Finite Group Databasebeta

← #11906208

Subgroups — #11906208

Order 1152.

2413 conjugacy classes of subgroups.

The subgroup lattice has 859 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2C3×#5539C212yesmaximal, complemented
3#10595274C211yesmaximal, characteristic, complemented
4D4×#627C211yesmaximal, characteristic, complemented
5#10595223C212yesmaximal
6#10594956C214yesmaximal, complemented
7#10594925C212yesmaximal, complemented
8C2×#63865C212yesmaximal, complemented
9#10594484C211yesmaximal, characteristic, complemented
10#10594379C211yesmaximal, characteristic, complemented
11#10594325C212yesmaximal, complemented
12#10594180C214yesmaximal, complemented
13#10594168C212yesmaximal, complemented
14#10594072C212yesmaximal, complemented
15#10593938C212yesmaximal, complemented
16#10593882C211yesmaximal, characteristic, complemented
17#10593854C211yesmaximal, characteristic, complemented
18#86949—32nomaximal
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C4×C3⋊D3C2212yes—
21C22×#627C2212yescomplemented
22C2×#3797C2212yescomplemented
23C32×C4×D4C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25C4×#638C2212yes—
26#64102C2211yescharacteristic
27C4⋊C4×C3⋊D3C2211yescharacteristic
28#64090C2212yes—
29C22⋊C4×C3⋊D3C2212yes—
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C42×C3⋊D3C2211yescharacteristic
32C3×D4×Dic3C2212yes—
33C3×D4×Dic3C2212yes—
34C3×#924C2214yescomplemented
35C2×C3×Dic3⋊C4C2214yescomplemented
36C3×#890C2212yescomplemented
37C3×#888C2212yescomplemented
38C3×#878C2214yescomplemented
39C3×#878C2214yescomplemented
40C3×#870C2212yescomplemented
41C3×C4×Dic6C2212yescomplemented
42#63982C2212yescomplemented
43#63982C2212yescomplemented
44#63974C2214yes—
45C2×#3724C2212yescomplemented
46#63964C2214yescomplemented
47#63964C2214yescomplemented
48C2×#3722C2214yes—
49#63952C2214yes—
50#63952C2214yes—
51#63919C2211yescharacteristic, complemented
52#63919C2211yescharacteristic, complemented
53#63919C2211yescharacteristic, complemented
54#63918C2212yescomplemented
55C4×#627C2211yescharacteristic, complemented
56C4×#627C2211yescharacteristic, complemented
57#63900C2212yescomplemented
58#63895C2214yescomplemented
59#63895C2214yescomplemented
60#63894C2212yes—
61#63894C2212yes—
62#63888C2214yescomplemented
63#63888C2214yescomplemented
64#63883C2214yescomplemented
65#63874C2212yes—
66#63873C2211yescharacteristic, complemented
67#63871C2214yes—
68#63871C2212yes—
69#63870C2212yescomplemented
70#63869C2212yescomplemented
71#63865C2214yes—
72#63865C2211yescharacteristic
73#63865C2212yes—
74#63865C2212yes—
75#63865C2211yescharacteristic
76#63865C2212yescomplemented
77#63865C2212yescomplemented
78#63865C2214yescomplemented
79#63849C2212yes—
