Finite Group Databasebeta

← #11904246

Subgroups — #11904246

Order 1152.

2522 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596034C211yesmaximal, characteristic, complemented
2C3×#5553C211yesmaximal, characteristic, complemented
3C3×C4×#237C211yesmaximal, characteristic, complemented
4#10595158C212yesmaximal, complemented
5#10595139C212yesmaximal, complemented
6#10595026C212yesmaximal, complemented
7#10595007C212yesmaximal, complemented
8Dic3×#235C212yesmaximal, complemented
9#10594910C212yesmaximal, complemented
10#10594555C212yesmaximal, complemented
11#10594360C212yesmaximal, complemented
12#10594104C214yesmaximal, complemented
13#10594058C214yesmaximal, complemented
14C4×#3799C211yesmaximal, characteristic, complemented
15#10593900C211yesmaximal, characteristic, complemented
16#10593897C211yesmaximal, characteristic, complemented
17Dic62C211yesmaximal, characteristic, complemented
18#86768—31nomaximal
19#85845—31nomaximal
20C2×C3×#237C2211yescharacteristic
21C2×C3×#235C2212yes—
22C2×#3804C2214yes—
23C2×#3799C2211yescharacteristic
24C2×#3796C2212yes—
25C2×#3795C2212yes—
26C32×C4×D4C2211yescharacteristic
27#64147C2212yes—
28#64139C2212yes—
29#64135C2212yes—
30#64101C2212yes—
31#64094C2214yes—
32C4×C4⋊(C3⋊D3)C2211yescharacteristic
33#64078C2211yescharacteristic
34C3×#940C2212yes—
35C3×D4×Dic3C2211yescharacteristic
36C3×#930C2212yes—
37C3×C4×#67C2212yes—
38C2×C3×C4×Dic3C2212yes—
39C3×#893C2212yes—
40C3×#892C2211yescharacteristic
41C3×#887C2211yescharacteristic
42C3×#884C2214yes—
43C3×#67⋊C4C2212yes—
44C3×#877C2212yes—
45C3×#874C2211yescharacteristic
46C3×C42×D3C2211yescharacteristic
47C3×C4×Dic6C2211yescharacteristic
48C3×C4×Dic6C2211yescharacteristic
49#63979C2214yes—
50#63978C2214yes—
51Dic3×#67C2214yes—
52Dic3×#67C2214yes—
53#63970C2214yes—
54#63959C2214yes—
55#63958C2214yes—
56#63918C2212yes—
57#63918C2212yes—
58#63916C2212yes—
59#63915C2214yes—
60#63911C2212yes—
61#63908C2212yes—
62#63908C2212yes—
63#63906C2214yes—
64#63904C2212yes—
65#63904C2214yes—
66C4×#626C2212yes—
67#63894C2211yescharacteristic
68Dic3×D12C2212yes—
69Dic3×D12C2212yes—
70Dic3×D12C2212yes—
71#63886C2214yes—
72C4×#624C2212yes—
73#63880C2214yes—
74#63878C2214yes—
75C4×D3×Dic3C2214yes—
76#63860C2212yes—
77#63855C2214yes—
78#63852C2214yes—
79Dic3×Dic6C2212yes—
80Dic3×Dic6C2212yes—
81Dic3×Dic6C2211yescharacteristic
82#63841C2211yescharacteristic
83#63840C2214yes—
84#63836C2212yes—
85C3×#550—31no—
86C3×C4×#41—31no—
87#5834—32no—
88#5834—32no—
89Dic3×#41—32no—
