Finite Group Databasebeta

← #11804765

Subgroups — #11804765

Order 1152.

3185 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#638C211yesmaximal, characteristic
2C22×C3×#217C211yesmaximal, characteristic, complemented
3C2×#63974C211yesmaximal, characteristic, complemented
4C2×#63952C212yesmaximal, complemented
5C3×#5247C211yesmaximal, characteristic, complemented
6#10591722C212yesmaximal, complemented
7#10591720C211yesmaximal, characteristic, complemented
8#10591714C211yesmaximal, characteristic, complemented
9#10591711C212yesmaximal, complemented
10#10591705C211yesmaximal, characteristic, complemented
11#10591704C212yesmaximal, complemented
12C22⋊C4×#67—31nomaximal
13#73850—31nomaximal
14C25×C32C2211yescharacteristic
15C24×C3⋊D3C2211yescharacteristic
16C22×#638—28no—
17C22×#638C418yescomplemented
18C22×#638C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×#638C2211yescharacteristic
21C22×#638C2211yescharacteristic
22C23×C3⋊Dic3C2211yescharacteristic
23C23×C3×Dic3C2212yescomplemented
24C22×#624C2212yescomplemented
25C2×C3×#217—24no—
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2212yescomplemented
31C2×C3×#217C2212yescomplemented
32C2×C3×#217C2212yescomplemented
33#63974—24no—
34C2×#3724C2212yescomplemented
35C2×#3722C2212yescomplemented
36C2×#3722C2212yescomplemented
37C2×#3722C2212yescomplemented
38C2×Dic32C2212yescomplemented
39#63952—28no—
40#63579C2212yescomplemented
41#63579C2212yescomplemented
42C23×#67—31no—
43C23×#67—31no—
44C23×#67—61no—
45C22×C3×C22⋊C4—31no—
46C22×#217D311yescharacteristic, complemented
47C2×C4×#67—32no—
48C2×#67⋊C4—32no—
49C2×D3×C22⋊C4—31no—
50C2×D3×C22⋊C4—31no—
51C3×#379—31no—
52#5247D311yescharacteristic, complemented
53#5213—32no—
54#4958—32no—
55#4957—32no—
56#4957—32no—
57#4956—32no—
58#4956—32no—
59#4955—31no—
60#4955—31no—
61#4942—31no—
62#4942—31no—
63Dic3×C22⋊C4—31no—
64Dic3×C22⋊C4—31no—
65C24×C32—24no—
66C24×C32—22no—
67C24×C32—22no—
68C24×C32—42no—
69C24×C32C2×C414yescomplemented
70C24×C32C2311yescharacteristic
71C24×C32C2311yescharacteristic
72C24×C32C2311yescharacteristic
73C23×C3⋊D3—22no—
74C23×C3⋊D3—22no—
75C23×C3⋊D3—24no—
76C23×C3⋊D3—42no—
77C23×C3⋊D3C2×C414yescomplemented
78C23×C3⋊D3C2311yescharacteristic
79C23×C3⋊D3C2311yescharacteristic
80C2×#638—24no—
81C2×#638—24no—
82C2×#638—232no—
83C2×#638—24no—
84C2×#638C2×C414yes—
85C2×#638C2×C414yescomplemented
86C2×#638C2×C414yescomplemented
87C2×#638C2×C414yescomplemented
88C2×#638D418yes—
89C22×C3⋊Dic3—24no—
90C22×C3⋊Dic3C2×C414yescomplemented
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3×Dic3—24no—
94C22×C3×Dic3—24no—
95C22×C3×Dic3—42no—
96C22×C3×Dic3C2312yes—
97C22×C3×Dic3C2312yes—
98C22×C3×Dic3C2312yes—
99C22×C3×Dic3C2312yes—
100C2×#624—24no—
101C2×#624—24no—
102C2×#624—42no—
