Finite Group Databasebeta

← #11906183

Subgroups — #11906183

Order 1152.

2361 conjugacy classes of subgroups.

The subgroup lattice has 853 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64155C211yesmaximal, characteristic, complemented
2C3×Q8×#67C212yesmaximal, complemented
3#10595434C212yesmaximal, complemented
4D3×#946C212yesmaximal, complemented
5#10595403C212yesmaximal, complemented
6#10595375C212yesmaximal, complemented
7#10595374C212yesmaximal, complemented
8#10595372C214yesmaximal, complemented
9#10595371C212yesmaximal, complemented
10#10595058C212yesmaximal
11C4×#3811C211yesmaximal, characteristic
12#10594993C212yesmaximal, complemented
13#10594981C212yesmaximal, complemented
14#10594959C214yesmaximal, complemented
15#10594925C211yesmaximal, characteristic, complemented
16#86761—32nomaximal
17C22×C32×Q8C2211yescharacteristic, complemented
18C22×C4×C3⋊D3C2211yescharacteristic
19C2×C3×D3×Q8C2212yescomplemented
20C2×#3811C2211yescharacteristic
21C2×C4×D32C2211yescharacteristic
22C2×#3797C2211yescharacteristic, complemented
23#64155C2212yes—
24#64155C2212yes—
25#64155C2212yescomplemented
26#64155C2212yescomplemented
27C2×#3752C2212yes—
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
29C2×#3750C2212yescomplemented
30C3×#946C2212yescomplemented
31C3×#946C2214yescomplemented
32C3×Q8×Dic3C2212yescomplemented
33C3×#944C2214yescomplemented
34C3×#944C2212yescomplemented
35C3×C4×#67C2214yes—
36C3×C4×#67C2212yes—
37C3×#924C2212yescomplemented
38C3×#924C2214yescomplemented
39#63982C2212yescomplemented
40#63982C2214yescomplemented
41#63974C2212yes—
42#63974C2211yescharacteristic
43#67⋊Dic3C2212yes—
44#67⋊Dic3C2214yes—
45#63921C2211yescharacteristic
46D3×(C2×D3)⋊C4C2214yes—
47#63918C2212yescomplemented
48#63904C2214yes—
49C4×#626C2212yes—
50#63900C2211yescharacteristic, complemented
51#63899C2214yescomplemented
52#63895C2214yes—
53#63895C2214yescomplemented
54#63893C2214yescomplemented
55D3×C4⋊Dic3C2212yescomplemented
56#63888C2214yes—
57#63888C2214yescomplemented
58#63887C2214yescomplemented
59#63883C2211yescharacteristic
60#63883C2212yescomplemented
61C4×#624C2211yescharacteristic
62#63881C2212yes—
63#63880C2214yes—
64D3×Dic3⋊C4C2214yescomplemented
65#63871C2212yes—
66#63867C2214yescomplemented
67#63865C2212yes—
68#63856C2212yescomplemented
69#63851C2214yescomplemented
70#63846C2214yescomplemented
71#63845C2214yescomplemented
72Dic3×Dic6C2212yescomplemented
73#63839C2214yescomplemented
74#63837C2214yescomplemented
75#63836C2214yes—
76C3×D4×Q8—32no—
77Q8×#67—32no—
78Q8×#67D312yescomplemented
79C2×#946—32no—
80C2×#946—32no—
81C2×#946—61no—
82#5730—34no—
83#5729—34no—
84#5728—32no—
