Finite Group Databasebeta

← #11872831

Subgroups — #11872831

Order 1152.

884 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596054C211yesmaximal, characteristic, complemented
2#10593996C211yesmaximal, characteristic
3C3×#5026C211yesmaximal, characteristic, complemented
4C3×C4×#215C211yesmaximal, characteristic, complemented
5#10591652C211yesmaximal, characteristic
6#10591569C211yesmaximal, characteristic, complemented
7#10591569C211yesmaximal, characteristic, complemented
8#10591561C211yesmaximal, characteristic, complemented
9#10590597C211yesmaximal, characteristic
10#10590474C211yesmaximal, characteristic, complemented
11#10590473C211yesmaximal, characteristic, complemented
12#10590450C211yesmaximal, characteristic, complemented
13#10590360C211yesmaximal, characteristic, complemented
14C4×#3716C211yesmaximal, characteristic, complemented
15#10590298C211yesmaximal, characteristic, complemented
16#79787—31nomaximal
17#79659—31nomaximal
18C2×#3802C2211yescharacteristic
19C32×C4×Q8C2211yescharacteristic, complemented
20#64155C2211yescharacteristic
21#64153C2211yescharacteristic, complemented
22#64107—21no—
23#64106C2211yescharacteristic
24#64099C2211yescharacteristic, complemented
25#64098—21no—
26#64085—21no—
27#64081C2211yescharacteristic
28#64079—21no—
29C4×#634C2211yescharacteristic, complemented
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×D12C2211yescharacteristic
34D3×(C2×D3)⋊C4—21no—
35D3×(C2×D3)⋊C4—21no—
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic
38#63879—21no—
39#63879—21no—
40#63849C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43C3×#835C2211yescharacteristic, complemented
44C3×#835C2211yescharacteristic, complemented
45C3×#809C2211yescharacteristic
46C3×#809C2211yescharacteristic
47C3×#808C2211yescharacteristic, complemented
48C3×#807C2211yescharacteristic, complemented
49C3×#803C2211yescharacteristic, complemented
50C3×C4×C3⋊C8C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63572C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63557C2211yescharacteristic
61#5583—31no—
62#5583—31no—
63#5583—61no—
64#5545—31no—
65#5545—31no—
66C3×#440—31no—
67C3×C4×SD16—31no—
68#5169—31no—
69#5169—31no—
70#5162—31no—
71#5162—31no—
72#5026D311yescharacteristic, complemented
73C4×#215D311yescharacteristic, complemented
74#5018—31no—
75C4×#214—31no—
76#4891—31no—
77#4888—31no—
78#4871—31no—
79#4868—31no—
80#4818—31no—
81#4818—31no—
82#4815—31no—
83#4814—31no—
84#4776—31no—
85#4776—31no—
86#4766—31no—
87#4763—31no—
88#4710—31no—
89#4709—31no—
90C4×#204—31no—
91#4690—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×#625—21no—
101C2×D3×Dic3—21no—
102C2×D3×Dic3—21no—
103#3802—22no—
104#3802—22no—
105C32×C4⋊C4—21no—
106C32×C4⋊C4C2311yescharacteristic
107C32×C42—21no—
108C32×C42C2311yescharacteristic
109#3752—21no—
110#3752—21no—
111#3752D411yescharacteristic
112#3752D411yescharacteristic
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117#3750—21no—
118#3750—21no—
119#3750—21no—
120#3750—21no—
121#3750D411yescharacteristic
122#3750D411yescharacteristic
123C4×C3⋊Dic3—21no—
124C4×C3⋊Dic3C2311yescharacteristic
125C3×#215—22no—
126C3×#215—22no—
127C3×(C2×D3)⋊C4—21no—
128C3×(C2×D3)⋊C4—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3722—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139#3716—22no—
140#3716—22no—
141#3123—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×C3×SD16—31no—
145C2×C3×SD16—31no—
146C3×C4×Q8—21no—
147C3×C4×Q8C2×D311yescharacteristic, complemented
148C3×C4×Q8C2×D311yescharacteristic, complemented
149C3×C4×D4—31no—
150C3×C4×D4—31no—
