Finite Group Databasebeta

← #11904795

Subgroups — #11904795

Order 1152.

3209 conjugacy classes of subgroups.

The subgroup lattice has 1023 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64309C211yesmaximal, characteristic, complemented
2C2×#64306C211yesmaximal, characteristic, complemented
3#10596077C211yesmaximal, characteristic, complemented
4C3×#5608C212yesmaximal, complemented
5#10595301C212yesmaximal, complemented
6#10595296C214yesmaximal, complemented
7#10595240C211yesmaximal, characteristic, complemented
8#10595142C212yesmaximal, complemented
9#10595134C212yesmaximal, complemented
10#10594925C211yesmaximal, characteristic, complemented
11#10594884C212yesmaximal, complemented
12D3×#897C212yesmaximal, complemented
13#10594529C211yesmaximal, characteristic, complemented
14#10594509C211yesmaximal, characteristic, complemented
15#10594276C212yesmaximal, complemented
16#10594072C212yesmaximal, complemented
17#10594065C214yesmaximal, complemented
18#86380—32nomaximal
19C2×#3830C2211yescharacteristic, complemented
20C22×C4×C3⋊D3C2211yescharacteristic
21C2×C3×#237C2212yescomplemented
22C2×C3×#235C2212yes—
23C2×#3811C2212yes—
24C22×#627C2212yescomplemented
25C2×#3805C2211yescharacteristic
26C2×#3805C2211yescharacteristic
27C2×#3805C2212yescomplemented
28C2×#3804C2214yescomplemented
29#64309—28no—
30#64306—28no—
31C2×#3802C2211yescharacteristic
32C2×C4×D32C2212yes—
33C2×#3798C2211yescharacteristic
34C2×#3798C2211yescharacteristic
35C2×#3797C2211yescharacteristic
36C2×#3797C2211yescharacteristic, complemented
37C2×#3796C2212yes—
38C2×D3×Dic6C2212yescomplemented
39C32×#121C2211yescharacteristic, complemented
40#64147C2211yescharacteristic
41#64146C2212yes—
42D4×C3⋊Dic3C2212yescomplemented
43#64133C2211yescharacteristic, complemented
44#64106C2211yescharacteristic
45#64101C2211yescharacteristic, complemented
46#64092C2212yescomplemented
47#64090C2212yes—
48C3×#939C2214yescomplemented
49C3×#938C2214yescomplemented
50C3×#938C2212yescomplemented
51C3×#924C2212yescomplemented
52C3×#897C2212yescomplemented
53C3×D3×C4⋊C4C2212yescomplemented
54C3×#884C2214yescomplemented
55C3×#878C2214yescomplemented
56#63983C2214yes—
57#63982C2212yescomplemented
58#63982C2212yescomplemented
59#63980C2212yescomplemented
60#63974C2212yes—
61Dic3×#67C2214yescomplemented
62#63969C2214yescomplemented
63#63969C2214yescomplemented
64#63959C2214yescomplemented
65#63958C2214yescomplemented
66#63952C2214yes—
67D3×(C2×D3)⋊C4C2214yes—
68#63919C2212yescomplemented
69#63915C2212yescomplemented
70#63904C2214yescomplemented
71C4×#625C2212yescomplemented
72#63900C2211yescharacteristic, complemented
73#63895C2214yes—
74#63893C2214yescomplemented
