Finite Group Databasebeta

← #11904244

Subgroups — #11904244

Order 1152.

2560 conjugacy classes of subgroups.

The subgroup lattice has 998 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596024C211yesmaximal, characteristic, complemented
2C3×#5563C211yesmaximal, characteristic, complemented
3C3×C4×#237C211yesmaximal, characteristic, complemented
4#10595236C212yesmaximal, complemented
5#10595131C212yesmaximal, complemented
6#10594954C212yesmaximal, complemented
7#10594919C212yesmaximal, complemented
8#10594910C212yesmaximal, complemented
9#10594838C212yesmaximal, complemented
10#10594575C212yesmaximal, complemented
11#10594362C212yesmaximal, complemented
12#10594109C214yesmaximal, complemented
13#10594068C214yesmaximal, complemented
14#10593970C211yesmaximal, characteristic, complemented
15#10593902C211yesmaximal, characteristic, complemented
16C4×#3795C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#86959—31nomaximal
19#85845—31nomaximal
20C2×#3828C2212yes—
21C2×C3×#237C2211yescharacteristic
22C2×#3804C2214yes—
23C2×#3799C2212yes—
24C2×#3799C2212yes—
25C2×#3795C2211yescharacteristic
26C32×C4×D4C2211yescharacteristic
27#64149C2212yes—
28#64139C2212yes—
29#64102C2212yes—
30#64093C2214yes—
31#64083C2211yescharacteristic
32C4×#634C2211yescharacteristic
33C3×#938C2212yes—
34C3×D4×Dic3C2211yescharacteristic
35C3×#930C2212yes—
36C3×C4×#67C2212yes—
37C3×#926C2212yes—
38C2×C3×C4×Dic3C2212yes—
39C3×#892C2211yescharacteristic
40C3×#892C2212yes—
41C3×#887C2211yescharacteristic
42C3×#885C2214yes—
43C3×#67⋊C4C2212yes—
44C3×#877C2212yes—
45C3×C4×D12C2211yescharacteristic
46C3×C42×D3C2211yescharacteristic
47C3×#869C2211yescharacteristic
48C3×C4×Dic6C2211yescharacteristic
49#63979C2214yes—
50#63978C2214yes—
51#63971C2214yes—
52#63958C2214yes—
53#63953C2214yes—
54#63952C2214yes—
55#63952C2214yes—
56#63919C2212yes—
57#63918C2212yes—
58#63912C2214yes—
59#63911C2212yes—
60#63910C2214yes—
61#63909C2212yes—
62#63909C2212yes—
63#63909C2212yes—
64C4×#625C2212yes—
65#63894C2212yes—
66#63894C2212yes—
67#63894C2212yes—
68Dic3×D12C2211yescharacteristic
69C4×#624C2214yes—
70#63881C2214yes—
71#63880C2214yes—
72#63879C2212yes—
73#63877C2212yes—
74C4×D3×Dic3C2212yes—
75#63874C2214yes—
76#63864C2212yes—
77#63852C2214yes—
78#63852C2214yes—
79#63844C2212yes—
80#63844C2211yescharacteristic
81#63843C2212yes—
82#63841C2211yescharacteristic
83#63839C2214yes—
84#63836C2214yes—
85C3×#555—31no—
86C3×C4×#41—31no—
87#5834—32no—
88#5725—31no—
89#5722—31no—
90#5670—34no—
91#5668—34no—
