Finite Group Databasebeta

← #11806905

Subgroups — #11806905

Order 1152.

1913 conjugacy classes of subgroups.

The subgroup lattice has 767 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×#63952C212yesmaximal, complemented
4C2×#63894C211yesmaximal, characteristic, complemented
5C3×#5221C211yesmaximal, characteristic, complemented
6#10591722C212yesmaximal, complemented
7#10591711C212yesmaximal, complemented
8#10591704C212yesmaximal, complemented
9C4×#3724C211yesmaximal, characteristic, complemented
10#10591320C211yesmaximal, characteristic, complemented
11#10591274C211yesmaximal, characteristic, complemented
12#82343—31nomaximal
13#76306—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×#638C2212yes—
16C22×#638C2212yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C23×C3×Dic3C2212yes—
19C22×#624C2212yes—
20#64149C418yescomplemented
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C3×D4×Dic3—24no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3722C2212yes—
33C2×#3722C2212yes—
34C2×#3722C2212yes—
35C2×Dic32C2212yes—
36#63952—28no—
37#63894—24no—
38#63579C2212yes—
39#63579C2211yescharacteristic
40#63579C2211yescharacteristic
41C2×C3×C4×D4—31no—
42C2×#940—31no—
43C2×#940—31no—
44C2×#940—61no—
45C2×D4×Dic3D311yescharacteristic, complemented
46C2×C4×#67—32no—
47C2×#893—31no—
48C2×#67⋊C4—32no—
49C2×C4×D12—31no—
50C3×#390—31no—
51#5221D311yescharacteristic, complemented
52#5213—32no—
53#4988—31no—
54Dic3×C4⋊C4—31no—
55Dic3×C4⋊C4—31no—
56#4958—32no—
57#4957—32no—
58#4957—32no—
59#4956—32no—
60#4956—32no—
61#4939—31no—
62C4×Dic3⋊C4—31no—
63C4×Dic3⋊C4—31no—
64C24×C32C2312yes—
65C23×C3⋊D3C2312yes—
66C2×C32×D4—22no—
67C2×C32×D4—22no—
68C2×C32×D4C2×C414yescomplemented
69C22×C32×C4C2311yescharacteristic
70C2×#638—24no—
71C2×#638—24no—
72C2×#638—42no—
73C2×#638—42no—
74C2×#638C2×C418yescomplemented
75C2×#638C2×C418yescomplemented
76C22×C3⋊Dic3C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C2×C4⋊(C3⋊D3)—22no—
79C2×C4⋊(C3⋊D3)—22no—
80C2×C4⋊(C3⋊D3)C2×C414yescomplemented
81C22×C3×Dic3—24no—
82C22×C3×Dic3—24no—
83C22×C3×Dic3—42no—
84C22×C3×Dic3C2311yescharacteristic
85C22×C3×Dic3C2311yescharacteristic
86C22×C3×Dic3C2312yes—
87C22×C3×Dic3C2311yescharacteristic
88C22×C3×Dic3C2311yescharacteristic
89C22×C3×Dic3C2312yes—
90C2×#624—24no—
91C2×#624—24no—
92C2×#624—42no—
93C4×C3⋊Dic3C2×C414yescomplemented
94C3×#217—24no—
95C3×#217—24no—
96C3×#217—42no—
97C3×C4⋊Dic3—22no—
98C3×C4⋊Dic3D414yescomplemented
99C3×C4×Dic3—22no—
100C3×C4×Dic3—22no—
101#3724—22no—
102#3724D414yescomplemented
103#3722—24no—
104#3722—24no—
105#3722—42no—
106Dic32—24no—
107#2366—91noSylow
108C22×C3×D4—21no—
109C22×C3×D4C2×D311yescharacteristic
110C22×C3×D4C2×D311yescharacteristic
111C23×C3×C4—32no—
112C22×#67—32no—
113C22×#67—32no—
114C22×#67—32no—
115C22×#67—32no—
116C22×#67—62no—
117C22×#67—62no—
118C23×Dic3C2×D312yes—
119C22×D12—31no—
120C22×D12—31no—
121C22×D12—61no—
122C22×C4×D3—32no—
123C22×C4×D3—32no—
124C3×C4×D4—64no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C22⋊C4—32no—
128C2×C3×C22⋊C4—32no—
129C2×C3×C22⋊C4—32no—
130C2×C3×C42—31no—
131C2×C3×C42—31no—
132C2×#217C2×D312yes—
133C2×#217C2×D312yes—
134C2×#217C2×D312yes—
135#940—38no—
136#940—38no—
137#940—68no—
