Finite Group Databasebeta

← #11864593

Subgroups — #11864593

Order 1152.

1622 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C2×#63933C211yesmaximal, characteristic, complemented
3C2×#63932C211yesmaximal, characteristic, complemented
4#10595004C211yesmaximal, characteristic, complemented
5#10592917C211yesmaximal, characteristic, complemented
6C3×#5217C211yesmaximal, characteristic, complemented
7#10591463C211yesmaximal, characteristic, complemented
8#10591459C211yesmaximal, characteristic, complemented
9#10591450C211yesmaximal, characteristic, complemented
10#10591447C211yesmaximal, characteristic, complemented
11#10591414C211yesmaximal, characteristic, complemented
12D3×#832C211yesmaximal, characteristic, complemented
13#10591173C211yesmaximal, characteristic, complemented
14#10591161C211yesmaximal, characteristic, complemented
15#10591145C211yesmaximal, characteristic, complemented
16#84102—31nomaximal
17#80005—31nomaximal
18C22×C32×D4C2211yescharacteristic
19C22×C3×#67—21no—
20C22×C3×#67—21no—
21C3×#1004—24no—
22C3×#1004—24no—
23C2×C3×#237—21no—
24C2×C3×#237C2211yescharacteristic
25C2×C3×#237C2211yescharacteristic
26C2×C3×D3×D4—21no—
27C2×C3×D3×D4C2211yescharacteristic
28C2×C3×D3×D4C2211yescharacteristic
29C2×C3×#235C2211yescharacteristic
30C2×C3×#235C2211yescharacteristic
31C2×#3795C2211yescharacteristic, complemented
32C2×#3754C2211yescharacteristic, complemented
33C2×#3754C2211yescharacteristic, complemented
34#64133C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic, complemented
37C3×#930C2211yescharacteristic, complemented
38#63970—21no—
39#63970—21no—
40#63933—24no—
41#63932—24no—
42#63908C2211yescharacteristic, complemented
43D3×C4⋊Dic3C2211yescharacteristic, complemented
44#63887—21no—
45#63885—21no—
46#63857C2211yescharacteristic, complemented
47C2×#3719C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63565C2211yescharacteristic, complemented
61#63563C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×C3×H(5,𝔽2)—31no—
66C2×#1004D311yescharacteristic, complemented
67#5833—31no—
68C2×#950—31no—
69C2×#932—31no—
70C2×#912—31no—
71C2×#911—31no—
72#5608—31no—
73C3×#447—31no—
74#5239—31no—
75#5239—31no—
76#5238—31no—
77#5238—31no—
78#5234—31no—
79#5232—31no—
80#5218—31no—
81#5218—31no—
82#5218—31no—
83#5218—61no—
84#5217—31no—
85#5217D311yescharacteristic, complemented
86C2×#832—31no—
87#5158—31no—
88#5156—31no—
89#5037—31no—
90#4783—31no—
91#4776—31no—
92#4771—31no—
93D3×#102—31no—
94#4733—31no—
95#4727—31no—
96C24×C32—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C2×C32×D4—22no—
100C2×C32×D4—22no—
101C2×C32×D4—21no—
102C2×C32×D4C2311yescharacteristic
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C2×#634C2311yescharacteristic
106C2×C3×#67—28no—
107C2×C3×#67—28no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C2×C3×#67D411yescharacteristic
