Finite Group Databasebeta

← #11902021

Subgroups — #11902021

Order 1152.

2533 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic, complemented
2C3×#5791C212yesmaximal, complemented
3#10595528C212yesmaximal, complemented
4#10595508C212yesmaximal, complemented
5#10595089C214yesmaximal, complemented
6#10595084C211yesmaximal, characteristic, complemented
7#10595060C214yesmaximal, complemented
8C4×#3811C212yesmaximal, complemented
9#10595033C212yesmaximal, complemented
10#10594981C211yesmaximal, characteristic, complemented
11#10594974C212yesmaximal, complemented
12#10594968C214yesmaximal, complemented
13#10594836C214yesmaximal, complemented
14#86036—32nomaximal
15C23×C32×C4C2211yescharacteristic, complemented
16C22×#638C2211yescharacteristic
17C22×C4×C3⋊D3C2211yescharacteristic
18C2×C3×#235C2212yescomplemented
19C2×#3811C2212yes—
20C2×C4×D32C2212yescomplemented
21C2×#3757C2211yescharacteristic, complemented
22C4×#638C2214yescomplemented
23C4×#638C2214yescomplemented
24C2×#3752C2211yescharacteristic
25C2×#3750C2211yescharacteristic, complemented
26C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C3×#953C2214yescomplemented
28C3×#930C2212yes—
29C3×#930C2212yescomplemented
30C3×#929C2214yescomplemented
31C3×C4×#67C2214yescomplemented
32C3×C4×#67C2214yescomplemented
33C3×#926C2212yescomplemented
34C3×#924C2212yescomplemented
35C3×#924C2212yescomplemented
36#63983C2214yescomplemented
37#63982C2212yescomplemented
38#63980C2212yes—
39#63975C2214yescomplemented
40#63974C2212yes—
41#67⋊Dic3C2214yescomplemented
42#63970C2214yescomplemented
43#63969C2214yescomplemented
44#63962C2214yescomplemented
45#63959C2214yescomplemented
46#63958C2214yes—
47#63958C2214yes—
48#63956C2214yescomplemented
49#63922C2214yescomplemented
50#63921C2212yescomplemented
51C4×#627C2212yescomplemented
52#63915C2212yescomplemented
53C4×#626C2214yescomplemented
54C4×#625C2212yescomplemented
55#63895C2214yescomplemented
56#63888C2214yescomplemented
57#63887C2214yescomplemented
58#63884C2214yescomplemented
59#63883C2212yescomplemented
60C4×#624C2212yescomplemented
61#63881C2214yescomplemented
62#63870C2212yescomplemented
63#63862C2214yescomplemented
64#63858C2214yescomplemented
65#63855C2214yescomplemented
66#63854C2214yescomplemented
67#63846C2214yescomplemented
68C3×#525—32no—
69#5828—34no—
70#5791D312yescomplemented
71C2×C4×#67—32no—
72C2×C4×#67—61no—
73#5660—34no—
74#5657—34no—
75#5645—32no—
76#5638—34no—
77#5634—32no—
78#5613—34no—