92#5599—32no—
93#5599—32no—
94#5596—32no—
95#5596—32no—
96#5577—31no—
97C4×#239—32no—
98Q8×Dic6—31no—
99#5563—32no—
100#5563D311yescharacteristic, complemented
101#5553—31no—
102#5553—31no—
103#5553—32no—
104#5553—31no—
105#5553—61no—
106#5548—32no—
107#5548—34no—
108C4×#237—31no—
109C4×#237D311yescharacteristic, complemented
110#5532—32no—
111#5532—32no—
112#5532—32no—
113#5532—34no—
114#5522—32no—
115#5522—32no—
116#5477—32no—
117#5477—31no—
118C4×#235—32no—
119C4×#235—31no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C2×#638C2314yes—
123C2×#638C2314yes—
124#3828—28no—
125C2×C4⋊(C3⋊D3)C2312yes—
126C2×C4⋊(C3⋊D3)C2312yes—
127C2×C4⋊(C3⋊D3)C2312yes—
128C2×C4×C3⋊D3C2314yes—
129C2×#634C2311yescharacteristic
130C2×C3×#67C2312yes—
131C2×C3×#67C2314yes—
132C22×C3×Dic3C2312yes—
133C22×C3×Dic3C2312yes—
134C3×#237—24no—
135C2×C3×D12C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2312yes—
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×Dic6C2312yes—
141C2×C3×Dic6C2311yescharacteristic
142C2×#627C2314yes—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#626C2314yes—
146C2×#625C2312yes—
147C2×#624C2314yes—
148C2×#624C2314yes—
149#3804—48no—
150C2×D3×Dic3C2312yes—
151C2×D3×Dic3C2312yes—
152#3799—28no—
153#3799—44no—
154#3795—24no—
155C32×C4⋊C4C2311yescharacteristic
156C32×C22⋊C4C2312yes—
157C32×C42C2311yescharacteristic
158#3752C2314yes—
159C4⋊(C3⋊Dic3)C2311yescharacteristic
160#3750C2312yes—
161C4×C3⋊Dic3C2312yes—
162C3×#217C2312yes—
163C3×#217C2314yes—
164C3×(C2×D3)⋊C4C2312yes—
165C3×(C2×D3)⋊C4C2312yes—
166C3×(C2×D3)⋊C4C2314yes—
167C3×C4⋊Dic3C2311yescharacteristic
168C3×C4⋊Dic3C2312yes—
169C3×C4⋊Dic3C2311yescharacteristic
170C3×C4⋊Dic3C2312yes—
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2312yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2312yes—
176C3×C4×Dic3C2314yes—
177C3×C4×Dic3C2311yescharacteristic
178C3×C4×Dic3C2311yescharacteristic
179C3×C4×Dic3C2312yes—
180#3724C2314yes—
181#3724C2312yes—
182Dic3⋊Dic3C2314yes—
183#3722C2314yes—
184#3722C2314yes—
185#3722C2314yes—
186(C2×D3)⋊Dic3C2312yes—
187(C2×D3)⋊Dic3C2312yes—
188Dic32C2312yes—
189Dic32C2314yes—
190Dic32C2312yes—
191#3483—91noSylow
192C2×C3×#41—31no—
193C2×#239—32no—
194C2×#239—32no—
195C2×#237—34no—
196C2×#237—31no—
197C2×#237C2×D311yescharacteristic
198C2×#235—32no—
199C2×#235—32no—
200C2×#235—34no—
201C2×#235—31no—
202C2×#235—32no—
203C2×#235—32no—
204C2×#235—62no—
205C3×C4⋊Q8—31no—
206C3×#124—34no—
207C3×#121—32no—
208C3×#121—32no—
209C3×C4×Q8—31no—
210C3×C4×Q8—31no—
