Finite Group Databasebeta

← #11887118

Subgroups — #11887118

Order 1152.

986 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D12×#67C211yesmaximal, characteristic
2#10594988C211yesmaximal, characteristic, complemented
3#10592813C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591125C211yesmaximal, characteristic, complemented
8#10590946C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590879C211yesmaximal, characteristic, complemented
11#10590878C211yesmaximal, characteristic, complemented
12#10590825C211yesmaximal, characteristic, complemented
13#10590757C211yesmaximal, characteristic, complemented
14#10590744C211yesmaximal, characteristic, complemented
15#10590676C211yesmaximal, characteristic, complemented
16#79439—31nomaximal
17#78758—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic, complemented
22#64139C2211yescharacteristic
23#64133C2211yescharacteristic, complemented
24C2×#3744C2211yescharacteristic, complemented
25C3×C4×#67C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
27C2×C3×D3×C8C2211yescharacteristic, complemented
28#63977—21no—
29Dic3×#67—21no—
30#63964—21no—
31#63922—21no—
32#63918C2211yescharacteristic, complemented
33#63911C2211yescharacteristic
34#63908C2211yescharacteristic
35#63899—21no—
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic, complemented
38#63886—21no—
39#63857C2211yescharacteristic, complemented
40#63846—21no—
41#63844C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic, complemented
44#63648C2211yescharacteristic, complemented
45#63644C2211yescharacteristic, complemented
46#63643C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×#821C2211yescharacteristic, complemented
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61D4×#67—31no—
62D4×D12—31no—
63#5543—31no—
64#5511—31no—
65C3×C8×D4—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5114—31no—
69#5114—31no—
70#5114—31no—
71#5114—61no—
72C2×#821—31no—
73C2×#821D311yescharacteristic, complemented
74C8×#67D311yescharacteristic, complemented
75#4968—31no—
76#4848—31no—
77#4842—31no—
78#4778—31no—
79#4777—31no—
80#4776—31no—
81D3×#102—31no—
82#4762—31no—
83#4761—31no—
84#4760—31no—
85#4758—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
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×#634C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C22×C3×Dic3—21no—
100C2×C3×D12—22no—
101C2×C3×D12—21no—
102C2×C3×D12—41no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106D3×#67—44no—
107C2×#627—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#625—21no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114D3×D12—22no—
115D3×D12—41no—
116C2×C32×C8—41no—
117C2×C32×C8C2311yescharacteristic
118C2×C32×C8C2311yescharacteristic
119#3757—21no—
120#3752—21no—
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123#3750—21no—
124#3744—41no—
125C3×#217D411yescharacteristic
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C3×D3×C8—41no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3716—22no—
144#3716—41no—
145#3295—91noSylow
146C22×C3×D4—31no—
147C22×#67—61no—
148C2×D3×D4—31no—
149C2×D3×D4—61no—
150C22×D12—31no—
151C22×D12C2×D311yescharacteristic
152C22×C3×C8—21no—
153C22×C3×C8—31no—
154C22×C3×C8C2×D311yescharacteristic, complemented
155C22×C3×C8C2×D311yescharacteristic, complemented
156C3×C4×D4—31no—
157C2×C3×C4⋊C4—31no—
158#953—61no—
159#940—31no—
160#939—61no—
161#938—31no—
162#937—61no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165C2×#214—31no—
166C2×#214—31no—
167#930—31no—
168#930—31no—
169#930—31no—
170#930—61no—
171C4×#67—61no—
172C4×#67C2×D311yescharacteristic
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3C2×D311yescharacteristic, complemented
175#924—31no—
176#924—31no—
177#924—31no—
178#924—61no—
179#924—61no—
180C2×#204—31no—
181C2×#204—31no—
182C2×#204—31no—
183C2×#204—31no—
184C2×#204—61no—
185C2×D3×C8C2×D311yescharacteristic, complemented
186#897—31no—
187#896—61no—
188#895—61no—
189D3×C4⋊C4—31no—
190#890—61no—
191#889—61no—
192#888—31no—
193#887—31no—
194#882—61no—
195#882—61no—