115C2×C3×#67D411yescharacteristic
116C22×C3×Dic3—21no—
117C22×C3×Dic3—21no—
118C3×#237—28no—
119C3×#237—22no—
120C3×#237—22no—
121C3×#237—22no—
122C3×#237D414yescomplemented
123C3×D3×D4—28no—
124C3×D3×D4—22no—
125C3×D3×D4—22no—
126C3×D3×D4—22no—
127C3×D3×D4D414yescomplemented
128C3×#235—22no—
129C3×#235—22no—
130C3×#235—22no—
131C3×#235—22no—
132C2×C3×D12D411yescharacteristic
133C2×C3×D12C2311yescharacteristic
134C2×C3×D12C2311yescharacteristic
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6D411yescharacteristic
139C2×C3×Dic6C2311yescharacteristic
140C2×#625—21no—
141C2×#625—21no—
142C2×D3×Dic3—21no—
143C2×D3×Dic3—21no—
144#3795—22no—
145#3795—22no—
146#3757—21no—
147#3754—22no—
148#3754—22no—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150#3750—21no—
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153C3×#213—22no—
154C3×#213—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159Dic3⋊Dic3—21no—
160Dic3⋊Dic3—21no—
161(C2×D3)⋊Dic3—21no—
162(C2×D3)⋊Dic3—21no—
163#3719—22no—
164#3716—22no—
165#3715—22no—
166#3713—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3012—91noSylow
170C3×H(5,𝔽2)—64no—
171C3×H(5,𝔽2)—64no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C22×C3×D4—21no—
178C22×C3×D4—31no—
179C22×C3×D4—31no—
180C22×C3×D4—61no—
181C22×C3×D4—61no—
182C22×C3×D4—61no—
183C22×C3×D4C2×D311yescharacteristic
184C22×C3×D4C2×D311yescharacteristic
185C22×#67—21no—
186C22×#67—21no—
187#1004—24no—
188#1004—24no—
189C2×#237—21no—
190C2×#237—31no—
191C2×#237C2×D311yescharacteristic
192C2×#237C2×D311yescharacteristic
193C2×D3×D4—21no—
194C2×D3×D4C2×D311yescharacteristic
195C2×D3×D4C2×D311yescharacteristic
196C2×#235—31no—
197C2×#235C2×D311yescharacteristic
198C2×#235C2×D311yescharacteristic
199C2×C3×D8—31no—
200C2×C3×D8—31no—
201C3×#121—31no—
202#950—64no—
203#946—61no—
204C2×#216—31no—
205C2×#215—31no—
206#939—61no—
207#939—61no—
208#939—61no—
209#938—31no—
210#938—61no—
211#938—61no—
212C2×#214—31no—
213C2×#214—31no—
214C2×#214—31no—
215C2×#214—31no—
216C2×#214—31no—
217C2×#214—31no—
218C2×#214—61no—
219C2×#214—61no—
220#932—64no—
221C2×#213—31no—
222C2×#213—31no—
223C2×#213C2×D311yescharacteristic, complemented
224C2×#213C2×D311yescharacteristic, complemented
225#930—31no—
226#930C2×D311yescharacteristic, complemented
227C2×C4⋊Dic3—31no—
228#924—31no—
229#924—31no—
230#924—31no—
231#924—61no—
232C2×#208—31no—
233C22×C3⋊C8—31no—
234#912—64no—
235#911—64no—
236C2×Dic12—31no—
237C2×#204—31no—
238C2×ΓL(1,𝔽25)—31no—
239C2×D3×C8—31no—
240#897—31no—
241D3×C4⋊C4—31no—
242#884—61no—
243#878—61no—
244C3×#102—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#832—31no—
250#832—31no—
251#832—31no—
252#832—31no—
253#832—31no—
254#832—31no—
255#832—61no—
256#832—61no—
257#832C2×D311yescharacteristic, complemented
258#832C2×D311yescharacteristic, complemented
259#830—31no—
260#830—31no—