211C3×C4×D4—21no—
212C3×C4×D4—31no—
213C3×C4×D4—32no—
214C3×C4×D4—32no—
215C3×C4×D4—31no—
216C3×C4×D4C2×D311yescharacteristic
217C3×C4×D4C2×D311yescharacteristic
218C3×#117—32no—
219C3×#117—32no—
220C3×#117—31no—
221C3×#117—32no—
222C2×C3×C42—32no—
223C2×C3×C42—31no—
224#947—32no—
225Q8×Dic3—32no—
226#944—34no—
227#940—32no—
228#940—32no—
229#940—34no—
230#940—34no—
231#940—32no—
232#940—62no—
233#939—34no—
234#939—34no—
235#938—34no—
236#938C2×D312yes—
237D4×Dic3—31no—
238D4×Dic3C2×D311yescharacteristic
239#930—32no—
240#930—32no—
241#930—34no—
242#930—32no—
243#930—32no—
244#930—32no—
245#930—62no—
246#930C2×D312yes—
247C4×#67—32no—
248C4×#67—32no—
249C4×#67—34no—
250C4×#67—34no—
251C4×#67—32no—
252C4×#67C2×D312yes—
253#926—31no—
254#926C2×D312yes—
255C2×C4×Dic3—32no—
256C2×C4×Dic3C2×D312yes—
257#895—32no—
258#895—32no—
259#895—32no—
260#895—34no—
261#893—32no—
262#893—32no—
263#893—34no—
264#893—32no—
265#893—32no—
266#893—32no—
267#893—62no—
268#892—31no—
269#892—34no—
270#892C2×D311yescharacteristic
271#892C2×D312yes—
272#888—34no—
273#888—32no—
274#888—32no—
275#888—32no—
276#887—32no—
277#887—32no—
278#887—31no—
279#887C2×D311yescharacteristic
280#885—34no—
281#885—34no—
282#885—34no—
283#885—34no—
284#885C2×D314yes—
285#884—34no—
286#884—34no—
287#884—34no—
288#884—34no—
289#884—34no—
290#884—34no—
291#884—34no—
292#884—64no—
293#67⋊C4—34no—
294#67⋊C4—34no—
295#67⋊C4—32no—
296#67⋊C4—34no—
297#67⋊C4—34no—
298#67⋊C4C2×D312yes—
299#877—32no—
300#877C2×D312yes—
301#875—32no—
302#875—34no—
303#875—34no—
304#874—32no—
305#874—31no—
306#874—31no—
307#874—61no—
308C4×D12—31no—
309C4×D12—34no—
310C4×D12—32no—
311C4×D12—32no—
312C4×D12—32no—
313C4×D12C2×D311yescharacteristic
314#872—32no—
315#872—34no—
316#872—34no—
317#872—34no—
318C42×D3—32no—
319C42×D3—34no—
320C42×D3—34no—
321C42×D3C2×D311yescharacteristic
322#869—32no—
323#869C2×D311yescharacteristic
324C4×Dic6—31no—
325C4×Dic6—31no—
326C4×Dic6—31no—
327C4×Dic6—32no—
328C4×Dic6—61no—
329C4×Dic6C2×D311yescharacteristic
330C23×C32C2412yes—
331C22×C3⋊D3C2414yes—
332C22×C3×D3C2411yescharacteristic
333C22×C3×D3C2412yes—
334C32×D4—22no—
335C2×C32×C4—24no—
336C2×C32×C4C2412yes—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340#638—28no—
341#638—44no—
342C2×C3⋊Dic3C2412yes—
343C2×C3⋊Dic3C2412yes—
344C4⋊(C3⋊D3)—24no—
345C4⋊(C3⋊D3)—24no—
346C4⋊(C3⋊D3)—42no—
347C4×C3⋊D3—28no—
348#634#4114yescomplemented
349C3×#67—24no—
350C3×#67—44no—
351C2×C3×Dic3—24no—