85#5727—32no—
86#5636—34no—
87#5636—34no—
88#5635—32no—
89#5635—32no—
90#5634—34no—
91#5634—34no—
92D3×C22⋊Q8—32no—
93D3×C22⋊Q8—32no—
94#5579—32no—
95#5578—32no—
96#5545—34no—
97C4×D3×D4—32no—
98#5543—32no—
99#5539—34no—
100C23×C3⋊D3C2311yescharacteristic
101C22×D32C2311yescharacteristic
102C2×C32×Q8—42no—
103C2×C32×Q8C2312yes—
104C2×C32×Q8C2312yes—
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2312yes—
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2312yes—
109C2×C4×C3⋊D3—42no—
110C2×C4×C3⋊D3C2311yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C3×#67C2312yes—
115C3×D3×Q8—44no—
116C2×C3×C4×D3C2312yes—
117C2×C3×C4×D3C2314yes—
118C2×C3×Dic6C2312yes—
119C2×C3×Dic6C2314yes—
120#3811Q818yescomplemented
121C2×#627C2312yes—
122C2×#627C2314yes—
123C2×#626C2312yes—
124C2×#624C2312yes—
125C2×#624C2311yescharacteristic
126C2×#624C2312yes—
127C2×#624C2311yescharacteristic
128C2×#624C2311yescharacteristic
129C2×D3×Dic3C2312yes—
130C2×D3×Dic3C2314yes—
131C4×D32—42no—
132#3797—42no—
133#3752C2314yes—
134#3752C2314yes—
135C4⋊(C3⋊Dic3)C2312yes—
136C4⋊(C3⋊Dic3)C2312yes—
137#3750C2314yes—
138#3750C2314yes—
139C3×#217C2314yes—
140C3×#217C2312yes—
141C3×(C2×D3)⋊C4C2314yes—
142C3×(C2×D3)⋊C4C2312yes—
143C3×C4⋊Dic3C2314yes—
144C3×C4⋊Dic3C2312yes—
145C3×Dic3⋊C4C2314yes—
146C3×Dic3⋊C4C2314yes—
147C3×Dic3⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×Dic3⋊C4C2312yes—
150C3×C4×Dic3C2314yes—
151C3×C4×Dic3C2312yes—
152#3724C2314yes—
153#3724C2312yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2314yes—
156Dic3⋊Dic3C2312yes—
157Dic3⋊Dic3C2314yes—
158Dic3⋊Dic3C2314yes—
159#3722C2314yes—
160#3722C2312yes—
161(C2×D3)⋊Dic3C2312yes—
162(C2×D3)⋊Dic3C2314yes—
163Dic32C2314yes—
164Dic32C2312yes—
165#3501—91noSylow
166C22×C3×Q8—21no—
167C22×C3×Q8—32no—
168C22×C3×Q8C2×D312yescomplemented
169C2×D3×Q8—32no—
170C2×D3×Q8C2×D312yescomplemented
171C2×D3×D4—32no—
172C22×C4×D3—32no—
173C22×C4×D3—32no—
174C22×C4×D3—61no—
175C3×C4⋊Q8—32no—
176C3×C4⋊Q8—34no—
177C3×C22⋊Q8—34no—
178C3×C22⋊Q8—32no—
179C3×C22⋊Q8—34no—
180C3×C22⋊Q8—32no—
181C3×C4×Q8—32no—
182C3×C4×D4—34no—
183C3×C4×D4—32no—
184#946—34no—
185#946—32no—
186#946—34no—
187#946—32no—
188#946—32no—
189#946—32no—
190#946—32no—
191#946—34no—
192#946—32no—
193#946—34no—
194#946—34no—
195#946—62no—
196#946—62no—
197#946—62no—
198#946—62no—
199#946C2×D314yescomplemented
200#946C2×D312yescomplemented
201Q8×Dic3—32no—
202Q8×Dic3C2×D312yescomplemented
203#944—34no—
204#944C2×D314yescomplemented
205#944C2×D312yescomplemented
206D4×Dic3—32no—
207D4×Dic3—34no—
208C4×#67—34no—
209C4×#67—32no—
210C4×#67C2×D312yes—
211C4×#67C2×D314yes—
212C2×(C2×D3)⋊C4—34no—
