Finite Group Databasebeta

← #11887122

Subgroups — #11887122

Order 1152.

1018 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D4×#67C211yesmaximal, characteristic
2#10594988C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic, complemented
6#10591460C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591439C211yesmaximal, characteristic, complemented
9#10591415C211yesmaximal, characteristic, complemented
10D3×#832C211yesmaximal, characteristic, complemented
11#10591408C211yesmaximal, characteristic, complemented
12#10591401C211yesmaximal, characteristic, complemented
13#10591175C211yesmaximal, characteristic, complemented
14C3⋊C8×#67C211yesmaximal, characteristic, complemented
15#10591091C211yesmaximal, characteristic, complemented
16#83483—31nomaximal
17#78758—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C2×C3×D3×D4C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C2×#3754C2211yescharacteristic, complemented
23#64133C2211yescharacteristic, complemented
24C3×#953—21no—
25C3×#940C2211yescharacteristic
26C3×#939—21no—
27C3×#938C2211yescharacteristic
28C3×#937—21no—
29C3×D4×Dic3C2211yescharacteristic
30C3×#930C2211yescharacteristic
31C3×C4×#67C2211yescharacteristic
32C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34Dic3×#67—21no—
35#63964—21no—
36#63918C2211yescharacteristic, complemented
37#63899—21no—
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63857C2211yescharacteristic, complemented
40#63846—21no—
41#63844C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63659C2211yescharacteristic
45#63659C2211yescharacteristic, complemented
46#63657C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic, complemented
50C3×#832C2211yescharacteristic, complemented
51#63574C2211yescharacteristic, complemented
52#63574C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×D42—31no—
62D4×#67D311yescharacteristic
63#5543—31no—
64#5511—31no—
65C2×C3×#102—31no—
66#5218—31no—
67#5218—31no—
68#5218—31no—
69#5218—61no—
70C2×#832—31no—
71C2×#832D311yescharacteristic, complemented
72#5114—31no—
73C8×#67—31no—
74#5075—31no—
75#5070—31no—
76#5041—31no—
77#5041—31no—
78#5034—31no—
79#5034—31no—
80C4×#214—31no—
81D4×C3⋊C8—31no—
82#5008—31no—
83#4968—31no—
84#4778—31no—
85#4777—31no—
86#4776—31no—
87D3×#102—31no—
88#4762—31no—
89#4761—31no—
90#4760—31no—
91#4758—31no—
92C24×C32—21no—
93C23×C3×D3—21no—
94C2×C32×D4—22no—
95C2×C32×D4—21no—
96C2×C32×D4—41no—
97C2×C32×D4C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×#67—21no—
103C2×C3×#67—21no—
104C2×C3×#67—21no—
105C2×C3×#67—21no—
106C2×C3×#67—44no—
107C2×C3×#67D411yescharacteristic
108C22×C3×Dic3—21no—
109C22×C3×Dic3—21no—
110C3×D3×D4—22no—
111C3×D3×D4—41no—
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3C2311yescharacteristic
114C2×#627—21no—
115C2×D3×Dic3—21no—
116#3757—21no—
117#3754—22no—
118#3754—41no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217—21no—
124C3×#217—21no—
125C3×#217D411yescharacteristic
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4D411yescharacteristic
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3C2311yescharacteristic
134C2×C3×C3⋊C8—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3716—41no—
144D3×C3⋊C8—41no—
145#3295—91noSylow
146C22×C3×D4—21no—
147C22×C3×D4—31no—
148C22×C3×D4—61no—
149C22×C3×D4C2×D311yescharacteristic
150C22×C3×D4C2×D311yescharacteristic
151C22×#67—21no—
152C2×D3×D4C2×D311yescharacteristic
153C22×C3×C8—31no—
154C3×#127—31no—