352C2×C3×Dic3—24no—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2411yescharacteristic
355C2×C3×Dic3C2414yes—
356C2×C3×Dic3C2411yescharacteristic
357C2×C3×Dic3C2412yes—
358C2×C3×Dic3C2412yes—
359C2×C3×Dic3C2411yescharacteristic
360C3×D12—22no—
361C3×C4×D3—22no—
362C3×C4×D3—24no—
363C3×C4×D3—22no—
364C3×C4×D3—22no—
365C3×Dic6—42no—
366C3×Dic6#4114yescomplemented
367#627—44no—
368#626—28no—
369#626—44no—
370#626—44no—
371#625—24no—
372#624—28no—
373#624—28no—
374D3×Dic3—24no—
375D3×Dic3—24no—
376Q82—91no—
377#555—31no—
378#555—92no—
379#555—92no—
380#555—94no—
381#550—91no—
382#550—92no—
383#550—92no—
384#550—91no—
385#532—92no—
386#532—91no—
387#532—92no—
388#532—94no—
389C4×#41—31no—
390C4×#41—92no—
391C4×#41—91no—
392C4×#41—92no—
393C3×#41—64no—
394C2×C3×Q8—31no—
395C2×C3×Q8—32no—
396C2×C3×D4—21no—
397C2×C3×D4—32no—
398C2×C3×D4—34no—
399C2×C3×D4—31no—
400C2×C3×D4C22×D311yescharacteristic
401C2×C3×D4C22×D311yescharacteristic
402C22×C3×C4—22no—
403C22×C3×C4—32no—
404C22×C3×C4—32no—
405C22×C3×C4—32no—
406C22×C3×C4—31no—
407C22×C3×C4—31no—
408C22×C3×C4—31no—
409C22×C3×C4C22×D312yes—
410C22×C3×C4C22×D312yes—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—32no—
414C2×#67—32no—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—34no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—64no—
421C2×#67—64no—
422C2×#67C22×D312yes—
423C2×#67C22×D314yes—
424C22×Dic3—32no—
425C22×Dic3—32no—
426C22×Dic3C22×D312yes—
427C22×Dic3C22×D312yes—
428#239—68no—
429#239—124no—
430#237—24no—
431#237—64no—
432#237—128no—
433#235—64no—
434#235—68no—
435#235—68no—
436#235—68no—
437#235—128no—
438#235—124no—
439#235—128no—
440C2×D12—34no—
441C2×D12—32no—
442C2×D12—32no—
443C2×D12—32no—
444C2×D12—32no—
445C2×D12—34no—
446C2×D12—34no—
447C2×D12—32no—
448C2×D12—32no—
449C2×D12—62no—
450C2×D12—62no—
451C2×D12—62no—
452C2×D12C22×D311yescharacteristic
453C2×C4×D3—32no—
454C2×C4×D3—32no—
455C2×C4×D3—34no—
456C2×C4×D3—34no—
457C2×C4×D3—34no—
458C2×C4×D3—34no—
459C2×C4×D3—34no—
460C2×C4×D3—34no—
461C2×C4×D3—64no—
462C2×C4×D3C22×D312yes—
463C2×C4×D3C22×D311yescharacteristic
464C2×C4×D3C22×D311yescharacteristic
465C2×C4×D3C22×D311yescharacteristic
466C2×Dic6—31no—
467C2×Dic6—31no—
468C2×Dic6—34no—
469C2×Dic6—34no—
470C2×Dic6—61no—
471C2×Dic6C22×D312yes—
472C2×Dic6C22×D311yescharacteristic
473C3×C4⋊C4—21no—
474C3×C4⋊C4—32no—
475C3×C4⋊C4—32no—
476C3×C4⋊C4—31no—
477C3×C4⋊C4—32no—
478C3×C4⋊C4—31no—
479C3×C4⋊C4—32no—
480C3×C4⋊C4C22×D311yescharacteristic
481C3×C4⋊C4C22×D311yescharacteristic
482C3×C22⋊C4—22no—
483C3×C22⋊C4—34no—