80#63847C2214yescomplemented
81#63839C2214yescomplemented
82#63838C2212yescomplemented
83#63838C2212yescomplemented
84C3×#554—32no—
85#5729—32no—
86#5727—32no—
87#5690—32no—
88#5690—32no—
89#5689—32no—
90#5688—32no—
91#5636—34no—
92#5636—34no—
93#5634—34no—
94#5634—34no—
95#5632—34no—
96D3×C22⋊Q8—34no—
97#5579—32no—
98#5578—32no—
99#5545—32no—
100#5545—32no—
101C4×D3×D4—32no—
102C4×D3×D4—61no—
103#5539—32no—
104#5539D312yescomplemented
105D4×Dic6—32no—
106#5511—34no—
107C2×#896—34no—
108C23×C3⋊D3C2312yes—
109C2×C32×D4C2311yescharacteristic
110C22×C32×C4C2312yes—
111C2×#638C2312yes—
112C22×C3⋊Dic3C2312yes—
113D4×C3⋊D3Q818yescomplemented
114C2×C4⋊(C3⋊D3)C2311yescharacteristic
115C2×C4×C3⋊D3—44no—
116C2×C4×C3⋊D3C2312yes—
117C2×C4×C3⋊D3C2311yescharacteristic
118C2×C4×C3⋊D3C2311yescharacteristic
119C2×C4×C3⋊D3C2312yes—
120C2×C4×C3⋊D3C2312yes—
121C2×C4×C3⋊D3C2311yescharacteristic
122C22×C3×Dic3C2314yes—
123C22×C3×Dic3C2314yes—
124C2×C3×Dic6C2312yes—
125C2×C3×Dic6C2314yes—
126C2×#627—44no—
127C2×#627C2311yescharacteristic
128C2×#627C2312yes—
129C2×#627C2311yescharacteristic
130C2×#627C2314yes—
131C2×#627C2312yes—
132C2×#624C2314yes—
133C2×#624C2314yes—
134#3797—44no—
135C32×C4⋊C4C2311yescharacteristic
136C32×C22⋊C4C2312yes—
137C32×C42C2311yescharacteristic
138#3757C2312yes—
139#3752C2312yes—
140#3752C2312yes—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142#3750C2312yes—
143C4×C3⋊Dic3C2311yescharacteristic
144C4×C3⋊Dic3C2311yescharacteristic
145C4×C3⋊Dic3C2311yescharacteristic
146C3×#217C2314yes—
147C3×#217C2314yes—
148C3×C4⋊Dic3C2312yes—
149C3×C4⋊Dic3C2314yes—
150C3×C4⋊Dic3C2312yes—
151C3×C4⋊Dic3C2312yes—
152C3×Dic3⋊C4C2314yes—
153C3×Dic3⋊C4C2314yes—
154C3×Dic3⋊C4C2314yes—
155C3×Dic3⋊C4C2312yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2312yes—
158C3×C4×Dic3C2312yes—
159C3×C4×Dic3C2312yes—
160#3724C2312yes—
161#3724C2312yes—
162#3724C2312yes—
163#3724C2312yes—
164#3724C2314yes—
165#3724C2311yescharacteristic
166#3724C2311yescharacteristic
167Dic3⋊Dic3C2314yes—
168Dic3⋊Dic3C2314yes—
169Dic3⋊Dic3C2312yes—
170Dic3⋊Dic3C2312yes—
171#3722C2314yes—
172#3722C2312yes—
173#3722C2312yes—
174#3722C2314yes—
175#3722C2314yes—
176Dic32C2314yes—
177#3501—91noSylow
178C2×D3×Q8—34no—
179C2×D3×D4—32no—
180C2×D3×D4—61no—
181C22×C4×D3—34no—
182C22×C4×D3—62no—
183C22×Dic6—34no—
184C3×C4⋊Q8—32no—
185C3×#125—32no—
186C3×#125—32no—
187C3×C22⋊Q8—34no—
188C3×C22⋊Q8—34no—
189C3×C22⋊Q8—34no—
190C3×C4×Q8—32no—
191C3×C4×D4—21no—
192C3×C4×D4—32no—
193C3×C4×D4—32no—
194C3×C4×D4C2×D312yes—
195C2×C3×C4⋊C4—34no—
196#946—32no—
197#946—34no—
198#946—34no—
199#946—34no—
200#944—32no—
201#944—34no—
202D4×Dic3—32no—
203D4×Dic3—61no—
204D4×Dic3C2×D312yes—
205D4×Dic3C2×D312yes—
206C4×#67—34no—