79#5605—32no—
80#5602—32no—
81#5593—34no—
82#5589—34no—
83#5557—34no—
84#5547—34no—
85C4×D3×D4—34no—
86#5538—34no—
87#5528—34no—
88C24×C32C2311yescharacteristic
89C23×C3⋊D3C2311yescharacteristic
90C22×D32C2312yes—
91C22×C32×C4—42no—
92C22×C32×C4C2312yes—
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2312yes—
96C2×#638—24no—
97C2×#638C2314yes—
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C2×C4×C3⋊D3—42no—
102C2×C4×C3⋊D3C2312yes—
103C2×C4×C3⋊D3C2312yes—
104C2×C3×#67C2314yes—
105C2×C3×#67C2314yes—
106C2×C3×#67C2314yes—
107C3×#235—44no—
108C2×C3×D12C2312yes—
109C2×C3×C4×D3C2314yes—
110C2×C3×Dic6C2312yes—
111#3811—28no—
112C2×#627C2312yes—
113C2×#626C2314yes—
114C2×#625C2312yes—
115C2×#624C2312yes—
116C2×#624C2312yes—
117C2×#624C2312yes—
118C2×D3×Dic3C2314yes—
119C4×D32—44no—
120#3757C2314yes—
121#3752C2314yes—
122#3750C2314yes—
123C4×C3⋊Dic3C2312yes—
124C4×C3⋊Dic3C2312yes—
125C3×#217C2314yes—
126C3×#217C2314yes—
127C3×#217C2314yes—
128C3×(C2×D3)⋊C4C2314yes—
129C3×(C2×D3)⋊C4C2314yes—
130C3×C4⋊Dic3C2312yes—
131C3×C4⋊Dic3C2312yes—
132C3×Dic3⋊C4C2314yes—
133C3×Dic3⋊C4C2314yes—
134C3×C4×Dic3C2314yes—
135#3724C2312yes—
136#3724C2312yes—
137Dic3⋊Dic3C2314yes—
138Dic3⋊Dic3C2314yes—
139Dic3⋊Dic3C2314yes—
140Dic3⋊Dic3C2314yes—
141#3722C2314yes—
142(C2×D3)⋊Dic3C2314yes—
143(C2×D3)⋊Dic3C2314yes—
144(C2×D3)⋊Dic3C2314yes—
145(C2×D3)⋊Dic3C2314yes—
146Dic32C2314yes—
147#3459—91noSylow
148C2×C3×#41—32no—
149C23×C3×C4—21no—
150C23×C3×C4C2×D312yescomplemented
151C22×#67—32no—
152C22×#67—61no—
153C2×D3×D4—34no—
154C2×#235C2×D312yescomplemented
155C22×C4×D3—32no—
156C22×C4×D3—34no—
157C22×C4×D3—61no—
158C3×#123—34no—
159C3×C22⋊Q8—32no—
160C3×C22⋊Q8—32no—
161C3×#121—32no—
162C3×#121—32no—
163C3×#120—34no—
164C3×C4×D4—34no—
165C3×C4×D4—34no—
166C3×#117—32no—
167#953C2×D314yescomplemented
168C2×#217—32no—
169C2×#217—61no—
170#946—34no—
171#946—34no—
172#939—34no—
173#939—34no—
174#938—34no—
175#938—34no—
176#938—34no—
177#937—34no—
178#937—34no—
179#937—34no—
180#936—34no—
181#935—34no—
182#935—34no—
183#935—34no—
184D4×Dic3—34no—
185#930C2×D312yes—
186#930C2×D312yescomplemented
187#929C2×D314yescomplemented
188C4×#67—34no—
189C4×#67—34no—
190C4×#67—34no—
191C4×#67—34no—
192C4×#67—34no—
193C4×#67—34no—
194C4×#67—64no—
195C4×#67—64no—
196C4×#67C2×D314yescomplemented
197C4×#67C2×D314yescomplemented
198C2×(C2×D3)⋊C4—32no—
199C2×(C2×D3)⋊C4—61no—
200#926—34no—
201#926C2×D312yescomplemented
202#924C2×D312yescomplemented