75D3×C4⋊Dic3C2214yescomplemented
76#63884C2214yescomplemented
77#63883C2212yescomplemented
78#63871C2212yes—
79#63865C2212yes—
80#63857C2212yescomplemented
81#63856C2212yescomplemented
82#63854C2214yescomplemented
83#63841C2212yescomplemented
84#63839C2214yescomplemented
85#63838C2212yescomplemented
86C2×#1010—32no—
87C2×D3×#41—32no—
88C3×#537—32no—
89#5828—32no—
90#5825—32no—
91#5632—34no—
92#5631—34no—
93#5628—32no—
94#5628—32no—
95D3×C22⋊Q8—32no—
96D3×C22⋊Q8—32no—
97#5612—34no—
98#5611—34no—
99#5611—34no—
100#5610—34no—
101#5610—34no—
102#5608—32no—
103#5608D312yescomplemented
104#5606—32no—
105#5606—32no—
106#5606—61no—
107#5598—34no—
108C2×#897—32no—
109#5504—32no—
110C23×C3⋊D3C2311yescharacteristic
111C22×D32C2312yes—
112C2×C32×D4C2311yescharacteristic
113C2×C32×D4C2312yes—
114C22×C32×C4C2311yescharacteristic
115C2×#638C2312yes—
116C2×#638C2312yes—
117C22×C3⋊Dic3C2311yescharacteristic
118C22×C3⋊Dic3C2312yes—
119#3830—24no—
120C2×C4×C3⋊D3—24no—
121C2×C4×C3⋊D3C2311yescharacteristic
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2311yescharacteristic
124C2×C4×C3⋊D3C2311yescharacteristic
125C2×#634C2311yescharacteristic
126C2×C3×#67C2314yes—
127C2×C3×#67C2312yes—
128C2×C3×#67C2312yes—
129C2×C3×#67C2314yes—
130C22×C3×Dic3C2314yes—
131C3×#237—28no—
132C3×#235—28no—
133C2×C3×D12C2312yes—
134C2×C3×C4×D3C2312yes—
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×Dic6C2312yes—
138C2×C3×Dic6C2312yes—
139#3811—28no—
140C2×#627—28no—
141C2×#627C2314yes—
142C2×#627C2311yescharacteristic
143C2×#627C2312yes—
144C2×#627C2311yescharacteristic
145C2×#626C2312yes—
146C2×#626C2312yes—
147C2×#625C2311yescharacteristic
148C2×#625C2311yescharacteristic
149C2×#624C2312yes—
150C2×#624C2312yes—
151C2×#624C2312yes—
152#3805—24no—
153#3805—24no—
154#3805—28no—
155#3804—216no—
156C2×D3×Dic3C2314yes—
157C2×D3×Dic3C2312yes—
158C2×D3×Dic3C2312yes—
159#3802—24no—
160C4×D32—28no—
161#3798—24no—
162#3798D418yescomplemented
163#3797—24no—
164#3797—24no—
165#3796—28no—
166D3×Dic6—28no—
167C32×C4⋊C4C2311yescharacteristic
168C32×C22⋊C4C2312yes—
169#3757C2312yes—
170#3757C2312yes—
171#3752C2312yes—
172#3752C2312yes—
173C4⋊(C3⋊Dic3)C2312yes—
174C4⋊(C3⋊Dic3)C2311yescharacteristic
175#3750C2312yes—
176C4×C3⋊Dic3C2312yes—
177C3×#217C2314yes—
178C3×#217C2314yes—
179C3×(C2×D3)⋊C4C2314yes—
180C3×C4⋊Dic3C2314yes—
181C3×C4⋊Dic3C2312yes—
182C3×Dic3⋊C4C2314yes—
183C3×Dic3⋊C4C2314yes—
184#3724C2312yes—
185#3724C2314yes—
186Dic3⋊Dic3C2314yes—
187Dic3⋊Dic3C2314yes—
188#3722C2314yes—
189(C2×D3)⋊Dic3C2314yes—
190(C2×D3)⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2314yes—
192Dic32C2314yes—
193#3489—91noSylow
194C2×C3×#41—32no—
195C2×C3×#41—32no—
196#1010—616no—
197D3×#41—616no—
