Finite Group Databasebeta

← #11867164

Subgroups — #11867164

Order 1152.

1309 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic, complemented
3C22×C3×#208C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5#10591178C212yesmaximal, complemented
6#10591177C212yesmaximal, complemented
7#10591165C212yesmaximal, complemented
8#10591164C212yesmaximal, complemented
9#10591131C211yesmaximal, characteristic, complemented
10#10591096C211yesmaximal, characteristic, complemented
11#10591088C211yesmaximal, characteristic, complemented
12#83772—31nomaximal
13#82924—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638—21no—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18#64139—21no—
19#64139—21no—
20#64139C2212yes—
21#64139C2212yes—
22C2×#3752—21no—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C3×#953—21no—
25C3×#930C2211yescharacteristic, complemented
26C3×#930C2211yescharacteristic, complemented
27C3×#929—21no—
28C3×C4×#67—21no—
29C3×C4×#67—21no—
30C3×#926C2211yescharacteristic
31C3×#924C2211yescharacteristic, complemented
32C3×#924C2211yescharacteristic, complemented
33C2×C3×#208—24no—
34C2×C3×#208C2211yescharacteristic
35C2×C3×#208C2211yescharacteristic
36C2×C3×#208C2212yescomplemented
37C22×C3×C3⋊C8C2212yescomplemented
38C2×#3717C2212yescomplemented
39#63825—24no—
40C2×#3714C2212yescomplemented
41#63575C2212yescomplemented
42#63573C2212yescomplemented
43#63566C2212yescomplemented
44#63564C2212yescomplemented
45#63564C2212yescomplemented
46#63563C2212yescomplemented
47C22×C3×M16—31no—
48C3×#525—31no—
49C2×#949—31no—
50#5791D311yescharacteristic, complemented
51C2×#930—31no—
52C2×#930—31no—
53C2×#930—61no—
54C22×#208D311yescharacteristic, complemented
55C2×#908—31no—
56#5232—31no—
57#5135—32no—
58#5134—32no—
59#5133—31no—
60#5131—31no—
61#5121—31no—
62#5115—32no—
63#5114—32no—
64#5049—32no—
65#5048—32no—
66#5039—32no—
67#5038—32no—
68#5001—31no—
69#4995—31no—
70C24×C32D411yescharacteristic
71C23×C3⋊D3—21no—
72C22×C32×C4—22no—
73C22×C32×C4—22no—
74C22×C32×C4D411yescharacteristic
75C22×C32×C4D411yescharacteristic
76C22×C32×C4D411yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C2×#638—22no—
81C2×#638—22no—
82C2×#638—44no—
83C22×C3⋊Dic3—21no—
84C2×C4⋊(C3⋊D3)—22no—
85C2×C4⋊(C3⋊D3)—22no—
86C2×C4⋊(C3⋊D3)—21no—
87C2×C4⋊(C3⋊D3)C2312yes—
88C2×C3×#67—21no—
89C2×C3×#67—21no—
90C2×C3×#67—21no—
91C3×#235—22no—
92C3×#235—22no—
93C2×C3×D12C2311yescharacteristic
94C2×C3×C4×D3—21no—
95C2×C3×Dic6C2311yescharacteristic
96#3752—22no—
97#3752—22no—
98C4⋊(C3⋊Dic3)—21no—
99C4⋊(C3⋊Dic3)C2312yes—
100C3×#217—21no—
101C3×#217—21no—
102C3×#217—21no—
103C3×(C2×D3)⋊C4—21no—
104C3×(C2×D3)⋊C4—21no—
105C3×C4⋊Dic3C2311yescharacteristic
106C3×C4⋊Dic3C2311yescharacteristic
107C3×Dic3⋊C4—21no—
108C3×Dic3⋊C4—21no—
109C3×C4×Dic3—21no—
110C3×#208—22no—
111C3×#208—24no—
112C3×#208D414yescomplemented
113C2×C3×C3⋊C8—24no—
114C2×C3×C3⋊C8C2312yes—
115C2×C3×C3⋊C8C2312yes—
116#3717—24no—
117#3714—24no—
118#3055—91noSylow
119C2×C3×#41—31no—
120C23×C3×C4—21no—
121C23×C3×C4C2×D311yescharacteristic
122C23×C3×C4C2×D311yescharacteristic
123C22×#67—62no—
124C22×#67—61no—
125C22×#67—61no—
126C2×#235C2×D311yescharacteristic
127C22×D12—31no—
128C22×D12—31no—
129C22×D12—61no—