213C2×(C2×D3)⋊C4—34no—
214C2×(C2×D3)⋊C4—62no—
215C2×C4⋊Dic3—32no—
216C2×C4⋊Dic3—32no—
217C2×C4⋊Dic3—61no—
218#924—32no—
219#924—34no—
220#924C2×D314yescomplemented
221#924C2×D312yescomplemented
222C2×Dic3⋊C4—34no—
223C2×Dic3⋊C4—34no—
224C2×Dic3⋊C4—62no—
225#897—32no—
226#897—34no—
227#897—34no—
228#897—34no—
229#896—34no—
230#896—34no—
231#896—34no—
232#896—34no—
233#896—34no—
234#896—34no—
235#896—34no—
236#893—34no—
237#893—32no—
238#892—34no—
239D3×C4⋊C4—32no—
240D3×C4⋊C4—34no—
241D3×C4⋊C4—32no—
242D3×C4⋊C4—34no—
243D3×C4⋊C4—32no—
244#890—34no—
245#890—34no—
246#889—34no—
247#889—34no—
248#889—34no—
249#888—34no—
250#888—32no—
251#887—34no—
252#67⋊C4—34no—
253#67⋊C4—32no—
254#67⋊C4—32no—
255#67⋊C4—34no—
256D3×C22⋊C4—34no—
257D3×C22⋊C4—32no—
258D3×C22⋊C4—34no—
259D3×C22⋊C4—32no—
260#878—34no—
261#878—34no—
262#878—34no—
263#878—34no—
264#878—34no—
265#878—34no—
266C4×D12—32no—
267C4×D12—34no—
268#872—34no—
269C42×D3—32no—
270#870—34no—
271#869—32no—
272C4×Dic6—32no—
273C4×Dic6—34no—
274C23×C32C2411yescharacteristic
275C22×C3⋊D3—41no—
276C22×C3⋊D3—41no—
277C22×C3⋊D3C2×Q814yescomplemented
278C22×C3⋊D3C2411yescharacteristic
279C22×C3⋊D3C2411yescharacteristic
280C22×C3×D3C2412yes—
281C2×D32—41no—
282C2×D32—41no—
283C2×D32C2×Q814yescomplemented
284C32×Q8—24no—
285C32×Q8—42no—
286C2×C32×C4—22no—
287C2×C32×C4—42no—
288C2×C32×C4C2414yes—
289C2×C32×C4C2411yescharacteristic
290C2×C32×C4C2411yescharacteristic
291C2×C3⋊Dic3—41no—
292C2×C3⋊Dic3—42no—
293C2×C3⋊Dic3C2411yescharacteristic
294C2×C3⋊Dic3C2414yes—
295C2×C3⋊Dic3C2411yescharacteristic
296C4×C3⋊D3—22no—
297C4×C3⋊D3—22no—
298C4×C3⋊D3—41no—
299C4×C3⋊D3—41no—
300C3×#67C2×Q818yescomplemented
301C2×C3×Dic3C2414yes—
302C2×C3×Dic3C2412yes—
303C2×C3×Dic3C2412yes—
304C2×C3×Dic3C2414yes—
305C2×C3×Dic3C2412yes—
306C3×C4×D3—24no—
307C3×C4×D3—44no—
308C3×Dic6—24no—
309C3×Dic6—44no—
310#627—42no—
311#627—44no—
312#626C2×Q818yescomplemented
313#624—42no—
314#624—41no—
315#624—42no—
316#624—41no—
317#624C2×Q814yescomplemented
318D3×Dic3—42no—
319D3×Dic3—44no—
320#554—92no—
321#554—94no—
322#554—92no—
323#554—94no—
324D4×Q8—32no—
325D4×Q8—92no—
326#544—92no—
327#543—92no—
328#543—92no—
329#533—92no—
330C2×C22⋊Q8—91no—
331C2×C22⋊Q8—92no—
332C2×C22⋊Q8—91no—
333#518—92no—
334C2×C4×D4—91no—
335C23×D3—32no—
336C23×D3—32no—
337C23×D3—61no—
338C2×C3×Q8—22no—
339C2×C3×Q8—22no—
340C2×C3×Q8—32no—
341C2×C3×Q8—34no—
342C2×C3×Q8—44no—
343C2×C3×Q8—44no—
344C2×C3×Q8—124no—
345C2×C3×Q8C22×D312yes—
346C2×C3×Q8C22×D312yes—
347C2×C3×Q8C22×D314yes—
348C2×C3×D4—32no—
349C22×C3×C4—21no—
350C22×C3×C4—22no—
351C22×C3×C4—32no—
352C22×C3×C4—34no—
353C22×C3×C4C22×D312yes—
354C22×C3×C4C22×D314yes—