103C3×#217—22no—
104C3×#217—22no—
105C3×#217—24no—
106C3×#217—22no—
107C3×#217—24no—
108C3×#217—42no—
109C3×#217D414yescomplemented
110#3724—24no—
111#3722—24no—
112#3722—24no—
113#3722—42no—
114Dic32—24no—
115D4×C22⋊C4—91noSylow
116C25×C3—21no—
117C25×C3C2×D311yescharacteristic
118C25×C3C2×D311yescharacteristic
119C24×D3—31no—
120C24×D3—31no—
121C24×D3—61no—
122C23×C3×C4—32no—
123C22×#67—31no—
124C22×#67—31no—
125C22×#67—38no—
126C22×#67—38no—
127C22×#67—31no—
128C22×#67—31no—
129C22×#67—31no—
130C22×#67—31no—
131C22×#67—31no—
132C22×#67—31no—
133C22×#67—68no—
134C22×#67—61no—
135C22×#67—61no—
136C22×#67—61no—
137C22×#67—61no—
138C22×#67—68no—
139C22×#67—68no—
140C22×#67—616no—
141C23×Dic3—31no—
142C23×Dic3—31no—
143C23×Dic3—61no—
144C23×Dic3C2×D312yescomplemented
145C22×C4×D3—32no—
146C22×C4×D3—32no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×C3×C22⋊C4—31no—
150C2×C3×C22⋊C4—31no—
151C2×C3×C22⋊C4—32no—
152C2×C3×C22⋊C4—32no—
153C2×C3×C22⋊C4—32no—
154C2×C3×C22⋊C4—64no—
155C2×#217—24no—
156C2×#217C2×D311yescharacteristic
157C2×#217C2×D311yescharacteristic
158C2×#217C2×D311yescharacteristic
159C2×#217C2×D311yescharacteristic
160C2×#217C2×D312yescomplemented
161C2×#217C2×D312yescomplemented
162C2×#217C2×D312yescomplemented
163C4×#67—68no—
164C2×(C2×D3)⋊C4—32no—
165C2×(C2×D3)⋊C4—32no—
166C2×(C2×D3)⋊C4—32no—
167C2×(C2×D3)⋊C4—32no—
168C2×(C2×D3)⋊C4—32no—
169C2×(C2×D3)⋊C4—32no—
170C2×Dic3⋊C4—32no—
171C2×Dic3⋊C4—32no—
172C2×C4×Dic3—32no—
173C2×C4×Dic3—32no—
174#67⋊C4—68no—
175D3×C22⋊C4—64no—
176D3×C22⋊C4—64no—
177C3⋊#95—32no—
178C3⋊#95—32no—
179C3⋊#95—32no—
180C3⋊#95—32no—
181C23×C32—22no—
182C23×C32—22no—
183C23×C32—28no—
184C23×C32—22no—
185C23×C32—21no—
186C23×C32—21no—
187C23×C32—22no—
188C23×C32—28no—
189C23×C32—21no—
190C23×C32—21no—
191C23×C32—22no—
192C23×C32—44no—
193C23×C32—48no—
194C23×C32—48no—
195C23×C32C22×C412yes—
196C23×C32C22×C412yes—
197C23×C32C22×C412yes—
198C23×C32C2×D414yes—
199C23×C32C2×D412yes—
200C23×C32#4112yes—
201C23×C32C2411yescharacteristic
202C22×C3⋊D3—22no—
203C22×C3⋊D3—28no—
204C22×C3⋊D3—21no—
205C22×C3⋊D3—21no—
206C22×C3⋊D3—22no—
207C22×C3⋊D3—28no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—22no—
211C22×C3⋊D3—44no—
212C22×C3⋊D3—48no—
213C22×C3⋊D3—48no—
214C22×C3⋊D3C22×C412yes—
215C22×C3⋊D3C22×C412yes—
216C22×C3⋊D3C2×D414yes—
217#638—28no—
218#638—28no—
219#638—28no—
220#638C22⋊C4116yescomplemented
221C2×C3⋊Dic3—22no—
222C2×C3⋊Dic3—28no—
223C2×C3⋊Dic3C22×C412yes—
224C2×C3⋊Dic3C22×C412yes—
225C2×C3⋊Dic3C2×D414yes—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3—22no—
231C2×C3×Dic3—22no—
232C2×C3×Dic3—22no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—22no—
237C2×C3×Dic3—48no—
238C2×C3×Dic3C2×D414yescomplemented
239#624—48no—
240C23×D4—91no—