155C3×#121—31no—
156C3×#121—31no—
157C3×#121—61no—
158C3×#120—61no—
159C3×#120—61no—
160C3×C4×D4—31no—
161C3×C4×D4—31no—
162C2×C3×C4⋊C4—31no—
163#953—21no—
164#940C2×D311yescharacteristic
165#939—21no—
166#938C2×D311yescharacteristic
167#937—21no—
168D4×Dic3—61no—
169D4×Dic3C2×D311yescharacteristic
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—31no—
174C2×#214—31no—
175C2×#214—61no—
176C2×#214—61no—
177#930C2×D311yescharacteristic
178C4×#67—61no—
179C4×#67C2×D311yescharacteristic
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3C2×D311yescharacteristic, complemented
182#924—31no—
183#924—31no—
184#924—31no—
185#924—61no—
186#924—61no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8C2×D311yescharacteristic, complemented
189C2×#204—31no—
190C2×D3×C8—31no—
191#897—31no—
192#896—61no—
193D3×C4⋊C4—31no—
194#890—61no—
195#889—61no—
196#888—31no—
197#887—31no—
198#878—61no—
199#878—61no—
200#869—31no—
201C4×Dic6—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—61no—
214#832—61no—
215#832C2×D311yescharacteristic
216#832C2×D311yescharacteristic
217#832C2×D311yescharacteristic, complemented
218#832C2×D311yescharacteristic, complemented
219#830—31no—
220#830—31no—
221#830—31no—
222#830—61no—
223#821—31no—
224(C2×D3)⋊C8—31no—
225#817—31no—
226#816—31no—
227Dic3⋊C8—31no—
228C8×Dic3—31no—
229#810—31no—
230#809—31no—
231#809—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237C4⋊(C3⋊C8)—31no—
238C4×C3⋊C8—31no—
239C23×C32—21no—
240C23×C32—21no—
241C23×C32—42no—
242C23×C32—42no—
243C23×C32—81no—
244C23×C32C2×D411yescharacteristic
245C22×C3×D3—21no—
246C22×C3×D3—42no—
247C22×C3×D3—42no—
248C22×C3×D3—81no—
249C22×C3×D3C2×D411yescharacteristic
250C32×D4—21no—
251C32×D4—21no—
252C32×D4—21no—
253C32×D4—42no—
254C32×D4#4112yes—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D411yescharacteristic
258C2×C32×C4C2411yescharacteristic
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261#634—21no—
262#634—21no—
263C3×#67—42no—
264C3×#67—42no—
265C3×#67—42no—
266C3×#67—42no—
267C3×#67—81no—
268C3×#67SD1614yescomplemented
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—42no—
273C2×C3×Dic3—81no—
274C2×C3×Dic3C2×D411yescharacteristic
275C2×C3×Dic3C2×D411yescharacteristic
276C2×C3×Dic3C2×D411yescharacteristic
277C3×D12—21no—
278C3×D12—21no—
279C3×C4×D3—21no—
280C3×C4×D3—21no—
281#627—81no—
282D3×Dic3—81no—
283C3⋊(C3⋊C8)—21no—
284C3⋊(C3⋊C8)—21no—
285C3×C3⋊C8—21no—
286C3×C3⋊C8—21no—
287#554—91no—
288D42—31no—
289#486—91no—
290#481—91no—
291#481—91no—
292#476—91no—
293#465—91no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—91no—
300C2×#102—31no—
301C2×#102—91no—
302C24×C3—21no—
303C24×C3—21no—
304C24×C3—41no—
305C24×C3—61no—
306C23×D3—21no—
307C2×C3×D4—22no—
308C2×C3×D4—22no—
309C2×C3×D4—21no—
310C2×C3×D4—21no—
311C2×C3×D4—21no—
312C2×C3×D4—21no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C2×C3×D4—41no—
316C2×C3×D4—42no—
317C2×C3×D4—41no—
318C2×C3×D4—41no—
319C2×C3×D4—42no—
320C2×C3×D4—61no—
321C2×C3×D4—61no—
322C2×C3×D4—61no—
323C2×C3×D4—62no—
324C2×C3×D4—61no—
325C2×C3×D4—61no—
326C2×C3×D4—121no—
327C2×C3×D4—124no—
328C2×C3×D4C22×D311yescharacteristic
329C2×C3×D4C22×D311yescharacteristic
330C2×C3×D4C22×D311yescharacteristic
331C2×C3×D4C22×D311yescharacteristic
332C22×C3×C4—21no—
333C22×C3×C4—31no—
334C22×C3×C4—61no—
335C22×C3×C4—61no—
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C2×#67—21no—
339C2×#67—21no—
340C2×#67—21no—
341C2×#67—21no—