90#5718—32no—
91#5718—31no—
92#5716—32no—
93#5716—31no—
94#5616—32no—
95#5616—34no—
96#5596—32no—
97#5596—34no—
98#5577—31no—
99C4×#239—32no—
100C4×#239—31no—
101Q8×Dic6—31no—
102Q8×Dic6—31no—
103#5563—31no—
104#5563—31no—
105#5563—32no—
106#5563—32no—
107#5563—61no—
108#5553—32no—
109#5553D311yescharacteristic, complemented
110#5548—32no—
111#5548—34no—
112C4×#237—32no—
113C4×#237D311yescharacteristic, complemented
114#5532—32no—
115#5532—34no—
116#5477—32no—
117#5477—31no—
118C4×#235—32no—
119C4×#235—31no—
120C2×C32×D4C2311yescharacteristic
121C22×C32×C4C2312yes—
122C2×#638C2314yes—
123C2×C4⋊(C3⋊D3)C2311yescharacteristic
124C2×C4×C3⋊D3C2312yes—
125C2×#634C2312yes—
126C2×C3×#67C2312yes—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C22×C3×Dic3C2312yes—
130C22×C3×Dic3C2312yes—
131C3×#237—24no—
132C3×#235—28no—
133C2×C3×D12C2312yes—
134C2×C3×D12C2312yes—
135C2×C3×D12C2312yes—
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2314yes—
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×Dic6C2311yescharacteristic
141C2×C3×Dic6C2311yescharacteristic
142C2×#627C2314yes—
143C2×#626C2314yes—
144C2×#626C2312yes—
145C2×#626C2314yes—
146C2×#625C2314yes—
147C2×#624C2312yes—
148C2×#624C2312yes—
149#3804—48no—
150C2×D3×Dic3C2314yes—
151C2×D3×Dic3C2314yes—
152#3799—24no—
153#3796—28no—
154#3795—44no—
155C32×C4⋊C4C2311yescharacteristic
156C32×C22⋊C4C2312yes—
157C32×C42C2311yescharacteristic
158#3757C2314yes—
159#3752C2312yes—
160#3752C2314yes—
161C4⋊(C3⋊Dic3)C2312yes—
162C4⋊(C3⋊Dic3)C2312yes—
163C4⋊(C3⋊Dic3)C2311yescharacteristic
164C4×C3⋊Dic3C2314yes—
165C3×#217C2312yes—
166C3×(C2×D3)⋊C4C2312yes—
167C3×(C2×D3)⋊C4C2314yes—
168C3×C4⋊Dic3C2311yescharacteristic
169C3×C4⋊Dic3C2311yescharacteristic
170C3×Dic3⋊C4C2312yes—
171C3×Dic3⋊C4C2312yes—
172C3×Dic3⋊C4C2312yes—
173C3×C4×Dic3C2311yescharacteristic
174C3×C4×Dic3C2312yes—
175C3×C4×Dic3C2312yes—
176C3×C4×Dic3C2311yescharacteristic
177C3×C4×Dic3C2312yes—
178C3×C4×Dic3C2311yescharacteristic
179C3×C4×Dic3C2312yes—
180Dic3⋊Dic3C2312yes—
181Dic3⋊Dic3C2314yes—
182Dic3⋊Dic3C2314yes—
183#3722C2312yes—
184(C2×D3)⋊Dic3C2312yes—
185(C2×D3)⋊Dic3C2314yes—
186(C2×D3)⋊Dic3C2314yes—
187(C2×D3)⋊Dic3C2314yes—
188Dic32C2312yes—
189Dic32C2314yes—
190Dic32C2312yes—
191#3483—91noSylow
192C2×C3×#41—31no—
193C2×C3×#41—32no—
194C2×#239—32no—
195C2×#239—31no—
196C2×#237—34no—
197C2×#237—32no—
198C2×#237—32no—
199C2×#237C2×D311yescharacteristic
200C2×#235—34no—
201C2×#235—32no—
202C2×#235—31no—
203C2×#235C2×D312yes—