130C2×C3×M16—31no—
131C2×C3×M16—31no—
132C2×C3×M16—32no—
133C2×C3×M16—64no—
134C22×C3×C8—32no—
135C3×#123—61no—
136C3×C22⋊Q8—31no—
137C3×C22⋊Q8—31no—
138C3×#121—31no—
139C3×#121—31no—
140C3×#120—61no—
141C3×C4×D4—61no—
142C3×C4×D4—61no—
143C3×#117—31no—
144#953—21no—
145#949—64no—
146C2×#215—32no—
147C2×#213—32no—
148#930—32no—
149#930—32no—
150#930—32no—
151#930—32no—
152#930—62no—
153#930—62no—
154#930—62no—
155#930—62no—
156#930—61no—
157#930—61no—
158#930—61no—
159#930—61no—
160#930C2×D311yescharacteristic, complemented
161#930C2×D311yescharacteristic, complemented
162#929—21no—
163C4×#67—21no—
164C4×#67—21no—
165C2×(C2×D3)⋊C4—62no—
166C2×(C2×D3)⋊C4—61no—
167C2×(C2×D3)⋊C4—61no—
168#926C2×D311yescharacteristic
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—61no—
172#924C2×D311yescharacteristic, complemented
173#924C2×D311yescharacteristic, complemented
174C2×#208—24no—
175C2×#208C2×D311yescharacteristic
176C2×#208C2×D311yescharacteristic
177C2×#208C2×D312yescomplemented
178C22×C3⋊C8C2×D312yescomplemented
179#908—64no—
180C2×D24—32no—
181C2×#204—32no—
182#835—32no—
183#832—32no—
184#821—32no—
185#821—32no—
186#821—32no—
187#818—32no—
188#817—32no—
189#816—32no—
190#809—32no—
191#809—32no—
192#808—32no—
193#807—32no—
194C23×C32—22no—
195C23×C32—22no—
196C23×C32—41no—
197C23×C32C2×D411yescharacteristic
198C23×C32C2×D411yescharacteristic
199C23×C32C2×D411yescharacteristic
200C22×C3⋊D3—22no—
201C22×C3⋊D3—42no—
202C22×C3⋊D3—42no—
203C22×C3⋊D3—42no—
204C22×C3×D3—21no—
205C2×C32×C4—22no—
206C2×C32×C4—22no—
207C2×C32×C4—22no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4C2×D411yescharacteristic
213C2×C32×C4C2×D411yescharacteristic
214C2×C32×C4C2×D411yescharacteristic
215C2×C32×C4C2×D412yes—
216C2×C32×C4#4112yes—
217C2×C32×C4C2411yescharacteristic
218#638—44no—
219#638—44no—
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3—42no—
222C4⋊(C3⋊D3)—22no—
223C4⋊(C3⋊D3)—22no—
224C4⋊(C3⋊D3)—42no—
225C3×#67—42no—
226C3×#67—42no—
227C3×#67—42no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C3×D12—21no—
232C3×D12—21no—
233C3×C4×D3—42no—
234C3×Dic6—21no—
235C3×Dic6—21no—
236C3×C3⋊C8—22no—
237C3×C3⋊C8C2×D414yescomplemented
238C2×AGL(1,ℤ/8)—91no—
239C22×M16—31no—
240#525—31no—
241C2×#121—91no—
242#469—92no—
243#468—92no—
244#466—92no—
245#465—92no—
246#428—91no—
247#418—91no—
248#417—91no—
249C24×C3—21no—
250C24×C3D1211yescharacteristic
251C24×C3#6711yescharacteristic
252C23×D3—62no—
253C23×D3—61no—
254C23×D3—61no—
255C3×#41—62no—
256C3×#41—62no—
257C2×C3×Q8—31no—
258C2×C3×D4—31no—
259C2×C3×D4—61no—
260C2×C3×D4—61no—
261C2×C3×D4—61no—
262C22×C3×C4—22no—
263C22×C3×C4—22no—
264C22×C3×C4—22no—
265C22×C3×C4—22no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—42no—
273C22×C3×C4—42no—
274C22×C3×C4—61no—
275C22×C3×C4D1211yescharacteristic
276C22×C3×C4D1211yescharacteristic
277C22×C3×C4D1211yescharacteristic
278C22×C3×C4#6711yescharacteristic
279C22×C3×C4#6711yescharacteristic
280C22×C3×C4#6711yescharacteristic
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C2×#67—21no—
288C2×#67—21no—
289C2×#67—21no—
290C2×#67—64no—
291C2×#67—64no—
292C2×#67—62no—
293C2×#67—62no—
294C2×#67—62no—
295C2×#67—62no—
296C2×#67—128no—
297C2×#67—124no—
298C2×#67—124no—