198C2×#239—32no—
199C2×D3×Q8—32no—
200C2×D3×Q8—32no—
201C2×D3×Q8—32no—
202C2×#237—32no—
203C2×#237—32no—
204C2×#237—32no—
205C2×#237—34no—
206C2×#237—34no—
207C2×#237—32no—
208C2×#237—61no—
209C2×#237C2×D312yescomplemented
210C2×D3×D4—32no—
211C2×D3×D4—32no—
212C2×D3×D4—32no—
213C2×#235—34no—
214C2×#235—32no—
215C2×#235—32no—
216C2×#235C2×D312yes—
217C22×C4×D3—32no—
218C22×C4×D3—32no—
219C22×C4×D3—32no—
220C22×C4×D3—61no—
221C22×Dic6—34no—
222C22×Dic6—32no—
223C3×C22⋊Q8—32no—
224C3×C22⋊Q8—32no—
225C3×C22⋊Q8—34no—
226C3×#121—21no—
227C3×#121—32no—
228C3×#121—34no—
229C3×#121—34no—
230C3×#121—34no—
231C3×#121C2×D312yescomplemented
232C2×C3×C4⋊C4—32no—
233#946—32no—
234#946—32no—
235#944—34no—
236#939—34no—
237#939C2×D314yescomplemented
238#938—32no—
239#938—34no—
240#938—61no—
241#938C2×D312yescomplemented
242#938C2×D314yescomplemented
243#937—34no—
244#937—34no—
245#937—34no—
246#937—62no—
247#936—34no—
248#935—34no—
249#935—34no—
250#935—34no—
251D4×Dic3—34no—
252D4×Dic3—34no—
253D4×Dic3—62no—
254C4×#67—34no—
255C4×#67—34no—
256C4×#67—34no—
257C4×#67—34no—
258C2×(C2×D3)⋊C4—34no—
259#926—32no—
260C2×C4⋊Dic3—34no—
261#924—32no—
262#924—32no—
263#924—32no—
264#924—61no—
265#924C2×D312yescomplemented
266#897—32no—
267#897—32no—
268#897—32no—
269#897—34no—
270#897—34no—
271#897—61no—
272#897C2×D312yescomplemented
273#896—34no—
274#896—34no—
275#894—34no—
276#894—34no—
277#893—34no—
278#892—32no—
279#892—32no—
280#892—61no—
281D3×C4⋊C4—34no—
282D3×C4⋊C4—32no—
283D3×C4⋊C4—34no—
284D3×C4⋊C4C2×D312yescomplemented
285#888—34no—
286#888—34no—
287#887—34no—
288#885—34no—
289#885—34no—
290#884—34no—
291#884C2×D314yescomplemented
292#883—34no—
293#883—34no—
294#883—34no—
295#883—34no—
296#883—62no—
297#67⋊C4—34no—
298#67⋊C4—34no—
299#67⋊C4—62no—
300D3×C22⋊C4—34no—
301D3×C22⋊C4—34no—
302#878—34no—
303#878—34no—
304#878—34no—
305#878C2×D314yescomplemented
306C23×C32C2411yescharacteristic
307C23×C32C2412yes—
308C22×C3⋊D3—22no—
309C22×C3⋊D3—22no—
310C22×C3⋊D3—41no—
311C22×C3⋊D3C2411yescharacteristic
312C22×C3⋊D3C2411yescharacteristic
313C22×C3×D3C2412yes—
314C22×C3×D3C2412yes—
315C2×D32—24no—
316C2×D32—24no—
317C2×D32—42no—
318C32×D4—22no—
319C32×D4—42no—
320C2×C32×C4—22no—
321C2×C32×C4C2411yescharacteristic
322C2×C32×C4C2412yes—
323C2×C32×C4C2411yescharacteristic
324#638—24no—
325#638—24no—
326C2×C3⋊Dic3—22no—
327C2×C3⋊Dic3—24no—
328C2×C3⋊Dic3C2412yes—
329C2×C3⋊Dic3C2412yes—
330C2×C3⋊Dic3C2411yescharacteristic
331C2×C3⋊Dic3C2411yescharacteristic
332C4×C3⋊D3—22no—
333C4×C3⋊D3—22no—
334C4×C3⋊D3—22no—
335C4×C3⋊D3C2×D414yes—
336#634—22no—
337C3×#67—28no—
338C3×#67—24no—
339C3×#67—24no—
340C3×#67—44no—
341C2×C3×Dic3—28no—
342C2×C3×Dic3C2414yes—