261#830—31no—
262#830—31no—
263#830—61no—
264#830C2×D311yescharacteristic, complemented
265#821—31no—
266(C2×D3)⋊C8—31no—
267(C2×D3)⋊C8—31no—
268#816—31no—
269#810—31no—
270#809—31no—
271C23×C32—24no—
272C23×C32—21no—
273C23×C32—21no—
274C23×C32—81no—
275C23×C32—81no—
276C23×C32C2×D411yescharacteristic
277C22×C3×D3—21no—
278C22×C3×D3—24no—
279C22×C3×D3—24no—
280C22×C3×D3—21no—
281C22×C3×D3—81no—
282C22×C3×D3—81no—
283C22×C3×D3—81no—
284C22×C3×D3—81no—
285C22×C3×D3C2×D411yescharacteristic
286C22×C3×D3C2×D411yescharacteristic
287C32×D4—24no—
288C32×D4—21no—
289C32×D4—21no—
290C32×D4C2×D412yes—
291C32×D4C2×D412yes—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4C2×D411yescharacteristic
295C2×C32×C4C2411yescharacteristic
296C2×C3⋊Dic3—21no—
297C2×C3⋊Dic3—21no—
298#634—21no—
299#634—21no—
300C3×#67—24no—
301C3×#67—24no—
302C3×#67—24no—
303C3×#67—22no—
304C3×#67—24no—
305C3×#67—22no—
306C3×#67—24no—
307C3×#67—81no—
308C2×C3×Dic3—24no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—24no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3C2×D411yescharacteristic
313C2×C3×Dic3C2×D411yescharacteristic
314C3×D12—22no—
315C3×D12—21no—
316C3×D12—21no—
317C3×D12—21no—
318C3×D12C2×D412yes—
319C3×C4×D3—24no—
320C3×C4×D3—21no—
321C3×C4×D3—21no—
322C3×C4×D3C2×D412yes—
323C3×C4×D3C2×D412yes—
324C3×Dic6—21no—
325C3×Dic6—22no—
326C3×Dic6C2×D412yes—
327#625—42no—
328#625—81no—
329D3×Dic3—42no—
330D3×Dic3—81no—
331C3⋊(C3⋊C8)—21no—
332C3⋊(C3⋊C8)—21no—
333C3×C3⋊C8—21no—
334C3×C3⋊C8—21no—
335C2×H(5,𝔽2)—31no—
336C2×AGL(1,ℤ/8)—91no—
337C2×#135—91no—
338#537—91no—
339#452—91no—
340#452—91no—
341#450—91no—
342#450—91no—
343#449—91no—
344#449—91no—
345#447—31no—
346#447—91no—
347#417—91no—
348C2×#102—91no—
349#408—91no—
350C24×C3—21no—
351C24×C3—21no—
352C24×C3—41no—
353C24×C3—61no—
354C24×C3—61no—
355C23×D3—21no—
356C23×D3—21no—
357C3×#41—34no—
358C3×#41—62no—
359C3×#41—62no—
360C3×#41—62no—
361C3×#41—62no—
362C3×#41—62no—
363C3×#41—62no—
364C3×#41—68no—
365C3×#41—62no—
366C2×C3×Q8—31no—
367C2×C3×Q8—31no—
368C2×C3×D4—22no—
369C2×C3×D4—22no—
370C2×C3×D4—22no—
371C2×C3×D4—22no—
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—21no—
375C2×C3×D4—21no—
376C2×C3×D4—34no—
377C2×C3×D4—31no—
378C2×C3×D4—31no—
379C2×C3×D4—31no—
380C2×C3×D4—31no—
381C2×C3×D4—31no—
382C2×C3×D4—41no—
383C2×C3×D4—42no—
384C2×C3×D4—42no—
385C2×C3×D4—62no—
386C2×C3×D4—61no—
387C2×C3×D4—61no—
388C2×C3×D4—62no—
389C2×C3×D4—68no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—68no—
393C2×C3×D4—68no—
394C2×C3×D4—61no—
395C2×C3×D4—62no—
396C2×C3×D4—61no—
397C2×C3×D4C22×D311yescharacteristic
398C2×C3×D4C22×D311yescharacteristic
399C2×C3×D4C22×D311yescharacteristic
400C2×C3×D4C22×D311yescharacteristic
401C22×C3×C4—21no—
402C22×C3×C4—31no—
403C22×C3×C4—31no—
404C22×C3×C4—61no—
405C22×C3×C4—61no—
406C22×C3×C4—61no—
407C22×C3×C4C22×D311yescharacteristic