207C4×#67—34no—
208C4×#67—34no—
209C4×#67—62no—
210C2×(C2×D3)⋊C4—34no—
211C2×(C2×D3)⋊C4—34no—
212#924—34no—
213#924—34no—
214#924C2×D314yescomplemented
215C2×Dic3⋊C4—34no—
216C2×Dic3⋊C4C2×D314yescomplemented
217#897—32no—
218#897—34no—
219#897—34no—
220#897—34no—
221#896—34no—
222#896—34no—
223#896—34no—
224#896—34no—
225#896—34no—
226#896—34no—
227#896—34no—
228#896—34no—
229#896—34no—
230#896—34no—
231#896—34no—
232#896—32no—
233#896—32no—
234#896—34no—
235#893—32no—
236#893—32no—
237#893—32no—
238#893—61no—
239#892—32no—
240#892—32no—
241D3×C4⋊C4—32no—
242D3×C4⋊C4—34no—
243D3×C4⋊C4—34no—
244D3×C4⋊C4—34no—
245D3×C4⋊C4—61no—
246#890—32no—
247#890C2×D312yescomplemented
248#889—34no—
249#889—34no—
250#889—32no—
251#889—32no—
252#888—34no—
253#888—32no—
254#888—32no—
255#888—32no—
256#888—32no—
257#888C2×D312yescomplemented
258#887—34no—
259#887—34no—
260#67⋊C4—34no—
261#67⋊C4—34no—
262#67⋊C4—34no—
263#67⋊C4—62no—
264D3×C22⋊C4—34no—
265D3×C22⋊C4—34no—
266D3×C22⋊C4—34no—
267D3×C22⋊C4—62no—
268#878—34no—
269#878—34no—
270#878—34no—
271#878—34no—
272#878C2×D314yescomplemented
273#878C2×D314yescomplemented
274C4×D12—32no—
275C4×D12—32no—
276C4×D12—32no—
277C4×D12—61no—
278#872—32no—
279#872—32no—
280C42×D3—32no—
281C42×D3—61no—
282#870—32no—
283#870C2×D312yescomplemented
284#869—32no—
285C4×Dic6—32no—
286C4×Dic6—32no—
287C4×Dic6C2×D312yescomplemented
288C23×C32C2412yes—
289C22×C3⋊D3—42no—
290C22×C3⋊D3—42no—
291C22×C3⋊D3C2×Q818yescomplemented
292C22×C3⋊D3C2411yescharacteristic
293C22×C3⋊D3C2412yes—
294C32×D4C2×Q814yescomplemented
295C2×C32×C4—42no—
296C2×C32×C4C2411yescharacteristic
297C2×C32×C4C2411yescharacteristic
298C2×C32×C4C2412yes—
299C2×C32×C4C2411yescharacteristic
300#638C2×Q818yescomplemented
301C2×C3⋊Dic3—24no—
302C2×C3⋊Dic3C2411yescharacteristic
303C2×C3⋊Dic3C2412yes—
304C2×C3⋊Dic3C2411yescharacteristic
305C2×C3⋊Dic3C2411yescharacteristic
306C4⋊(C3⋊D3)C2×Q814yescomplemented
307C4×C3⋊D3—22no—
308C4×C3⋊D3—24no—
309C4×C3⋊D3—42no—
310C4×C3⋊D3—42no—
311C4×C3⋊D3—41no—
312C4×C3⋊D3C2×Q814yescomplemented
313C2×C3×Dic3—44no—
314C2×C3×Dic3—44no—
315C2×C3×Dic3C2414yes—
316C2×C3×Dic3C2414yes—
317C2×C3×Dic3C2412yes—
318C2×C3×Dic3C2412yes—
319C2×C3×Dic3C2412yes—
320C2×C3×Dic3C2412yes—
321C3×Dic6—44no—
322C3×Dic6—42no—
323#627—22no—
324#627—24no—
325#627—22no—
326#627—44no—
327#627—42no—
328#624—44no—
329#624—44no—
330#554—32no—
331#554—94no—
332#554—91no—
333#554—92no—
334#554—92no—
335#554—91no—
336D4×Q8—91no—
337D4×Q8—92no—
338D4×Q8—91no—
339#544—92no—
340#543—94no—
341#533—91no—
342#533—91no—
343C2×C22⋊Q8—92no—
344C2×C22⋊Q8—92no—
345#518—92no—
346C2×C4×D4—91no—
347C23×D3—34no—
348C23×D3—62no—
349C2×C3×Q8—32no—
350C2×C3×Q8—34no—
351C2×C3×D4—21no—