484C3×C22⋊C4—32no—
485C3×C22⋊C4—32no—
486C3×C22⋊C4—34no—
487C3×C22⋊C4—32no—
488C3×C22⋊C4C22×D312yes—
489C3×C22⋊C4C22×D312yes—
490C3×C42—21no—
491C3×C42—32no—
492C3×C42—31no—
493C3×C42—32no—
494C3×C42—31no—
495C3×C42—34no—
496C3×C42—31no—
497C3×C42—32no—
498C3×C42C22×D311yescharacteristic
499C3×C42C22×D311yescharacteristic
500#217—32no—
501#217—32no—
502#217C22×D312yes—
503#217C22×D314yes—
504(C2×D3)⋊C4—32no—
505(C2×D3)⋊C4—32no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—34no—
508(C2×D3)⋊C4—34no—
509(C2×D3)⋊C4—34no—
510(C2×D3)⋊C4—34no—
511(C2×D3)⋊C4—34no—
512(C2×D3)⋊C4—34no—
513(C2×D3)⋊C4—34no—
514(C2×D3)⋊C4—64no—
515(C2×D3)⋊C4C22×D312yes—
516(C2×D3)⋊C4C22×D314yes—
517(C2×D3)⋊C4C22×D312yes—
518C4⋊Dic3—31no—
519C4⋊Dic3—31no—
520C4⋊Dic3—34no—
521C4⋊Dic3—61no—
522C4⋊Dic3C22×D312yes—
523C4⋊Dic3C22×D311yescharacteristic
524C4⋊Dic3C22×D311yescharacteristic
525C4⋊Dic3C22×D312yes—
526Dic3⋊C4—32no—
527Dic3⋊C4—32no—
528Dic3⋊C4—32no—
529Dic3⋊C4—34no—
530Dic3⋊C4—32no—
531Dic3⋊C4—34no—
532Dic3⋊C4—34no—
533Dic3⋊C4—62no—
534Dic3⋊C4C22×D312yes—
535Dic3⋊C4C22×D312yes—
536C4×Dic3—32no—
537C4×Dic3—32no—
538C4×Dic3—32no—
539C4×Dic3—34no—
540C4×Dic3—32no—
541C4×Dic3—32no—
542C4×Dic3—34no—
543C4×Dic3—32no—
544C4×Dic3—62no—
545C4×Dic3C22×D312yes—
546C4×Dic3C22×D312yes—
547C4×Dic3C22×D314yes—
548C4×Dic3C22×D311yescharacteristic
549C4×Dic3C22×D311yescharacteristic
550C4×Dic3C22×D311yescharacteristic
551C4×Dic3C22×D312yes—
552C22×C32—22no—
553C22×C32—22no—
554C22×C32—22no—
555C22×C32C2511yescharacteristic
556C2×C3⋊D3—24no—
557C2×C3⋊D3—24no—
558C2×C3⋊D3—24no—
559C2×C3×D3—22no—
560C2×C3×D3—21no—
561C2×C3×D3—22no—
562C2×C3×D3—21no—
563C2×C3×D3—22no—
564C2×C3×D3—21no—
565C32×C4—22no—
566C32×C4—21no—
567C32×C4C2×#4112yes—
568C32×C4C2×#4112yes—
569C3⋊Dic3—22no—
570C3⋊Dic3C2×#4114yes—
571C3×Dic3—21no—
572C3×Dic3—22no—
573C3×Dic3—21no—
574C3×Dic3—24no—
575C3×Dic3—22no—
576C3×Dic3C2×#4114yes—
577C3×Dic3H(5,𝔽2)12yes—
578C2×#41—31no—
579C2×#41—91no—
580C2×#41—94no—
581C2×#41—92no—
582C2×#41—92no—
583C2×#41—92no—
584C4⋊Q8—31no—
585C4⋊Q8—92no—
586C4⋊Q8—92no—
587C4⋊Q8—94no—
588#127—92no—
589#127—94no—
590#127—92no—
591#127—91no—
592#124—34no—
593#124—94no—
594#124—94no—
595#124—92no—
596#124—94no—
597#121—32no—
598#121—32no—
599#121—94no—
600#121—94no—
601#121—94no—
602#121—94no—
603#121—92no—
604#121—92no—
605#121—92no—
606#121—94no—
607#121—92no—
608#121—94no—
609C4×Q8—31no—
610C4×Q8—31no—
611C4×Q8—91no—
612C4×Q8—92no—
613C4×Q8—92no—
614C4×Q8—91no—
615C4×D4—31no—
616C4×D4—32no—