138D4×Dic3—24no—
139C4×#67—68no—
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×C4⋊Dic3C2×D311yescharacteristic
147C2×C4⋊Dic3C2×D311yescharacteristic
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—32no—
155C2×C4×Dic3—32no—
156C2×C4×Dic3—61no—
157C2×C4×Dic3C2×D311yescharacteristic
158C2×C4×Dic3C2×D311yescharacteristic
159#893—64no—
160#67⋊C4—68no—
161C4×D12—64no—
162C3⋊#95—31no—
163C3⋊#95—31no—
164C3⋊#95—31no—
165C3⋊#95—31no—
166C3⋊#95—32no—
167C3⋊#95—32no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—22no—
172C23×C32—22no—
173C23×C32—22no—
174C23×C32C22×C414yes—
175C23×C32C2411yescharacteristic
176C22×C3⋊D3—22no—
177C22×C3⋊D3—22no—
178C22×C3⋊D3—22no—
179C22×C3⋊D3—22no—
180C22×C3⋊D3—22no—
181C22×C3⋊D3—22no—
182C22×C3⋊D3C22×C414yes—
183C32×D4—28no—
184C2×C32×C4C22×C412yes—
185C2×C32×C4C2×D412yes—
186C2×C32×C4#4112yes—
187#638—216no—
188#638—48no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3C22×C412yes—
192C2×C3⋊Dic3C22×C412yes—
193C2×C3⋊Dic3C2×D412yes—
194C2×C3⋊Dic3#4112yes—
195C4⋊(C3⋊D3)—28no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—21no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—22no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3—21no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—21no—
209C2×C3×Dic3—22no—
210C2×C3×Dic3—21no—
211C2×C3×Dic3—48no—
212C2×C3×Dic3C2×D412yes—
213C2×C3×Dic3C2×D412yes—
214C2×C3×Dic3C2×D414yes—
215#624—48no—
216C2×#127—91no—
217C2×C4×D4—31no—
218C2×C4×D4—91no—
219C2×C4×D4—92no—
220#390—31no—
221#390—91no—
222#390—92no—
223#386—92no—
224#386—92no—
225C4×C4⋊C4—91no—
226C4×C4⋊C4—91no—
227C24×C3—22no—
228C24×C3C22×D312yes—
229C24×C3C22×D312yes—
230C23×D3—32no—
231C23×D3—32no—
232C23×D3—62no—
233C2×C3×D4—22no—
234C2×C3×D4—22no—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—24no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4C4×D314yescomplemented
241C2×C3×D4C4×D314yescomplemented
242C22×C3×C4—21no—
243C22×C3×C4—32no—
244C22×C3×C4—31no—
245C22×C3×C4—31no—
246C22×C3×C4—32no—
247C22×C3×C4—31no—
248C22×C3×C4—31no—
249C22×C3×C4—64no—
250C22×C3×C4—64no—
251C22×C3×C4—122no—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C22×D311yescharacteristic
254C2×#67—38no—
255C2×#67—38no—
256C2×#67—38no—
257C2×#67—38no—
258C2×#67—68no—
259C2×#67—68no—
260C2×#67—64no—
261C2×#67—64no—
262C2×#67—64no—
263C2×#67—64no—
264C2×#67—124no—
265C2×#67—124no—
266C2×#67—122no—
267C2×#67—122no—
268C2×#67—122no—
269C2×#67—122no—
270C2×#67—124no—
271C2×#67—124no—
272C22×Dic3—24no—
273C22×Dic3—24no—
274C22×Dic3—31no—
275C22×Dic3—31no—
276C22×Dic3—31no—
277C22×Dic3—31no—
278C22×Dic3—42no—
279C22×Dic3—61no—
280C22×Dic3—61no—
281C22×Dic3C22×D312yes—
282C22×Dic3C22×D311yescharacteristic
283C22×Dic3C22×D311yescharacteristic
284C22×Dic3C22×D311yescharacteristic
285C22×Dic3C22×D311yescharacteristic
286C22×Dic3C22×D312yes—
287C2×D12—34no—
288C2×D12—34no—
289C2×D12—64no—
290C2×D12—62no—
291C2×D12—62no—
292C2×D12—62no—
293C2×D12—62no—
294C2×D12—122no—
295C2×D12—122no—
296C2×C4×D3—64no—
297C2×C4×D3—64no—
298C2×C4×D3—64no—
299C2×C4×D3—64no—
300C2×C4×D3—122no—
301C2×C4×D3—122no—
302C3×C4⋊C4—34no—
303C3×C4⋊C4—62no—
304C3×C22⋊C4—64no—
305C3×C22⋊C4—64no—
306C3×C22⋊C4—122no—
307C3×C42—62no—
308C3×C42—62no—
