect
179. C2×#204C2×D3semidirect
180. C2×D3×C8C2×D3semidirect
210. #830C2×D3semidirect
227. #821C2×D3semidirect
228. (C2×D3)⋊C8C2×D3semidirect
231. #817C2×D3semidirect
232. #816C2×D3semidirect
233. Dic3⋊C8C2×D3semidirect
234. C8×Dic3C2×D3semidirect
263. C3×#67SD16semidirect
458. C22×C8D32semidirect
553. #67#204semidirect
745. C32#3295semidirect
846. C3#79439semidirect
847. C3#80680semidirect

Maximal subgroups

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

subgroupindex
#105950742
#105949932
C2×#636482
C3×#51142
C3×C8×#672
#105911832
#105910922
#105909422
D3×#8212
#105908782
#105908472
#105907992
#105907922
#105907592
#105906772
#806803
#794393