196#878—61no—
197#878—61no—
198#874—31no—
199C4×D12—31no—
200#869—31no—
201C4×Dic6—31no—
202C3×C4⋊C8—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8—31no—
209C3×C4×C8—31no—
210#832—31no—
211#832—31no—
212#830C2×D311yescharacteristic, complemented
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic
221#821C2×D311yescharacteristic
222#821C2×D311yescharacteristic, complemented
223#821C2×D311yescharacteristic, complemented
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225#817—31no—
226#817—31no—
227#817—31no—
228#817—31no—
229#817—61no—
230#816—31no—
231#816—31no—
232#816—61no—
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—21no—
243C22×C3×D3—42no—
244C22×C3×D3—42no—
245C22×C3×D3—81no—
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
254#638—42no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3—21no—
258C4⋊(C3⋊D3)—21no—
259C4⋊(C3⋊D3)—21no—
260#634—21no—
261#634—21no—
262C3×#67SD1614yescomplemented
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—81no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×D12—21no—
272C3×D12—42no—
273C3×D12#4112yes—
274C3×C4×D3—21no—
275C3×C4×D3—21no—
276#627—81no—
277#626—42no—
278#626—42no—
279#626—81no—
280#625—42no—
281D3×Dic3—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—91no—
294#465—91no—
295#460—91no—
296#450—91no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—31no—
300C2×#102—31no—
301C2×#102—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×D4—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—62no—
310C2×C3×D4—61no—
311C2×C3×D4—121no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—61no—
315C22×C3×C4C22×D311yescharacteristic
316C22×C3×C4C22×D311yescharacteristic
317C2×#67—61no—
318C2×#67—61no—
319C2×#67—61no—
320C2×#67—61no—
321C2×#67—61no—
322C2×#67—61no—
323C2×#67—61no—
324C2×#67—121no—
325C2×#67—124no—
326C2×#67D1211yescharacteristic
327C22×Dic3—21no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330D3×D4—62no—
331D3×D4—121no—
332D3×D4—124no—
333C2×D12—22no—
334C2×D12—21no—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—41no—
338C2×D12—61no—
339C2×D12—62no—
340C2×D12—61no—
341C2×D12—61no—
342C2×D12—61no—
343C2×D12—121no—
344C2×D12C22×D311yescharacteristic
345C2×D12C22×D311yescharacteristic
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3C22×D311yescharacteristic
349C2×Dic6—31no—
350C2×Dic6—31no—
351C2×Dic6—61no—
352C2×Dic6—61no—
353C2×Dic6—61no—
354C2×C3×C8—21no—
355C2×C3×C8—21no—
356C2×C3×C8—31no—
357C2×C3×C8—31no—
358C2×C3×C8—41no—
359C2×C3×C8—41no—
360C2×C3×C8—42no—
361C2×C3×C8—121no—
362C2×C3×C8C22×D311yescharacteristic
363C2×C3×C8C22×D311yescharacteristic
364C2×C3×C8C22×D311yescharacteristic
365C2×C3×C8C22×D311yescharacteristic
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—31no—
369C3×C4⋊C4—61no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—31no—
372C3×C42—31no—
373#217—61no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217—61no—
378#217—121no—
379#217D1211yescharacteristic
380#214—62no—
381#214—121no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—121no—
388(C2×D3)⋊C4D1211yescharacteristic
389C4⋊Dic3—21no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—121no—
409Dic3⋊C4D1211yescharacteristic
410C4×Dic3—61no—
411C4×Dic3—61no—
412C4×Dic3C22×D311yescharacteristic
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415#204—62no—
416#204—121no—
417#204—121no—
418#204—122no—
419#204—121no—
420D3×C8—41no—
421C22×C32—21no—
422C22×C32—21no—
423C22×C32C2×SD1612yes—
424C22×C32C22×D411yescharacteristic
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3×D3—21no—
429C2×C3×D3—21no—
430C2×C3×D3—22no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—41no—
435C2×C3×D3—41no—
436C2×C3×D3—84no—
437C2×C3×D3C2×SD1612yes—
438D32—84no—
439C32×C4—21no—
440C32×C4C2×#4111yescharacteristic
441C32×C4H(5,𝔽2)11yescharacteristic
442C3⋊Dic3—41no—
443C3⋊Dic3—41no—
444C3⋊Dic3—41no—
445C3×Dic3—21no—
446C3×Dic3—21no—
447C3×Dic3—41no—
448C3×Dic3—41no—
449C3×Dic3C2×SD1612yes—
450C22×D4—31no—
451C22×D4—91no—
452C22×D4—181no—