352C2×C3×D4C22×D312yes—
353C22×C3×C4—22no—
354C22×C3×C4—34no—
355C22×C3×C4—34no—
356C22×C3×C4C22×D314yes—
357C2×#67—34no—
358C2×#67—62no—
359C22×Dic3—34no—
360C22×Dic3—62no—
361C22×Dic3C22×D314yes—
362C22×Dic3C22×D314yes—
363D3×Q8—128no—
364D3×D4—316no—
365D3×D4—68no—
366C2×D12—32no—
367C2×D12—61no—
368C2×C4×D3—32no—
369C2×C4×D3—32no—
370C2×C4×D3—34no—
371C2×C4×D3—32no—
372C2×C4×D3—34no—
373C2×C4×D3—34no—
374C2×C4×D3—34no—
375C2×C4×D3—34no—
376C2×C4×D3—34no—
377C2×C4×D3—34no—
378C2×C4×D3—61no—
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—128no—
385C2×C4×D3—128no—
386C2×Dic6—32no—
387C2×Dic6—32no—
388C2×Dic6—34no—
389C2×Dic6—34no—
390C2×Dic6—34no—
391C2×Dic6—34no—
392C2×Dic6—128no—
393C2×Dic6C22×D312yes—
394C2×Dic6C22×D314yes—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—34no—
397C3×C4⋊C4—34no—
398C3×C4⋊C4—32no—
399C3×C4⋊C4—32no—
400C3×C4⋊C4—34no—
401C3×C4⋊C4—32no—
402C3×C4⋊C4—32no—
403C3×C4⋊C4—34no—
404C3×C4⋊C4—32no—
405C3×C4⋊C4—34no—
406C3×C4⋊C4C22×D312yes—
407C3×C22⋊C4—22no—
408C3×C22⋊C4—34no—
409C3×C22⋊C4—34no—
410C3×C22⋊C4C22×D314yes—
411C3×C42—21no—
412C3×C42—32no—
413C3×C42—32no—
414C3×C42C22×D312yes—
415#217—34no—
416#217—62no—
417#217C22×D314yes—
418#217C22×D314yes—
419(C2×D3)⋊C4—34no—
420(C2×D3)⋊C4—34no—
421(C2×D3)⋊C4—32no—
422(C2×D3)⋊C4—32no—
423(C2×D3)⋊C4—32no—
424(C2×D3)⋊C4—32no—
425(C2×D3)⋊C4—34no—
426(C2×D3)⋊C4—34no—
427(C2×D3)⋊C4—34no—
428(C2×D3)⋊C4—34no—
429(C2×D3)⋊C4—34no—
430(C2×D3)⋊C4—34no—
431(C2×D3)⋊C4—62no—
432(C2×D3)⋊C4—62no—
433C4⋊Dic3—32no—
434C4⋊Dic3—32no—
435C4⋊Dic3—32no—
436C4⋊Dic3—34no—
437C4⋊Dic3—34no—
438C4⋊Dic3—61no—
439C4⋊Dic3C22×D312yes—
440C4⋊Dic3C22×D312yes—
441C4⋊Dic3C22×D312yes—
442C4⋊Dic3C22×D314yes—
443Dic3⋊C4—34no—
444Dic3⋊C4—32no—
445Dic3⋊C4—32no—
446Dic3⋊C4—32no—
447Dic3⋊C4—32no—
448Dic3⋊C4—34no—
449Dic3⋊C4—34no—
450Dic3⋊C4—32no—
451Dic3⋊C4—32no—
452Dic3⋊C4—32no—
453Dic3⋊C4—32no—
454Dic3⋊C4—34no—
455Dic3⋊C4—34no—
456Dic3⋊C4—34no—
457Dic3⋊C4—34no—
458Dic3⋊C4—62no—
459Dic3⋊C4C22×D312yes—
460Dic3⋊C4C22×D312yes—
461Dic3⋊C4C22×D314yes—
462Dic3⋊C4C22×D314yes—
463Dic3⋊C4C22×D314yes—
464Dic3⋊C4C22×D314yes—
465C4×Dic3—32no—
466C4×Dic3—32no—
467C4×Dic3—32no—
468C4×Dic3—34no—
469C4×Dic3—34no—
470C4×Dic3—61no—
471C4×Dic3—61no—
472C4×Dic3—61no—
473C4×Dic3C22×D312yes—
474C4×Dic3C22×D312yes—
475C22×C32—22no—
476C22×C32—22no—
477C22×C32C22×Q814yes—
478C22×C32C2511yescharacteristic
479C2×C3⋊D3—21no—
480C2×C3⋊D3—21no—
481C2×C3⋊D3—22no—
482C2×C3⋊D3—22no—
483C2×C3⋊D3—48no—
484C2×C3⋊D3C22×Q812yes—
485C2×C3⋊D3C22×Q814yes—
486C32×C4—21no—
487C32×C4—22no—
488C32×C4—21no—
489C32×C4C22×Q812yes—
490C3⋊Dic3—22no—
491C3⋊Dic3—21no—
492C3⋊Dic3C22×Q812yes—
493C3⋊Dic3H(5,𝔽2)12yes—
494C3×Dic3—22no—
495C3×Dic3—24no—
496C3×Dic3—22no—