355C2×#67—32no—
356C2×#67C22×D312yes—
357C22×Dic3—32no—
358C22×Dic3—34no—
359C22×Dic3—32no—
360C22×Dic3—34no—
361C22×Dic3—61no—
362C22×Dic3—62no—
363D3×Q8—44no—
364D3×Q8—124no—
365D3×D4—316no—
366C2×D12—32no—
367C2×C4×D3—32no—
368C2×C4×D3—32no—
369C2×C4×D3—32no—
370C2×C4×D3—34no—
371C2×C4×D3—32no—
372C2×C4×D3—32no—
373C2×C4×D3—32no—
374C2×C4×D3—32no—
375C2×C4×D3—34no—
376C2×C4×D3—34no—
377C2×C4×D3—32no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3—124no—
383C2×C4×D3—124no—
384C2×C4×D3—124no—
385C2×C4×D3C22×D312yes—
386C2×C4×D3C22×D314yes—
387C2×Dic6—34no—
388C2×Dic6—34no—
389C2×Dic6—34no—
390C2×Dic6C22×D312yes—
391C2×Dic6C22×D314yes—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—34no—
394C3×C4⋊C4—32no—
395C3×C4⋊C4—34no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—32no—
399C3×C22⋊C4—34no—
400C3×C22⋊C4—32no—
401C3×C22⋊C4—32no—
402C3×C22⋊C4—34no—
403C3×C42—32no—
404C3×C42—34no—
405#217—34no—
406#217—32no—
407#217C22×D312yes—
408#217C22×D314yes—
409(C2×D3)⋊C4—32no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—32no—
417(C2×D3)⋊C4—34no—
418(C2×D3)⋊C4—32no—
419(C2×D3)⋊C4—64no—
420(C2×D3)⋊C4—64no—
421(C2×D3)⋊C4C22×D314yes—
422(C2×D3)⋊C4C22×D312yes—
423C4⋊Dic3—32no—
424C4⋊Dic3—32no—
425C4⋊Dic3—34no—
426C4⋊Dic3—34no—
427C4⋊Dic3—34no—
428C4⋊Dic3—32no—
429C4⋊Dic3—34no—
430C4⋊Dic3—34no—
431C4⋊Dic3—62no—
432C4⋊Dic3—62no—
433C4⋊Dic3C22×D312yes—
434C4⋊Dic3C22×D314yes—
435Dic3⋊C4—34no—
436Dic3⋊C4—34no—
437Dic3⋊C4—34no—
438Dic3⋊C4—34no—
439Dic3⋊C4—34no—
440Dic3⋊C4—34no—
441Dic3⋊C4—34no—
442Dic3⋊C4—34no—
443Dic3⋊C4—34no—
444Dic3⋊C4—34no—
445Dic3⋊C4—34no—
446Dic3⋊C4—32no—
447Dic3⋊C4—64no—
448Dic3⋊C4—64no—
449Dic3⋊C4C22×D314yes—
450Dic3⋊C4C22×D314yes—
451Dic3⋊C4C22×D314yes—
452Dic3⋊C4C22×D314yes—
453Dic3⋊C4C22×D312yes—
454C4×Dic3—32no—
455C4×Dic3—34no—
456C4×Dic3—32no—
457C4×Dic3—34no—
458C4×Dic3C22×D312yes—
459C4×Dic3C22×D314yes—
460C22×C32—21no—
461C22×C32—21no—
462C22×C32C22×Q812yes—
463C22×C32C2511yescharacteristic
464C2×C3⋊D3—21no—
465C2×C3⋊D3—21no—
466C2×C3⋊D3—21no—
467C2×C3⋊D3—21no—
468C2×C3⋊D3—44no—
469C2×C3⋊D3C22×Q812yes—
470C2×C3⋊D3C22×Q812yes—
471C2×C3×D3—22no—
472C2×C3×D3—22no—
473C2×C3×D3C22×Q814yes—
474D32—44no—
475C32×C4—21no—
476C32×C4—24no—
477C32×C4H(5,𝔽2)12yes—
478C3⋊Dic3—21no—
479C3⋊Dic3—21no—
480C3⋊Dic3—24no—
481C3×Dic3—22no—
482C3×Dic3—24no—
483C3×Dic3—24no—
484C3×Dic3—22no—
485C3×Dic3C22×Q814yes—
486C22×Q8—32no—
487C22×Q8—91no—
488C22×Q8D3211yescharacteristic, complemented
489C22×D4—91no—
490C23×C4—91no—
491C23×C4—91no—
492C4⋊Q8—32no—
493C4⋊Q8—34no—
494C4⋊Q8—92no—
495C4⋊Q8—94no—
496#125—94no—
497#125—94no—
498#125—94no—
499C22⋊Q8—32no—
500C22⋊Q8—34no—