299C22×Dic3—62no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302#235—22no—
303#235—22no—
304C2×D12—32no—
305C2×D12—32no—
306C2×D12—62no—
307C2×D12—62no—
308C2×D12—62no—
309C2×D12—62no—
310C2×D12—62no—
311C2×D12—62no—
312C2×D12—61no—
313C2×D12—61no—
314C2×D12—122no—
315C2×D12—122no—
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—21no—
318C2×Dic6C22×D311yescharacteristic
319C3×M16—34no—
320C3×M16—64no—
321C3×M16—62no—
322C2×C3×C8—32no—
323C2×C3×C8—32no—
324C2×C3×C8—64no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C22⋊C4—61no—
330C3×C22⋊C4—61no—
331C3×C22⋊C4—61no—
332C3×C22⋊C4—61no—
333C3×C22⋊C4—61no—
334C3×C42—61no—
335#217—21no—
336#217—21no—
337#217—21no—
338#215—64no—
339#213—64no—
340(C2×D3)⋊C4—21no—
341(C2×D3)⋊C4—21no—
342(C2×D3)⋊C4—64no—
343(C2×D3)⋊C4—64no—
344(C2×D3)⋊C4—62no—
345(C2×D3)⋊C4—62no—
346(C2×D3)⋊C4—62no—
347(C2×D3)⋊C4—62no—
348C4⋊Dic3—32no—
349C4⋊Dic3—32no—
350C4⋊Dic3—62no—
351C4⋊Dic3—62no—
352C4⋊Dic3—61no—
353C4⋊Dic3—61no—
354C4⋊Dic3C22×D311yescharacteristic
355C4⋊Dic3C22×D311yescharacteristic
356Dic3⋊C4—21no—
357Dic3⋊C4—21no—
358C4×Dic3—21no—
359#208—22no—
360#208—24no—
361#208#6714yescomplemented
362C2×C3⋊C8—24no—
363C2×C3⋊C8C22×D312yes—
364C2×C3⋊C8C22×D312yes—
365D24—64no—
366#204—64no—
367C22×C32—21no—
368C22×C32—21no—
369C22×C32—21no—
370C22×C32—21no—
371C22×C32—21no—
372C22×C32—21no—
373C22×C32—21no—
374C22×C32—44no—
375C22×C32#12112yes—
376C22×C32AGL(1,ℤ/8)12yescomplemented
377C22×C32C22×D411yescharacteristic
378C2×C3⋊D3—42no—
379C2×C3⋊D3—42no—
380C2×C3⋊D3—42no—
381C2×C3⋊D3—84no—
382C2×C3×D3—41no—
383C2×C3×D3—41no—
384C2×C3×D3—41no—
385C32×C4—21no—
386C32×C4—21no—
387C32×C4#12112yes—
388C32×C4C22×D411yescharacteristic
389C32×C4C2×#4111yescharacteristic
390C3⋊Dic3—42no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C2×#41—31no—
395C22×D4—91no—
396C22×D4—181no—
397C23×C4D3211yescharacteristic
398AGL(1,ℤ/8)—184no—
399C2×SD16—92no—
400C2×D8—92no—
401C2×M16—31no—
402C2×M16—31no—
403C2×M16—32no—
404C2×M16—64no—
405C22×C8—32no—
406#123—61no—
407C22⋊Q8—31no—
408C22⋊Q8—31no—
409#121—31no—
410#121—31no—
411#121—92no—
412#121—92no—
413#121—181no—
414#121—181no—
415#120—61no—
416C4×D4—61no—
417C4×D4—61no—
418#117—31no—
419C2×C4⋊C4—91no—
420C2×C22⋊C4—181no—
421#107—92no—
422#106—92no—
423#103—92no—
424#102—92no—
425#102—92no—
426#102—92no—
427C23×C3—24no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—42no—
436C23×C3—41no—
437C23×C3—41no—
438C23×C3—42no—
439C23×C3—61no—
440C23×C3C2×D1211yescharacteristic
441C23×C3C2×D1211yescharacteristic
442C23×C3C2×D1211yescharacteristic
443C23×C3C2×#6711yescharacteristic
444C23×C3C2×#6711yescharacteristic
445C23×C3C2×#6711yescharacteristic
446C22×D3—21no—
447C22×D3—64no—
448C22×D3—62no—
449C22×D3—62no—
450C22×D3—124no—
451C22×D3—124no—
452C22×D3—122no—
453C22×D3—122no—
454C22×D3—124no—
455C22×D3—122no—
456C22×D3—122no—
457C22×D3—122no—
458C22×D3—122no—
459C3×Q8—61no—
460C3×Q8—61no—
461C3×D4—61no—
462C3×D4—61no—
463C3×D4—122no—
464C3×D4—122no—
465C3×D4—122no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—22no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—22no—
486C2×C3×C4—41no—
487C2×C3×C4—41no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—42no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—122no—