241C2×C4×D4—92no—
242C22×C22⋊C4—31no—
243C22×C22⋊C4—91no—
244#390—92no—
245#386—92no—
246#386—92no—
247#380—91no—
248#379—31no—
249#379—91no—
250C4×C22⋊C4—91no—
251C24×C3—28no—
252C24×C3—22no—
253C24×C3—22no—
254C24×C3—24no—
255C24×C3—24no—
256C24×C3—22no—
257C24×C3—22no—
258C24×C3—24no—
259C24×C3—21no—
260C24×C3—21no—
261C24×C3—21no—
262C24×C3—42no—
263C24×C3—42no—
264C24×C3—42no—
265C24×C3—42no—
266C24×C3—44no—
267C24×C3C4×D314yescomplemented
268C24×C3C4×D314yescomplemented
269C24×C3C22×D311yescharacteristic
270C24×C3C22×D311yescharacteristic
271C24×C3C22×D311yescharacteristic
272C24×C3C22×D311yescharacteristic
273C24×C3C22×D311yescharacteristic
274C24×C3C22×D311yescharacteristic
275C23×D3—31no—
276C23×D3—31no—
277C23×D3—31no—
278C23×D3—31no—
279C23×D3—34no—
280C23×D3—34no—
281C23×D3—64no—
282C23×D3—61no—
283C23×D3—61no—
284C23×D3—64no—
285C23×D3—64no—
286C23×D3—68no—
287C23×D3—62no—
288C23×D3—62no—
289C23×D3—62no—
290C23×D3—62no—
291C23×D3—122no—
292C23×D3—122no—
293C23×D3—122no—
294C23×D3—122no—
295C23×D3—124no—
296C22×C3×C4—32no—
297C22×C3×C4—32no—
298C22×C3×C4—32no—
299C22×C3×C4—32no—
300C22×C3×C4—64no—
301C22×C3×C4—64no—
302C22×C3×C4—122no—
303C2×#67—34no—
304C2×#67—34no—
305C2×#67—38no—
306C2×#67—38no—
307C2×#67—34no—
308C2×#67—34no—
309C2×#67—34no—
310C2×#67—34no—
311C2×#67—34no—
312C2×#67—34no—
313C2×#67—64no—
314C2×#67—64no—
315C2×#67—64no—
316C2×#67—64no—
317C2×#67—68no—
318C2×#67—64no—
319C2×#67—64no—
320C2×#67—632no—
321C2×#67—632no—
322C2×#67—64no—
323C2×#67—64no—
324C2×#67—68no—
325C2×#67—664no—
326C2×#67—68no—
327C2×#67—68no—
328C2×#67—64no—
329C2×#67—64no—
330C22×Dic3—24no—
331C22×Dic3—24no—
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—34no—
335C22×Dic3—34no—
336C22×Dic3—31no—
337C22×Dic3—31no—
338C22×Dic3—42no—
339C22×Dic3—64no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—64no—
343C22×Dic3—64no—
344C22×Dic3—68no—
345C22×Dic3C22×D312yes—
346C22×Dic3C22×D312yes—
347C22×Dic3C22×D312yes—
348C22×Dic3C22×D312yes—
349C2×C4×D3—64no—
350C2×C4×D3—64no—
351C2×C4×D3—64no—
352C2×C4×D3—64no—
353C2×C4×D3—122no—
354C2×C4×D3—122no—
355C3×C22⋊C4—34no—
356C3×C22⋊C4—64no—
357C3×C22⋊C4—62no—
358C3×C22⋊C4—64no—
359C3×C22⋊C4—62no—
360C3×C22⋊C4—62no—
361C3×C22⋊C4—122no—
362#217—22no—
363#217—24no—
364#217—22no—
365#217—22no—
366#217—24no—
367#217—42no—
368#217#6714yescomplemented
369(C2×D3)⋊C4—64no—
370(C2×D3)⋊C4—64no—
371(C2×D3)⋊C4—64no—
372(C2×D3)⋊C4—64no—
373(C2×D3)⋊C4—122no—
374(C2×D3)⋊C4—122no—
375Dic3⋊C4—64no—
376Dic3⋊C4—64no—
377C4×Dic3—64no—
378C4×Dic3—64no—
379C22×C32—22no—
380C22×C32—22no—
381C22×C32—24no—
382C22×C32—24no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32—22no—
386C22×C32—24no—
387C22×C32—24no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—416no—
391C22×C32—42no—