501C22⋊Q8—32no—
502C22⋊Q8—34no—
503C22⋊Q8—92no—
504C22⋊Q8—94no—
505C22⋊Q8—94no—
506C22⋊Q8—94no—
507C22⋊Q8—94no—
508C22⋊Q8—92no—
509C22⋊Q8—94no—
510C22⋊Q8—94no—
511C22⋊Q8—94no—
512C22⋊Q8—92no—
513C22⋊Q8—94no—
514C22⋊Q8—94no—
515C22⋊Q8—92no—
516C22⋊Q8—92no—
517C22⋊Q8—92no—
518C22⋊Q8—92no—
519C22⋊Q8—92no—
520C4×Q8—32no—
521C4×Q8—94no—
522C4×Q8—92no—
523C4×D4—32no—
524C4×D4—34no—
525C4×D4—94no—
526C4×D4—92no—
527C4×D4—92no—
528C4×D4—92no—
529C4×D4—94no—
530C4×D4—94no—
531#117—94no—
532C2×C4⋊C4—91no—
533C2×C4⋊C4—91no—
534C2×C4⋊C4—92no—
535C2×C4⋊C4—94no—
536C2×C4⋊C4—92no—
537C2×C4⋊C4—92no—
538C2×C4⋊C4—91no—
539C2×C22⋊C4—91no—
540C2×C22⋊C4—91no—
541C2×C22⋊C4—92no—
542C2×C22⋊C4—94no—
543C2×C22⋊C4—92no—
544C2×C42—91no—
545C23×C3—21no—
546C23×C3—32no—
547C23×C3C23×D312yes—
548C22×D3—32no—
549C22×D3—32no—
550C22×D3—38no—
551C22×D3—38no—
552C22×D3—64no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—122no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3C23×D312yes—
562C3×Q8—24no—
563C3×Q8—24no—
564C3×Q8—44no—
565C3×Q8—44no—
566C3×Q8—44no—
567C3×Q8—64no—
568C3×Q8—124no—
569C3×D4—38no—
570C2×C3×C4—24no—
571C2×C3×C4—24no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—24no—
575C2×C3×C4—32no—
576C2×C3×C4—34no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—34no—
580C2×C3×C4—44no—
581C2×C3×C4—44no—
582C2×C3×C4—64no—
583C2×C3×C4—124no—
584C2×C3×C4C23×D314yes—
585C2×C3×C4C23×D314yes—
586C2×C3×C4C23×D312yes—
587C2×C3×C4C23×D312yes—
588#67—38no—
589#67D3×Q818yescomplemented
590C2×Dic3—32no—
591C2×Dic3—34no—
592C2×Dic3—34no—
593C2×Dic3—32no—
594C2×Dic3—61no—
595C2×Dic3—61no—
596C2×Dic3—64no—
597C2×Dic3—122no—
598C2×Dic3—124no—
599C2×Dic3—122no—
600C2×Dic3—124no—
601C2×Dic3—122no—
602C2×Dic3—124no—
603C2×Dic3C23×D312yes—
604C2×Dic3C23×D314yes—
605C2×Dic3C23×D314yes—
606C2×Dic3C23×D312yes—
607C2×Dic3C23×D312yes—
608D12—38no—
609C4×D3—24no—
610C4×D3—38no—
611C4×D3—44no—
612C4×D3—64no—
613C4×D3—64no—
614C4×D3—122no—
615C4×D3—122no—
616C4×D3—122no—
617C4×D3—124no—
618C4×D3—122no—
619C4×D3—124no—
620C4×D3—122no—
621C4×D3—122no—
622C4×D3—124no—
623C4×D3—122no—
624C4×D3—122no—
625C4×D3—122no—
626Dic6—24no—
627Dic6—44no—
628Dic6—124no—
629Dic6—124no—
630Dic6—124no—
631C2×C32—22no—
632C2×C32C23×Q811yescharacteristic
633C2×C32C2×H(5,𝔽2)11yescharacteristic
634C2×C32#58511yescharacteristic
635C3⋊D3—22no—
636C3⋊D3—22no—
637C3×D3—24no—
638C24—91no—
639C24—91no—
640C2×Q8—32no—
641C2×Q8—34no—
642C2×Q8—42no—
643C2×Q8—94no—
644C2×Q8—92no—
645C2×Q8—124no—
646C2×Q8—362no—
647C2×Q8C2×D3212yes—
648C2×Q8C2×D3212yes—
649C2×D4—32no—
650C2×D4—92no—
651C2×D4—98no—
652C22×C4—32no—
653C22×C4—34no—
654C22×C4—91no—
655C22×C4—91no—