617C4×D4—32no—
618C4×D4—31no—
619C4×D4—94no—
620C4×D4—92no—
621C4×D4—92no—
622C4×D4—92no—
623C4×D4—91no—
624C4×D4—94no—
625C4×D4—94no—
626C4×D4—92no—
627C4×D4—94no—
628C4×D4—92no—
629C4×D4—92no—
630C4×D4D3211yescharacteristic
631#117—32no—
632#117—31no—
633#117—32no—
634#117—32no—
635#117—94no—
636#117—92no—
637#117—94no—
638#117—91no—
639C2×C42—32no—
640C2×C42—31no—
641C2×C42—94no—
642C2×C42—92no—
643C23×C3—22no—
644C23×C3—31no—
645C23×C3—32no—
646C23×C3C23×D312yes—
647C23×C3C23×D312yes—
648C22×D3—34no—
649C22×D3—34no—
650C22×D3—64no—
651C22×D3C23×D311yescharacteristic
652C22×D3C23×D312yes—
653C3×Q8—34no—
654C3×Q8—122no—
655C3×D4—22no—
656C3×D4—22no—
657C3×D4—42no—
658C3×D4—64no—
659C3×D4—62no—
660C3×D4—124no—
661C2×C3×C4—24no—
662C2×C3×C4—24no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—22no—
667C2×C3×C4—32no—
668C2×C3×C4—31no—
669C2×C3×C4—32no—
670C2×C3×C4—31no—
671C2×C3×C4—34no—
672C2×C3×C4—31no—
673C2×C3×C4—32no—
674C2×C3×C4—44no—
675C2×C3×C4—62no—
676C2×C3×C4—64no—
677C2×C3×C4—64no—
678C2×C3×C4—64no—
679C2×C3×C4—62no—
680C2×C3×C4—62no—
681C2×C3×C4C23×D312yes—
682C2×C3×C4C23×D312yes—
683C2×C3×C4C23×D311yescharacteristic
684C2×C3×C4C23×D311yescharacteristic
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D311yescharacteristic
687C2×C3×C4C23×D311yescharacteristic
688C2×C3×C4C23×D311yescharacteristic
689#67—24no—
690#67—44no—
691#67—64no—
692#67—64no—
693#67—68no—
694#67—68no—
695#67—68no—
696#67—128no—
697#67—124no—
698#67—124no—
699#67—124no—
700#67—124no—
701#67—244no—
702C2×Dic3—24no—
703C2×Dic3—24no—
704C2×Dic3—32no—
705C2×Dic3—32no—
706C2×Dic3—32no—
707C2×Dic3—32no—
708C2×Dic3—62no—
709C2×Dic3—62no—
710C2×Dic3—64no—
711C2×Dic3—64no—
712C2×Dic3C23×D312yes—
713C2×Dic3C23×D311yescharacteristic
714C2×Dic3C23×D314yes—
715C2×Dic3C23×D311yescharacteristic
716C2×Dic3C23×D312yes—
717C2×Dic3C23×D312yes—
718C2×Dic3C23×D311yescharacteristic
719D12—22no—
720D12—68no—
721D12—64no—
722D12—64no—
723D12—64no—
724D12—64no—
725D12—124no—
726D12—124no—
727D12—122no—
728D12—122no—
729D12—124no—
730D12—124no—
731D12—242no—
732C4×D3—22no—
733C4×D3—22no—
734C4×D3—24no—
735C4×D3—22no—
736C4×D3—68no—
737C4×D3—68no—
738C4×D3—68no—
739C4×D3—68no—
740C4×D3—64no—
741C4×D3—64no—
742C4×D3—68no—
743C4×D3—68no—
744C4×D3—128no—
745Dic6—34no—
746Dic6—34no—
747Dic6—42no—
748Dic6—64no—
749Dic6—124no—
750Dic6—124no—
751Dic6#23514yescomplemented
752C2×C32—42no—
753C2×C32C22×#4111yescharacteristic
754C2×C32C22×#4111yescharacteristic
755C2×C32C2×H(5,𝔽2)11yescharacteristic
