Finite Group Databasebeta

← #11803301

Subgroups — #11803301

Order 1152.

1947 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C22×#3722C211yesmaximal, characteristic, complemented
4C3×#5220C211yesmaximal, characteristic, complemented
5#10591714C211yesmaximal, characteristic, complemented
6#10591711C212yesmaximal, complemented
7#10591704C212yesmaximal, complemented
8Dic3×#217C211yesmaximal, characteristic, complemented
9#10591693C211yesmaximal, characteristic, complemented
10#10591266C212yesmaximal, complemented
11#10591202C212yesmaximal, complemented
12#82395—31nomaximal
13#74875—31nomaximal
14C24×C3⋊D3C2211yescharacteristic
15C22×C32×D4C2211yescharacteristic
16C22×#638C2212yes—
17C23×C3×Dic3C2211yescharacteristic
18C23×C3×Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic, complemented
20C2×#3757C2211yescharacteristic
21#64146C418yescomplemented
22C2×#3752C2212yes—
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic, complemented
26C2×C3×#217C2212yescomplemented
27C3×D4×Dic3—24no—
28C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
29C2×C3×C4×Dic3C2211yescharacteristic, complemented
30C2×#3724C2212yescomplemented
31C2×#3722—24no—
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35C2×#3722C2212yes—
36C2×Dic32C2212yescomplemented
37C3×C3⋊#95C2212yescomplemented
38#63579C2212yescomplemented
39#63579C2212yescomplemented
40C2×C3×C4×D4—31no—
41C2×#937—31no—
42C2×#937—31no—
43C2×#937—61no—
44C2×D4×Dic3D311yescharacteristic, complemented
45C22×(C2×D3)⋊C4—31no—
46C22×(C2×D3)⋊C4—31no—
47C3×#386—31no—
48#5220D311yescharacteristic, complemented
49#5213—32no—
50#5210—31no—
51C4×#217—31no—
52#4990—32no—
53#4958—32no—
54#4957—32no—
55#4957—32no—
56#4955—31no—
57#4955—31no—
58#4946—31no—
59Dic3×C22⋊C4—31no—
60#4940—32no—
61#4670—32no—
62#4669—32no—
63C24×C32C2311yescharacteristic
64C24×C32C2311yescharacteristic
65C23×C3⋊D3—22no—
66C23×C3⋊D3—22no—
67C23×C3⋊D3—42no—
68C23×C3⋊D3—42no—
69C23×C3⋊D3C2×C414yescomplemented
70C23×C3⋊D3C2312yes—
71C2×C32×D4—22no—
72C2×C32×D4—22no—
73C2×C32×D4C2×C414yes—
74C22×C32×C4C2311yescharacteristic
75C2×#638—42no—
76C2×#638—42no—
77C2×#638C2×C418yescomplemented
78C22×C3⋊Dic3C2312yes—
79C22×C3×Dic3—22no—
80C22×C3×Dic3—22no—
81C22×C3×Dic3—42no—
82C22×C3×Dic3—42no—
83C22×C3×Dic3—42no—
84C22×C3×Dic3D414yescomplemented
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2311yescharacteristic
87C22×C3×Dic3C2312yes—
88C22×C3×Dic3C2312yes—
89C22×C3×Dic3C2311yescharacteristic
90C22×C3×Dic3C2311yescharacteristic
91#3757C2×C414yescomplemented
92#3752C2×C418yescomplemented
93C3×#217—22no—
94C3×#217—22no—
95C3×#217—22no—
96C3×#217—42no—
97C3×C4⋊Dic3—22no—
98C3×C4×Dic3—22no—
99#3724—42no—
100#3722—24no—
101#3722—24no—
102#3722—42no—
103#3722—42no—
104Dic32—42no—
105#2321—91noSylow
106C24×D3—31no—
107C24×D3—31no—
108C24×D3—61no—
109C22×C3×D4—21no—
110C22×C3×D4C2×D311yescharacteristic
111C22×C3×D4C2×D311yescharacteristic
112C23×C3×C4—31no—
113C23×C3×C4—31no—
114C23×C3×C4—31no—
115C22×#67—32no—
116C22×#67—32no—
117C22×#67—62no—
118C23×Dic3C2×D311yescharacteristic
119C23×Dic3C2×D311yescharacteristic
120C23×Dic3C2×D311yescharacteristic, complemented
