Finite Group Databasebeta

← #11887112

Subgroups — #11887112

Order 1152.

981 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D12×#67C211yesmaximal, characteristic
2#10594993C211yesmaximal, characteristic, complemented
3#10592434C211yesmaximal, characteristic, complemented
4C3×#4731C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591177C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590942C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590878C211yesmaximal, characteristic, complemented
11#10590829C211yesmaximal, characteristic, complemented
12#10590799C211yesmaximal, characteristic, complemented
13#10590757C211yesmaximal, characteristic, complemented
14Dic3×#204C211yesmaximal, characteristic, complemented
15#10590676C211yesmaximal, characteristic, complemented
16#80158—31nomaximal
17#79439—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×D3×#67—21no—
20C2×D3×D12C2211yescharacteristic
21#64139C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
23C3×C4×#67C2211yescharacteristic
24C3×#924C2211yescharacteristic, complemented
25C22×C3×C3⋊C8C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic, complemented
28C2×C3×D3×C8C2211yescharacteristic, complemented
29#63982—21no—
30#63977—21no—
31#67⋊Dic3—21no—
32#63922—21no—
33#63918C2211yescharacteristic, complemented
34#63911C2211yescharacteristic
35#63908C2211yescharacteristic
36#63893—21no—
37Dic3×D12C2211yescharacteristic
38D3×C4⋊Dic3C2211yescharacteristic, complemented
39#63886—21no—
40#63856C2211yescharacteristic, complemented
41#63845—21no—
42Dic3×Dic6C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63648C2211yescharacteristic, complemented
47#63644C2211yescharacteristic, complemented
48#63644C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61D4×#67—31no—
62#5635—31no—
63D4×D12—31no—
64#5543—31no—
65C3×#450—31no—
66C3×C8×D4—31no—
67C2×#832—31no—
68#5171—31no—
69#5169—31no—
70#5163—31no—
71Dic3×SD16—31no—
72#5114—31no—
73#5114—31no—
74C2×#821—31no—
75C2×#821—31no—
76#5048—31no—
77#4848—31no—
78#4842—31no—
79#4777—31no—
80D3×#102—31no—
81#4761—31no—
82#4760—31no—
83#4735—31no—
84#4735—31no—
85#4735—31no—
86#4735—61no—
87#4731—31no—
88#4731D311yescharacteristic, complemented
89#67⋊C8D311yescharacteristic, complemented
90#4694—31no—
91C4×#204—31no—
92C23×C3×D3—21no—
93C22×D32—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67D411yescharacteristic
99C2×C3×D12—22no—
100C2×C3×D12—21no—
101C2×C3×D12—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
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×C8C2311yescharacteristic
117C2×C32×C8C2311yescharacteristic
118#3752—21no—
119C4⋊(C3⋊Dic3)—21no—
120C4⋊(C3⋊Dic3)C2311yescharacteristic
121C4⋊(C3⋊Dic3)C2311yescharacteristic
122C4⋊(C3⋊Dic3)C2311yescharacteristic
123C3×#217—21no—
124C3×#217D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×#204—22no—
134C3×#204—41no—
135C3×D3×C8—41no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144#3717—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
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C22×C3×C8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×D4—31no—
158#953—61no—
159#946—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162#940—31no—
163#939—61no—
164#938—31no—
165#937—61no—
166D4×Dic3—31no—
167D4×Dic3—61no—
168#930—31no—
169#930—31no—
170#930—31no—
171#930—61no—
172C4×#67C2×D311yescharacteristic
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—61no—
177#924—31no—
178#924C2×D311yescharacteristic, complemented
179C22×C3⋊C8C2×D311yescharacteristic, complemented
180C2×#204—31no—
181C2×#204C2×D311yescharacteristic
182C2×#204C2×D311yescharacteristic, complemented
183C2×D3×C8C2×D311yescharacteristic, complemented
184#897—61no—
185#895—61no—
186D3×C4⋊C4—31no—
187#890—61no—
188#889—61no—
189#888—31no—
190#882—61no—