392C22×C32—42no—
393C22×C32C2×C22⋊C414yescomplemented
394C22×C32C4×D414yescomplemented
395C22×C32C23×C411yescharacteristic
396C22×C32C22×D412yes—
397C22×C32C22×D411yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32H(5,𝔽2)12yes—
400C2×C3⋊D3—22no—
401C2×C3⋊D3—22no—
402C2×C3⋊D3—22no—
403C2×C3⋊D3—24no—
404C2×C3⋊D3—24no—
405C2×C3⋊D3—22no—
406C2×C3⋊D3—22no—
407C2×C3⋊D3—416no—
408C2×C3⋊D3—42no—
409C2×C3⋊D3—42no—
410C2×C3⋊D3C2×C22⋊C414yescomplemented
411C3⋊Dic3—22no—
412C3⋊Dic3C2×C22⋊C414yescomplemented
413C3×Dic3—24no—
414C3×Dic3—42no—
415C3×Dic3—42no—
416C3×Dic3—42no—
417C25—91no—
418C25D3211yescharacteristic
419C22×D4—91no—
420C22×D4—98no—
421C22×D4—91no—
422C22×D4—91no—
423C22×D4—91no—
424C22×D4—188no—
425C23×C4—32no—
426C23×C4—92no—
427C23×C4—91no—
428C4×D4—188no—
429C2×C4⋊C4—92no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—32no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—32no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—32no—
437C2×C22⋊C4—64no—
438C2×C22⋊C4—92no—
439C2×C22⋊C4—92no—
440C2×C22⋊C4—92no—
441C2×C22⋊C4—184no—
442C2×C42—92no—
443#95—92no—
444#95—92no—
445C23×C3—24no—
446C23×C3—24no—
447C23×C3—21no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—21no—
457C23×C3—24no—
458C23×C3—216no—
459C23×C3—28no—
460C23×C3—28no—
461C23×C3—28no—
462C23×C3—28no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—21no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—24no—
478C23×C3—41no—
479C23×C3—41no—
480C23×C3—42no—
481C23×C3—41no—
482C23×C3—41no—
483C23×C3—42no—
484C23×C3—48no—
485C23×C3—44no—
486C23×C3—44no—
487C23×C3—48no—
488C23×C3—48no—
489C23×C3—48no—
490C23×C3—48no—
491C23×C3—48no—
492C23×C3—416no—
493C23×C3—416no—
494C23×C3C2×C4×D312yes—
495C23×C3C2×C4×D312yes—
496C23×C3C2×C4×D312yes—
497C23×C3C2×C4×D312yes—
498C23×C3C2×C4×D312yes—
499C23×C3C2×C4×D312yes—
500C23×C3#23512yes—
501C23×C3D3×D412yes—
502C23×C3D3×D414yes—
503C23×C3D3×D414yes—
504C23×C3#23712yes—
505C23×C3C2×#6712yes—
506C23×C3C23×D311yescharacteristic
507C23×C3C23×D311yescharacteristic
508C22×D3—32no—
509C22×D3—32no—
510C22×D3—34no—
511C22×D3—34no—
512C22×D3—32no—
513C22×D3—32no—
514C22×D3—62no—
515C22×D3—62no—
516C22×D3—64no—
517C22×D3—68no—
518C22×D3—68no—
519C22×D3—61no—
520C22×D3—61no—
521C22×D3—61no—
522C22×D3—62no—
523C22×D3—62no—
524C22×D3—61no—
525C22×D3—616no—
526C22×D3—64no—
527C22×D3—68no—
528C22×D3—68no—
529C22×D3—61no—
530C22×D3—61no—
531C22×D3—62no—
532C22×D3—62no—
533C22×D3—61no—
534C22×D3—62no—
535C22×D3—62no—
536C22×D3—61no—
537C22×D3—121no—
538C22×D3—121no—
539C22×D3—122no—
540C22×D3—121no—
541C22×D3—121no—
542C22×D3—122no—
543C22×D3—128no—
544C22×D3—124no—
545C22×D3—124no—
546C22×D3—128no—
547C22×D3—128no—
548C22×D3—128no—
549C22×D3—128no—
550C22×D3—128no—
551C22×D3—1216no—