203#924C2×D312yescomplemented
204C2×Dic3⋊C4—32no—
205C2×Dic3⋊C4—61no—
206C2×C4×Dic3—32no—
207C2×C4×Dic3—61no—
208#898—34no—
209#898—34no—
210#897—34no—
211#896—34no—
212#896—34no—
213#894—34no—
214#894—34no—
215#893—34no—
216D3×C4⋊C4—34no—
217#890—34no—
218#889—34no—
219#889—34no—
220#886—34no—
221#885—34no—
222#885—34no—
223#884—34no—
224#884—34no—
225#883—34no—
226#883—34no—
227#883—34no—
228#883—34no—
229#882—34no—
230#67⋊C4—34no—
231#67⋊C4—34no—
232D3×C22⋊C4—34no—
233D3×C22⋊C4—34no—
234#879—34no—
235#879—34no—
236#879—34no—
237#879—34no—
238#878—34no—
239#878—34no—
240C4×D12—34no—
241#872—34no—
242C42×D3—34no—
243C4×Dic6—34no—
244C23×C32—22no—
245C23×C32—41no—
246C23×C32—41no—
247C23×C32C2412yes—
248C23×C32C2411yescharacteristic
249C22×C3⋊D3—41no—
250C22×C3⋊D3—41no—
251C22×C3⋊D3#4114yescomplemented
252C22×C3⋊D3C2412yes—
253C22×C3×D3C2414yes—
254C2×D32—24no—
255C2×D32—42no—
256C2×D32—42no—
257C2×C32×C4—22no—
258C2×C32×C4—24no—
259C2×C32×C4—42no—
260C2×C32×C4—41no—
261C2×C32×C4C2411yescharacteristic
262C2×C32×C4C2412yes—
263C2×C32×C4C2411yescharacteristic
264#638—28no—
265C2×C3⋊Dic3—22no—
266C2×C3⋊Dic3—41no—
267C2×C3⋊Dic3—41no—
268C2×C3⋊Dic3C2412yes—
269C2×C3⋊Dic3C2412yes—
270C2×C3⋊Dic3C2412yes—
271C4×C3⋊D3—24no—
272C4×C3⋊D3—42no—
273C3×#67—28no—
274C3×#67—44no—
275C3×#67—44no—
276C2×C3×Dic3C2414yes—
277C2×C3×Dic3C2414yes—
278C2×C3×Dic3C2414yes—
279C3×D12—42no—
280C3×C4×D3—28no—
281C3×Dic6—42no—
282#627—42no—
283#626—28no—
284#625—42no—
285#624—24no—
286#624—42no—
287#624—42no—
288D3×Dic3—44no—
289#543—91no—
290#539—92no—
291#539—94no—
292#538—92no—
293#538—94no—
294#534—92no—
295#534—91no—
296#529—94no—
297#529—92no—
298#525—32no—
299#525—94no—
300C2×C4×D4—92no—
301C2×C4×D4—91no—
302C24×C3—21no—
303C24×C3C22×D312yes—
304C23×D3—32no—
305C23×D3—34no—
306C23×D3—61no—
307C3×#41—124no—
308C2×C3×Q8—32no—
309C2×C3×D4—34no—
310C2×C3×D4—34no—
311C2×C3×D4—34no—
312C2×C3×D4—32no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—34no—
318C22×C3×C4—44no—
319C22×C3×C4—44no—
320C22×C3×C4C22×D312yes—
321C22×C3×C4C22×D312yes—
322C22×C3×C4C22×D312yes—
323C22×C3×C4C22×D312yes—
324C22×C3×C4C22×D312yes—
325C22×C3×C4C22×D312yes—
326C2×#67—34no—
327C2×#67—34no—
328C2×#67—34no—
329C2×#67—34no—
330C2×#67—64no—
331C2×#67—68no—
332C2×#67—68no—
333C2×#67C22×D314yes—
334C2×#67C22×D314yes—
335C2×#67C22×D314yes—
336C22×Dic3—32no—
337C22×Dic3—32no—
338C22×Dic3—32no—
339C22×Dic3—34no—
340C22×Dic3—61no—
341C22×Dic3—61no—