408C22×C3×C4C22×D311yescharacteristic
409C2×#67—28no—
410C2×#67—28no—
411C2×#67—21no—
412C2×#67—21no—
413C2×#67—21no—
414C2×#67—21no—
415C2×#67—21no—
416C2×#67—21no—
417C2×#67—61no—
418C2×#67—61no—
419C2×#67—61no—
420C2×#67—61no—
421C2×#67#6711yescharacteristic
422C2×#67#6711yescharacteristic
423C22×Dic3—21no—
424C22×Dic3—21no—
425C22×Dic3—61no—
426C22×Dic3—61no—
427#237—28no—
428#237—22no—
429#237—22no—
430#237—22no—
431#237—62no—
432#237—62no—
433#237#6714yescomplemented
434D3×D4—28no—
435D3×D4—22no—
436D3×D4—22no—
437D3×D4—22no—
438D3×D4#6714yescomplemented
439#235—22no—
440#235—22no—
441#235—22no—
442#235—22no—
443#235—62no—
444#235—62no—
445C2×D12#6711yescharacteristic
446C2×D12C22×D311yescharacteristic
447C2×D12C22×D311yescharacteristic
448C2×C4×D3—21no—
449C2×C4×D3—61no—
450C2×C4×D3—61no—
451C2×C4×D3C22×D311yescharacteristic
452C2×C4×D3C22×D311yescharacteristic
453C2×Dic6—31no—
454C2×Dic6—31no—
455C2×Dic6—61no—
456C2×Dic6#6711yescharacteristic
457C2×Dic6C22×D311yescharacteristic
458C3×D8—62no—
459C3×D8—62no—
460C2×C3×C8—31no—
461C2×C3×C8—31no—
462C3×C4⋊C4—31no—
463C3×C22⋊C4—61no—
464#217—61no—
465#217—61no—
466#217—61no—
467#217—61no—
468#217—121no—
469#216—62no—
470#215—62no—
471#214—62no—
472#214—62no—
473#214—62no—
474#214—62no—
475#214—62no—
476#214—62no—
477#214—122no—
478#214—122no—
479#213—22no—
480#213—22no—
481#213—62no—
482#213—62no—
483(C2×D3)⋊C4—21no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486C4⋊Dic3—31no—
487C4⋊Dic3—31no—
488C4⋊Dic3—61no—
489C4⋊Dic3—61no—
490C4⋊Dic3—61no—
491C4⋊Dic3C22×D311yescharacteristic
492Dic3⋊C4—61no—
493Dic3⋊C4—61no—
494Dic3⋊C4—61no—
495Dic3⋊C4—61no—
496Dic3⋊C4—121no—
497#208—62no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—31no—
500C2×C3⋊C8—31no—
501C2×C3⋊C8—31no—
502C2×C3⋊C8—61no—
503C2×C3⋊C8—61no—
504C2×C3⋊C8—62no—
505C2×C3⋊C8C22×D311yescharacteristic
506C2×C3⋊C8C22×D311yescharacteristic
507Dic12—62no—
508#204—62no—
509ΓL(1,𝔽25)—62no—
510D3×C8—62no—
511C22×C32—21no—
512C22×C32—22no—
513C22×C32—22no—
514C22×C32—21no—
515C22×C32—21no—
516C22×C32—41no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32—41no—
520C22×C32—84no—
521C22×C32C22×D411yescharacteristic
522C2×C3×D3—21no—
523C2×C3×D3—21no—
524C2×C3×D3—21no—
525C2×C3×D3—22no—
526C2×C3×D3—21no—
527C2×C3×D3—21no—
528C2×C3×D3—41no—
529C2×C3×D3—41no—
530C2×C3×D3—41no—
531C2×C3×D3—41no—
532C2×C3×D3—41no—
533C2×C3×D3—84no—
534C2×C3×D3—84no—
535C2×C3×D3#12012yes—
536C32×C4—21no—
537C32×C4C22×D411yescharacteristic
538C32×C4C22×D411yescharacteristic
539C3⋊Dic3—41no—
540C3⋊Dic3—41no—
541C3×Dic3—21no—
542C3×Dic3—22no—
543C3×Dic3—41no—
544C3×Dic3#12012yes—
545H(5,𝔽2)—64no—
546H(5,𝔽2)—64no—
547C2×#41—31no—
548C2×#41—31no—
549C2×#41—31no—
550C2×#41—31no—
551C2×#41—61no—
552C2×#41—91no—
553C22×D4—31no—
554C22×D4—31no—
555C22×D4—61no—
556C22×D4—61no—
557C22×D4—61no—