204C3×#127—32no—
205C3×#127—31no—
206C3×#121—32no—
207C3×#121—34no—
208C3×C4×Q8—31no—
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—32no—
216C3×C4×D4C2×D311yescharacteristic
217C3×C4×D4C2×D311yescharacteristic
218C3×#117—31no—
219C3×#117—32no—
220C2×C3×C42—32no—
221C2×C3×C42—31no—
222Q8×Dic3—32no—
223Q8×Dic3—32no—
224Q8×Dic3—31no—
225#940—34no—
226#940—34no—
227#940—32no—
228#940C2×D312yes—
229#939—34no—
230#939—34no—
231#939—34no—
232#938—32no—
233#938—32no—
234#938—34no—
235#938—32no—
236#938—32no—
237#938—34no—
238#938—32no—
239#938—62no—
240#936—34no—
241#936—32no—
242D4×Dic3—34no—
243D4×Dic3—34no—
244D4×Dic3—32no—
245D4×Dic3—32no—
246D4×Dic3—32no—
247D4×Dic3C2×D311yescharacteristic
248#930—32no—
249#930—32no—
250#930—34no—
251#930—32no—
252#930—32no—
253#930—34no—
254#930—62no—
255#930C2×D312yes—
256C4×#67—34no—
257C4×#67—34no—
258C4×#67—32no—
259C4×#67—34no—
260C4×#67—32no—
261C4×#67C2×D312yes—
262#926—32no—
263#926—32no—
264#926—31no—
265#926—34no—
266#926—62no—
267C2×C4×Dic3—34no—
268C2×C4×Dic3C2×D312yes—
269#895—34no—
270#895—32no—
271#893—34no—
272#893—32no—
273#893—31no—
274#893C2×D312yes—
275#892—31no—
276#892—32no—
277#892—32no—
278#892—34no—
279#892—32no—
280#892—62no—
281#892C2×D311yescharacteristic
282#888—34no—
283#888—34no—
284#888—32no—
285#888—32no—
286#887C2×D311yescharacteristic
287#885—34no—
288#885—34no—
289#885—34no—
290#885—34no—
291#885—34no—
292#885—34no—
293#885—64no—
294#884—34no—
295#884—34no—
296#884C2×D314yes—
297#67⋊C4—34no—
298#67⋊C4C2×D312yes—
299#877—34no—
300#877C2×D312yes—
301#875—32no—
302#875—34no—
303#874—32no—
304#874C2×D311yescharacteristic
305C4×D12—32no—
306C4×D12—32no—
307C4×D12—32no—
308C4×D12—32no—
309C4×D12—31no—
310C4×D12—31no—
311C4×D12—34no—
312C4×D12—31no—
313C4×D12—61no—
314#872—34no—
315#872—32no—
316C42×D3—34no—
317C42×D3—32no—
318C42×D3—32no—
319C42×D3C2×D311yescharacteristic
320#869—31no—
321#869—31no—
322#869—32no—
323#869—32no—
324#869—61no—
325C4×Dic6—32no—
326C4×Dic6—31no—
327C4×Dic6—32no—
328C4×Dic6C2×D311yescharacteristic
329C4×Dic6C2×D311yescharacteristic
330C23×C32C2412yes—
331C22×C3⋊D3C2412yes—
332C22×C3×D3C2414yes—
333C22×C3×D3C2411yescharacteristic
334C32×D4—22no—
335C2×C32×C4—24no—
336C2×C32×C4C2412yes—
337C2×C32×C4C2411yescharacteristic
338C2×C32×C4C2411yescharacteristic
339C2×C32×C4C2411yescharacteristic
340#638—44no—
341C2×C3⋊Dic3C2412yes—
342C2×C3⋊Dic3C2414yes—
343C4⋊(C3⋊D3)—22no—
344C4×C3⋊D3—24no—
345#634—42no—
346C3×#67—28no—
347C3×#67—24no—
348C3×#67—44no—