497C3×Dic3—22no—
498C3×Dic3—24no—
499C3×Dic3—22no—
500C22×Q8—92no—
501C22×Q8—92no—
502C22×D4—91no—
503C23×C4—92no—
504C4⋊Q8—32no—
505C4⋊Q8—92no—
506C4⋊Q8—91no—
507C4⋊Q8—91no—
508C4⋊Q8—91no—
509C4⋊Q8—94no—
510C4⋊Q8—91no—
511#125—32no—
512#125—32no—
513#125—92no—
514#125—92no—
515#125—94no—
516C22⋊Q8—34no—
517C22⋊Q8—34no—
518C22⋊Q8—34no—
519C22⋊Q8—92no—
520C22⋊Q8—92no—
521C22⋊Q8—94no—
522C22⋊Q8—94no—
523C22⋊Q8—91no—
524C22⋊Q8—92no—
525C22⋊Q8—91no—
526C22⋊Q8—94no—
527C22⋊Q8—92no—
528C22⋊Q8—92no—
529C22⋊Q8—94no—
530C22⋊Q8—92no—
531C22⋊Q8—94no—
532C22⋊Q8—94no—
533C22⋊Q8—94no—
534C22⋊Q8—92no—
535C22⋊Q8—94no—
536C22⋊Q8—94no—
537C4×Q8—32no—
538C4×Q8—91no—
539C4×Q8—91no—
540C4×Q8—92no—
541C4×Q8—92no—
542C4×D4—32no—
543C4×D4—32no—
544C4×D4—92no—
545C4×D4—92no—
546C4×D4—94no—
547C4×D4—94no—
548C4×D4—91no—
549C4×D4—92no—
550C4×D4—91no—
551C4×D4—92no—
552C4×D4—91no—
553C4×D4D3211yescharacteristic
554#117—92no—
555#117—92no—
556C2×C4⋊C4—34no—
557C2×C4⋊C4—94no—
558C2×C4⋊C4—92no—
559C2×C4⋊C4—92no—
560C2×C4⋊C4—91no—
561C2×C22⋊C4—94no—
562C2×C22⋊C4—94no—
563C2×C22⋊C4—92no—
564C2×C42—91no—
565C23×C3—22no—
566C23×C3C23×D314yes—
567C22×D3—32no—
568C22×D3—34no—
569C22×D3—316no—
570C22×D3—61no—
571C22×D3—68no—
572C22×D3—62no—
573C22×D3—124no—
574C22×D3—124no—
575C22×D3—124no—
576C22×D3—124no—
577C3×Q8—124no—
578C3×Q8—122no—
579C3×D4—24no—
580C3×D4D3×Q818yescomplemented
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—22no—
585C2×C3×C4—34no—
586C2×C3×C4—34no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—44no—
592C2×C3×C4—44no—
593C2×C3×C4—124no—
594C2×C3×C4—124no—
595C2×C3×C4C23×D312yes—
596C2×C3×C4C23×D312yes—
597C2×C3×C4C23×D314yes—
598C2×C3×C4C23×D312yes—
599#67—316no—
600#67—68no—
601C2×Dic3—32no—
602C2×Dic3—32no—
603C2×Dic3—32no—
604C2×Dic3—34no—
605C2×Dic3—44no—
606C2×Dic3—44no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—62no—
611C2×Dic3—68no—
612C2×Dic3—124no—
613C2×Dic3C23×D314yes—
614C2×Dic3C23×D314yes—
615C2×Dic3C23×D312yes—
616C2×Dic3C23×D312yes—
617C2×Dic3C23×D312yes—
618C2×Dic3C23×D312yes—
619D12—38no—
620D12—64no—
621C4×D3—38no—
622C4×D3—64no—
623C4×D3—64no—
624C4×D3—68no—
625C4×D3—64no—
626C4×D3—124no—
627C4×D3—124no—
628C4×D3—124no—
629C4×D3—124no—
630C4×D3—124no—
631C4×D3—122no—
632C4×D3—124no—
633C4×D3—124no—
634C4×D3—124no—
635C4×D3—122no—
636C4×D3—124no—
637Dic6—42no—
638Dic6—44no—
639Dic6—64no—
640Dic6—68no—
641Dic6—64no—
642Dic6—124no—
643Dic6—124no—
644Dic6—124no—
645C2×C32—24no—
646C2×C32C23×Q811yescharacteristic
647C2×C32C2×H(5,𝔽2)11yescharacteristic
648C2×C32#58511yescharacteristic
649C3⋊D3—22no—
650C3⋊D3—24no—
651C24—92no—
652C2×Q8—32no—
653C2×Q8—34no—
654C2×Q8—91no—
655C2×Q8—91no—
656C2×Q8—92no—
657C2×Q8—92no—
658C2×Q8—94no—