343C2×C3×Dic3C2414yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C3×D12—24no—
347C3×C4×D3—24no—
348C3×C4×D3—44no—
349C3×C4×D3C2×D418yes—
350C3×Dic6—24no—
351C3×Dic6—24no—
352#627—22no—
353#627—24no—
354#627—28no—
355#627C2×D414yes—
356#626—24no—
357#626C2×D418yes—
358#625—22no—
359#625C2×D414yes—
360#624—24no—
361#624—24no—
362#624—42no—
363D3×Dic3—28no—
364D3×Dic3—24no—
365D3×Dic3—24no—
366C2×2−1+4—91no—
367C22×#41—91no—
368D4×Q8—92no—
369#548—92no—
370#547—92no—
371#547—94no—
372#546—92no—
373#546—94no—
374#537—32no—
375#537—91no—
376#536—91no—
377#536—92no—
378#525—92no—
379#525—91no—
380C2×C22⋊Q8—92no—
381C2×C22⋊Q8—91no—
382#520—91no—
383C23×D3—32no—
384C23×D3—32no—
385C23×D3—32no—
386C23×D3—61no—
387C3×#41—68no—
388C3×#41—68no—
389C2×C3×Q8—32no—
390C2×C3×Q8—32no—
391C2×C3×D4—22no—
392C2×C3×D4—21no—
393C2×C3×D4—32no—
394C2×C3×D4—34no—
395C2×C3×D4—32no—
396C2×C3×D4—34no—
397C2×C3×D4—32no—
398C2×C3×D4C22×D312yes—
399C2×C3×D4C22×D314yes—
400C22×C3×C4—21no—
401C22×C3×C4—32no—
402C22×C3×C4—34no—
403C22×C3×C4—32no—
404C22×C3×C4—34no—
405C22×C3×C4C22×D312yes—
406C2×#67—32no—
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—32no—
410C2×#67—32no—
411C2×#67—32no—
412C2×#67—62no—
413C2×#67—62no—
414C2×#67C22×D312yes—
415C2×#67C22×D314yes—
416C2×#67C22×D312yes—
417C2×#67C22×D314yes—
418C22×Dic3—32no—
419C22×Dic3—34no—
420C22×Dic3—32no—
421C22×Dic3—32no—
422C22×Dic3—34no—
423C22×Dic3—62no—
424C22×Dic3—61no—
425C22×Dic3C22×D314yes—
426#239—68no—
427D3×Q8—68no—
428D3×Q8—68no—
429D3×Q8—68no—
430#237—28no—
431#237—68no—
432#237—68no—
433#237—68no—
434#237—616no—
435#237—68no—
436#237—616no—
437#237—124no—
438D3×D4—68no—
439D3×D4—68no—
440D3×D4—68no—
441#235—28no—
442#235—316no—
443#235—68no—
444#235—616no—
445C2×D12—32no—
446C2×D12—32no—
447C2×D12C22×D312yes—
448C2×C4×D3—32no—
449C2×C4×D3—34no—
450C2×C4×D3—32no—
451C2×C4×D3—32no—
452C2×C4×D3—32no—
453C2×C4×D3—32no—
454C2×C4×D3—32no—
455C2×C4×D3—34no—
456C2×C4×D3—32no—
457C2×C4×D3—32no—
458C2×C4×D3—34no—
459C2×C4×D3—61no—
460C2×C4×D3—61no—
461C2×C4×D3—61no—
462C2×C4×D3—61no—
463C2×C4×D3—68no—
464C2×C4×D3—68no—
465C2×C4×D3—68no—
466C2×C4×D3—124no—
467C2×C4×D3C22×D312yes—
468C2×C4×D3C22×D314yes—
469C2×C4×D3C22×D312yes—
470C2×Dic6—32no—
471C2×Dic6—32no—
472C2×Dic6—32no—
473C2×Dic6—34no—
474C2×Dic6—34no—
475C2×Dic6—34no—
476C2×Dic6—61no—
477C2×Dic6—68no—
478C2×Dic6—616no—
479C2×Dic6C22×D312yes—
480C2×Dic6C22×D312yes—
481C3×C4⋊C4—21no—
482C3×C4⋊C4—34no—
483C3×C4⋊C4—34no—
484C3×C4⋊C4—34no—
485C3×C4⋊C4—32no—
486C3×C4⋊C4C22×D312yes—
487C3×C22⋊C4—22no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4—34no—
490C3×C22⋊C4—34no—
491C3×C22⋊C4C22×D314yes—
492#217—34no—
493#217—34no—