349C2×C3×Dic3—24no—
350C2×C3×Dic3—24no—
351C2×C3×Dic3C2411yescharacteristic
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2411yescharacteristic
354C2×C3×Dic3C2412yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2412yes—
357C2×C3×Dic3C2411yescharacteristic
358C3×D12—24no—
359C3×D12—24no—
360C3×D12—42no—
361C3×C4×D3—22no—
362C3×C4×D3—22no—
363C3×C4×D3—28no—
364C3×C4×D3—22no—
365C3×Dic6#4114yescomplemented
366C3×Dic6#4114yescomplemented
367#627—44no—
368#626—28no—
369#626—24no—
370#626—44no—
371#625—44no—
372#624—24no—
373#624—24no—
374D3×Dic3—28no—
375D3×Dic3—28no—
376Q82—91no—
377#555—92no—
378#555—94no—
379#555—92no—
380#555—91no—
381#550—31no—
382#550—92no—
383#550—91no—
384#550—92no—
385#532—92no—
386#532—91no—
387#532—94no—
388#532—92no—
389C4×#41—31no—
390C4×#41—91no—
391C4×#41—92no—
392C4×#41—92no—
393C3×#41—68no—
394C3×#41—64no—
395C2×C3×Q8—31no—
396C2×C3×Q8—31no—
397C2×C3×D4—21no—
398C2×C3×D4—34no—
399C2×C3×D4—32no—
400C2×C3×D4—34no—
401C2×C3×D4—32no—
402C2×C3×D4—32no—
403C2×C3×D4—32no—
404C2×C3×D4C22×D311yescharacteristic
405C2×C3×D4C22×D311yescharacteristic
406C22×C3×C4—22no—
407C22×C3×C4—32no—
408C22×C3×C4—32no—
409C22×C3×C4—34no—
410C22×C3×C4—31no—
411C22×C3×C4—31no—
412C22×C3×C4—31no—
413C22×C3×C4C22×D312yes—
414C22×C3×C4C22×D312yes—
415C2×#67—34no—
416C2×#67—34no—
417C2×#67—34no—
418C2×#67—34no—
419C2×#67—34no—
420C2×#67—32no—
421C2×#67—34no—
422C2×#67—64no—
423C2×#67C22×D312yes—
424C2×#67C22×D314yes—
425C2×#67C22×D314yes—
426C22×Dic3—34no—
427C22×Dic3—34no—
428C22×Dic3C22×D312yes—
429C22×Dic3C22×D312yes—
430#239—64no—
431#239—68no—
432#237—24no—
433#237—68no—
434#237—124no—
435#237—128no—
436#235—28no—
437#235—64no—
438#235—124no—
439#235—128no—
440C2×D12—34no—
441C2×D12—32no—
442C2×D12—31no—
443C2×D12—31no—
444C2×D12—34no—
445C2×D12—61no—
446C2×D12C22×D312yes—
447C2×D12C22×D312yes—
448C2×D12C22×D312yes—
449C2×C4×D3—34no—
450C2×C4×D3—34no—
451C2×C4×D3—32no—
452C2×C4×D3—32no—
453C2×C4×D3—32no—
454C2×C4×D3—32no—
455C2×C4×D3—32no—
456C2×C4×D3—32no—
457C2×C4×D3—62no—
458C2×C4×D3C22×D314yes—
459C2×C4×D3C22×D311yescharacteristic
460C2×C4×D3C22×D311yescharacteristic
461C2×C4×D3C22×D311yescharacteristic
462C2×Dic6—32no—
463C2×Dic6—32no—
464C2×Dic6—34no—
465C2×Dic6—34no—
466C2×Dic6—62no—
467C2×Dic6C22×D311yescharacteristic
468C2×Dic6C22×D311yescharacteristic
469C3×C4⋊C4—21no—
470C3×C4⋊C4—32no—
471C3×C4⋊C4—31no—
472C3×C4⋊C4—32no—
473C3×C4⋊C4—31no—
474C3×C4⋊C4—32no—
475C3×C4⋊C4C22×D311yescharacteristic
476C3×C4⋊C4C22×D311yescharacteristic