552C22×D3—1216no—
553C2×C3×C4—34no—
554C2×C3×C4—62no—
555C2×C3×C4—62no—
556C2×C3×C4—62no—
557C2×C3×C4—62no—
558C2×C3×C4—62no—
559C2×C3×C4—62no—
560C2×C3×C4—62no—
561C2×C3×C4—62no—
562C2×C3×C4—62no—
563C2×C3×C4—62no—
564C2×C3×C4—62no—
565C2×C3×C4—128no—
566#67—316no—
567#67—316no—
568#67—616no—
569#67—68no—
570#67—68no—
571#67—68no—
572#67—68no—
573#67—616no—
574#67—616no—
575#67—616no—
576#67—68no—
577#67—68no—
578C2×Dic3—22no—
579C2×Dic3—22no—
580C2×Dic3—22no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—22no—
585C2×Dic3—22no—
586C2×Dic3—22no—
587C2×Dic3—22no—
588C2×Dic3—22no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—34no—
592C2×Dic3—34no—
593C2×Dic3—32no—
594C2×Dic3—32no—
595C2×Dic3—48no—
596C2×Dic3—62no—
597C2×Dic3—62no—
598C2×Dic3—64no—
599C2×Dic3—68no—
600C2×Dic3—68no—
601C2×Dic3—616no—
602C2×Dic3—64no—
603C2×Dic3—62no—
604C2×Dic3—62no—
605C2×Dic3C2×#6714yescomplemented
606C4×D3—128no—
607C4×D3—128no—
608C2×C32—24no—
609C2×C32—24no—
610C2×C32—42no—
611C2×C32C22×C22⋊C411yescharacteristic
612C2×C32C2×C4×D411yescharacteristic
613C2×C32#51811yescharacteristic
614C2×C32D4212yes—
615C2×C32#54612yes—
616C3⋊D3—24no—
617C3⋊D3—42no—
618C24—22no—
619C24—22no—
620C24—24no—
621C24—42no—
622C24—91no—
623C24—91no—
624C24—94no—
625C24—184no—
626C24—182no—
627C24—182no—
628C24—362no—
629C24#62414yescomplemented
630C24C2×D3211yescharacteristic
631C24C2×D3211yescharacteristic
632C24C2×D3211yescharacteristic
633C2×D4—94no—
634C2×D4—98no—
635C2×D4—94no—
636C2×D4—94no—
637C2×D4—94no—
638C2×D4—184no—
639C2×D4—1832no—
640C2×D4—184no—
641C2×D4—184no—
642C22×C4—32no—
643C22×C4—32no—
644C22×C4—32no—
645C22×C4—32no—
646C22×C4—64no—
647C22×C4—64no—
648C22×C4—91no—
649C22×C4—91no—
650C22×C4—94no—
651C22×C4—122no—
652C22×C4—184no—
653C22×C4—184no—
654C22×C4—184no—
655C22×C4—362no—
656C4⋊C4—184no—
657C22⋊C4—34no—
658C22⋊C4—64no—
659C22⋊C4—62no—
660C22⋊C4—62no—
661C22⋊C4—62no—
662C22⋊C4—64no—
663C22⋊C4—122no—
664C22⋊C4—184no—
665C22⋊C4—184no—
666C22⋊C4—362no—
667C42—184no—
668C22×C3—24no—
669C22×C3—28no—
670C22×C3—24no—
671C22×C3—28no—
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—22no—
676C22×C3—22no—
677C22×C3—22no—
678C22×C3—22no—
679C22×C3—24no—
680C22×C3—24no—
681C22×C3—22no—
682C22×C3—24no—
683C22×C3—24no—
684C22×C3—24no—
685C22×C3—24no—
686C22×C3—24no—
687C22×C3—24no—
688C22×C3—24no—
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—22no—
694C22×C3—22no—
695C22×C3—21no—
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—24no—
701C22×C3—24no—
702C22×C3—42no—
703C22×C3—44no—
704C22×C3—42no—
705C22×C3—44no—
706C22×C3—42no—
707C22×C3—42no—
708C22×C3—416no—
709C22×C3—416no—
710C22×C3—432no—
711C22×C3—44no—
712C22×C3—44no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3D3×C22⋊C414yescomplemented