494#217—34no—
495#217—34no—
496#217—34no—
497#217—62no—
498#217—62no—
499#217C22×D314yes—
500#217C22×D314yes—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—34no—
508(C2×D3)⋊C4—62no—
509(C2×D3)⋊C4—62no—
510(C2×D3)⋊C4C22×D314yes—
511C4⋊Dic3—34no—
512C4⋊Dic3—32no—
513C4⋊Dic3—34no—
514C4⋊Dic3—34no—
515C4⋊Dic3—62no—
516C4⋊Dic3—61no—
517C4⋊Dic3C22×D314yes—
518C4⋊Dic3C22×D312yes—
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4—34no—
522Dic3⋊C4—34no—
523Dic3⋊C4—34no—
524Dic3⋊C4—34no—
525Dic3⋊C4—62no—
526Dic3⋊C4C22×D314yes—
527Dic3⋊C4C22×D314yes—
528C4×Dic3—34no—
529C4×Dic3—34no—
530C4×Dic3—34no—
531C4×Dic3—62no—
532C22×C32—21no—
533C22×C32—22no—
534C22×C32—21no—
535C22×C32—22no—
536C22×C32—21no—
537C22×C32—22no—
538C22×C32C2511yescharacteristic
539C2×C3⋊D3—21no—
540C2×C3⋊D3—21no—
541C2×C3⋊D3—21no—
542C2×C3⋊D3—21no—
543C2×C3⋊D3—44no—
544C2×C3⋊D3C22×D412yes—
545C2×C3⋊D32−1+412yescomplemented
546C2×C3×D3—22no—
547C2×C3×D3—22no—
548C2×C3×D3—22no—
549C2×C3×D3—22no—
550C2×C3×D3—22no—
551C2×C3×D3C22×D414yes—
552D32—48no—
553C32×C4—21no—
554C32×C4—22no—
555C32×C4C22×D412yes—
556C3⋊Dic3—21no—
557C3⋊Dic3—22no—
558C3⋊Dic3—22no—
559C3⋊Dic3C22×D412yes—
560C3×Dic3—22no—
561C3×Dic3—24no—
562C3×Dic3—24no—
563C3×Dic3C22×D414yes—
5642−1+4—188no—
565C2×#41—32no—
566C2×#41—32no—
567C2×#41—91no—
568C2×#41—91no—
569C2×#41—94no—
570C2×#41—92no—
571C2×#41—91no—
572C2×#41—91no—
573C2×#41—92no—
574C2×#41—91no—
575C2×#41—188no—
576C22×Q8—92no—
577C22×Q8—92no—
578C22×Q8—91no—
579C22×Q8—91no—
580C22×D4—92no—
581C22×D4—91no—
582C23×C4—92no—
583C23×C4—91no—
584C4⋊Q8—92no—
585C4⋊Q8—94no—
586#124—92no—
587#124—94no—
588#123—94no—
589#123—94no—
590#123—94no—
591#123—94no—
592#123—92no—
593C22⋊Q8—32no—
594C22⋊Q8—32no—
595C22⋊Q8—34no—
596C22⋊Q8—92no—
597C22⋊Q8—92no—
598C22⋊Q8—94no—
599C22⋊Q8—92no—
600C22⋊Q8—94no—
601C22⋊Q8—92no—
602C22⋊Q8—92no—
603C22⋊Q8—92no—
604C22⋊Q8—91no—
605C22⋊Q8—91no—
606#121—32no—
607#121—34no—
608#121—34no—
609#121—34no—
610#121—94no—
611#121—92no—
612#121—91no—
613#121D3211yescharacteristic, complemented
614#120—94no—
615#120—92no—
616C4×Q8—92no—
617C4×D4—94no—
618C4×D4—94no—
619C4×D4—92no—
620C4×D4—94no—
621C4×D4—92no—
622C4×D4—92no—
623#117—92no—
624#117—91no—
625C2×C4⋊C4—32no—
626C2×C4⋊C4—91no—
627C2×C4⋊C4—92no—
628C2×C4⋊C4—94no—
629C2×C22⋊C4—92no—
630C2×C22⋊C4—94no—
631C23×C3—21no—
632C23×C3—22no—
633C23×C3—32no—
634C23×C3—32no—
635C23×C3C23×D312yes—
636C23×C3C23×D314yes—
637C22×D3—32no—
638C22×D3—32no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—64no—
642C22×D3—64no—
643C22×D3—64no—
644C22×D3—64no—
645C22×D3—64no—
646C22×D3—64no—
647C22×D3—122no—
648C22×D3—122no—
649C22×D3—122no—
650C22×D3—122no—
651C22×D3—122no—