477C3×C22⋊C4—22no—
478C3×C22⋊C4—32no—
479C3×C22⋊C4—34no—
480C3×C22⋊C4—32no—
481C3×C22⋊C4C22×D312yes—
482C3×C22⋊C4C22×D312yes—
483C3×C42—21no—
484C3×C42—32no—
485C3×C42—32no—
486C3×C42—31no—
487C3×C42—32no—
488C3×C42—31no—
489C3×C42—31no—
490C3×C42—32no—
491C3×C42C22×D311yescharacteristic
492C3×C42C22×D311yescharacteristic
493#217—34no—
494#217—34no—
495#217—34no—
496#217—32no—
497#217—34no—
498#217—34no—
499#217—64no—
500#217C22×D312yes—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—32no—
505(C2×D3)⋊C4—32no—
506(C2×D3)⋊C4—34no—
507(C2×D3)⋊C4—32no—
508(C2×D3)⋊C4—34no—
509(C2×D3)⋊C4—32no—
510(C2×D3)⋊C4—32no—
511(C2×D3)⋊C4—62no—
512(C2×D3)⋊C4—64no—
513(C2×D3)⋊C4C22×D314yes—
514(C2×D3)⋊C4C22×D312yes—
515C4⋊Dic3—32no—
516C4⋊Dic3—32no—
517C4⋊Dic3—31no—
518C4⋊Dic3—32no—
519C4⋊Dic3—32no—
520C4⋊Dic3—31no—
521C4⋊Dic3—34no—
522C4⋊Dic3—34no—
523C4⋊Dic3—32no—
524C4⋊Dic3—62no—
525C4⋊Dic3—62no—
526C4⋊Dic3—61no—
527C4⋊Dic3C22×D311yescharacteristic
528C4⋊Dic3C22×D311yescharacteristic
529Dic3⋊C4—32no—
530Dic3⋊C4—34no—
531Dic3⋊C4—34no—
532Dic3⋊C4C22×D312yes—
533Dic3⋊C4C22×D312yes—
534Dic3⋊C4C22×D312yes—
535C4×Dic3—34no—
536C4×Dic3—34no—
537C4×Dic3—32no—
538C4×Dic3—34no—
539C4×Dic3—34no—
540C4×Dic3—32no—
541C4×Dic3—32no—
542C4×Dic3—32no—
543C4×Dic3—64no—
544C4×Dic3C22×D312yes—
545C4×Dic3C22×D312yes—
546C4×Dic3C22×D311yescharacteristic
547C4×Dic3C22×D311yescharacteristic
548C4×Dic3C22×D311yescharacteristic
549C4×Dic3C22×D312yes—
550C4×Dic3C22×D312yes—
551C22×C32—22no—
552C22×C32—22no—
553C22×C32—22no—
554C22×C32C2511yescharacteristic
555C2×C3⋊D3—22no—
556C2×C3⋊D3—22no—
557C2×C3⋊D3—22no—
558C2×C3×D3—24no—
559C2×C3×D3—21no—
560C2×C3×D3—24no—
561C2×C3×D3—21no—
562C2×C3×D3—24no—
563C2×C3×D3—21no—
564C32×C4—22no—
565C32×C4—21no—
566C32×C4C2×#4112yes—
567C32×C4C2×#4112yes—
568C3⋊Dic3—22no—
569C3⋊Dic3—24no—
570C3×Dic3—21no—
571C3×Dic3—21no—
572C3×Dic3—22no—
573C3×Dic3—22no—
574C3×Dic3C2×#4114yes—
575C3×Dic3C2×#4114yes—
576C3×Dic3H(5,𝔽2)12yes—
577C2×#41—31no—
578C2×#41—32no—
579C2×#41—94no—
580C2×#41—92no—
581C2×#41—91no—
582C2×#41—92no—
583C4⋊Q8—92no—
584C4⋊Q8—92no—
585C4⋊Q8—94no—
586C4⋊Q8—91no—
587#127—32no—
588#127—31no—
589#127—92no—
590#127—94no—
591#124—94no—
592#124—92no—
593#124—94no—
594#124—94no—
595#124—94no—
596#121—32no—
597#121—34no—
598#121—94no—
599#121—94no—
600#121—92no—
601#121—94no—
602#121—92no—
603#121—92no—
604#121—94no—
605#121—94no—
606#121—92no—
607#121—92no—
608C4×Q8—31no—
609C4×Q8—31no—
610C4×Q8—31no—
611C4×Q8—91no—