558C22×D4D3211yescharacteristic
559AGL(1,ℤ/8)—184no—
560#135—184no—
561C2×Q16—91no—
562C2×SD16—91no—
563C2×SD16—91no—
564C2×SD16—91no—
565C2×SD16—91no—
566C2×D8—31no—
567C2×D8—31no—
568C2×D8—91no—
569C2×M16—91no—
570C22×C8—91no—
571C22⋊Q8—91no—
572C22⋊Q8—91no—
573C22⋊Q8—181no—
574#121—31no—
575#121—91no—
576#121—181no—
577#121—181no—
578#121—181no—
579C2×C4⋊C4—91no—
580#103—91no—
581#103—91no—
582#102—31no—
583#102—31no—
584#102—91no—
585#102—91no—
586#102—91no—
587#102—91no—
588C22⋊C8—31no—
589C22⋊C8—91no—
590C22⋊C8—91no—
591C22⋊C8—91no—
592C23×C3—24no—
593C23×C3—24no—
594C23×C3—21no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—31no—
600C23×C3—31no—
601C23×C3—41no—
602C23×C3—41no—
603C23×C3—44no—
604C23×C3—64no—
605C23×C3—64no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—81no—
609C23×C3—81no—
610C23×C3—81no—
611C23×C3—81no—
612C23×C3—82no—
613C23×C3—82no—
614C23×C3—241no—
615C23×C3—241no—
616C23×C3—241no—
617C23×C3—241no—
618C23×C3D3×D411yescharacteristic
619C23×C3C2×#6711yescharacteristic
620C22×D3—21no—
621C22×D3—24no—
622C22×D3—24no—
623C22×D3—21no—
624C22×D3—81no—
625C22×D3—81no—
626C22×D3—81no—
627C22×D3—81no—
628C22×D3C2×#6711yescharacteristic
629C22×D3C2×#6711yescharacteristic
630C3×Q8—32no—
631C3×Q8—62no—
632C3×Q8—61no—
633C3×D4—24no—
634C3×D4—24no—
635C3×D4—21no—
636C3×D4—21no—
637C3×D4—21no—
638C3×D4—21no—
639C3×D4—22no—
640C3×D4—22no—
641C3×D4—32no—
642C3×D4—41no—
643C3×D4—41no—
644C3×D4—44no—
645C3×D4—62no—
646C3×D4—62no—
647C3×D4—64no—
648C3×D4—62no—
649C3×D4—64no—
650C3×D4—64no—
651C3×D4—64no—
652C3×D4—64no—
653C3×D4—61no—
654C3×D4—61no—
655C3×D4—61no—
656C3×D4—241no—
657C3×D4D3×D412yes—
658C3×D4D3×D412yes—
659C3×D4C2×#6712yes—
660C3×D4C2×#6712yes—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—31no—
668C2×C3×C4—32no—
669C2×C3×C4—32no—
670C2×C3×C4—31no—
671C2×C3×C4—41no—
672C2×C3×C4—41no—
673C2×C3×C4—64no—
674C2×C3×C4—64no—
675C2×C3×C4—64no—
676C2×C3×C4—61no—
677C2×C3×C4—61no—
678C2×C3×C4—61no—
679C2×C3×C4—61no—
680C2×C3×C4D3×D411yescharacteristic
681C2×C3×C4C2×#6711yescharacteristic
682C2×C3×C4C23×D311yescharacteristic
683C2×C3×C4C23×D311yescharacteristic
684#67—24no—
685#67—24no—
686#67—24no—
687#67—22no—
688#67—24no—
689#67—22no—
690#67—24no—
691#67—81no—
692#67—122no—
693#67—122no—
694#67—241no—
695#67—241no—
696C2×Dic3—24no—
697C2×Dic3—21no—
698C2×Dic3—24no—
699C2×Dic3—21no—
700C2×Dic3—61no—
701C2×Dic3—61no—
702C2×Dic3—61no—
703C2×Dic3—61no—
704C2×Dic3—121no—
705C2×Dic3—121no—
706C2×Dic3—122no—
707C2×Dic3—241no—
708C2×Dic3C2×#6711yescharacteristic
709C2×Dic3C2×#6711yescharacteristic
710D12—22no—
711D12—21no—
712D12—21no—
713D12—21no—
714D12C2×#6712yes—
715C4×D3—24no—
716C4×D3—21no—
717C4×D3—21no—
718C4×D3—122no—
719C4×D3—241no—
720C4×D3C2×#6712yes—
721C4×D3C2×#6712yes—
722Dic6—21no—
723Dic6—22no—
724Dic6—61no—
725Dic6—61no—
726Dic6—61no—
727Dic6—61no—
728Dic6—121no—