342C22×Dic3—61no—
343D3×D4—616no—
344#235—44no—
345C2×D12—34no—
346C2×D12C22×D312yes—
347C2×C4×D3—34no—
348C2×C4×D3—34no—
349C2×C4×D3—34no—
350C2×C4×D3—34no—
351C2×C4×D3—34no—
352C2×C4×D3—34no—
353C2×C4×D3—62no—
354C2×C4×D3—62no—
355C2×C4×D3—128no—
356C2×C4×D3—124no—
357C2×C4×D3—124no—
358C2×C4×D3C22×D314yes—
359C2×Dic6—34no—
360C2×Dic6C22×D312yes—
361C3×C4⋊C4—32no—
362C3×C4⋊C4—34no—
363C3×C4⋊C4—34no—
364C3×C4⋊C4—32no—
365C3×C22⋊C4—34no—
366C3×C22⋊C4—34no—
367C3×C22⋊C4—34no—
368C3×C22⋊C4—34no—
369C3×C22⋊C4—34no—
370C3×C42—34no—
371#217—34no—
372#217—34no—
373#217—34no—
374#217—34no—
375#217—34no—
376#217—34no—
377#217—64no—
378#217C22×D314yes—
379#217C22×D314yes—
380#217C22×D314yes—
381(C2×D3)⋊C4—34no—
382(C2×D3)⋊C4—34no—
383(C2×D3)⋊C4—34no—
384(C2×D3)⋊C4—34no—
385(C2×D3)⋊C4—34no—
386(C2×D3)⋊C4—34no—
387(C2×D3)⋊C4—34no—
388(C2×D3)⋊C4—34no—
389(C2×D3)⋊C4—64no—
390(C2×D3)⋊C4C22×D314yes—
391(C2×D3)⋊C4C22×D314yes—
392C4⋊Dic3—34no—
393C4⋊Dic3—34no—
394C4⋊Dic3—34no—
395C4⋊Dic3—34no—
396C4⋊Dic3C22×D312yes—
397C4⋊Dic3C22×D312yes—
398Dic3⋊C4—34no—
399Dic3⋊C4—34no—
400Dic3⋊C4—34no—
401Dic3⋊C4—34no—
402Dic3⋊C4—34no—
403Dic3⋊C4—34no—
404Dic3⋊C4—34no—
405Dic3⋊C4—34no—
406Dic3⋊C4—64no—
407Dic3⋊C4C22×D314yes—
408Dic3⋊C4C22×D314yes—
409C4×Dic3—34no—
410C4×Dic3—34no—
411C4×Dic3—34no—
412C4×Dic3—34no—
413C4×Dic3—62no—
414C4×Dic3—62no—
415C4×Dic3C22×D314yes—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—22no—
419C22×C32—22no—
420C22×C32—22no—
421C22×C32—44no—
422C22×C32C2×#4112yes—
423C22×C32C2511yescharacteristic
424C2×C3⋊D3—22no—
425C2×C3⋊D3—22no—
426C2×C3⋊D3—44no—
427C2×C3⋊D3C2×#4114yes—
428C2×C3×D3—24no—
429C2×C3×D3—24no—
430C2×C3×D3—24no—
431D32—48no—
432C32×C4—21no—
433C32×C4—22no—
434C32×C4H(5,𝔽2)12yes—
435C3⋊Dic3—22no—
436C3⋊Dic3—22no—
437C3⋊Dic3—22no—
438C3×Dic3—24no—
439C3×Dic3—24no—
440C3×Dic3—24no—
441C2×#41—32no—
442C22×D4—92no—
443C22×D4—91no—
444C23×C4—92no—
445C23×C4—91no—
446C23×C4D3211yescharacteristic, complemented
447#126—94no—
448#126—94no—
449#126—94no—
450#125—92no—
451#125—94no—
452#124—92no—
453#124—94no—
454#123—34no—
455#123—94no—
456#123—94no—
457#123—94no—
458#123—94no—
459#123—94no—
460C22⋊Q8—32no—
461C22⋊Q8—32no—
462C22⋊Q8—92no—
463C22⋊Q8—94no—
464C22⋊Q8—94no—
465C22⋊Q8—94no—
466#121—32no—
467#121—32no—
468#121—94no—
469#121—94no—
470#121—94no—
471#121—92no—
472#120—34no—
473#120—94no—
474#120—94no—
475C4×Q8—92no—
476C4×D4—34no—
477C4×D4—34no—
478C4×D4—94no—
479C4×D4—94no—
480C4×D4—94no—