497C2×C3×C4C2×D1211yescharacteristic
498C2×C3×C4C2×D1211yescharacteristic
499C2×C3×C4C2×D1211yescharacteristic
500C2×C3×C4#23512yes—
501C2×C3×C4D3×D412yes—
502C2×C3×C4#23712yes—
503C2×C3×C4C2×#6711yescharacteristic
504C2×C3×C4C2×#6711yescharacteristic
505C2×C3×C4C2×#6711yescharacteristic
506C2×C3×C4C2×#6712yes—
507C2×C3×C4C23×D311yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509#67—42no—
510#67—42no—
511#67—42no—
512#67—128no—
513#67—124no—
514#67—124no—
515#67—128no—
516#67—124no—
517#67—124no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—64no—
522C2×Dic3—62no—
523C2×Dic3—62no—
524C2×Dic3—124no—
525C2×Dic3—122no—
526C2×Dic3—122no—
527D12—21no—
528D12—21no—
529D12—62no—
530D12—62no—
531D12—62no—
532D12—62no—
533D12—122no—
534D12—122no—
535D12—124no—
536D12—122no—
537D12—122no—
538C4×D3—42no—
539Dic6—21no—
540Dic6—21no—
541C3×C8—34no—
542C3×C8—62no—
543C3⋊C8—22no—
544C3⋊C8C2×#6714yescomplemented
545C2×C32—22no—
546C2×C32—22no—
547C2×C32—41no—
548C2×C32C2×#12111yescharacteristic
549C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
550C2×C32#57511yescharacteristic
551C3⋊D3—82no—
552C3×D3—81no—
553C24—181no—
554C24#62611yescharacteristic
555#41—62no—
556#41—62no—
557C2×Q8—31no—
558C2×D4—31no—
559C2×D4—61no—
560C2×D4—61no—
561C2×D4—61no—
562C2×D4—92no—
563C2×D4—182no—
564C2×D4—182no—
565C2×D4—182no—
566C2×D4—181no—
567C2×D4—182no—
568C2×D4—364no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—61no—
572C22×C4—181no—
573C22×C4#62611yescharacteristic
574C22×C4#62611yescharacteristic
575C22×C4#62611yescharacteristic
576C22×C4C2×D3211yescharacteristic
577C22×C4C2×D3211yescharacteristic
578C22×C4C2×D3211yescharacteristic
579SD16—184no—
580D8—184no—
581M16—34no—
582M16—64no—
583M16—62no—
584C2×C8—32no—
585C2×C8—32no—
586C2×C8—64no—
587C4⋊C4—31no—
588C4⋊C4—31no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—92no—
592C4⋊C4—181no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C22⋊C4—61no—
597C22⋊C4—61no—
598C22⋊C4—182no—
599C22⋊C4—182no—
600C42—61no—
601C22×C3—22no—
602C22×C3—22no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—22no—
620C22×C3—22no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—44no—
626C22×C3—44no—
627C22×C3—48no—
628C22×C3—121no—
629C22×C3—121no—
630C22×C3—121no—
631C22×C3#90812yescomplemented
632C22×C3#93012yes—
633C22×C3#93912yes—
634C22×C3#94912yescomplemented
635C22×C3C22×D1211yescharacteristic
636C22×C3C22×#6711yescharacteristic
637C2×D3—41no—
638C2×D3—41no—
639C2×D3—41no—
640C2×D3—124no—
641C2×D3—124no—
642C2×D3—124no—
643C2×D3—122no—
644C2×D3—122no—
645C2×D3—122no—
646C2×D3—122no—
647C2×D3—122no—
648C2×D3—122no—
649C2×D3—248no—
650C2×D3—244no—
651C2×D3—244no—
652C3×C4—21no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—22no—
659C3×C4—41no—
660C3×C4—41no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4#93012yes—
665C3×C4#93912yes—
666C3×C4C2×#23511yescharacteristic
667C3×C4C2×D3×D411yescharacteristic
668C3×C4C2×#23711yescharacteristic
669C3×C4C22×#6711yescharacteristic
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—124no—
674Dic3—122no—
675Dic3—122no—
676C32#305511yescharacteristic, complemented, Sylow