718C22×C3D3×C22⋊C414yescomplemented
719C22×C3#67⋊C414yescomplemented
720C22×C3C4×#6714yescomplemented
721C22×C3C22×C4×D311yescharacteristic
722C22×C3C22×C4×D311yescharacteristic
723C22×C3C2×#23511yescharacteristic
724C22×C3C2×D3×D411yescharacteristic
725C22×C3C2×D3×D412yes—
726C22×C3C2×D3×D412yes—
727C22×C3C2×#23711yescharacteristic
728C22×C3#100412yes—
729C22×C3#100412yes—
730C22×C3C22×#6711yescharacteristic
731C2×D3—34no—
732C2×D3—34no—
733C2×D3—64no—
734C2×D3—62no—
735C2×D3—62no—
736C2×D3—62no—
737C2×D3—64no—
738C2×D3—62no—
739C2×D3—64no—
740C2×D3—64no—
741C2×D3—64no—
742C2×D3—64no—
743C2×D3—62no—
744C2×D3—62no—
745C2×D3—62no—
746C2×D3—62no—
747C2×D3—62no—
748C2×D3—62no—
749C2×D3—122no—
750C2×D3—124no—
751C2×D3—122no—
752C2×D3—124no—
753C2×D3—122no—
754C2×D3—122no—
755C2×D3—1216no—
756C2×D3—1216no—
757C2×D3—1232no—
758C2×D3—124no—
759C2×D3—124no—
760C2×D3—122no—
761C2×D3—122no—
762C2×D3—122no—
763C2×D3—122no—
764C3×C4—64no—
765C3×C4—122no—
766C3×C4—122no—
767C3×C4—122no—
768Dic3—24no—
769Dic3—34no—
770Dic3—34no—
771Dic3—42no—
772Dic3—42no—
773Dic3—42no—
774Dic3—64no—
775Dic3—64no—
776Dic3—62no—
777Dic3—62no—
778C32D4×C22⋊C411yescharacteristic, complemented, Sylow
779C23—21no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—22no—
788C23—28no—
789C23—28no—
790C23—44no—
791C23—48no—
792C23—48no—
793C23—92no—
794C23—94no—
795C23—92no—
796C23—188no—
797C23—181no—
798C23—181no—
799C23—182no—
800C23—181no—
801C23—181no—
802C23—182no—
803C23—182no—
804C23—188no—
805C23—364no—
806C23—368no—
807C23—368no—
808C23#380412yes—
809C23C2×#62412yes—
810C23C2×#62412yes—
811C23C2×#62412yes—
812C23D3×#6712yes—
813C23#381114yes—
814C23C22×D3211yescharacteristic
815D4—916no—
816D4—188no—
817D4—188no—
818D4—188no—
819C2×C4—34no—
820C2×C4—62no—
821C2×C4—62no—
822C2×C4—62no—
823C2×C4—62no—
824C2×C4—62no—
825C2×C4—62no—
826C2×C4—62no—
827C2×C4—62no—
828C2×C4—62no—
829C2×C4—62no—
830C2×C4—62no—
831C2×C4—92no—
832C2×C4—94no—
833C2×C4—92no—
834C2×C4—128no—
835C2×C4—188no—
836C2×C4—182no—
837C2×C4—368no—
838C2×C3—28no—
839C2×C3—24no—
840C2×C3—24no—
841C2×C3—24no—
842C2×C3—24no—
843C2×C3—21no—
844C2×C3—22no—
845C2×C3—21no—
846C2×C3—21no—
847C2×C3—22no—
848C2×C3—44no—
849C2×C3—44no—
850C2×C3—42no—
851C2×C3—42no—
852C2×C3C2×D3×C22⋊C411yescharacteristic
853C2×C3C2×D3×C22⋊C411yescharacteristic
854C2×C3C2×#67⋊C411yescharacteristic
855C2×C3#548611yescharacteristic
856C2×C3#548611yescharacteristic
857C2×C3#549012yes—
858C2×C3#559012yes—
859C2×C3#559112yes—
860C2×C3C2×C4×#6711yescharacteristic
861C2×C3D4×#6712yes—
862D3—64no—
863D3—64no—
864D3—124no—
865D3—124no—
866D3—122no—
867D3—122no—
868C22—22no—
869C22—24no—
870C22—24no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—24no—