656C22×C4—92no—
657C22×C4—92no—
658C22×C4—91no—
659C22×C4—94no—
660C22×C4—92no—
661C22×C4—92no—
662C22×C4—91no—
663C22×C4—91no—
664C22×C4—91no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—362no—
668C22×C4—362no—
669C22×C4C2×D3211yescharacteristic
670C22×C4C2×D3212yes—
671C4⋊C4—32no—
672C4⋊C4—32no—
673C4⋊C4—34no—
674C4⋊C4—34no—
675C4⋊C4—34no—
676C4⋊C4—34no—
677C4⋊C4—34no—
678C4⋊C4—94no—
679C4⋊C4—92no—
680C4⋊C4—92no—
681C4⋊C4—94no—
682C4⋊C4—94no—
683C4⋊C4—94no—
684C4⋊C4—94no—
685C4⋊C4—94no—
686C4⋊C4—92no—
687C4⋊C4—92no—
688C4⋊C4—94no—
689C22⋊C4—32no—
690C22⋊C4—34no—
691C22⋊C4—32no—
692C22⋊C4—34no—
693C22⋊C4—94no—
694C22⋊C4—92no—
695C22⋊C4—92no—
696C22⋊C4—94no—
697C22⋊C4—94no—
698C22⋊C4—94no—
699C42—32no—
700C42—34no—
701C42—92no—
702C42—94no—
703C22×C3—22no—
704C22×C3—22no—
705C22×C3—22no—
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—21no—
709C22×C3—34no—
710C22×C3—62no—
711C22×C3—62no—
712C22×C3C2×D3×Q814yes—
713C22×C3C24×D312yes—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—34no—
717C2×D3—34no—
718C2×D3—62no—
719C2×D3—62no—
720C2×D3—62no—
721C2×D3—62no—
722C2×D3—62no—
723C2×D3—62no—
724C2×D3—121no—
725C2×D3—121no—
726C2×D3—121no—
727C2×D3—121no—
728C2×D3—128no—
729C2×D3—128no—
730C2×D3—128no—
731C2×D3C2×D3×Q814yes—
732C3×C4—22no—
733C3×C4—24no—
734C3×C4—22no—
735C3×C4—24no—
736C3×C4—22no—
737C3×C4—34no—
738C3×C4—44no—
739C3×C4—64no—
740C3×C4—62no—
741C3×C4—62no—
742C3×C4—64no—
743C3×C4#100414yes—
744Dic3—24no—
745Dic3—22no—
746Dic3—22no—
747Dic3—24no—
748Dic3—62no—
749Dic3—62no—
750Dic3—64no—
751Dic3—64no—
752Dic3—121no—
753Dic3—121no—
754Dic3—124no—
755Dic3C2×D3×Q814yes—
756C32#350111yescharacteristic, complemented, Sylow
757C23—32no—
758C23—94no—
759C23—91no—
760C23—91no—
761C23—94no—
762C23—361no—
763C23—361no—
764C23—361no—
765C23—361no—
766C23C22×D3211yescharacteristic
767Q8—24no—
768Q8—42no—
769Q8—64no—
770Q8—124no—
771Q8—362no—
772Q8—364no—
773D4—38no—
774D4—98no—
775C2×C4—22no—
776C2×C4—32no—
777C2×C4—32no—
778C2×C4—34no—
779C2×C4—34no—
780C2×C4—32no—
781C2×C4—42no—
782C2×C4—64no—
783C2×C4—94no—
784C2×C4—91no—
785C2×C4—94no—
786C2×C4—91no—
787C2×C4—124no—
788C2×C4—182no—
789C2×C4—182no—
790C2×C4—361no—
791C2×C4—361no—
792C2×C4—361no—
793C2×C4—362no—
794C2×C4—362no—
795C2×C4—361no—
796C2×C4—362no—
797C2×C4—364no—
798C2×C4—361no—
799C2×C4—362no—
800C2×C4C22×D3214yes—
801C2×C4C22×D3211yescharacteristic
802C2×C4C22×D3211yescharacteristic
803C2×C3—24no—
804C2×C3—24no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—64no—
809C2×C3C2×#100412yes—
810C2×C3C22×D3×Q812yes—
811C2×C3#596812yes—
812D3—24no—
813D3—64no—
814D3—64no—
815D3—122no—
816D3—122no—
817C22—21no—