677C23—22no—
678C23—22no—
679C23—41no—
680C23—61no—
681C23—182no—
682C23—362no—
683C23—362no—
684C23—362no—
685C23C2×#62611yescharacteristic
686C23C2×#62611yescharacteristic
687C23C2×#62611yescharacteristic
688Q8—61no—
689Q8—61no—
690D4—61no—
691D4—61no—
692D4—122no—
693D4—122no—
694D4—122no—
695D4—182no—
696D4—182no—
697D4—364no—
698D4—364no—
699D4—362no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—122no—
711C2×C4—182no—
712C2×C4—362no—
713C2×C4#380412yes—
714C2×C4C2×#62611yescharacteristic
715C2×C4C2×#62611yescharacteristic
716C2×C4C2×#62611yescharacteristic
717C2×C4D3×#6712yes—
718C2×C4C22×D3211yescharacteristic
719C8—34no—
720C8—62no—
721C2×C3—24no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—22no—
725C2×C3—22no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—42no—
730C2×C3—42no—
731C2×C3—41no—
732C2×C3—41no—
733C2×C3—241no—
734C2×C3C2×#90811yescharacteristic
735C2×C3#574811yescharacteristic
736C2×C3C2×#93011yescharacteristic
737C2×C3C2×#93911yescharacteristic
738C2×C3C2×#94911yescharacteristic
739C2×C3#582211yescharacteristic
740D3—81no—
741D3—244no—
742D3—242no—
743D3—242no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—44no—
752C22—121no—
753C22—121no—
754C22—121no—
755C22—362no—
756C22—362no—
757C22—362no—
758C22—724no—
759C22#6382512yescomplemented
760C22#6397812yes—
761C22C22×#62611yescharacteristic
762C4—21no—
763C4—21no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—362no—
768C4#6397812yes—
769C4C2×#380411yescharacteristic
770C4C2×D3×#6711yescharacteristic
771C3—21no—
772C3#8292411yescharacteristic, complemented
773C3#8377211yescharacteristic, complemented
774C2—22no—
775C2—22no—
776C2—41no—
777C2—241no—
778C2—722no—
779C2C2×#6382511yescharacteristic
780C2#1059479511yescharacteristic
781C2C2×#6397811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
hypercenterC23×C4D32
hypocenterC32#3055
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64139C2semidirect
2. C3×#5791C2semidirect
3. C22×C3×#208C2semidirect
4. C2×#63825C2semidirect
5. #10591178C2semidirect
6. #10591177C2semidirect
7. #10591165C2semidirect
8. #10591164C2semidirect
9. #10591131C2semidirect
10. #10591096C2semidirect
11. #10591088C2semidirect
25. C3×#930C22semidirect
26. C3×#930C22semidirect
31. C3×#924C22semidirect
32. C3×#924C22semidirect
36. C2×C3×#208C22semidirect
37. C22×C3×C3⋊C8C22semidirect
38. C2×#3717C22semidirect
40. C2×#3714C22semidirect
41. #63575C22semidirect
42. #63573C22semidirect
43. #63566C22semidirect
44. #63564C22semidirect
45. #63564C22semidirect
46. #63563C22semidirect
50. #5791D3semidirect
54. C22×#208D3semidirect
112. C3×#208D4semidirect
160. #930C2×D3semidirect
161. #930C2×D3semidirect
172. #924C2×D3semidirect
173. #924C2×D3semidirect
177. C2×#208C2×D3semidirect
178. C22×C3⋊C8C2×D3semidirect
237. C3×C3⋊C8C2×D4semidirect
361. #208#67semidirect
376. C22×C32AGL(1,ℤ/8)semidirect
544. C3⋊C8C2×#67semidirect
631. C22×C3#908semidirect
634. C22×C3#949semidirect
676. C32#3055semidirect
759. C22#63825semidirect
772. C3#82924semidirect
773. C3#83772semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C3×#57912
C22×C3×#2082
C2×#638252
#105911782
#105911772
#105911652
#105911642
#105911312
#105910962
#105910882
#837723
#829243