756C3⋊D3—44no—
757C3×D3—41no—
758C3×D3—42no—
759#41—64no—
760#41—188no—
761#41—184no—
762#41—188no—
763#41—368no—
764#41—364no—
765C2×Q8—31no—
766C2×Q8—32no—
767C2×Q8—94no—
768C2×Q8—91no—
769C2×D4—32no—
770C2×D4—34no—
771C2×D4—31no—
772C2×D4—94no—
773C2×D4—94no—
774C2×D4—94no—
775C2×D4—92no—
776C2×D4—94no—
777C2×D4—94no—
778C2×D4—92no—
779C2×D4—92no—
780C2×D4—92no—
781C2×D4C2×D3211yescharacteristic
782C22×C4—32no—
783C22×C4—32no—
784C22×C4—31no—
785C22×C4—31no—
786C22×C4—31no—
787C22×C4—32no—
788C22×C4—94no—
789C22×C4—94no—
790C22×C4—92no—
791C22×C4—92no—
792C22×C4—94no—
793C22×C4C2×D3212yes—
794C4⋊C4—31no—
795C4⋊C4—32no—
796C4⋊C4—32no—
797C4⋊C4—31no—
798C4⋊C4—32no—
799C4⋊C4—32no—
800C4⋊C4—92no—
801C4⋊C4—94no—
802C4⋊C4—94no—
803C4⋊C4—92no—
804C4⋊C4—91no—
805C4⋊C4C2×D3211yescharacteristic
806C22⋊C4—32no—
807C22⋊C4—34no—
808C22⋊C4—32no—
809C22⋊C4—34no—
810C22⋊C4—32no—
811C22⋊C4—94no—
812C22⋊C4—94no—
813C22⋊C4—94no—
814C22⋊C4—92no—
815C22⋊C4—92no—
816C22⋊C4—94no—
817C22⋊C4C2×D3212yes—
818C42—31no—
819C42—32no—
820C42—31no—
821C42—31no—
822C42—32no—
823C42—32no—
824C42—34no—
825C42—92no—
826C42—92no—
827C42—94no—
828C42—92no—
829C42C2×D3211yescharacteristic
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—22no—
836C22×C3—21no—
837C22×C3—42no—
838C22×C3—42no—
839C22×C3—42no—
840C22×C3—62no—
841C22×C3—62no—
842C22×C3—61no—
843C22×C3—61no—
844C22×C3—62no—
845C22×C3—61no—
846C22×C3C24×D311yescharacteristic
847C22×C3C24×D311yescharacteristic
848C2×D3—21no—
849C2×D3—22no—
850C2×D3—21no—
851C2×D3—22no—
852C2×D3—21no—
853C2×D3—22no—
854C2×D3—64no—
855C2×D3—64no—
856C2×D3—64no—
857C2×D3—64no—
858C2×D3—64no—
859C2×D3—64no—
860C2×D3—124no—
861C2×D3—124no—
862C2×D3—124no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—21no—
866C3×C4—21no—
867C3×C4—22no—
868C3×C4—22no—
869C3×C4—34no—
870C3×C4—32no—
871C3×C4—42no—
872C3×C4—41no—
873C3×C4—62no—
874C3×C4—61no—
875C3×C4—61no—
876C3×C4—64no—
877C3×C4—62no—
878C3×C4C2×#23512yes—
879C3×C4D3×#4112yes—
880C3×C4D3×#4112yes—
881C3×C4D3×#4112yes—
882Dic3—21no—
883Dic3—22no—
884Dic3—21no—
885Dic3—22no—
886Dic3—24no—
887Dic3—34no—
888Dic3—34no—
889Dic3—64no—
890Dic3—62no—
891Dic3—62no—
892Dic3—122no—
893Dic3C2×#23514yes—
894Dic3#100912yes—
895C32#348311yescharacteristic, complemented, Sylow
896C23—32no—
897C23—31no—
898C23—94no—
899C23C22×D3212yes—
900Q8—34no—
901Q8—94no—
902Q8—122no—
903Q8—364no—
904D4—22no—
905D4—64no—
906D4—62no—
907D4—124no—
908D4—188no—
909D4—188no—
910D4—184no—
911D4—184no—
912D4—184no—
913D4—362no—
914D4—364no—