151#946—31no—
152#946—31no—
153#946—61no—
154#944—31no—
155#944—31no—
156#944—61no—
157C2×#215C2×D311yescharacteristic
158C2×#215C2×D311yescharacteristic
159D4×Dic3—31no—
160D4×Dic3—31no—
161C2×#214—31no—
162C2×#214—31no—
163C4×#67—61no—
164C4×#67—61no—
165C2×(C2×D3)⋊C4—61no—
166C2×(C2×D3)⋊C4—61no—
167C2×#204—31no—
168C2×#204—31no—
169#898—61no—
170#898—61no—
171#898—62no—
172#897—31no—
173#897—31no—
174#897—61no—
175#893—31no—
176#893—31no—
177#892—31no—
178#892—31no—
179#890—31no—
180#890—31no—
181#890—61no—
182#889—61no—
183#889—61no—
184#889—62no—
185#67⋊C4—61no—
186#67⋊C4—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189#876—61no—
190#876—61no—
191#876—62no—
192C4×D12C2×D311yescharacteristic
193C4×D12C2×D311yescharacteristic
194#872—31no—
195#872—31no—
196#872—61no—
197#870—61no—
198#870—61no—
199#870—62no—
200C4×Dic6—31no—
201C4×Dic6—31no—
202C4×Dic6—61no—
203C3×#107—31no—
204C3×#106—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#102—31no—
208C3×#102—31no—
209C3×#97—31no—
210C3×C4×C8—31no—
211#835C2×D311yescharacteristic, complemented
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#832—31no—
215#821—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221#818—31no—
222#817—31no—
223#816—31no—
224#816—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229#810—31no—
230#810—31no—
231#809C2×D311yescharacteristic
232#809C2×D311yescharacteristic
233#808—31no—
234#808C2×D311yescharacteristic, complemented
235#807—31no—
236#807C2×D311yescharacteristic, complemented
237#803C2×D311yescharacteristic, complemented
238C4×C3⋊C8C2×D311yescharacteristic, complemented
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C2×D32—24no—
243C2×D32—81no—
244C2×D32—81no—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2×D411yescharacteristic
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3C2×D411yescharacteristic
255C2×C3⋊Dic3C2×D411yescharacteristic
256C2×C3⋊Dic3C2×D411yescharacteristic
257C4×C3⋊D3—21no—
258C4×C3⋊D3—21no—
259#634—21no—
260#634—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12#4112yes—
266C3×D12#4112yes—
267C3×C4×D3—81no—
268C3×C4×D3—81no—
269#625—24no—
270D3×Dic3—81no—
271D3×Dic3—81no—
272C3×C3⋊C8—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#541—91no—
277#518—91no—
278#485—91no—
279#485—91no—
280#478—91no—
281#478—91no—
282#461—91no—
283#461—91no—
284#450—91no—
285#450—91no—
286#440—31no—
287#440—91no—
288C4×SD16—31no—
289C4×SD16—91no—
290#433—91no—
291C23×D3—61no—
292C23×D3—61no—
293C2×C3×Q8—21no—
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C22×C3×C4—61no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C2×#67—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304D3×D4—62no—
305D3×D4—62no—
306D3×D4—62no—
307D3×D4—62no—
308C2×D12C22×D311yescharacteristic
309C2×D12C22×D311yescharacteristic
310C2×C4×D3—21no—
311C2×C4×D3—21no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×Dic6—31no—
318C2×Dic6—31no—
319C2×Dic6—61no—
320C3×SD16—62no—
321C3×SD16—62no—
322C2×C3×C8—31no—
323C2×C3×C8—31no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C3×C4⋊C4—22no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4C22×D311yescharacteristic
333C3×C4⋊C4C22×D311yescharacteristic
334C3×C22⋊C4—61no—
335C3×C22⋊C4—61no—
336C3×C42—22no—
337C3×C42—21no—
338C3×C42—21no—
339C3×C42—21no—
340C3×C42C22×D311yescharacteristic
341C3×C42C22×D311yescharacteristic
342#217—61no—
343#217—61no—
344#215—22no—
345#215—22no—
346#214—62no—
347#214—62no—
348(C2×D3)⋊C4—21no—
349(C2×D3)⋊C4—21no—
350(C2×D3)⋊C4—31no—
351(C2×D3)⋊C4—31no—
352(C2×D3)⋊C4—31no—
353(C2×D3)⋊C4—31no—
354(C2×D3)⋊C4—61no—