309#217—24no—
310#217—24no—
311#217—42no—
312(C2×D3)⋊C4—64no—
313(C2×D3)⋊C4—64no—
314(C2×D3)⋊C4—64no—
315(C2×D3)⋊C4—64no—
316(C2×D3)⋊C4—122no—
317(C2×D3)⋊C4—122no—
318C4⋊Dic3—22no—
319C4⋊Dic3#6714yescomplemented
320Dic3⋊C4—34no—
321Dic3⋊C4—34no—
322Dic3⋊C4—62no—
323Dic3⋊C4—62no—
324C4×Dic3—22no—
325C4×Dic3—22no—
326C4×Dic3—34no—
327C4×Dic3—34no—
328C4×Dic3—64no—
329C4×Dic3—64no—
330C4×Dic3—64no—
331C22×C32—24no—
332C22×C32—24no—
333C22×C32—24no—
334C22×C32—42no—
335C22×C32—42no—
336C22×C32—42no—
337C22×C32—42no—
338C22×C32C23×C411yescharacteristic
339C22×C32C22×D411yescharacteristic
340C22×C32C22×D411yescharacteristic
341C22×C32C2×#4111yescharacteristic
342C22×C32C2×#4111yescharacteristic
343C22×C32H(5,𝔽2)11yescharacteristic
344C22×C32H(5,𝔽2)11yescharacteristic
345C2×C3⋊D3—24no—
346C2×C3⋊D3—24no—
347C2×C3⋊D3—24no—
348C2×C3⋊D3—42no—
349C2×C3⋊D3—42no—
350C2×C3⋊D3—42no—
351C2×C3⋊D3—42no—
352C32×C4C4×D414yescomplemented
353C3⋊Dic3—22no—
354C3⋊Dic3C4×D414yescomplemented
355C3×Dic3—22no—
356C3×Dic3—24no—
357C3×Dic3—22no—
358C3×Dic3—42no—
359C3×Dic3—41no—
360C3×Dic3—41no—
361C22×D4—92no—
362C22×D4—92no—
363C22×D4—91no—
364C22×D4D3211yescharacteristic
365C23×C4—32no—
366C23×C4—92no—
367#127—98no—
368C4×D4—64no—
369C4×D4—184no—
370C4×D4—188no—
371C2×C4⋊C4—31no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—91no—
374C2×C4⋊C4—91no—
375C2×C22⋊C4—32no—
376C2×C22⋊C4—32no—
377C2×C22⋊C4—32no—
378C2×C22⋊C4—92no—
379C2×C22⋊C4—92no—
380C2×C22⋊C4—92no—
381C2×C42—31no—
382C2×C42—31no—
383C2×C42—91no—
384C2×C42—92no—
385#95—91no—
386#95—91no—
387#95—92no—
388C23×C3—22no—
389C23×C3—22no—
390C23×C3—22no—
391C23×C3—22no—
392C23×C3—22no—
393C23×C3—22no—
394C23×C3—22no—
395C23×C3—22no—
396C23×C3—22no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—24no—
402C23×C3—42no—
403C23×C3—42no—
404C23×C3—42no—
405C23×C3—42no—
406C23×C3—42no—
407C23×C3—42no—
408C23×C3C2×C4×D314yes—
409C23×C3C2×C4×D314yes—
410C23×C3C23×D311yescharacteristic
411C23×C3C23×D311yescharacteristic
412C22×D3—34no—
413C22×D3—34no—
414C22×D3—64no—
415C22×D3—62no—
416C22×D3—62no—
417C22×D3—62no—
418C22×D3—62no—
419C22×D3—62no—
420C22×D3—62no—
421C22×D3—62no—
422C22×D3—62no—
423C22×D3—62no—
424C22×D3—62no—
425C22×D3—62no—
426C22×D3—62no—
427C22×D3—122no—
428C22×D3—122no—
429C22×D3—122no—
430C22×D3—122no—
431C22×D3—122no—
432C22×D3—122no—
433C3×D4—28no—
434C3×D4—28no—
435C3×D4—48no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—32no—
440C2×C3×C4—32no—
441C2×C3×C4—34no—
442C2×C3×C4—62no—
443C2×C3×C4—61no—
444C2×C3×C4—61no—
445C2×C3×C4—62no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—62no—
449C2×C3×C4—62no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—61no—
453C2×C3×C4—61no—
454C2×C3×C4—62no—
455C2×C3×C4—61no—
456C2×C3×C4—61no—
457C2×C3×C4—128no—
458C2×C3×C4C2×C4×D312yes—
459C2×C3×C4C2×C4×D312yes—
460C2×C3×C4#23512yes—
461C2×C3×C4D3×D412yes—
462C2×C3×C4#23712yes—
463C2×C3×C4C2×#6712yes—
464#67—616no—
465#67—616no—
466#67—1216no—
467#67—128no—
468#67—128no—
469#67—1216no—
470C2×Dic3—21no—
471C2×Dic3—22no—
472C2×Dic3—22no—
473C2×Dic3—21no—
474C2×Dic3—21no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—22no—
478C2×Dic3—22no—
479C2×Dic3—22no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—32no—