342C2×#67—21no—
343C2×#67—44no—
344C2×#67#6711yescharacteristic
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—61no—
348D3×D4—22no—
349D3×D4—41no—
350C2×D12C22×D311yescharacteristic
351C2×C4×D3—61no—
352C2×C4×D3C22×D311yescharacteristic
353C2×Dic6—31no—
354C2×Dic6—31no—
355C2×Dic6—61no—
356C2×Dic6—61no—
357C2×Dic6—61no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—121no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—31no—
365C3×C4⋊C4—61no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—31no—
368C3×C22⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C22⋊C4—61no—
371C3×C42—31no—
372#217—21no—
373#217—21no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—121no—
378#217#6711yescharacteristic
379#214—62no—
380#214—62no—
381#214—122no—
382#214—121no—
383#214—121no—
384#214—121no—
385#214—122no—
386(C2×D3)⋊C4—21no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4#6711yescharacteristic
389C4⋊Dic3—21no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—121no—
407Dic3⋊C4#6711yescharacteristic
408C4×Dic3—61no—
409C4×Dic3—61no—
410C4×Dic3C22×D311yescharacteristic
411C2×C3⋊C8—31no—
412C2×C3⋊C8—31no—
413C2×C3⋊C8—31no—
414C2×C3⋊C8—31no—
415C2×C3⋊C8—41no—
416C2×C3⋊C8—61no—
417C2×C3⋊C8—61no—
418C2×C3⋊C8—121no—
419C2×C3⋊C8C22×D311yescharacteristic
420C2×C3⋊C8C22×D311yescharacteristic
421#204—121no—
422D3×C8—121no—
423C22×C32—21no—
424C22×C32—21no—
425C22×C32—22no—
426C22×C32—41no—
427C22×C32—41no—
428C22×C32—41no—
429C22×C32—41no—
430C22×C32—41no—
431C22×C32—84no—
432C22×C32C2×SD1612yes—
433C22×C32C22×D411yescharacteristic
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—41no—
437C2×C3×D3—41no—
438C2×C3×D3—41no—
439C2×C3×D3—84no—
440C2×C3×D3C2×SD1612yes—
441C32×C4—21no—
442C32×C4C2×#4111yescharacteristic
443C32×C4H(5,𝔽2)11yescharacteristic
444C3⋊Dic3—41no—
445C3⋊Dic3—41no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—41no—
449C3×Dic3—41no—
450C3×Dic3—41no—
451C3×Dic3C2×SD1612yes—
452C22×D4—31no—
453C22×D4—61no—
454C22×D4D3211yescharacteristic
455C2×SD16—91no—
456C2×SD16—91no—
457C2×SD16—91no—
458C22×C8—31no—
459C22×C8—91no—
460C4⋊Q8—91no—
461#127—31no—
462#125—181no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465C22⋊Q8—181no—
466C22⋊Q8—181no—
467#121—31no—
468#121—31no—
469#121—61no—
470#120—61no—
471#120—61no—
472C4×Q8—91no—
473C4×D4—31no—
474C4×D4—31no—
475C4×D4—181no—
476C2×C4⋊C4—31no—
477C2×C4⋊C4—91no—
478#106—91no—
479#106—91no—
480#106—91no—
481C4⋊C8—91no—
482#103—91no—
483#102—31no—
484#102—31no—
485#102—31no—
486#102—31no—
487#102—91no—
488#102—91no—
489#102—91no—
490#102—91no—
491#102—91no—
492C22⋊C8—91no—
493C22⋊C8—91no—
494C4×C8—91no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—21no—
500C23×C3—31no—
501C23×C3—41no—
502C23×C3—41no—
503C23×C3—42no—
504C23×C3—42no—
505C23×C3—44no—
506C23×C3—42no—
507C23×C3—42no—
508C23×C3—61no—
509C23×C3—82no—
510C23×C3—81no—
511C23×C3—81no—
512C23×C3—82no—
513C23×C3—122no—
514C23×C3—122no—
515C23×C3—241no—
516C23×C3D3×D411yescharacteristic
517C23×C3C2×#6711yescharacteristic
518C22×D3—21no—
519C22×D3—42no—
520C22×D3—42no—
521C22×D3—81no—
522C22×D3C2×#6711yescharacteristic
523C3×D4—22no—
524C3×D4—21no—
525C3×D4—21no—
526C3×D4—21no—
527C3×D4—21no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—22no—
531C3×D4—34no—
532C3×D4—41no—
533C3×D4—41no—
534C3×D4—42no—
535C3×D4—42no—
536C3×D4—44no—
537C3×D4—61no—
538C3×D4—61no—
539C3×D4—122no—
540C3×D4—122no—
541C3×D4—122no—
542C3×D4—122no—