191#882—61no—
192#67⋊C4—61no—
193#878—61no—
194#878—61no—
195#878—61no—
196#874—31no—
197C4×D12—31no—
198#869—31no—
199C4×Dic6—31no—
200C3×C4⋊C8—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C22⋊C8—21no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8C2×D311yescharacteristic, complemented
206C3×C22⋊C8C2×D311yescharacteristic, complemented
207C3×C4×C8—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—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—61no—
223#821—61no—
224#821C2×D311yescharacteristic
225#821C2×D311yescharacteristic, complemented
226(C2×D3)⋊C8C2×D311yescharacteristic, complemented
227#817—31no—
228#817—31no—
229#817—31no—
230#817—31no—
231#817—31no—
232#817—61no—
233#817—61no—
234#816—31no—
235Dic3⋊C8C2×D311yescharacteristic, complemented
236C8×Dic3C2×D311yescharacteristic, complemented
237#809—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—
258C2×C3⋊Dic3—81no—
259C4⋊(C3⋊D3)—21no—
260C4⋊(C3⋊D3)—21no—
261C3×#67SD1614yescomplemented
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—42no—
271C3×D12#4112yes—
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—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—31no—
297#450—91no—
298C4×SD16—91no—
299C8×D4—31no—
300C2×#102—91no—
301C2×#102—91no—
302C24×C3—61no—
303C23×D3—21no—
304C23×D3—61no—
305C23×D3—61no—
306C2×C3×Q8—31no—
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—31no—
310C2×C3×D4—62no—
311C2×C3×D4—61no—
312C2×C3×D4—121no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
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—61no—
328C22×Dic3—61no—
329C22×Dic3—61no—
330C22×Dic3—61no—
331C22×Dic3—121no—
332D3×D4—62no—
333D3×D4—121no—
334D3×D4—124no—
335C2×D12—22no—
336C2×D12—21no—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—41no—
340C2×D12—61no—
341C2×D12—62no—
342C2×D12—61no—
343C2×D12—61no—
344C2×D12—61no—
345C2×D12—121no—
346C2×D12C22×D311yescharacteristic
347C2×D12C22×D311yescharacteristic
348C2×C4×D3—61no—
349C2×C4×D3—61no—
350C2×C4×D3C22×D311yescharacteristic
351C2×Dic6—61no—
352C2×Dic6—61no—
353C2×Dic6C22×D311yescharacteristic
354C3×SD16—62no—
355C3×SD16—121no—
356C2×C3×C8—21no—
357C2×C3×C8—21no—
358C2×C3×C8—31no—
359C2×C3×C8—31no—
360C2×C3×C8—121no—
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—61no—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—31no—
371C3×C22⋊C4—61no—
372C3×C42—31no—
373#217—21no—
374#217—61no—
375#217—61no—
376#217—61no—
377#217D1211yescharacteristic
378#215—121no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4D1211yescharacteristic
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3—61no—
400C4⋊Dic3—121no—
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4D1211yescharacteristic
409C4×Dic3—61no—
410C4×Dic3—61no—
411C4×Dic3C22×D311yescharacteristic
412C2×C3⋊C8—41no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415#204—22no—
416#204—41no—
417#204—121no—
418D3×C8—41no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32C2×SD1612yes—
422C22×C32C22×D411yescharacteristic
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—22no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3—41no—
432C2×C3×D3—41no—
433C2×C3×D3—41no—
434C2×C3×D3—84no—
435C2×C3×D3C2×SD1612yes—
436D32—84no—
437C32×C4—21no—
438C32×C4C2×#4111yescharacteristic
439C32×C4H(5,𝔽2)11yescharacteristic
440C3⋊Dic3—41no—
441C3⋊Dic3—41no—
442C3⋊Dic3—41no—
443C3×Dic3—21no—
444C3×Dic3—21no—
445C3×Dic3—41no—
446C3×Dic3—41no—
447C3×Dic3C2×SD1612yes—
448C22×D4—31no—
449C22×D4—91no—
450C22×D4—181no—
451C2×SD16—31no—
452C2×SD16—31no—
453C2×SD16—91no—
454C22×C8—31no—
455C22×C8—31no—
456C4⋊Q8—91no—
457#127—91no—
458#125—181no—
459C22⋊Q8—31no—
460C22⋊Q8—91no—
461C22⋊Q8—181no—
462C22⋊Q8—181no—
463#121—91no—
464#121—91no—
465#121—181no—
466#120—181no—
467#120—181no—
468C4×Q8—91no—
469C4×D4—31no—