453C2×SD16—91no—
454C2×SD16—91no—
455C2×SD16—91no—
456C22×C8—31no—
457C22×C8D3211yescharacteristic, complemented
458C4⋊Q8—91no—
459#127—91no—
460#125—181no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—181no—
464C22⋊Q8—181no—
465#121—91no—
466#121—91no—
467#121—181no—
468#120—181no—
469#120—181no—
470C4×Q8—91no—
471C4×D4—31no—
472C4×D4—91no—
473C4×D4—181no—
474C2×C4⋊C4—31no—
475C2×C4⋊C4—91no—
476#106—91no—
477#106—91no—
478#106—91no—
479C4⋊C8—31no—
480#103—91no—
481#102—31no—
482#102—31no—
483#102—31no—
484#102—31no—
485#102—91no—
486#102—91no—
487#102—91no—
488#102—91no—
489#102—91no—
490C22⋊C8—31no—
491C22⋊C8—31no—
492C4×C8—31no—
493C23×C3—21no—
494C23×C3—31no—
495C23×C3—61no—
496C23×C3—61no—
497C23×C3—122no—
498C23×C3—122no—
499C23×C3—241no—
500C23×C3C2×D1211yescharacteristic
501C23×C3D3×D411yescharacteristic
502C22×D3—21no—
503C22×D3—21no—
504C22×D3—42no—
505C22×D3—42no—
506C22×D3—61no—
507C22×D3—61no—
508C22×D3—81no—
509C22×D3—121no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—241no—
515C22×D3—241no—
516C22×D3C2×D1211yescharacteristic
517C3×D4—34no—
518C3×D4—32no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4—61no—
522C3×D4—122no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—31no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—41no—
533C2×C3×C4—41no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—241no—
539C2×C3×C4C2×D1211yescharacteristic
540C2×C3×C4D3×D411yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542C2×C3×C4C23×D311yescharacteristic
543#67—122no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—122no—
549#67—242no—
550#67—241no—
551#67#20414yescomplemented
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—81no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—122no—
565C2×Dic3—241no—
566C2×Dic3C2×D1211yescharacteristic
567C2×Dic3C2×D1211yescharacteristic
568C2×Dic3C2×D1211yescharacteristic
569D12—21no—
570D12—21no—
571D12—21no—
572D12—42no—
573D12—61no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—121no—
578D12—121no—
579D12—122no—
580D12—122no—
581D12—241no—
582D12#23512yes—
583C4×D3—21no—
584C4×D3—21no—
585C4×D3—122no—
586C4×D3—241no—
587Dic6—61no—
588Dic6—61no—
589Dic6—61no—
590Dic6—61no—
591Dic6—121no—
592Dic6—121no—
593Dic6—241no—
594Dic6—241no—
595C3×C8—22no—
596C3×C8—21no—
597C3×C8—21no—
598C3×C8—21no—
599C3×C8—21no—
600C3×C8—41no—
601C3×C8—61no—
602C3×C8—61no—
603C3⋊C8—21no—
604C3⋊C8—21no—
605C2×C32—22no—
606C2×C32#54611yescharacteristic
607C2×C32C22×SD1611yescharacteristic
608C2×C32#57611yescharacteristic
609C3⋊D3—81no—
610C3×D3—22no—
611C3×D3—42no—
612C3×D3—81no—
613C24—61no—
614C24—181no—
615C2×Q8—91no—
616C2×Q8—181no—
617C2×D4—31no—
618C2×D4—31no—
619C2×D4—31no—
620C2×D4—62no—
621C2×D4—61no—
622C2×D4—91no—
623C2×D4—121no—
624C2×D4—181no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—182no—
628C2×D4—181no—
629C2×D4—181no—
630C2×D4—361no—
631C2×D4—364no—
632C22×C4—31no—
633C22×C4—61no—
634C22×C4—181no—
635C22×C4—181no—
636C22×C4C2×D3211yescharacteristic
637SD16—182no—
638SD16—361no—
639SD16—361no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—41no—
643C2×C8—121no—
644C2×C8C2×D3211yescharacteristic
645C2×C8C2×D3211yescharacteristic
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—91no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4—181no—
657C22⋊C4—31no—
658C22⋊C4—31no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C42—31no—
665C42—181no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—22no—
672C22×C3—32no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—61no—
676C22×C3—61no—
677C22×C3—62no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—121no—
681C22×C3—121no—
682C22×C3—121no—
683C22×C3—244no—
684C22×C3C2×#20412yes—
685C22×C3D3×SD1612yes—
686C22×C3C22×D1211yescharacteristic
687C22×C3C2×D3×D411yescharacteristic
688C2×D3—21no—
689C2×D3—21no—
690C2×D3—22no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—41no—
694C2×D3—41no—
695C2×D3—41no—
696C2×D3—84no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—121no—
701C2×D3—121no—
702C2×D3—121no—