543C3×D4—241no—
544C3×D4#23512yes—
545C3×D4#23712yes—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—31no—
553C2×C3×C4—31no—
554C2×C3×C4—31no—
555C2×C3×C4—41no—
556C2×C3×C4—41no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—61no—
561C2×C3×C4—61no—
562C2×C3×C4—122no—
563C2×C3×C4—241no—
564C2×C3×C4D3×D411yescharacteristic
565C2×C3×C4C2×#6711yescharacteristic
566C2×C3×C4C23×D311yescharacteristic
567C2×C3×C4C23×D311yescharacteristic
568#67—42no—
569#67—42no—
570#67—42no—
571#67—42no—
572#67—81no—
573#67#21414yescomplemented
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—42no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—81no—
583C2×Dic3—121no—
584C2×Dic3—121no—
585C2×Dic3—241no—
586C2×Dic3C2×#6711yescharacteristic
587C2×Dic3C2×#6711yescharacteristic
588C2×Dic3C2×#6711yescharacteristic
589D12—21no—
590D12—21no—
591C4×D3—21no—
592C4×D3—21no—
593C4×D3—241no—
594Dic6—61no—
595Dic6—61no—
596Dic6—61no—
597Dic6—61no—
598Dic6—121no—
599Dic6—121no—
600Dic6—241no—
601Dic6—241no—
602C3×C8—61no—
603C3×C8—61no—
604C3⋊C8—21no—
605C3⋊C8—21no—
606C3⋊C8—61no—
607C3⋊C8—61no—
608C3⋊C8—61no—
609C3⋊C8—61no—
610C3⋊C8—121no—
611C3⋊C8—121no—
612C2×C32—22no—
613C2×C32—42no—
614C2×C32—81no—
615C2×C32#54611yescharacteristic
616C2×C32C22×SD1611yescharacteristic
617C2×C32#57611yescharacteristic
618C3×D3—22no—
619C3×D3—81no—
620C24—21no—
621C24—61no—
622C2×Q8—91no—
623C2×Q8—181no—
624C2×D4—22no—
625C2×D4—21no—
626C2×D4—31no—
627C2×D4—31no—
628C2×D4—41no—
629C2×D4—61no—
630C2×D4—61no—
631C2×D4—61no—
632C2×D4—62no—
633C2×D4—61no—
634C2×D4—61no—
635C2×D4—121no—
636C2×D4—124no—
637C2×D4C2×D3211yescharacteristic
638C2×D4C2×D3211yescharacteristic
639C22×C4—31no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—181no—
643C22×C4C2×D3211yescharacteristic
644SD16—182no—
645SD16—361no—
646SD16—361no—
647C2×C8—31no—
648C2×C8—31no—
649C2×C8—91no—
650C2×C8—91no—
651C2×C8—121no—
652C2×C8—361no—
653C4⋊C4—31no—
654C4⋊C4—31no—
655C4⋊C4—31no—
656C4⋊C4—31no—
657C4⋊C4—61no—
658C4⋊C4—91no—
659C4⋊C4—181no—
660C4⋊C4—181no—
661C4⋊C4—181no—
662C4⋊C4—181no—
663C4⋊C4—181no—
664C22⋊C4—31no—
665C22⋊C4—31no—
666C22⋊C4—61no—
667C22⋊C4—61no—
668C22⋊C4—61no—
669C22⋊C4—181no—
670C22⋊C4—181no—
671C42—31no—
672C42—181no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—21no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—21no—
680C22×C3—22no—
681C22×C3—32no—
682C22×C3—41no—
683C22×C3—41no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3—41no—
689C22×C3—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—61no—
697C22×C3—61no—
698C22×C3—81no—
699C22×C3—81no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3—84no—
703C22×C3—84no—
704C22×C3—88no—
705C22×C3—121no—
706C22×C3—121no—
707C22×C3—121no—
708C22×C3—244no—
709C22×C3D3×SD1612yes—
710C22×C3C2×#21412yes—
711C22×C3C2×D3×D411yescharacteristic
712C22×C3C22×#6711yescharacteristic
713C2×D3—21no—
714C2×D3—21no—
715C2×D3—41no—
716C2×D3—41no—
717C2×D3—41no—
718C2×D3—84no—
719C2×D3C2×#21412yes—
720C3×C4—21no—
721C3×C4—21no—
722C3×C4—21no—
723C3×C4—21no—
724C3×C4—32no—
725C3×C4—41no—
726C3×C4—61no—
727C3×C4—61no—
728C3×C4—121no—
729C3×C4—121no—
730C3×C4—121no—
731C3×C4C2×#23511yescharacteristic
732C3×C4C2×#23711yescharacteristic
733C3×C4#100411yescharacteristic
734C3×C4#100411yescharacteristic
735Dic3—21no—
736Dic3—21no—
737Dic3—41no—
738Dic3—41no—
739Dic3—41no—
740Dic3—121no—
741Dic3—121no—
742Dic3—121no—
743Dic3—121no—
744Dic3—241no—
745Dic3—241no—
746Dic3C2×#21412yes—