470C4×D4—91no—
471C4×D4—181no—
472C2×C4⋊C4—91no—
473C2×C4⋊C4—91no—
474#106—91no—
475#106—91no—
476#106—91no—
477C4⋊C8—31no—
478#103—91no—
479#102—31no—
480#102—31no—
481#102—91no—
482#102—91no—
483#102—91no—
484#102—91no—
485#102—91no—
486#102—91no—
487#102—91no—
488C22⋊C8—31no—
489C22⋊C8D3211yescharacteristic, complemented
490C4×C8—31no—
491C23×C3—21no—
492C23×C3—31no—
493C23×C3—61no—
494C23×C3—61no—
495C23×C3—122no—
496C23×C3—122no—
497C23×C3—241no—
498C23×C3C2×D1211yescharacteristic
499C23×C3D3×D411yescharacteristic
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—42no—
503C22×D3—42no—
504C22×D3—61no—
505C22×D3—61no—
506C22×D3—81no—
507C22×D3—121no—
508C22×D3—122no—
509C22×D3—122no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—241no—
513C22×D3—241no—
514C22×D3C2×D1211yescharacteristic
515C3×Q8—61no—
516C3×Q8—61no—
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×C4C2×D1211yescharacteristic
539C2×C3×C4D3×D411yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542#67—122no—
543#67—122no—
544#67—122no—
545#67—122no—
546#67—122no—
547#67—122no—
548#67—242no—
549#67—241no—
550#67#20414yescomplemented
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—122no—
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—21no—
573D12—42no—
574D12—61no—
575D12—61no—
576D12—61no—
577D12—61no—
578D12—121no—
579D12—121no—
580D12—122no—
581D12—122no—
582D12—241no—
583D12#23712yes—
584C4×D3—21no—
585C4×D3—21no—
586C4×D3—122no—
587C4×D3—241no—
588Dic6—21no—
589Dic6—21no—
590Dic6—241no—
591Dic6—241no—
592C3×C8—21no—
593C3×C8—21no—
594C3×C8—21no—
595C3×C8—21no—
596C3×C8—41no—
597C3×C8—41no—
598C3×C8—61no—
599C3×C8—61no—
600C3⋊C8—21no—
601C3⋊C8—21no—
602C2×C32—22no—
603C2×C32#54611yescharacteristic
604C2×C32C22×SD1611yescharacteristic
605C2×C32#57611yescharacteristic
606C3⋊D3—81no—
607C3×D3—22no—
608C3×D3—42no—
609C3×D3—81no—
610C24—61no—
611C24—181no—
612C2×Q8—31no—
613C2×Q8—181no—
614C2×D4—31no—
615C2×D4—31no—
616C2×D4—31no—
617C2×D4—62no—
618C2×D4—61no—
619C2×D4—91no—
620C2×D4—121no—
621C2×D4—181no—
622C2×D4—181no—
623C2×D4—181no—
624C2×D4—182no—
625C2×D4—181no—
626C2×D4—181no—
627C2×D4—361no—
628C2×D4—364no—
629C22×C4—31no—
630C22×C4—181no—
631C22×C4—181no—
632C22×C4—181no—
633C22×C4C2×D3211yescharacteristic
634SD16—62no—
635SD16—121no—
636SD16—361no—
637C2×C8—31no—
638C2×C8—31no—
639C2×C8—121no—
640C2×C8—121no—
641C2×C8C2×D3211yescharacteristic
642C2×C8C2×D3211yescharacteristic
643C4⋊C4—31no—
644C4⋊C4—31no—
645C4⋊C4—61no—
646C4⋊C4—91no—
647C4⋊C4—91no—
648C4⋊C4—91no—
649C4⋊C4—181no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C22⋊C4—31no—
655C22⋊C4—31no—
656C22⋊C4—61no—
657C22⋊C4—181no—
658C22⋊C4—181no—
659C22⋊C4—181no—
660C22⋊C4—181no—
661C42—31no—
662C42—181no—
663C22×C3—21no—
664C22×C3—21no—
665C22×C3—21no—
666C22×C3—21no—
667C22×C3—21no—
668C22×C3—22no—
669C22×C3—32no—
670C22×C3—41no—
671C22×C3—41no—
672C22×C3—61no—
673C22×C3—61no—
674C22×C3—62no—
675C22×C3—121no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3—121no—
680C22×C3—244no—
681C22×C3C2×#20412yes—
682C22×C3D3×SD1612yes—
683C22×C3C22×D1211yescharacteristic
684C22×C3C2×D3×D411yescharacteristic
685C2×D3—21no—
686C2×D3—21no—
687C2×D3—22no—
688C2×D3—41no—
689C2×D3—41no—
690C2×D3—41no—
691C2×D3—41no—
692C2×D3—41no—
693C2×D3—84no—
694C2×D3—121no—
695C2×D3—121no—
696C2×D3—121no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—121no—
700C2×D3—241no—
701C2×D3—241no—
702C2×D3—241no—
703C2×D3—244no—
704C2×D3—244no—
705C2×D3C2×#20412yes—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—21no—
710C3×C4—32no—
711C3×C4—41no—
712C3×C4—61no—
713C3×C4—61no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4C2×#23711yescharacteristic
717C3×C4#100411yescharacteristic
718C3×C4#100411yescharacteristic
719C3×C4D3×#4111yescharacteristic
720Dic3—21no—
721Dic3—21no—