659C2×Q8—364no—
660C2×Q8—364no—
661C2×D4—92no—
662C2×D4—98no—
663C2×D4—91no—
664C2×D4C2×D3211yescharacteristic
665C22×C4—34no—
666C22×C4—34no—
667C22×C4—94no—
668C22×C4—94no—
669C22×C4—91no—
670C22×C4—92no—
671C22×C4—91no—
672C22×C4—92no—
673C22×C4—91no—
674C22×C4—92no—
675C22×C4—92no—
676C22×C4—364no—
677C22×C4C2×D3212yes—
678C4⋊C4—32no—
679C4⋊C4—34no—
680C4⋊C4—34no—
681C4⋊C4—34no—
682C4⋊C4—32no—
683C4⋊C4—34no—
684C4⋊C4—32no—
685C4⋊C4—32no—
686C4⋊C4—32no—
687C4⋊C4—34no—
688C4⋊C4—91no—
689C4⋊C4—91no—
690C4⋊C4—92no—
691C4⋊C4—94no—
692C4⋊C4—94no—
693C4⋊C4—94no—
694C4⋊C4—92no—
695C4⋊C4—92no—
696C4⋊C4—92no—
697C4⋊C4—92no—
698C4⋊C4—92no—
699C4⋊C4—92no—
700C4⋊C4—91no—
701C4⋊C4C2×D3211yescharacteristic
702C22⋊C4—34no—
703C22⋊C4—34no—
704C22⋊C4—92no—
705C22⋊C4—92no—
706C22⋊C4—94no—
707C22⋊C4—94no—
708C22⋊C4—94no—
709C22⋊C4—92no—
710C22⋊C4—92no—
711C22⋊C4—92no—
712C22⋊C4C2×D3212yes—
713C42—32no—
714C42—32no—
715C42—94no—
716C42—91no—
717C42—91no—
718C42—91no—
719C42C2×D3211yescharacteristic
720C22×C3—24no—
721C22×C3—24no—
722C22×C3—24no—
723C22×C3—21no—
724C22×C3—42no—
725C22×C3—42no—
726C22×C3C2×D3×Q818yes—
727C22×C3C24×D312yes—
728C2×D3—34no—
729C2×D3—38no—
730C2×D3—62no—
731C2×D3—64no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—64no—
735C2×D3—62no—
736C2×D3—64no—
737C2×D3—62no—
738C2×D3—122no—
739C2×D3—122no—
740C2×D3—1216no—
741C2×D3—1216no—
742C3×C4—22no—
743C3×C4—22no—
744C3×C4—24no—
745C3×C4—22no—
746C3×C4—22no—
747C3×C4—42no—
748C3×C4—41no—
749C3×C4—64no—
750C3×C4—62no—
751C3×C4—62no—
752C3×C4—62no—
753C3×C4—64no—
754C3×C4—62no—
755C3×C4C2×D3×Q814yes—
756Dic3—22no—
757Dic3—22no—
758Dic3—24no—
759Dic3—22no—
760Dic3—24no—
761Dic3—22no—
762Dic3—34no—
763Dic3—34no—
764Dic3—62no—
765Dic3—62no—
766Dic3—62no—
767Dic3—64no—
768Dic3—122no—
769Dic3—121no—
770C32#350111yescharacteristic, complemented, Sylow
771C23—91no—
772C23—92no—
773C23—98no—
774C23—362no—
775C23—362no—
776C23C22×D3212yes—
777Q8—124no—
778Q8—122no—
779Q8—182no—
780Q8—184no—
781Q8—182no—
782Q8—364no—
783Q8—362no—
784D4—98no—
785D4—94no—
786D4#379714yescomplemented
787C2×C4—32no—
788C2×C4—32no—
789C2×C4—32no—
790C2×C4—32no—
791C2×C4—34no—
792C2×C4—34no—
793C2×C4—42no—
794C2×C4—91no—
795C2×C4—91no—
796C2×C4—94no—
797C2×C4—91no—
798C2×C4—92no—
799C2×C4—124no—
800C2×C4—124no—
801C2×C4—182no—
802C2×C4—184no—
803C2×C4—184no—
804C2×C4—362no—
805C2×C4—362no—
806C2×C4—361no—
807C2×C4—364no—
808C2×C4—364no—
809C2×C4C22×D3211yescharacteristic
810C2×C4C22×D3211yescharacteristic
811C2×C4C22×D3212yes—
812C2×C4C22×D3211yescharacteristic
813C2×C3—28no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—44no—
818C2×C3C22×D3×Q812yes—
819C2×C3#596412yes—
820C2×C3D3×H(5,𝔽2)12yes—
821D3—64no—
822D3—64no—
823D3—68no—