481C4×D4—92no—
482C4×D4—94no—
483C4×D4—94no—
484#117—32no—
485#117—94no—
486C2×C4⋊C4—92no—
487C2×C4⋊C4—91no—
488C2×C22⋊C4—92no—
489C2×C22⋊C4—92no—
490C2×C22⋊C4—91no—
491C2×C22⋊C4—91no—
492C2×C42—92no—
493C2×C42—91no—
494C23×C3—24no—
495C23×C3—24no—
496C23×C3—21no—
497C23×C3—22no—
498C23×C3—34no—
499C23×C3—42no—
500C23×C3—42no—
501C23×C3—42no—
502C23×C3—42no—
503C23×C3C23×D312yes—
504C23×C3C23×D312yes—
505C23×C3C23×D312yes—
506C22×D3—34no—
507C22×D3—38no—
508C22×D3—64no—
509C22×D3—62no—
510C22×D3—68no—
511C22×D3—124no—
512C22×D3—124no—
513C22×D3—122no—
514C22×D3—122no—
515C22×D3—122no—
516C22×D3—122no—
517C22×D3C23×D314yes—
518C3×Q8—122no—
519C3×D4—68no—
520C3×D4—122no—
521C3×D4—124no—
522C3×D4—124no—
523C2×C3×C4—24no—
524C2×C3×C4—24no—
525C2×C3×C4—24no—
526C2×C3×C4—24no—
527C2×C3×C4—21no—
528C2×C3×C4—22no—
529C2×C3×C4—21no—
530C2×C3×C4—34no—
531C2×C3×C4—34no—
532C2×C3×C4—34no—
533C2×C3×C4—44no—
534C2×C3×C4—42no—
535C2×C3×C4—42no—
536C2×C3×C4—42no—
537C2×C3×C4—44no—
538C2×C3×C4—42no—
539C2×C3×C4—68no—
540C2×C3×C4C23×D312yes—
541C2×C3×C4C23×D312yes—
542C2×C3×C4C23×D312yes—
543C2×C3×C4C23×D312yes—
544#67—28no—
545#67—44no—
546#67—44no—
547#67—68no—
548#67—68no—
549#67—68no—
550#67—616no—
551#67—124no—
552C2×Dic3—34no—
553C2×Dic3—34no—
554C2×Dic3—34no—
555C2×Dic3—62no—
556C2×Dic3—62no—
557C2×Dic3—62no—
558C2×Dic3—64no—
559C2×Dic3—64no—
560C2×Dic3—124no—
561C2×Dic3—122no—
562C2×Dic3—122no—
563C2×Dic3—122no—
564C2×Dic3—122no—
565C2×Dic3C23×D314yes—
566C2×Dic3C23×D314yes—
567C2×Dic3C23×D314yes—
568D12—42no—
569D12—68no—
570C4×D3—28no—
571C4×D3—68no—
572C4×D3—68no—
573C4×D3—124no—
574C4×D3—124no—
575C4×D3—124no—
576C4×D3—124no—
577C4×D3—124no—
578C4×D3—124no—
579Dic6—42no—
580Dic6—124no—
581C2×C32—22no—
582C2×C32—42no—
583C2×C32C22×#4111yescharacteristic
584C2×C32C2×H(5,𝔽2)11yescharacteristic
585C2×C32#58511yescharacteristic
586C3⋊D3—24no—
587C3×D3—44no—
588C24—92no—
589C24—91no—
590C24C2×D3211yescharacteristic
591#41—124no—
592C2×Q8—32no—
593C2×Q8—92no—
594C2×D4—34no—
595C2×D4—34no—
596C2×D4—34no—
597C2×D4—32no—
598C2×D4—94no—
599C2×D4—94no—
600C2×D4—92no—
601C2×D4—188no—
602C2×D4—184no—
603C22×C4—34no—
604C22×C4—42no—
605C22×C4—92no—
606C22×C4—92no—
607C22×C4—92no—
608C22×C4—94no—
609C22×C4—91no—
610C22×C4—91no—
611C22×C4—91no—
612C22×C4—92no—
613C22×C4—92no—
614C22×C4—362no—
615C22×C4—364no—
616C22×C4C2×D3211yescharacteristic
617C22×C4C2×D3212yes—
618C22×C4C2×D3211yescharacteristic
619C22×C4C2×D3212yes—