612C4×Q8—92no—
613C4×Q8—92no—
614C4×D4—31no—
615C4×D4—32no—
616C4×D4—32no—
617C4×D4—32no—
618C4×D4—94no—
619C4×D4—91no—
620C4×D4—92no—
621C4×D4—92no—
622C4×D4—92no—
623C4×D4—92no—
624C4×D4—92no—
625C4×D4—94no—
626C4×D4—94no—
627C4×D4—94no—
628C4×D4—91no—
629C4×D4D3211yescharacteristic
630#117—31no—
631#117—32no—
632#117—92no—
633#117—94no—
634#117—94no—
635#117—91no—
636#117—92no—
637#117—92no—
638C2×C42—32no—
639C2×C42—31no—
640C2×C42—92no—
641C2×C42—94no—
642C23×C3—22no—
643C23×C3—34no—
644C23×C3—31no—
645C23×C3C23×D312yes—
646C23×C3C23×D312yes—
647C22×D3—32no—
648C22×D3—32no—
649C22×D3—62no—
650C22×D3C23×D314yes—
651C22×D3C23×D311yescharacteristic
652C3×Q8—34no—
653C3×Q8—34no—
654C3×D4—22no—
655C3×D4—22no—
656C3×D4—42no—
657C3×D4—64no—
658C3×D4—68no—
659C3×D4—64no—
660C3×D4—64no—
661C3×D4—122no—
662C3×D4—124no—
663C2×C3×C4—24no—
664C2×C3×C4—24no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—22no—
668C2×C3×C4—21no—
669C2×C3×C4—32no—
670C2×C3×C4—32no—
671C2×C3×C4—31no—
672C2×C3×C4—31no—
673C2×C3×C4—32no—
674C2×C3×C4—31no—
675C2×C3×C4—32no—
676C2×C3×C4—44no—
677C2×C3×C4—62no—
678C2×C3×C4—68no—
679C2×C3×C4—64no—
680C2×C3×C4—64no—
681C2×C3×C4—62no—
682C2×C3×C4—62no—
683C2×C3×C4C23×D312yes—
684C2×C3×C4C23×D312yes—
685C2×C3×C4C23×D311yescharacteristic
686C2×C3×C4C23×D311yescharacteristic
687C2×C3×C4C23×D311yescharacteristic
688C2×C3×C4C23×D311yescharacteristic
689C2×C3×C4C23×D311yescharacteristic
690C2×C3×C4C23×D311yescharacteristic
691#67—24no—
692#67—28no—
693#67—44no—
694#67—68no—
695#67—64no—
696#67—124no—
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—34no—
707C2×Dic3—34no—
708C2×Dic3—62no—
709C2×Dic3—64no—
710C2×Dic3—68no—
711C2×Dic3—68no—
712C2×Dic3C23×D311yescharacteristic
713C2×Dic3C23×D312yes—
714C2×Dic3C23×D311yescharacteristic
715C2×Dic3C23×D312yes—
716C2×Dic3C23×D312yes—
717C2×Dic3C23×D312yes—
718C2×Dic3C23×D311yescharacteristic
719D12—24no—
720D12—24no—
721D12—42no—
722D12—68no—
723D12—64no—
724D12—62no—
725D12—62no—
726D12—122no—
727D12—124no—
728C4×D3—22no—
729C4×D3—22no—
730C4×D3—28no—
731C4×D3—22no—
732C4×D3—64no—
733C4×D3—64no—
734C4×D3—68no—
735C4×D3—68no—
736C4×D3—64no—
737C4×D3—64no—
738C4×D3—64no—
739C4×D3—64no—
740C4×D3—124no—
741Dic6—124no—
742Dic6—124no—
743Dic6—122no—
744Dic6—122no—
745Dic6—242no—
746Dic6#23514yescomplemented
747Dic6#23714yescomplemented
748C2×C32—42no—
749C2×C32C22×#4111yescharacteristic
750C2×C32C22×#4111yescharacteristic
751C2×C32C2×H(5,𝔽2)11yescharacteristic
752C3⋊D3—42no—