824D3—124no—
825C22—22no—
826C22—22no—
827C22—92no—
828C22—94no—
829C22—182no—
830C22—181no—
831C22—182no—
832C22—181no—
833C22—368no—
834C22C2×#379714yes—
835C22C23×D3211yescharacteristic
836C4—21no—
837C4—22no—
838C4—21no—
839C4—62no—
840C4—64no—
841C4—62no—
842C4—62no—
843C4—64no—
844C4—62no—
845C4—92no—
846C4—92no—
847C4—182no—
848C4—181no—
849C4C2×#379712yes—
850C3—21no—
851C3#8694912yescomplemented
852C2—24no—
853C2—182no—
854C2—184no—
855C2C22×#379711yescharacteristic
856C2#1059667511yescharacteristic
857C2#1059669511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC2×D4×C3⋊D3C22
hypercenterC4×D4D32
hypocenterC32#3501
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5539C2semidirect
3. #10595274C2semidirect
4. D4×#627C2semidirect
6. #10594956C2semidirect
7. #10594925C2semidirect
8. C2×#63865C2semidirect
9. #10594484C2semidirect
10. #10594379C2semidirect
11. #10594325C2semidirect
12. #10594180C2semidirect
13. #10594168C2semidirect
14. #10594072C2semidirect
15. #10593938C2semidirect
16. #10593882C2semidirect
17. #10593854C2semidirect
21. C22×#627C22semidirect
22. C2×#3797C22semidirect
34. C3×#924C22semidirect
35. C2×C3×Dic3⋊C4C22semidirect
36. C3×#890C22semidirect
37. C3×#888C22semidirect
38. C3×#878C22semidirect
39. C3×#878C22semidirect
40. C3×#870C22semidirect
41. C3×C4×Dic6C22semidirect
42. #63982C22semidirect
43. #63982C22semidirect
45. C2×#3724C22semidirect
46. #63964C22semidirect
47. #63964C22semidirect
51. #63919C22semidirect
52. #63919C22semidirect
53. #63919C22semidirect
54. #63918C22semidirect
55. C4×#627C22semidirect
56. C4×#627C22semidirect
57. #63900C22semidirect
58. #63895C22semidirect
59. #63895C22semidirect
62. #63888C22semidirect
63. #63888C22semidirect
64. #63883C22semidirect
66. #63873C22semidirect
69. #63870C22semidirect
70. #63869C22semidirect
76. #63865C22semidirect
77. #63865C22semidirect
78. #63865C22semidirect
80. #63847C22semidirect
81. #63839C22semidirect
82. #63838C22semidirect
83. #63838C22semidirect
104. #5539D3semidirect
113. D4×C3⋊D3Q8semidirect
214. #924C2×D3semidirect
216. C2×Dic3⋊C4C2×D3semidirect
247. #890C2×D3semidirect
257. #888C2×D3semidirect
272. #878C2×D3semidirect
273. #878C2×D3semidirect
283. #870C2×D3semidirect
287. C4×Dic6C2×D3semidirect
291. C22×C3⋊D3C2×Q8semidirect
294. C32×D4C2×Q8semidirect
300. #638C2×Q8semidirect
306. C4⋊(C3⋊D3)C2×Q8semidirect
312. C4×C3⋊D3C2×Q8semidirect
580. C3×D4D3×Q8semidirect
770. C32#3501semidirect
786. D4#3797semidirect
851. C3#86949semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
C3×#55392
#105952742
D4×#6272
#105952232
#105949562
#105949252
C2×#638652
#105944842
#105943792
#105943252
#105941802
#105941682
#105940722
#105939382
#105938822
#105938542
#869493