620C4⋊C4—34no—
621C4⋊C4—32no—
622C4⋊C4—32no—
623C4⋊C4—34no—
624C4⋊C4—94no—
625C4⋊C4—94no—
626C4⋊C4—94no—
627C4⋊C4—92no—
628C4⋊C4—92no—
629C4⋊C4—94no—
630C4⋊C4—94no—
631C22⋊C4—34no—
632C22⋊C4—34no—
633C22⋊C4—34no—
634C22⋊C4—34no—
635C22⋊C4—34no—
636C22⋊C4—94no—
637C22⋊C4—94no—
638C22⋊C4—94no—
639C22⋊C4—94no—
640C22⋊C4—94no—
641C22⋊C4—94no—
642C22⋊C4—94no—
643C42—34no—
644C42—94no—
645C42—92no—
646C42—92no—
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—24no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—22no—
657C22×C3—22no—
658C22×C3—22no—
659C22×C3—21no—
660C22×C3—42no—
661C22×C3—42no—
662C22×C3—48no—
663C22×C3—48no—
664C22×C3—64no—
665C22×C3—64no—
666C22×C3—64no—
667C22×C3D3×#4114yes—
668C22×C3C24×D312yes—
669C2×D3—24no—
670C2×D3—24no—
671C2×D3—24no—
672C2×D3—38no—
673C2×D3—64no—
674C2×D3—64no—
675C2×D3—64no—
676C2×D3—122no—
677C2×D3—122no—
678C2×D3—1216no—
679C2×D3—128no—
680C2×D3—128no—
681C3×C4—22no—
682C3×C4—22no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—42no—
687C3×C4—64no—
688C3×C4—64no—
689C3×C4—64no—
690C3×C4#100414yes—
691Dic3—24no—
692Dic3—24no—
693Dic3—24no—
694Dic3—64no—
695Dic3—64no—
696Dic3—64no—
697Dic3—64no—
698Dic3—122no—
699Dic3—122no—
700C32#345911yescharacteristic, complemented, Sylow
701C23—22no—
702C23—34no—
703C23—41no—
704C23—41no—
705C23—92no—
706C23—94no—
707C23—184no—
708C23—361no—
709C23—361no—
710C23—362no—
711C23—362no—
712C23C22×D3212yes—
713C23C22×D3211yescharacteristic
714Q8—122no—
715Q8—362no—
716D4—68no—
717D4—122no—
718D4—124no—
719D4—124no—
720D4—188no—
721D4—188no—
722D4—362no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—34no—
726C2×C4—34no—
727C2×C4—34no—
728C2×C4—42no—
729C2×C4—41no—
730C2×C4—68no—
731C2×C4—92no—
732C2×C4—92no—
733C2×C4—92no—
734C2×C4—184no—
735C2×C4—182no—
736C2×C4—184no—
737C2×C4—362no—
738C2×C4—362no—
739C2×C4—362no—
740C2×C4—364no—
741C2×C4—361no—
742C2×C4—361no—
743C2×C4C22×D3211yescharacteristic
744C2×C4C22×D3212yes—
745C2×C4C22×D3211yescharacteristic
746C2×C3—24no—
747C2×C3—24no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—44no—
752C2×C3—42no—
753C2×C3—42no—
754C2×C3—124no—
755C2×C3C2×#100412yes—
756C2×C3C2×D3×#4112yes—
757C2×C3#596412yes—
758D3—44no—
759D3—68no—
760D3—124no—
761C22—21no—
762C22—21no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—44no—
767C22—64no—
768C22—64no—
769C22—64no—
770C22—94no—
771C22—182no—
772C22—182no—
773C22—364no—
774C22—368no—
775C22#6430612yes—