121C3×C4×D4—64no—
122C2×C3×C4⋊C4—31no—
123C2×C3×C22⋊C4—31no—
124C2×C3×C22⋊C4—31no—
125C2×C3×C22⋊C4—31no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C42—31no—
128C2×#217—31no—
129C2×#217—31no—
130C2×#217—61no—
131C2×#217C2×D311yescharacteristic
132C2×#217C2×D311yescharacteristic
133C2×#217C2×D311yescharacteristic, complemented
134C2×#217C2×D312yescomplemented
135#937—38no—
136#937—38no—
137#937—68no—
138D4×Dic3—24no—
139C2×(C2×D3)⋊C4—32no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—32no—
149C2×(C2×D3)⋊C4—62no—
150C2×(C2×D3)⋊C4—64no—
151C2×(C2×D3)⋊C4—64no—
152C2×C4⋊Dic3C2×D311yescharacteristic, complemented
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×C4×Dic3—32no—
156C2×C4×Dic3—32no—
157C2×C4×Dic3C2×D311yescharacteristic, complemented
158C3×#95—32no—
159C3⋊#95—32no—
160C3⋊#95—32no—
161C3⋊#95—32no—
162C3⋊#95—32no—
163C3⋊#95C2×D312yescomplemented
164C23×C32—22no—
165C23×C32—22no—
166C23×C32—21no—
167C23×C32—21no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32C22×C412yes—
171C23×C32C22×C412yes—
172C23×C32C2×D412yes—
173C23×C32#4112yes—
174C23×C32C2411yescharacteristic
175C22×C3⋊D3—22no—
176C22×C3⋊D3—22no—
177C22×C3⋊D3—28no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3—48no—
183C22×C3⋊D3—44no—
184C22×C3⋊D3—44no—
185C22×C3⋊D3—48no—
186C22×C3⋊D3C22×C414yes—
187C32×D4—28no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4C22×C412yes—
191#638—48no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3—22no—
194C2×C3⋊Dic3C22×C414yes—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—22no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—44no—
208C2×C3×Dic3—44no—
209C2×C3×Dic3—44no—
210C2×C3×Dic3C2×D412yes—
211C2×C3×Dic3C2×D412yes—
212C2×#120—91no—
213C2×C4×D4—31no—
214C22×C22⋊C4—91no—
215#390—92no—
216#388—92no—
217#388—92no—
218#386—31no—
219#386—92no—
220#385—91no—
221#379—91no—
222C4×C22⋊C4—91no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3C22×D311yescharacteristic
226C24×C3C22×D311yescharacteristic
227C24×C3C22×D311yescharacteristic
228C24×C3C22×D311yescharacteristic
229C23×D3—32no—
230C23×D3—32no—
231C23×D3—34no—
232C23×D3—34no—
233C23×D3—62no—
234C23×D3—64no—
235C23×D3—62no—
236C23×D3—62no—
237C23×D3—62no—
238C23×D3—62no—
239C23×D3—122no—
240C23×D3—122no—
241C23×D3—122no—
242C23×D3—122no—
243C23×D3—122no—
244C23×D3—122no—
245C23×D3—124no—
246C23×D3—124no—
247C2×C3×D4—22no—
248C2×C3×D4—22no—
249C2×C3×D4—22no—
250C2×C3×D4—22no—
251C2×C3×D4—24no—
252C2×C3×D4—42no—
253C2×C3×D4—42no—
254C2×C3×D4C4×D314yes—
255C2×C3×D4C4×D314yes—
256C22×C3×C4—21no—
257C22×C3×C4—31no—
258C22×C3×C4—31no—
259C22×C3×C4—34no—
260C22×C3×C4—31no—
261C22×C3×C4—32no—
262C22×C3×C4—32no—
263C22×C3×C4—31no—
264C22×C3×C4—62no—
265C22×C3×C4—62no—
266C22×C3×C4—122no—
267C22×C3×C4—122no—
268C22×C3×C4—122no—
269C22×C3×C4C22×D311yescharacteristic
270C22×C3×C4C22×D311yescharacteristic
271C2×#67—38no—
272C2×#67—38no—
273C2×#67—68no—
274C2×#67—122no—
275C2×#67—122no—
276C2×#67—122no—
277C2×#67—122no—
278C2×#67—124no—
279C2×#67—124no—
280C22×Dic3—22no—
281C22×Dic3—22no—
282C22×Dic3—32no—
283C22×Dic3—32no—
284C22×Dic3—42no—