652C22×D3—122no—
653C22×D3C23×D312yes—
654C22×D3C23×D312yes—
655C3×Q8—64no—
656C3×Q8—64no—
657C3×D4—24no—
658C3×D4—42no—
659C3×D4—44no—
660C3×D4—44no—
661C3×D4—64no—
662C3×D4—64no—
663C3×D4—64no—
664C3×D4—68no—
665C3×D4—124no—
666C2×C3×C4—24no—
667C2×C3×C4—21no—
668C2×C3×C4—22no—
669C2×C3×C4—21no—
670C2×C3×C4—32no—
671C2×C3×C4—38no—
672C2×C3×C4—34no—
673C2×C3×C4—32no—
674C2×C3×C4—34no—
675C2×C3×C4—42no—
676C2×C3×C4—68no—
677C2×C3×C4—64no—
678C2×C3×C4—124no—
679C2×C3×C4C23×D314yes—
680C2×C3×C4C23×D312yes—
681C2×C3×C4C23×D312yes—
682#67—24no—
683#67—28no—
684#67—24no—
685#67—38no—
686#67—38no—
687#67—44no—
688#67—64no—
689#67—64no—
690#67—68no—
691#67—68no—
692#67—124no—
693#67—124no—
694C2×Dic3—28no—
695C2×Dic3—32no—
696C2×Dic3—34no—
697C2×Dic3—32no—
698C2×Dic3—34no—
699C2×Dic3—61no—
700C2×Dic3—62no—
701C2×Dic3—62no—
702C2×Dic3—61no—
703C2×Dic3—68no—
704C2×Dic3—64no—
705C2×Dic3—68no—
706C2×Dic3—64no—
707C2×Dic3—64no—
708C2×Dic3—122no—
709C2×Dic3—124no—
710C2×Dic3C23×D314yes—
711C2×Dic3C23×D312yes—
712C2×Dic3C23×D314yes—
713C2×Dic3C23×D312yes—
714D12—24no—
715D12—38no—
716D12—64no—
717C4×D3—24no—
718C4×D3—38no—
719C4×D3—44no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—68no—
723C4×D3—64no—
724C4×D3—64no—
725C4×D3—64no—
726C4×D3—64no—
727C4×D3—68no—
728C4×D3—64no—
729C4×D3—64no—
730C4×D3—122no—
731C4×D3—122no—
732C4×D3—122no—
733C4×D3—124no—
734C4×D3D3×D418yes—
735Dic6—24no—
736Dic6—24no—
737Dic6—38no—
738Dic6—68no—
739Dic6—64no—
740Dic6—68no—
741Dic6—64no—
742Dic6—68no—
743Dic6—122no—
744C2×C32—41no—
745C2×C32—42no—
746C2×C32C23×D411yescharacteristic
747C2×C32C2×2−1+411yescharacteristic
748C2×C32#58511yescharacteristic
749C3⋊D3—22no—
750C3⋊D3—22no—
751C3×D3—24no—
752C3×D3—42no—
753C24—92no—
754C24—91no—
755#41—68no—
756#41—68no—
757#41—98no—
758#41—184no—
759#41—1816no—
760#41—184no—
761#41—184no—
762#41—188no—
763#41—184no—
764#41—188no—
765C2×Q8—32no—
766C2×Q8—32no—
767C2×Q8—91no—
768C2×Q8—94no—
769C2×Q8—92no—
770C2×Q8—91no—
771C2×Q8—91no—
772C2×Q8—188no—
773C2×Q8—188no—
774C2×Q8—184no—
775C2×Q8—184no—
776C2×D4—34no—
777C2×D4—32no—
778C2×D4—32no—
779C2×D4—34no—
780C2×D4—32no—
781C2×D4—92no—
782C2×D4—92no—
783C2×D4—91no—
784C2×D4—91no—
785C2×D4—92no—
786C2×D4—92no—
787C2×D4—184no—
788C2×D4—188no—
789C2×D4C2×D3211yescharacteristic
790C2×D4C2×D3212yes—
791C22×C4—32no—
792C22×C4—34no—
793C22×C4—32no—
794C22×C4—34no—
795C22×C4—92no—
796C22×C4—92no—
797C22×C4—92no—
798C22×C4—94no—
799C22×C4—92no—
800C22×C4—92no—
801C22×C4—91no—
802C22×C4—92no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—184no—
808C22×C4—188no—
809C22×C4C2×D3211yescharacteristic
810C4⋊C4—32no—
811C4⋊C4—34no—
812C4⋊C4—34no—
813C4⋊C4—34no—
814C4⋊C4—94no—