753C3×D3—41no—
754C3×D3—44no—
755#41—68no—
756#41—64no—
757#41—184no—
758#41—188no—
759#41—364no—
760#41—368no—
761C2×Q8—31no—
762C2×Q8—31no—
763C2×Q8—94no—
764C2×Q8—92no—
765C2×D4—32no—
766C2×D4—34no—
767C2×D4—34no—
768C2×D4—32no—
769C2×D4—32no—
770C2×D4—32no—
771C2×D4—94no—
772C2×D4—92no—
773C2×D4—94no—
774C2×D4—94no—
775C2×D4—94no—
776C2×D4—91no—
777C2×D4C2×D3211yescharacteristic
778C22×C4—32no—
779C22×C4—32no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—31no—
783C22×C4—34no—
784C22×C4—92no—
785C22×C4—92no—
786C22×C4—94no—
787C22×C4—94no—
788C22×C4—92no—
789C22×C4C2×D3212yes—
790C4⋊C4—32no—
791C4⋊C4—32no—
792C4⋊C4—31no—
793C4⋊C4—32no—
794C4⋊C4—31no—
795C4⋊C4—92no—
796C4⋊C4—94no—
797C4⋊C4—94no—
798C4⋊C4—91no—
799C4⋊C4—92no—
800C4⋊C4—92no—
801C4⋊C4C2×D3211yescharacteristic
802C22⋊C4—32no—
803C22⋊C4—32no—
804C22⋊C4—34no—
805C22⋊C4—92no—
806C22⋊C4—94no—
807C22⋊C4—94no—
808C22⋊C4—94no—
809C22⋊C4—92no—
810C22⋊C4—94no—
811C22⋊C4—92no—
812C22⋊C4—94no—
813C22⋊C4C2×D3212yes—
814C42—31no—
815C42—32no—
816C42—31no—
817C42—31no—
818C42—32no—
819C42—32no—
820C42—32no—
821C42—92no—
822C42—92no—
823C42—94no—
824C42—94no—
825C42C2×D3211yescharacteristic
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—21no—
833C22×C3—42no—
834C22×C3—42no—
835C22×C3—42no—
836C22×C3—64no—
837C22×C3—61no—
838C22×C3—61no—
839C22×C3—64no—
840C22×C3—64no—
841C22×C3—61no—
842C22×C3C24×D311yescharacteristic
843C22×C3C24×D311yescharacteristic
844C2×D3—21no—
845C2×D3—24no—
846C2×D3—21no—
847C2×D3—24no—
848C2×D3—21no—
849C2×D3—24no—
850C2×D3—62no—
851C2×D3—62no—
852C2×D3—62no—
853C2×D3—62no—
854C2×D3—62no—
855C2×D3—62no—
856C2×D3—122no—
857C2×D3—122no—
858C2×D3—122no—
859C3×C4—22no—
860C3×C4—22no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—34no—
866C3×C4—34no—
867C3×C4—32no—
868C3×C4—41no—
869C3×C4—42no—
870C3×C4—61no—
871C3×C4—61no—
872C3×C4—62no—
873C3×C4—62no—
874C3×C4C2×#23512yes—
875C3×C4C2×#23712yes—
876C3×C4D3×#4112yes—
877C3×C4D3×#4112yes—
878Dic3—21no—
879Dic3—21no—
880Dic3—22no—
881Dic3—22no—
882Dic3—62no—
883Dic3—62no—
884Dic3—64no—
885Dic3—64no—
886Dic3—124no—
887Dic3—122no—
888Dic3C2×#23514yes—
889Dic3C2×#23714yes—
890Dic3#100912yes—
891C32#348311yescharacteristic, complemented, Sylow
892C23—31no—
893C23—34no—
894C23—92no—
895C23C22×D3212yes—
896Q8—34no—
897Q8—34no—
898Q8—362no—
899Q8—364no—
900D4—22no—
901D4—64no—
902D4—68no—
903D4—64no—
904D4—64no—
905D4—122no—
906D4—124no—
907D4—188no—
908D4—184no—
909D4—182no—
910D4—364no—
911D4—364no—
912D4—364no—