729Dic6—121no—
730Dic6C2×#6712yes—
731C3×C8—61no—
732C3×C8—61no—
733C3⋊C8—21no—
734C3⋊C8—21no—
735C3⋊C8—61no—
736C3⋊C8—61no—
737C3⋊C8—61no—
738C3⋊C8—61no—
739C3⋊C8—121no—
740C3⋊C8—121no—
741C2×C32—41no—
742C2×C32—42no—
743C2×C32—42no—
744C2×C32C2×#12011yescharacteristic
745C2×C32#57611yescharacteristic
746C2×C32#57711yescharacteristic
747C3×D3—22no—
748C3×D3—41no—
749C3×D3—42no—
750C3×D3—81no—
751C24—21no—
752C24—61no—
753C24—61no—
754#41—34no—
755#41—62no—
756#41—62no—
757#41—62no—
758#41—62no—
759#41—62no—
760#41—62no—
761#41—68no—
762#41—62no—
763#41—182no—
764#41—182no—
765C2×Q8—31no—
766C2×Q8—31no—
767C2×Q8—91no—
768C2×D4—22no—
769C2×D4—22no—
770C2×D4—21no—
771C2×D4—34no—
772C2×D4—31no—
773C2×D4—31no—
774C2×D4—31no—
775C2×D4—31no—
776C2×D4—31no—
777C2×D4—62no—
778C2×D4—61no—
779C2×D4—61no—
780C2×D4—62no—
781C2×D4—68no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—68no—
785C2×D4—68no—
786C2×D4—61no—
787C2×D4—62no—
788C2×D4—61no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4C2×D3211yescharacteristic
792C2×D4C2×D3211yescharacteristic
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—181no—
799C22×C4—181no—
800C22×C4C2×D3211yescharacteristic
801Q16—182no—
802SD16—182no—
803SD16—182no—
804SD16—182no—
805SD16—182no—
806D8—62no—
807D8—62no—
808D8—182no—
809M16—182no—
810C2×C8—31no—
811C2×C8—31no—
812C2×C8—91no—
813C2×C8—91no—
814C2×C8—182no—
815C4⋊C4—31no—
816C4⋊C4—91no—
817C4⋊C4—181no—
818C4⋊C4—181no—
819C4⋊C4—181no—
820C22⋊C4—61no—
821C22⋊C4—181no—
822C22⋊C4—181no—
823C22⋊C4—181no—
824C22×C3—22no—
825C22×C3—21no—
826C22×C3—21no—
827C22×C3—21no—
828C22×C3—21no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—21no—
832C22×C3—21no—
833C22×C3—22no—
834C22×C3—22no—
835C22×C3—21no—
836C22×C3—32no—
837C22×C3—41no—
838C22×C3—41no—
839C22×C3—42no—
840C22×C3—42no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—61no—
850C22×C3—61no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—62no—
854C22×C3—61no—
855C22×C3—81no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—84no—
860C22×C3—84no—
861C22×C3—88no—
862C22×C3—121no—
863C22×C3—121no—
864C22×C3—121no—
865C22×C3—121no—
866C22×C3—121no—
867C22×C3—244no—
868C22×C3—244no—
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C22×#6711yescharacteristic
871C2×D3—21no—
872C2×D3—21no—
873C2×D3—21no—
874C2×D3—21no—
875C2×D3—21no—
876C2×D3—22no—
877C2×D3—41no—
878C2×D3—41no—
879C2×D3—41no—
880C2×D3—41no—
881C2×D3—41no—
882C2×D3—84no—
883C2×D3—84no—
884C2×D3#95312yes—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—32no—
890C3×C4—41no—
891C3×C4—61no—
892C3×C4—62no—
893C3×C4—121no—
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896C3×C4C22×#6711yescharacteristic
897C3×C4C22×#6711yescharacteristic
898Dic3—21no—
899Dic3—22no—
900Dic3—41no—
901Dic3—121no—
902Dic3—121no—
903Dic3—121no—
904Dic3—121no—
905Dic3—241no—