815C4⋊C4—92no—
816C4⋊C4—94no—
817C4⋊C4—94no—
818C4⋊C4—92no—
819C4⋊C4—91no—
820C4⋊C4—92no—
821C4⋊C4C2×D3211yescharacteristic
822C22⋊C4—34no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C22⋊C4—94no—
828C22⋊C4—94no—
829C22⋊C4—92no—
830C22⋊C4—92no—
831C22⋊C4—92no—
832C22⋊C4—92no—
833C22⋊C4C2×D3212yes—
834C42—94no—
835C42—92no—
836C22×C3—22no—
837C22×C3—24no—
838C22×C3—22no—
839C22×C3—24no—
840C22×C3—22no—
841C22×C3—24no—
842C22×C3—22no—
843C22×C3—21no—
844C22×C3—34no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3C24×D312yes—
856C2×D3—22no—
857C2×D3—22no—
858C2×D3—22no—
859C2×D3—22no—
860C2×D3—22no—
861C2×D3—34no—
862C2×D3—34no—
863C2×D3—62no—
864C2×D3—62no—
865C2×D3—62no—
866C2×D3—62no—
867C2×D3—62no—
868C2×D3—62no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—128no—
874C2×D3—128no—
875C2×D3—128no—
876C2×D3—128no—
877C2×D3C2×D3×D414yes—
878C3×C4—22no—
879C3×C4—24no—
880C3×C4—22no—
881C3×C4—34no—
882C3×C4—41no—
883C3×C4—42no—
884C3×C4—64no—
885C3×C4—62no—
886C3×C4—64no—
887C3×C4C2×D3×D414yes—
888Dic3—24no—
889Dic3—22no—
890Dic3—24no—
891Dic3—34no—
892Dic3—62no—
893Dic3—64no—
894Dic3—62no—
895Dic3—64no—
896Dic3—122no—
897Dic3—121no—
898Dic3—122no—
899Dic3C2×D3×D414yes—
900C32#348911yescharacteristic, complemented, Sylow
901C23—32no—
902C23—32no—
903C23—91no—
904C23—91no—
905C23—182no—
906C23—182no—
907C23—184no—
908C23—184no—
909C23—361no—
910C23—362no—
911C23C22×D3211yescharacteristic
912C23C22×D3212yes—
913Q8—64no—
914Q8—64no—
915Q8—94no—
916Q8—188no—
917Q8—184no—
918Q8—182no—
919Q8—182no—
920D4—22no—
921D4—42no—
922D4—64no—
923D4—64no—
924D4—64no—
925D4—68no—
926D4—98no—
927D4—94no—
928D4—124no—
929D4—184no—
930D4—182no—
931D4—184no—
932D4—184no—
933C2×C4—22no—
934C2×C4—32no—
935C2×C4—38no—
936C2×C4—34no—
937C2×C4—34no—
938C2×C4—32no—
939C2×C4—68no—
940C2×C4—64no—
941C2×C4—91no—
942C2×C4—94no—
943C2×C4—92no—
944C2×C4—92no—
945C2×C4—91no—
946C2×C4—124no—
947C2×C4—182no—
948C2×C4—182no—
949C2×C4—184no—
950C2×C4—184no—
951C2×C4—184no—
952C2×C4—184no—
953C2×C4—188no—
954C2×C4—182no—
955C2×C4—184no—
956C2×C4—182no—
957C2×C4—362no—
958C2×C4C22×D3212yes—
959C2×C4C22×D3211yescharacteristic
960C2×C4C22×D3211yescharacteristic
961C2×C3—21no—
962C2×C3—21no—
963C2×C3—21no—
964C2×C3—42no—
965C2×C3—42no—
966C2×C3—44no—
967C2×C3—64no—
968C2×C3—82no—
969C2×C3—122no—
970C2×C3C22×D3×D412yes—
971C2×C3#596612yes—
972C2×C3D3×2−1+412yes—
973D3—24no—
974D3—42no—
975D3—64no—
976D3—64no—
977D3—122no—
978D3—122no—
979C22—21no—
980C22—22no—
981C22—21no—
982C22—22no—
983C22—22no—
984C22—21no—
985C22—34no—
986C22—62no—
987C22—62no—
988C22—62no—
989C22—62no—
990C22—62no—
991C22—92no—
992C22—92no—
993C22—181no—
994C22—181no—