915D4—364no—
916D4—364no—
917C2×C4—24no—
918C2×C4—31no—
919C2×C4—32no—
920C2×C4—31no—
921C2×C4—32no—
922C2×C4—31no—
923C2×C4—32no—
924C2×C4—34no—
925C2×C4—62no—
926C2×C4—64no—
927C2×C4—64no—
928C2×C4—62no—
929C2×C4—64no—
930C2×C4—62no—
931C2×C4—92no—
932C2×C4—92no—
933C2×C4—188no—
934C2×C4—188no—
935C2×C4—188no—
936C2×C4—184no—
937C2×C4—184no—
938C2×C4C22×D3212yes—
939C2×C4C22×D3211yescharacteristic
940C2×C4C22×D3211yescharacteristic
941C2×C4C22×D3211yescharacteristic
942C2×C3—21no—
943C2×C3—21no—
944C2×C3—21no—
945C2×C3—42no—
946C2×C3—42no—
947C2×C3—82no—
948C2×C3—122no—
949C2×C3—121no—
950C2×C3C22×#23511yescharacteristic
951C2×C3C2×D3×#4111yescharacteristic
952C2×C3C2×D3×#4111yescharacteristic
953C2×C3C2×D3×#4111yescharacteristic
954C2×C3C2×#100911yescharacteristic
955C2×C3D3×H(5,𝔽2)11yescharacteristic
956D3—41no—
957D3—42no—
958D3—124no—
959D3—124no—
960D3—244no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—61no—
965C22—62no—
966C22—61no—
967C22—62no—
968C22—61no—
969C22—62no—
970C22—184no—
971C22—184no—
972C22—184no—
973C22C23×D3211yescharacteristic
974C4—22no—
975C4—21no—
976C4—34no—
977C4—32no—
978C4—61no—
979C4—62no—
980C4—61no—
981C4—62no—
982C4—64no—
983C4—94no—
984C4—182no—
985C4D3×#23512yes—
986C4#6431212yes—
987C3—21no—
988C3#8584511yescharacteristic, complemented
989C3#8695911yescharacteristic, complemented
990C2—42no—
991C2—121no—
992C2—122no—
993C2—364no—
994C2C2×D3×#23511yescharacteristic
995C2C2×#6431211yescharacteristic
996C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3483
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596024C2semidirect
2. C3×#5563C2semidirect
3. C3×C4×#237C2semidirect
4. #10595236C2semidirect
5. #10595131C2semidirect
6. #10594954C2semidirect
7. #10594919C2semidirect
8. #10594910C2semidirect
9. #10594838C2semidirect
10. #10594575C2semidirect
11. #10594362C2semidirect
12. #10594109C2semidirect
13. #10594068C2semidirect
14. #10593970C2semidirect
15. #10593902C2semidirect
16. C4×#3795C2semidirect
17. #10593856C2semidirect
100. #5563D3semidirect
109. C4×#237D3semidirect
348. #634#41semidirect
366. C3×Dic6#41semidirect
751. Dic6#235semidirect
895. C32#3483semidirect
988. C3#85845semidirect
989. C3#86959semidirect

Maximal subgroups

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

subgroupindex
#105960242
C3×#55632
C3×C4×#2372
#105952362
#105951312
#105949542
#105949192
#105949102
#105948382
#105945752
#105943622
#105941092
#105940682
#105939702
#105939022
C4×#37952
#105938562
#869593
#858453