486C2×Dic3—32no—
487C2×Dic3—32no—
488C2×Dic3—32no—
489C2×Dic3—32no—
490C2×Dic3—32no—
491C2×Dic3—32no—
492C2×Dic3—32no—
493C2×Dic3—48no—
494C2×Dic3—62no—
495C2×Dic3—62no—
496C2×Dic3—62no—
497C2×Dic3—62no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—61no—
501C2×Dic3—61no—
502C2×Dic3—61no—
503C2×Dic3—61no—
504C2×Dic3D3×D412yes—
505C2×Dic3D3×D412yes—
506C2×Dic3C2×#6714yes—
507D12—68no—
508D12—68no—
509D12—128no—
510C4×D3—128no—
511C4×D3—128no—
512C2×C32—44no—
513C2×C32C2×C4×D411yescharacteristic
514C2×C32C2×C4×D411yescharacteristic
515C2×C32#51811yescharacteristic
516C2×C32D4211yescharacteristic
517C2×C32#55011yescharacteristic
518C2×C32#55011yescharacteristic
519C2×C32#55911yescharacteristic
520C3⋊D3—44no—
521C24—92no—
522C24C2×D3212yes—
523C2×D4—22no—
524C2×D4—22no—
525C2×D4—98no—
526C2×D4—98no—
527C2×D4—94no—
528C2×D4—184no—
529C2×D4—184no—
530C2×D4—182no—
531C2×D4—182no—
532C2×D4—362no—
533C2×D4—362no—
534C2×D4#62414yescomplemented
535C22×C4—31no—
536C22×C4—31no—
537C22×C4—32no—
538C22×C4—31no—
539C22×C4—31no—
540C22×C4—32no—
541C22×C4—64no—
542C22×C4—64no—
543C22×C4—91no—
544C22×C4—91no—
545C22×C4—122no—
546C22×C4—184no—
547C22×C4—184no—
548C22×C4—362no—
549C22×C4C2×D3211yescharacteristic
550C4⋊C4—34no—
551C4⋊C4—62no—
552C4⋊C4—94no—
553C4⋊C4—182no—
554C22⋊C4—64no—
555C22⋊C4—64no—
556C22⋊C4—122no—
557C22⋊C4—184no—
558C22⋊C4—184no—
559C22⋊C4—362no—
560C42—62no—
561C42—62no—
562C42—94no—
563C42—184no—
564C22×C3—24no—
565C22×C3—24no—
566C22×C3—24no—
567C22×C3—24no—
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—21no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—44no—
578C22×C3—44no—
579C22×C3—44no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—42no—
584C22×C3—42no—
585C22×C3—42no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—82no—
589C22×C3—82no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3C22×C4×D311yescharacteristic
593C22×C3C22×C4×D311yescharacteristic
594C22×C3C2×#23511yescharacteristic
595C22×C3C2×D3×D411yescharacteristic
596C22×C3C2×D3×D411yescharacteristic
597C22×C3C2×D3×D411yescharacteristic
598C22×C3C2×#23711yescharacteristic
599C22×C3#100411yescharacteristic
600C22×C3#100411yescharacteristic
601C22×C3D3×#4111yescharacteristic
602C22×C3D3×#4111yescharacteristic
603C22×C3#100911yescharacteristic
604C22×C3#100911yescharacteristic
605C22×C3C22×#6711yescharacteristic
606C2×D3—64no—
607C2×D3—64no—
608C2×D3—64no—
609C2×D3—64no—
610C2×D3—64no—
611C2×D3—64no—
612C2×D3—124no—
613C2×D3—124no—
614C2×D3—124no—
615C2×D3—122no—
616C2×D3—122no—
617C2×D3—122no—
618C2×D3—122no—
619C2×D3—122no—
620C2×D3—122no—
621C2×D3—122no—
622C2×D3—122no—
623C2×D3—242no—
624C2×D3—242no—
625C2×D3—242no—
626C2×D3—242no—
627C3×C4—24no—
628C3×C4—62no—
629C3×C4—64no—
630C3×C4—62no—
631C3×C4—122no—
632C3×C4—121no—
633C3×C4—121no—
634C3×C4#67⋊C414yescomplemented
635C3×C4C4×#6714yescomplemented
636Dic3—24no—
637Dic3—22no—
638Dic3—22no—
639Dic3—34no—
640Dic3—34no—
641Dic3—42no—
642Dic3—41no—
643Dic3—41no—
644Dic3—64no—
645Dic3—64no—
646Dic3—62no—
647Dic3—62no—
648C32#236611yescharacteristic, complemented, Sylow
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—94no—
656C23—182no—
657C23—182no—
658C23—182no—
659C23—182no—
660C23—182no—