285C22×Dic3—42no—
286C22×Dic3—42no—
287C22×Dic3—62no—
288C22×Dic3#6714yescomplemented
289C22×Dic3C22×D311yescharacteristic
290C22×Dic3C22×D312yes—
291C22×Dic3C22×D312yes—
292C22×Dic3C22×D311yescharacteristic
293C22×Dic3C22×D311yescharacteristic
294C22×Dic3C22×D311yescharacteristic
295C3×C4⋊C4—62no—
296C3×C22⋊C4—62no—
297C3×C22⋊C4—62no—
298C3×C22⋊C4—62no—
299C3×C22⋊C4—122no—
300C3×C42—62no—
301#217—22no—
302#217—22no—
303#217—22no—
304#217—34no—
305#217—34no—
306#217—42no—
307#217—64no—
308(C2×D3)⋊C4—38no—
309(C2×D3)⋊C4—38no—
310(C2×D3)⋊C4—68no—
311(C2×D3)⋊C4—64no—
312(C2×D3)⋊C4—64no—
313(C2×D3)⋊C4—64no—
314(C2×D3)⋊C4—64no—
315(C2×D3)⋊C4—122no—
316(C2×D3)⋊C4—122no—
317(C2×D3)⋊C4—122no—
318(C2×D3)⋊C4—122no—
319C4⋊Dic3—22no—
320Dic3⋊C4—122no—
321Dic3⋊C4—122no—
322C4×Dic3—22no—
323C4×Dic3—122no—
324C4×Dic3—122no—
325C22×C32—24no—
326C22×C32—22no—
327C22×C32—22no—
328C22×C32—24no—
329C22×C32—22no—
330C22×C32—24no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—42no—
334C22×C32C4×D414yes—
335C22×C32C23×C411yescharacteristic
336C22×C32C22×D411yescharacteristic
337C22×C32C2×#4111yescharacteristic
338C22×C32H(5,𝔽2)12yes—
339C22×C32H(5,𝔽2)12yes—
340C2×C3⋊D3—24no—
341C2×C3⋊D3—24no—
342C2×C3⋊D3—24no—
343C2×C3⋊D3—416no—
344C2×C3⋊D3—42no—
345C2×C3⋊D3—42no—
346C2×C3⋊D3—42no—
347C2×C3⋊D3—42no—
348C32×C4—22no—
349C3⋊Dic3—24no—
350C3×Dic3—22no—
351C3×Dic3—22no—
352C3×Dic3—41no—
353C3×Dic3—41no—
354C3×Dic3—42no—
355C3×Dic3—42no—
356C25—91no—
357C22×D4—92no—
358C22×D4D3211yescharacteristic
359C23×C4—31no—
360C23×C4—31no—
361C23×C4—31no—
362#120—98no—
363C4×D4—64no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—92no—
366C2×C22⋊C4—31no—
367C2×C22⋊C4—31no—
368C2×C22⋊C4—31no—
369C2×C22⋊C4—32no—
370C2×C22⋊C4—91no—
371C2×C22⋊C4—92no—
372C2×C22⋊C4—92no—
373C2×C22⋊C4—92no—
374C2×C22⋊C4—92no—
375C2×C22⋊C4—92no—
376C2×C22⋊C4—184no—
377C2×C42—31no—
378C2×C42—92no—
379#95—32no—
380#95—92no—
381#95—92no—
382C23×C3—22no—
383C23×C3—22no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—42no—
400C23×C3—42no—
401C23×C3—42no—
402C23×C3—42no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3C2×C4×D312yes—
406C23×C3C2×C4×D312yes—
407C23×C3C2×C4×D312yes—
408C23×C3C2×C4×D312yes—
409C23×C3#23512yes—
410C23×C3D3×D412yes—
411C23×C3#23712yes—
412C23×C3C2×#6712yes—
413C23×C3C23×D311yescharacteristic
414C23×C3C23×D311yescharacteristic
415C22×D3—34no—
416C22×D3—34no—
417C22×D3—64no—
418C22×D3—64no—
419C22×D3—64no—
420C22×D3—68no—
421C22×D3—68no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—62no—
427C22×D3—62no—
428C22×D3—62no—
429C22×D3—62no—
430C22×D3—62no—
431C22×D3—62no—
432C22×D3—62no—
433C22×D3—62no—
434C22×D3—122no—
435C22×D3—122no—
436C22×D3—122no—
437C22×D3—122no—
438C22×D3—128no—
439C22×D3—128no—
440C22×D3—128no—
441C22×D3—1216no—
442C22×D3—124no—
443C22×D3—124no—
444C22×D3—128no—
445C22×D3—124no—
446C22×D3—124no—
447C22×D3—128no—
448C22×D3—1216no—
449C22×D3—128no—
450C22×D3—128no—
451C3×D4—28no—
452C3×D4—28no—
453C3×D4—48no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—22no—
459C2×C3×C4—32no—
460C2×C3×C4—32no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—62no—