818C22—21no—
819C22—34no—
820C22—62no—
821C22—62no—
822C22—92no—
823C22—92no—
824C22—181no—
825C22—181no—
826C22—181no—
827C22—181no—
828C22—364no—
829C22—364no—
830C22D32×Q812yes—
831C22C23×D3211yescharacteristic
832C4—21no—
833C4—24no—
834C4—34no—
835C4—64no—
836C4—62no—
837C4—62no—
838C4—64no—
839C4—184no—
840C4—181no—
841C4—181no—
842C4#6433012yes—
843C3—21no—
844C3#8676112yescomplemented
845C2—22no—
846C2—64no—
847C2—182no—
848C2—182no—
849C2C2×D32×Q811yescharacteristic
850C2#1059668911yescharacteristic
851C2C2×#6433011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
prime radicalC2×#3811C22
hypercenterC22×Q8D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64155C2semidirect
2. C3×Q8×#67C2semidirect
3. #10595434C2semidirect
4. D3×#946C2semidirect
5. #10595403C2semidirect
6. #10595375C2semidirect
7. #10595374C2semidirect
8. #10595372C2semidirect
9. #10595371C2semidirect
12. #10594993C2semidirect
13. #10594981C2semidirect
14. #10594959C2semidirect
15. #10594925C2semidirect
17. C22×C32×Q8C22semidirect
19. C2×C3×D3×Q8C22semidirect
22. C2×#3797C22semidirect
25. #64155C22semidirect
26. #64155C22semidirect
28. C2×C4⋊(C3⋊Dic3)C22semidirect
29. C2×#3750C22semidirect
30. C3×#946C22semidirect
31. C3×#946C22semidirect
32. C3×Q8×Dic3C22semidirect
33. C3×#944C22semidirect
34. C3×#944C22semidirect
37. C3×#924C22semidirect
38. C3×#924C22semidirect
39. #63982C22semidirect
40. #63982C22semidirect
47. #63918C22semidirect
50. #63900C22semidirect
51. #63899C22semidirect
53. #63895C22semidirect
54. #63893C22semidirect
55. D3×C4⋊Dic3C22semidirect
57. #63888C22semidirect
58. #63887C22semidirect
60. #63883C22semidirect
64. D3×Dic3⋊C4C22semidirect
66. #63867C22semidirect
68. #63856C22semidirect
69. #63851C22semidirect
70. #63846C22semidirect
71. #63845C22semidirect
72. Dic3×Dic6C22semidirect
73. #63839C22semidirect
74. #63837C22semidirect
78. Q8×#67D3semidirect
120. #3811Q8semidirect
168. C22×C3×Q8C2×D3semidirect
170. C2×D3×Q8C2×D3semidirect
199. #946C2×D3semidirect
200. #946C2×D3semidirect
202. Q8×Dic3C2×D3semidirect
204. #944C2×D3semidirect
205. #944C2×D3semidirect
220. #924C2×D3semidirect
221. #924C2×D3semidirect
277. C22×C3⋊D3C2×Q8semidirect
283. C2×D32C2×Q8semidirect
300. C3×#67C2×Q8semidirect
312. #626C2×Q8semidirect
317. #624C2×Q8semidirect
488. C22×Q8D32semidirect
589. #67D3×Q8semidirect
756. C32#3501semidirect
844. C3#86761semidirect

Maximal subgroups

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

subgroupindex
C2×#641552
C3×Q8×#672
#105954342
D3×#9462
#105954032
#105953752
#105953742
#105953722
#105953712
#105950582
C4×#38112
#105949932
#105949812
#105949592
#105949252
#867613