875C22—24no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—416no—
880C22—42no—
881C22—42no—
882C22—94no—
883C22—182no—
884C22—184no—
885C22—182no—
886C22—184no—
887C22—182no—
888C22—182no—
889C22—182no—
890C22—3616no—
891C22—362no—
892C22—362no—
893C22#6395214yescomplemented
894C22#6397414yescomplemented
895C22C2×#380411yescharacteristic
896C22C22×#62411yescharacteristic
897C22C2×D3×#6711yescharacteristic
898C22C2×#381112yes—
899C22#6433012yes—
900C4—64no—
901C4—94no—
902C4—122no—
903C4—122no—
904C4—122no—
905C4—182no—
906C3—21no—
907C3#7385011yescharacteristic, complemented
908C3C22⋊C4×#6711yescharacteristic, complemented
909C2—24no—
910C2—24no—
911C2—42no—
912C2—184no—
913C2—362no—
914C2C2×#6395211yescharacteristic
915C2#1059550012yes—
916C2C2×#6397411yescharacteristic
917C2#1059551011yescharacteristic
918C2#1059552612yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC25×C32C22
socle, cosocleC23×C32C24
prime radicalC23×#638C2
hypercenterC25D32
hypocenterC32D4×C22⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
2. C22×C3×#217C2semidirect
3. C2×#63974C2semidirect
4. C2×#63952C2semidirect
5. C3×#5247C2semidirect
6. #10591722C2semidirect
7. #10591720C2semidirect
8. #10591714C2semidirect
9. #10591711C2semidirect
10. #10591705C2semidirect
11. #10591704C2semidirect
17. C22×#638C4semidirect
23. C23×C3×Dic3C22semidirect
24. C22×#624C22semidirect
30. C2×C3×#217C22semidirect
31. C2×C3×#217C22semidirect
32. C2×C3×#217C22semidirect
34. C2×#3724C22semidirect
35. C2×#3722C22semidirect
36. C2×#3722C22semidirect
37. C2×#3722C22semidirect
38. C2×Dic32C22semidirect
40. #63579C22semidirect
41. #63579C22semidirect
46. C22×#217D3semidirect
52. #5247D3semidirect
69. C24×C32C2×C4semidirect
77. C23×C3⋊D3C2×C4semidirect
85. C2×#638C2×C4semidirect
86. C2×#638C2×C4semidirect
87. C2×#638C2×C4semidirect
90. C22×C3⋊Dic3C2×C4semidirect
109. C3×#217D4semidirect
144. C23×Dic3C2×D3semidirect
160. C2×#217C2×D3semidirect
161. C2×#217C2×D3semidirect
162. C2×#217C2×D3semidirect
220. #638C22⋊C4semidirect
238. C2×C3×Dic3C2×D4semidirect
267. C24×C3C4×D3semidirect
268. C24×C3C4×D3semidirect
368. #217#67semidirect
393. C22×C32C2×C22⋊C4semidirect
394. C22×C32C4×D4semidirect
410. C2×C3⋊D3C2×C22⋊C4semidirect
412. C3⋊Dic3C2×C22⋊C4semidirect
605. C2×Dic3C2×#67semidirect
629. C24#624semidirect
717. C22×C3D3×C22⋊C4semidirect
718. C22×C3D3×C22⋊C4semidirect
719. C22×C3#67⋊C4semidirect
720. C22×C3C4×#67semidirect
778. C32D4×C22⋊C4semidirect
893. C22#63952semidirect
894. C22#63974semidirect
907. C3#73850semidirect
908. C3C22⋊C4×#67semidirect

Maximal subgroups

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

subgroupindex
C23×#6382
C22×C3×#2172
C2×#639742
C2×#639522
C3×#52472
#105917222
#105917202
#105917142
#105917112
#105917052
#105917042
C22⋊C4×#673
#738503