464C2×C3×C4—62no—
465C2×C3×C4—62no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—62no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—124no—
476C2×C3×C4—124no—
477C2×C3×C4—124no—
478C2×C3×C4C2×C4×D312yes—
479C2×C3×C4C2×C4×D312yes—
480#67—128no—
481#67—128no—
482#67—1216no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—34no—
496C2×Dic3—34no—
497C2×Dic3—44no—
498C2×Dic3—44no—
499C2×Dic3—44no—
500C2×Dic3—64no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—62no—
504C2×Dic3—62no—
505C2×Dic3—122no—
506C2×Dic3—122no—
507C2×Dic3C2×#6712yes—
508C2×Dic3C2×#6712yes—
509C2×C32—24no—
510C2×C32—42no—
511C2×C32C2×C4×D411yescharacteristic
512C2×C32#51812yes—
513C2×C32#53411yescharacteristic
514C2×C32#53511yescharacteristic
515C2×C32#53812yes—
516C3⋊D3—44no—
517C24—92no—
518C24—94no—
519C24—182no—
520C24—182no—
521C24—362no—
522C24—362no—
523C24C2×D3211yescharacteristic
524C24C2×D3211yescharacteristic
525C2×D4—22no—
526C2×D4—22no—
527C2×D4—98no—
528C2×D4—362no—
529C2×D4—362no—
530C2×D4#62414yes—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—34no—
534C22×C4—32no—
535C22×C4—32no—
536C22×C4—31no—
537C22×C4—31no—
538C22×C4—62no—
539C22×C4—62no—
540C22×C4—92no—
541C22×C4—122no—
542C22×C4—122no—
543C22×C4—122no—
544C22×C4C2×D3211yescharacteristic
545C4⋊C4—62no—
546C4⋊C4—362no—
547C22⋊C4—62no—
548C22⋊C4—62no—
549C22⋊C4—62no—
550C22⋊C4—94no—
551C22⋊C4—98no—
552C22⋊C4—122no—
553C22⋊C4—184no—
554C22⋊C4—184no—
555C22⋊C4—362no—
556C22⋊C4—362no—
557C42—62no—
558C42—362no—
559C22×C3—22no—
560C22×C3—24no—
561C22×C3—24no—
562C22×C3—22no—
563C22×C3—24no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—24no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—24no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—44no—
582C22×C3—42no—
583C22×C3—41no—
584C22×C3—41no—
585C22×C3—42no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3—42no—
589C22×C3—82no—
590C22×C3—81no—
591C22×C3—81no—
592C22×C3#67⋊C414yes—
593C22×C3C4×#6714yes—
594C22×C3C22×C4×D311yescharacteristic
595C22×C3C22×C4×D311yescharacteristic
596C22×C3C2×#23511yescharacteristic
597C22×C3C2×D3×D411yescharacteristic
598C22×C3C2×#23711yescharacteristic
599C22×C3#100412yes—
600C22×C3#100412yes—
601C22×C3#100912yes—
602C22×C3#100912yes—
603C22×C3C22×#6711yescharacteristic
604C2×D3—68no—
605C2×D3—64no—
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—64no—
609C2×D3—64no—
610C2×D3—64no—
611C2×D3—124no—
612C2×D3—124no—
613C2×D3—1216no—
614C2×D3—1216no—
615C2×D3—124no—
616C2×D3—124no—
617C2×D3—124no—
618C2×D3—124no—
619C2×D3—1232no—
620C2×D3—122no—
621C2×D3—122no—
622C2×D3—122no—
623C2×D3—122no—
624C2×D3—122no—
625C2×D3—122no—
626C2×D3—122no—
627C2×D3—122no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—42no—
631C3×C4—62no—
632C3×C4—62no—
633C3×C4—121no—
634C3×C4—122no—
635C3×C4—122no—
636C3×C4—121no—
637Dic3—22no—
638Dic3—22no—
639Dic3—41no—
640Dic3—41no—
641Dic3—42no—
642Dic3—42no—
643Dic3—64no—
644Dic3—64no—
645Dic3—124no—
646C32#232111yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—21no—
652C23—21no—
653C23—94no—
654C23—182no—
655C23—182no—
656C23—182no—
657C23—182no—
658C23—182no—