995C22—181no—
996C22—181no—
997C22—364no—
998C22—368no—
999C22C23×D3211yescharacteristic
1000C4—21no—
1001C4—22no—
1002C4—34no—
1003C4—62no—
1004C4—64no—
1005C4—64no—
1006C4—92no—
1007C4—181no—
1008C4—182no—
1009C4—182no—
1010C4D32×D412yes—
1011C3—21no—
1012C3#8638012yescomplemented
1013C2—41no—
1014C2—42no—
1015C2—64no—
1016C2—122no—
1017C2—182no—
1018C2—182no—
1019C2C2×D32×D411yescharacteristic
1020C2#1059667911yescharacteristic
1021C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#64309C2semidirect
2. C2×#64306C2semidirect
3. #10596077C2semidirect
4. C3×#5608C2semidirect
5. #10595301C2semidirect
6. #10595296C2semidirect
7. #10595240C2semidirect
8. #10595142C2semidirect
9. #10595134C2semidirect
10. #10594925C2semidirect
11. #10594884C2semidirect
12. D3×#897C2semidirect
13. #10594529C2semidirect
14. #10594509C2semidirect
15. #10594276C2semidirect
16. #10594072C2semidirect
17. #10594065C2semidirect
19. C2×#3830C22semidirect
21. C2×C3×#237C22semidirect
24. C22×#627C22semidirect
27. C2×#3805C22semidirect
28. C2×#3804C22semidirect
36. C2×#3797C22semidirect
38. C2×D3×Dic6C22semidirect
39. C32×#121C22semidirect
42. D4×C3⋊Dic3C22semidirect
43. #64133C22semidirect
45. #64101C22semidirect
46. #64092C22semidirect
48. C3×#939C22semidirect
49. C3×#938C22semidirect
50. C3×#938C22semidirect
51. C3×#924C22semidirect
52. C3×#897C22semidirect
53. C3×D3×C4⋊C4C22semidirect
54. C3×#884C22semidirect
55. C3×#878C22semidirect
57. #63982C22semidirect
58. #63982C22semidirect
59. #63980C22semidirect
61. Dic3×#67C22semidirect
62. #63969C22semidirect
63. #63969C22semidirect
64. #63959C22semidirect
65. #63958C22semidirect
68. #63919C22semidirect
69. #63915C22semidirect
70. #63904C22semidirect
71. C4×#625C22semidirect
72. #63900C22semidirect
74. #63893C22semidirect
75. D3×C4⋊Dic3C22semidirect
76. #63884C22semidirect
77. #63883C22semidirect
80. #63857C22semidirect
81. #63856C22semidirect
82. #63854C22semidirect
83. #63841C22semidirect
84. #63839C22semidirect
85. #63838C22semidirect
103. #5608D3semidirect
162. #3798D4semidirect
209. C2×#237C2×D3semidirect
231. C3×#121C2×D3semidirect
237. #939C2×D3semidirect
241. #938C2×D3semidirect
242. #938C2×D3semidirect
265. #924C2×D3semidirect
272. #897C2×D3semidirect
284. D3×C4⋊C4C2×D3semidirect
291. #884C2×D3semidirect
305. #878C2×D3semidirect
545. C2×C3⋊D32−1+4semidirect
613. #121D32semidirect
900. C32#3489semidirect
1012. C3#86380semidirect

Maximal subgroups

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

subgroupindex
C2×#643092
C2×#643062
#105960772
C3×#56082
#105953012
#105952962
#105952402
#105951422
#105951342
#105949252
#105948842
D3×#8972
#105945292
#105945092
#105942762
#105940722
#105940652
#863803