355(C2×D3)⋊C4—61no—
356(C2×D3)⋊C4—61no—
357(C2×D3)⋊C4—61no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—62no—
365(C2×D3)⋊C4—62no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—62no—
374C4⋊Dic3—62no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—31no—
378Dic3⋊C4—31no—
379Dic3⋊C4—31no—
380Dic3⋊C4—31no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—62no—
392Dic3⋊C4—62no—
393Dic3⋊C4—62no—
394Dic3⋊C4—62no—
395Dic3⋊C4—62no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—62no—
404C4×Dic3—61no—
405C4×Dic3—61no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—62no—
411#204—62no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3×D3—22no—
417C2×C3×D3—22no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422D32—84no—
423C32×C4—21no—
424C32×C4—21no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4C2×#4111yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C22×D4—91no—
437C2×SD16—31no—
438C2×SD16—31no—
439C2×SD16—91no—
440C2×SD16—91no—
441C4⋊Q8—91no—
442#126—181no—
443#126—181no—
444#125—91no—
445#125—181no—
446#125—181no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449C4×Q8—91no—
450C4×Q8D3211yescharacteristic, complemented
451C4×D4—31no—
452C4×D4—31no—
453C4×D4—91no—
454C4×D4—91no—
455C4×D4—181no—
456C4×D4—181no—
457#117—91no—
458#117—91no—
459C2×C22⋊C4—181no—
460C2×C22⋊C4—181no—
461#107—31no—
462#107—91no—
463#106—31no—
464#106—91no—
465C4⋊C8—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477#97—31no—
478C4×C8—31no—
479C23×C3—61no—
480C23×C3—61no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—31no—
484C22×D3—31no—
485C22×D3—61no—
486C22×D3—64no—
487C22×D3—64no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3—241no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—32no—
499C3×D4—32no—
500C3×D4—61no—
501C3×D4—61no—
502C2×C3×C4—22no—
503C2×C3×C4—22no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—241no—
514C2×C3×C4—241no—
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—64no—
522#67—64no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—62no—
535C2×Dic3—62no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—241no—
541C2×Dic3—241no—
542D12—21no—
543D12—21no—
544D12#23512yes—
545D12#23512yes—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—61no—
550C4×D3—81no—
551C4×D3—81no—
552C4×D3—121no—
553C4×D3—121no—
554C4×D3—241no—
555C4×D3—241no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—121no—
561Dic6—121no—
562C3×C8—61no—
563C3×C8—61no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C2×C32#52511yescharacteristic
571C2×C32#57711yescharacteristic
572C2×C32#57711yescharacteristic
573C3⋊D3—41no—
574C3×D3—42no—
575C3×D3—42no—
576C24—181no—
577C2×Q8—91no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—181no—
582C2×D4—182no—
583C2×D4—182no—
584C22×C4—61no—
585C22×C4—61no—
586C22×C4—91no—
587C22×C4—181no—
588C22×C4—181no—
589SD16—62no—
590SD16—62no—
591SD16—182no—
592SD16—182no—
593C2×C8—31no—
594C2×C8—31no—
595C2×C8—31no—
596C2×C8—31no—
597C4⋊C4—21no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—91no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4C2×D3211yescharacteristic
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C42—21no—
621C42—91no—
622C42—181no—
623C42—181no—
624C42C2×D3211yescharacteristic
625C22×C3—21no—
626C22×C3—62no—
627C22×C3—62no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3C2×D3×D411yescharacteristic
633C22×C3C2×D3×D411yescharacteristic
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—41no—
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—61no—
641C2×D3—61no—
642C2×D3—61no—