776C22C23×D3211yescharacteristic
777C4—21no—
778C4—22no—
779C4—64no—
780C4—64no—
781C4—64no—
782C4—182no—
783C4—182no—
784C4—182no—
785C4#6433012yes—
786C3—21no—
787C3#8603612yescomplemented
788C2—22no—
789C2—42no—
790C2—124no—
791C2—184no—
792C2C2×#6430611yescharacteristic
793C2#1059666911yescharacteristic
794C2C2×#6433011yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
hypercenterC23×C4D32
hypocenterC32#3459
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×#638C2semidirect
2. C3×#5791C2semidirect
3. #10595528C2semidirect
4. #10595508C2semidirect
5. #10595089C2semidirect
6. #10595084C2semidirect
7. #10595060C2semidirect
8. C4×#3811C2semidirect
9. #10595033C2semidirect
10. #10594981C2semidirect
11. #10594974C2semidirect
12. #10594968C2semidirect
13. #10594836C2semidirect
15. C23×C32×C4C22semidirect
18. C2×C3×#235C22semidirect
20. C2×C4×D32C22semidirect
21. C2×#3757C22semidirect
22. C4×#638C22semidirect
23. C4×#638C22semidirect
25. C2×#3750C22semidirect
26. C2×C4×C3⋊Dic3C22semidirect
27. C3×#953C22semidirect
29. C3×#930C22semidirect
30. C3×#929C22semidirect
31. C3×C4×#67C22semidirect
32. C3×C4×#67C22semidirect
33. C3×#926C22semidirect
34. C3×#924C22semidirect
35. C3×#924C22semidirect
36. #63983C22semidirect
37. #63982C22semidirect
39. #63975C22semidirect
41. #67⋊Dic3C22semidirect
42. #63970C22semidirect
43. #63969C22semidirect
44. #63962C22semidirect
45. #63959C22semidirect
48. #63956C22semidirect
49. #63922C22semidirect
50. #63921C22semidirect
51. C4×#627C22semidirect
52. #63915C22semidirect
53. C4×#626C22semidirect
54. C4×#625C22semidirect
55. #63895C22semidirect
56. #63888C22semidirect
57. #63887C22semidirect
58. #63884C22semidirect
59. #63883C22semidirect
60. C4×#624C22semidirect
61. #63881C22semidirect
62. #63870C22semidirect
63. #63862C22semidirect
64. #63858C22semidirect
65. #63855C22semidirect
66. #63854C22semidirect
67. #63846C22semidirect
70. #5791D3semidirect
150. C23×C3×C4C2×D3semidirect
154. C2×#235C2×D3semidirect
167. #953C2×D3semidirect
186. #930C2×D3semidirect
187. #929C2×D3semidirect
196. C4×#67C2×D3semidirect
197. C4×#67C2×D3semidirect
201. #926C2×D3semidirect
202. #924C2×D3semidirect
203. #924C2×D3semidirect
251. C22×C3⋊D3#41semidirect
446. C23×C4D32semidirect
700. C32#3459semidirect
787. C3#86036semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C3×#57912
#105955282
#105955082
#105950892
#105950842
#105950602
C4×#38112
#105950332
#105949812
#105949742
#105949682
#105948362
#860363