661C23—182no—
662C23C2×#62414yes—
663C23C22×D3211yescharacteristic
664D4—28no—
665D4—1816no—
666D4—188no—
667D4—368no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—34no—
671C2×C4—62no—
672C2×C4—61no—
673C2×C4—62no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—62no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—62no—
682C2×C4—61no—
683C2×C4—62no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—92no—
687C2×C4—92no—
688C2×C4—92no—
689C2×C4—92no—
690C2×C4—128no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—368no—
694C2×C4#380412yes—
695C2×C4C2×#62412yes—
696C2×C4D3×#6712yes—
697C2×C3—21no—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—44no—
705C2×C3—44no—
706C2×C3—84no—
707C2×C3C2×#67⋊C411yescharacteristic
708C2×C3C4×D3×D411yescharacteristic
709C2×C3C4×D3×D411yescharacteristic
710C2×C3#554511yescharacteristic
711C2×C3#554511yescharacteristic
712C2×C3#555311yescharacteristic
713C2×C3#555911yescharacteristic
714C2×C3#559911yescharacteristic
715C2×C3#560911yescharacteristic
716C2×C3#568111yescharacteristic
717C2×C3#571811yescharacteristic
718C2×C3C2×C4×#6711yescharacteristic
719C2×C3D4×#6711yescharacteristic
720C2×C3#583411yescharacteristic
721D3—124no—
722D3—124no—
723D3—244no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—184no—
732C22—184no—
733C22—184no—
734C22—362no—
735C22—362no—
736C22—362no—
737C22—362no—
738C22D32×D411yescharacteristic
739C22#6431211yescharacteristic
740C22#6431411yescharacteristic
741C22#6431411yescharacteristic
742C22C2×#380411yescharacteristic
743C22C22×#62411yescharacteristic
744C22C2×D3×#6711yescharacteristic
745C4—62no—
746C4—64no—
747C4—62no—
748C4—94no—
749C4—122no—
750C4—121no—
751C4—121no—
752C4—182no—
753C4#6395214yescomplemented
754C3—21no—
755C3#7630611yescharacteristic, complemented
756C3#8234311yescharacteristic, complemented
757C2—44no—
758C2—364no—
759C2D4×#62411yescharacteristic
760C2#1059514311yescharacteristic
761C2#1059521011yescharacteristic
762C2#1059522311yescharacteristic
763C2#1059523611yescharacteristic
764C2#1059528811yescharacteristic
765C2C2×#6395211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×#64149C2
hypercenterC22×D4D32
hypocenterC32#2366
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. C2×#63952C2semidirect
4. C2×#63894C2semidirect
5. C3×#5221C2semidirect
6. #10591722C2semidirect
7. #10591711C2semidirect
8. #10591704C2semidirect
9. C4×#3724C2semidirect
10. #10591320C2semidirect
11. #10591274C2semidirect
20. #64149C4semidirect
45. C2×D4×Dic3D3semidirect
51. #5221D3semidirect
68. C2×C32×D4C2×C4semidirect
74. C2×#638C2×C4semidirect
75. C2×#638C2×C4semidirect
80. C2×C4⋊(C3⋊D3)C2×C4semidirect
93. C4×C3⋊Dic3C2×C4semidirect
98. C3×C4⋊Dic3D4semidirect
102. #3724D4semidirect
240. C2×C3×D4C4×D3semidirect
241. C2×C3×D4C4×D3semidirect
319. C4⋊Dic3#67semidirect
352. C32×C4C4×D4semidirect
354. C3⋊Dic3C4×D4semidirect
534. C2×D4#624semidirect
634. C3×C4#67⋊C4semidirect
635. C3×C4C4×#67semidirect
648. C32#2366semidirect
753. C4#63952semidirect
755. C3#76306semidirect
756. C3#82343semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×C3×D4×Dic32
C2×#639522
C2×#638942
C3×#52212
#105917222
#105917112
#105917042
C4×#37242
#105913202
#105912742
#823433
#763063