643C2×D3—61no—
644C2×D3—61no—
645C2×D3—61no—
646C2×D3—121no—
647C2×D3—121no—
648C2×D3—121no—
649C2×D3—244no—
650C2×D3—244no—
651C3×C4—21no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—42no—
660C3×C4—42no—
661C3×C4—41no—
662C3×C4—41no—
663C3×C4—41no—
664C3×C4—41no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4C2×#23511yescharacteristic
668C3×C4C2×#23511yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—41no—
672Dic3—41no—
673Dic3—61no—
674Dic3—61no—
675Dic3—61no—
676Dic3—61no—
677Dic3—61no—
678Dic3—61no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—122no—
683Dic3—122no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688C32#312311yescharacteristic, complemented, Sylow
689C23—61no—
690C23—61no—
691C23—91no—
692C23—184no—
693C23—721no—
694C23—721no—
695Q8—21no—
696Q8—21no—
697Q8—181no—
698Q8—181no—
699D4—32no—
700D4—32no—
701D4—61no—
702D4—61no—
703D4—184no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—91no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—241no—
716C2×C4—241no—
717C2×C4—721no—
718C2×C4—721no—
719C2×C4#381111yescharacteristic
720C2×C4#381111yescharacteristic
721C2×C4C22×D3211yescharacteristic
722C8—61no—
723C8—61no—
724C8—61no—
725C8—61no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—122no—
730C2×C3—122no—
731C2×C3#554711yescharacteristic
732C2×C3#554711yescharacteristic
733C2×C3#576211yescharacteristic
734C2×C3#577011yescharacteristic
735C2×C3#577511yescharacteristic
736C2×C3#577811yescharacteristic
737D3—42no—
738D3—42no—
739D3—121no—
740D3—121no—
741D3—241no—
742C22—62no—
743C22—62no—
744C22—121no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—181no—
749C22—181no—
750C22—181no—
751C22—724no—
752C22C2×#381111yescharacteristic
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—121no—
758C4—121no—
759C4—181no—
760C4—181no—
761C4—181no—
762C4—361no—
763C4—361no—
764C4D3×#23511yescharacteristic
765C4D3×#23511yescharacteristic
766C3—21no—
767C3#7965911yescharacteristic, complemented
768C3#7978711yescharacteristic, complemented
769C2—122no—
770C2—122no—
771C2—361no—
772C2#1059507611yescharacteristic
773C2#1059532411yescharacteristic
774C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×#3802C22
hypercenterC4×Q8D32
hypocenterC32#3123
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596054C2semidirect
3. C3×#5026C2semidirect
4. C3×C4×#215C2semidirect
6. #10591569C2semidirect
7. #10591569C2semidirect
8. #10591561C2semidirect
10. #10590474C2semidirect
11. #10590473C2semidirect
12. #10590450C2semidirect
13. #10590360C2semidirect
14. C4×#3716C2semidirect
15. #10590298C2semidirect
19. C32×C4×Q8C22semidirect
21. #64153C22semidirect
24. #64099C22semidirect
29. C4×#634C22semidirect
43. C3×#835C22semidirect
44. C3×#835C22semidirect
47. C3×#808C22semidirect
48. C3×#807C22semidirect
49. C3×#803C22semidirect
50. C3×C4×C3⋊C8C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63572C22semidirect
54. #63572C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
72. #5026D3semidirect
73. C4×#215D3semidirect
147. C3×C4×Q8C2×D3semidirect
148. C3×C4×Q8C2×D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
234. #808C2×D3semidirect
236. #807C2×D3semidirect
237. #803C2×D3semidirect
238. C4×C3⋊C8C2×D3semidirect
450. C4×Q8D32semidirect
688. C32#3123semidirect
767. C3#79659semidirect
768. C3#79787semidirect

Maximal subgroups

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

subgroupindex
#105960542
#105939962
C3×#50262
C3×C4×#2152
#105916522
#105915692
#105915612
#105905972
#105904742
#105904732
#105904502
#105903602
C4×#37162
#105902982
#797873
#796593