722Dic3—41no—
723Dic3—41no—
724Dic3—121no—
725Dic3—121no—
726Dic3—121no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—241no—
731Dic3—241no—
732Dic3—241no—
733Dic3C2×#20412yes—
734C32#329511yescharacteristic, complemented, Sylow
735C23—31no—
736C23—61no—
737C23—61no—
738C23—122no—
739C23—122no—
740C23—181no—
741C23—241no—
742C23—362no—
743C23—362no—
744C23—721no—
745C23D3×D1211yescharacteristic
746Q8—61no—
747Q8—61no—
748Q8—721no—
749D4—34no—
750D4—32no—
751D4—61no—
752D4—61no—
753D4—61no—
754D4—122no—
755D4—181no—
756D4—181no—
757D4—362no—
758D4—362no—
759D4—362no—
760D4—362no—
761D4—721no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—31no—
765C2×C4—31no—
766C2×C4—31no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—181no—
772C2×C4—181no—
773C2×C4—181no—
774C2×C4—362no—
775C2×C4—721no—
776C2×C4—721no—
777C2×C4D3×D1211yescharacteristic
778C2×C4C22×D3211yescharacteristic
779C8—21no—
780C8—21no—
781C8—61no—
782C8—61no—
783C2×C3—22no—
784C2×C3—22no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—42no—
789C2×C3—62no—
790C2×C3—122no—
791C2×C3—241no—
792C2×C3#555411yescharacteristic
793C2×C3#559111yescharacteristic
794C2×C3C22×#20411yescharacteristic
795C2×C3#575211yescharacteristic
796C2×C3C2×D3×SD1611yescharacteristic
797C2×C3#577411yescharacteristic
798D3—22no—
799D3—42no—
800D3—81no—
801D3—241no—
802D3—241no—
803D3—481no—
804C22—21no—
805C22—21no—
806C22—32no—
807C22—61no—
808C22—61no—
809C22—62no—
810C22—121no—
811C22—121no—
812C22—121no—
813C22—121no—
814C22—121no—
815C22—244no—
816C22—361no—
817C22—361no—
818C22—361no—
819C22—724no—
820C22D3×#20412yes—
821C22C2×D3×D1211yescharacteristic
822C4—21no—
823C4—32no—
824C4—61no—
825C4—61no—
826C4—121no—
827C4—121no—
828C4—361no—
829C4—361no—
830C4—361no—
831C4D3×#23711yescharacteristic
832C4#6431311yescharacteristic
833C3—21no—
834C3#7943911yescharacteristic, complemented
835C3#8015811yescharacteristic, complemented
836C2—22no—
837C2—62no—
838C2—122no—
839C2—241no—
840C2—721no—
841C2#1059429211yescharacteristic
842C2C2×D3×#20411yescharacteristic
843C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊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. #10594993C2semidirect
3. #10592434C2semidirect
4. C3×#4731C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591177C2semidirect
7. C2×#63563C2semidirect
8. #10590942C2semidirect
9. D3×#821C2semidirect
10. #10590878C2semidirect
11. #10590829C2semidirect
12. #10590799C2semidirect
13. #10590757C2semidirect
14. Dic3×#204C2semidirect
15. #10590676C2semidirect
22. C2×C4⋊(C3⋊Dic3)C22semidirect
24. C3×#924C22semidirect
25. C22×C3×C3⋊C8C22semidirect
27. C2×C3×#204C22semidirect
28. C2×C3×D3×C8C22semidirect
33. #63918C22semidirect
38. D3×C4⋊Dic3C22semidirect
40. #63856C22semidirect
42. Dic3×Dic6C22semidirect
43. C2×#3717C22semidirect
44. C32×C22⋊C8C22semidirect
45. #63648C22semidirect
46. #63648C22semidirect
47. #63644C22semidirect
48. #63644C22semidirect
50. C3×#821C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
56. #63564C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
88. #4731D3semidirect
89. #67⋊C8D3semidirect
178. #924C2×D3semidirect
179. C22×C3⋊C8C2×D3semidirect
182. C2×#204C2×D3semidirect
183. C2×D3×C8C2×D3semidirect
205. C3×C22⋊C8C2×D3semidirect
206. C3×C22⋊C8C2×D3semidirect
225. #821C2×D3semidirect
226. (C2×D3)⋊C8C2×D3semidirect
235. Dic3⋊C8C2×D3semidirect
236. C8×Dic3C2×D3semidirect
261. C3×#67SD16semidirect
489. C22⋊C8D32semidirect
550. #67#204semidirect
734. C32#3295semidirect
834. C3#79439semidirect
835. C3#80158semidirect

Maximal subgroups

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

subgroupindex
D12×#672
#105949932
#105924342
C3×#47312
C3×#67⋊C82
#105911772
C2×#635632
#105909422
D3×#8212
#105908782
#105908292
#105907992
#105907572
Dic3×#2042
#105906762
#801583
#794393