747C32#329511yescharacteristic, complemented, Sylow
748C23—21no—
749C23—21no—
750C23—31no—
751C23—42no—
752C23—42no—
753C23—61no—
754C23—81no—
755C23—122no—
756C23—122no—
757C23—241no—
758C23D3×#6711yescharacteristic
759Q8—181no—
760Q8—181no—
761Q8—721no—
762D4—21no—
763D4—21no—
764D4—21no—
765D4—34no—
766D4—42no—
767D4—61no—
768D4—61no—
769D4—122no—
770D4—122no—
771D4—122no—
772D4—122no—
773D4—241no—
774D4#380412yes—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—31no—
778C2×C4—31no—
779C2×C4—31no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—122no—
786C2×C4—181no—
787C2×C4—181no—
788C2×C4—241no—
789C2×C4—721no—
790C2×C4D3×#6711yescharacteristic
791C2×C4C22×D3211yescharacteristic
792C8—61no—
793C8—61no—
794C8—181no—
795C8—181no—
796C2×C3—22no—
797C2×C3—22no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—42no—
802C2×C3—42no—
803C2×C3—42no—
804C2×C3—62no—
805C2×C3—82no—
806C2×C3—82no—
807C2×C3—81no—
808C2×C3—81no—
809C2×C3—241no—
810C2×C3#549011yescharacteristic
811C2×C3#575711yescharacteristic
812C2×C3C2×D3×SD1611yescharacteristic
813C2×C3C22×#21411yescharacteristic
814C2×C3#580611yescharacteristic
815C2×C3#583511yescharacteristic
816D3—22no—
817D3—81no—
818C22—21no—
819C22—21no—
820C22—22no—
821C22—32no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—61no—
828C22—61no—
829C22—84no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—244no—
834C22D3×#21412yes—
835C22C2×D3×#6711yescharacteristic
836C4—21no—
837C4—32no—
838C4—61no—
839C4—61no—
840C4—121no—
841C4—121no—
842C4—121no—
843C4—361no—
844C4—361no—
845C4C2×#380411yescharacteristic
846C4#6433011yescharacteristic
847C3—21no—
848C3#7875811yescharacteristic, complemented
849C3#8348311yescharacteristic, complemented
850C2—22no—
851C2—42no—
852C2—62no—
853C2—81no—
854C2—241no—
855C2#1059509611yescharacteristic
856C2C2×D3×#21411yescharacteristic
857C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC3×D4×#67C2
hypercenterC22×D4D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10594988C2semidirect
3. #10592917C2semidirect
4. C2×C3×#832C2semidirect
5. #10591487C2semidirect
6. #10591460C2semidirect
7. #10591459C2semidirect
8. #10591439C2semidirect
9. #10591415C2semidirect
10. D3×#832C2semidirect
11. #10591408C2semidirect
12. #10591401C2semidirect
13. #10591175C2semidirect
14. C3⋊C8×#67C2semidirect
15. #10591091C2semidirect
22. C2×#3754C22semidirect
23. #64133C22semidirect
32. C2×C3×C4⋊Dic3C22semidirect
33. C22×C3×C3⋊C8C22semidirect
36. #63918C22semidirect
38. D3×C4⋊Dic3C22semidirect
39. #63857C22semidirect
41. #63844C22semidirect
42. C2×#3716C22semidirect
43. C2×D3×C3⋊C8C22semidirect
45. #63659C22semidirect
46. #63657C22semidirect
49. C3×#832C22semidirect
50. C3×#832C22semidirect
51. #63574C22semidirect
52. #63574C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63563C22semidirect
57. #63562C22semidirect
58. #63562C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
71. C2×#832D3semidirect
181. C2×C4⋊Dic3C2×D3semidirect
188. C22×C3⋊C8C2×D3semidirect
217. #832C2×D3semidirect
218. #832C2×D3semidirect
268. C3×#67SD16semidirect
573. #67#214semidirect
747. C32#3295semidirect
848. C3#78758semidirect
849. C3#83483semidirect

Maximal subgroups

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

subgroupindex
C3×D4×#672
#105949882
#105929172
C2×C3×#8322
#105914872
#105914602
#105914592
#105914392
#105914152
D3×#8322
#105914082
#105914012
#105911752
C3⋊C8×#672
#105910912
#834833
#787583