659C23—182no—
660C23—188no—
661C23—368no—
662C23—368no—
663C23—364no—
664C23—364no—
665C23#380412yes—
666C23C2×#62412yes—
667C23C2×#62412yes—
668C23D3×#6712yes—
669C23C22×D3211yescharacteristic
670D4—28no—
671D4—368no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—32no—
675C2×C4—32no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—62no—
688C2×C4—94no—
689C2×C4—124no—
690C2×C4—124no—
691C2×C4—124no—
692C2×C4—182no—
693C2×C4—182no—
694C2×C4C2×#62412yes—
695C2×C3—24no—
696C2×C3—24no—
697C2×C3—21no—
698C2×C3—22no—
699C2×C3—22no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—44no—
703C2×C3—42no—
704C2×C3—42no—
705C2×C3—82no—
706C2×C3C2×#67⋊C411yescharacteristic
707C2×C3#554512yes—
708C2×C3#554512yes—
709C2×C3#556012yes—
710C2×C3#559211yescharacteristic
711C2×C3#561712yes—
712C2×C3#565311yescharacteristic
713C2×C3C2×C4×#6711yescharacteristic
714C2×C3#580411yescharacteristic
715C2×C3#583011yescharacteristic
716D3—128no—
717D3—124no—
718D3—124no—
719C22—24no—
720C22—24no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—24no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—184no—
729C22—184no—
730C22—184no—
731C22—3616no—
732C22—362no—
733C22—362no—
734C22—362no—
735C22—362no—
736C22#6395214yes—
737C22#6431412yes—
738C22#6431412yes—
739C22C2×#380411yescharacteristic
740C22C22×#62411yescharacteristic
741C22C2×D3×#6711yescharacteristic
742C4—22no—
743C4—62no—
744C4—62no—
745C4—122no—
746C4—121no—
747C4—122no—
748C4—121no—
749C4—184no—
750C3—21no—
751C3#7487511yescharacteristic, complemented
752C3#8239511yescharacteristic, complemented
753C2—24no—
754C2—42no—
755C2—364no—
756C2#1059522112yes—
757C2#1059522312yes—
758C2#1059523411yescharacteristic
759C2#1059523811yescharacteristic
760C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×#64146C2
hypercenterC22×D4D32
hypocenterC32#2321
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic3C2semidirect
3. C22×#3722C2semidirect
4. C3×#5220C2semidirect
5. #10591714C2semidirect
6. #10591711C2semidirect
7. #10591704C2semidirect
8. Dic3×#217C2semidirect
9. #10591693C2semidirect
10. #10591266C2semidirect
11. #10591202C2semidirect
19. C23×C3×Dic3C22semidirect
21. #64146C4semidirect
25. C2×C3×#217C22semidirect
26. C2×C3×#217C22semidirect
28. C2×C3×C4⋊Dic3C22semidirect
29. C2×C3×C4×Dic3C22semidirect
30. C2×#3724C22semidirect
36. C2×Dic32C22semidirect
37. C3×C3⋊#95C22semidirect
38. #63579C22semidirect
39. #63579C22semidirect
44. C2×D4×Dic3D3semidirect
48. #5220D3semidirect
69. C23×C3⋊D3C2×C4semidirect
77. C2×#638C2×C4semidirect
84. C22×C3×Dic3D4semidirect
91. #3757C2×C4semidirect
92. #3752C2×C4semidirect
120. C23×Dic3C2×D3semidirect
133. C2×#217C2×D3semidirect
134. C2×#217C2×D3semidirect
152. C2×C4⋊Dic3C2×D3semidirect
157. C2×C4×Dic3C2×D3semidirect
163. C3⋊#95C2×D3semidirect
288. C22×Dic3#67semidirect
646. C32#2321semidirect
751. C3#74875semidirect
752. C3#82395semidirect

Maximal subgroups

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

subgroupindex
C2×#641462
C2×C3×D4×Dic32
C22×#37222
C3×#52202
#105917142
#105917112
#105917042
Dic3×#2172
#105916932
#105912662
#105912022
#823953
#748753