913C2×C4—24no—
914C2×C4—31no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—31no—
918C2×C4—31no—
919C2×C4—32no—
920C2×C4—32no—
921C2×C4—68no—
922C2×C4—62no—
923C2×C4—64no—
924C2×C4—64no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4—92no—
928C2×C4—94no—
929C2×C4—184no—
930C2×C4—184no—
931C2×C4—188no—
932C2×C4—188no—
933C2×C4—184no—
934C2×C4C22×D3212yes—
935C2×C4C22×D3211yescharacteristic
936C2×C4C22×D3211yescharacteristic
937C2×C4C22×D3211yescharacteristic
938C2×C3—21no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—42no—
942C2×C3—42no—
943C2×C3—82no—
944C2×C3—124no—
945C2×C3—121no—
946C2×C3C22×#23511yescharacteristic
947C2×C3C22×#23711yescharacteristic
948C2×C3C2×D3×#4111yescharacteristic
949C2×C3C2×D3×#4111yescharacteristic
950C2×C3C2×#100911yescharacteristic
951C2×C3D3×H(5,𝔽2)11yescharacteristic
952D3—41no—
953D3—44no—
954D3—122no—
955D3—122no—
956D3—242no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—61no—
961C22—64no—
962C22—64no—
963C22—61no—
964C22—61no—
965C22—64no—
966C22—182no—
967C22—182no—
968C22—182no—
969C22C23×D3211yescharacteristic
970C4—22no—
971C4—21no—
972C4—34no—
973C4—34no—
974C4—32no—
975C4—61no—
976C4—61no—
977C4—62no—
978C4—62no—
979C4—182no—
980C4—184no—
981C4D3×#23512yes—
982C4D3×#23712yes—
983C3—21no—
984C3#8584511yescharacteristic, complemented
985C3#8676811yescharacteristic, complemented
986C2—42no—
987C2—121no—
988C2—124no—
989C2—362no—
990C2C2×D3×#23511yescharacteristic
991C2C2×D3×#23711yescharacteristic
992C2D3×#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. #10596034C2semidirect
2. C3×#5553C2semidirect
3. C3×C4×#237C2semidirect
4. #10595158C2semidirect
5. #10595139C2semidirect
6. #10595026C2semidirect
7. #10595007C2semidirect
8. Dic3×#235C2semidirect
9. #10594910C2semidirect
10. #10594555C2semidirect
11. #10594360C2semidirect
12. #10594104C2semidirect
13. #10594058C2semidirect
14. C4×#3799C2semidirect
15. #10593900C2semidirect
16. #10593897C2semidirect
17. Dic62C2semidirect
109. #5553D3semidirect
113. C4×#237D3semidirect
365. C3×Dic6#41semidirect
366. C3×Dic6#41semidirect
746. Dic6#235semidirect
747. Dic6#237semidirect
891. C32#3483semidirect
984. C3#85845semidirect
985. C3#86768semidirect

Maximal subgroups

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

subgroupindex
#105960342
C3×#55532
C3×C4×#2372
#105951582
#105951392
#105950262
#105950072
Dic3×#2352
#105949102
#105945552
#105943602
#105941042
#105940582
C4×#37992
#105939002
#105938972
Dic622
#867683
#858453