703C2×D3—241no—
704C2×D3—241no—
705C2×D3—241no—
706C2×D3—244no—
707C2×D3—244no—
708C2×D3C2×#20412yes—
709C3×C4—21no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—32no—
714C3×C4—41no—
715C3×C4—61no—
716C3×C4—61no—
717C3×C4—121no—
718C3×C4—121no—
719C3×C4C2×#23511yescharacteristic
720C3×C4#100411yescharacteristic
721C3×C4#100411yescharacteristic
722C3×C4D3×#4111yescharacteristic
723Dic3—21no—
724Dic3—21no—
725Dic3—41no—
726Dic3—41no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731Dic3—121no—
732Dic3—121no—
733Dic3—241no—
734Dic3—241no—
735Dic3—241no—
736Dic3C2×#20412yes—
737C32#329511yescharacteristic, complemented, Sylow
738C23—31no—
739C23—61no—
740C23—61no—
741C23—122no—
742C23—122no—
743C23—181no—
744C23—241no—
745C23—362no—
746C23—362no—
747C23—721no—
748C23D3×D1211yescharacteristic
749Q8—181no—
750Q8—181no—
751Q8—721no—
752D4—34no—
753D4—32no—
754D4—61no—
755D4—61no—
756D4—61no—
757D4—122no—
758D4—181no—
759D4—181no—
760D4—362no—
761D4—362no—
762D4—362no—
763D4—362no—
764D4—721no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—241no—
778C2×C4—362no—
779C2×C4—721no—
780C2×C4D3×D1211yescharacteristic
781C2×C4C22×D3211yescharacteristic
782C8—21no—
783C8—21no—
784C8—61no—
785C8—61no—
786C2×C3—22no—
787C2×C3—22no—
788C2×C3—21no—
789C2×C3—21no—
790C2×C3—21no—
791C2×C3—42no—
792C2×C3—62no—
793C2×C3—122no—
794C2×C3—241no—
795C2×C3#549011yescharacteristic
796C2×C3#555411yescharacteristic
797C2×C3C22×#20411yescharacteristic
798C2×C3#575211yescharacteristic
799C2×C3#575711yescharacteristic
800C2×C3C2×D3×SD1611yescharacteristic
801D3—22no—
802D3—42no—
803D3—81no—
804D3—241no—
805D3—241no—
806D3—481no—
807C22—21no—
808C22—21no—
809C22—32no—
810C22—61no—
811C22—61no—
812C22—62no—
813C22—121no—
814C22—121no—
815C22—121no—
816C22—121no—
817C22—121no—
818C22—244no—
819C22—361no—
820C22—361no—
821C22—361no—
822C22—724no—
823C22D3×#20412yes—
824C22C2×D3×D1211yescharacteristic
825C4—21no—
826C4—32no—
827C4—61no—
828C4—61no—
829C4—121no—
830C4—121no—
831C4—361no—
832C4—361no—
833C4—361no—
834C4D3×#23511yescharacteristic
835C4#6433011yescharacteristic
836C3—21no—
837C3#7875811yescharacteristic, complemented
838C3#7943911yescharacteristic, complemented
839C2—22no—
840C2—62no—
841C2—122no—
842C2—241no—
843C2—721no—
844C2C2×D3×#20411yescharacteristic
845C2#1059467811yescharacteristic
846C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalD12×#67C2
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. #10594988C2semidirect
3. #10592813C2semidirect
4. C2×C3×#821C2semidirect
5. C3×C8×#67C2semidirect
6. #10591172C2semidirect
7. #10591125C2semidirect
8. #10590946C2semidirect
9. D3×#821C2semidirect
10. #10590879C2semidirect
11. #10590878C2semidirect
12. #10590825C2semidirect
13. #10590757C2semidirect
14. #10590744C2semidirect
15. #10590676C2semidirect
21. C22×C32×C8C22semidirect
23. #64133C22semidirect
24. C2×#3744C22semidirect
26. C2×C3×C4⋊Dic3C22semidirect
27. C2×C3×D3×C8C22semidirect
32. #63918C22semidirect
37. D3×C4⋊Dic3C22semidirect
39. #63857C22semidirect
41. #63844C22semidirect
43. C2×#3716C22semidirect
44. #63648C22semidirect
45. #63644C22semidirect
46. #63643C22semidirect
47. C3×#830C22semidirect
50. C3×#821C22semidirect
51. C3×#821C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
60. #63563C22semidirect
73. C2×#821D3semidirect
74. C8×#67D3semidirect
154. C22×C3×C8C2×D3semidirect
155. C22×C3×C8C2×D3semidirect
174. C2×C4⋊Dic3C2×D3semidirect
185. C2×D3×C8C2×D3semidirect
212. #830C2×D3semidirect
222. #821C2×D3semidirect
223. #821C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
233. Dic3⋊C8C2×D3semidirect
234. C8×Dic3C2×D3semidirect
262. C3×#67SD16semidirect
457. C22×C8D32semidirect
551. #67#204semidirect
737. C32#3295semidirect
837. C3#78758semidirect
838. C3#79439semidirect

Maximal subgroups

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

subgroupindex
D12×#672
#105949882
#105928132
C2×C3×#8212
C3×C8×#672
#105911722
#105911252
#105909462
D3×#8212
#105908792
#105908782
#105908252
#105907572
#105907442
#105906762
#794393
#787583