906Dic3—241no—
907Dic3#95312yes—
908C32#301211yescharacteristic, complemented, Sylow
909C23—24no—
910C23—21no—
911C23—21no—
912C23—31no—
913C23—31no—
914C23—64no—
915C23—64no—
916C23—61no—
917C23—61no—
918C23—81no—
919C23—81no—
920C23—241no—
921C23—241no—
922C23—241no—
923C23—241no—
924C23D3×#6711yescharacteristic
925Q8—32no—
926Q8—62no—
927Q8—61no—
928Q8—181no—
929Q8—181no—
930D4—24no—
931D4—21no—
932D4—21no—
933D4—32no—
934D4—62no—
935D4—62no—
936D4—64no—
937D4—62no—
938D4—64no—
939D4—64no—
940D4—64no—
941D4—64no—
942D4—61no—
943D4—61no—
944D4—61no—
945D4—241no—
946D4—362no—
947D4—721no—
948D4D3×#6712yes—
949D4D3×#6712yes—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—31no—
953C2×C4—32no—
954C2×C4—32no—
955C2×C4—31no—
956C2×C4—64no—
957C2×C4—64no—
958C2×C4—64no—
959C2×C4—61no—
960C2×C4—61no—
961C2×C4—61no—
962C2×C4—61no—
963C2×C4—181no—
964C2×C4—181no—
965C2×C4—362no—
966C2×C4—721no—
967C2×C4D3×#6711yescharacteristic
968C2×C4C22×D3211yescharacteristic
969C8—61no—
970C8—61no—
971C8—181no—
972C8—181no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—42no—
977C2×C3—41no—
978C2×C3—42no—
979C2×C3—42no—
980C2×C3—42no—
981C2×C3—42no—
982C2×C3—41no—
983C2×C3—62no—
984C2×C3—82no—
985C2×C3—82no—
986C2×C3—121no—
987C2×C3—122no—
988C2×C3—241no—
989C2×C3D3×#12011yescharacteristic
990C2×C3#575711yescharacteristic
991C2×C3#577511yescharacteristic
992C2×C3#583511yescharacteristic
993C2×C3#583611yescharacteristic
994C2×C3C2×#95311yescharacteristic
995D3—22no—
996D3—41no—
997D3—42no—
998D3—81no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—22no—
1003C22—22no—
1004C22—32no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—61no—
1010C22—61no—
1011C22—61no—
1012C22—61no—
1013C22—62no—
1014C22—61no—
1015C22—84no—
1016C22—121no—
1017C22—121no—
1018C22—121no—
1019C22—121no—
1020C22—121no—
1021C22—244no—
1022C22—244no—
1023C22C2×D3×#6711yescharacteristic
1024C4—21no—
1025C4—32no—
1026C4—61no—
1027C4—62no—
1028C4—121no—
1029C4—361no—
1030C4—361no—
1031C4C2×D3×#6711yescharacteristic
1032C4C2×D3×#6711yescharacteristic
1033C3—21no—
1034C3#8000511yescharacteristic, complemented
1035C3#8410211yescharacteristic, complemented
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—62no—
1040C2—121no—
1041C2—122no—
1042C2—241no—
1043C2#1059509611yescharacteristic
1044C2#1059510611yescharacteristic
1045C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3012
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C2×#63933C2semidirect
3. C2×#63932C2semidirect
4. #10595004C2semidirect
5. #10592917C2semidirect
6. C3×#5217C2semidirect
7. #10591463C2semidirect
8. #10591459C2semidirect
9. #10591450C2semidirect
10. #10591447C2semidirect
11. #10591414C2semidirect
12. D3×#832C2semidirect
13. #10591173C2semidirect
14. #10591161C2semidirect
15. #10591145C2semidirect
31. C2×#3795C22semidirect
32. C2×#3754C22semidirect
33. C2×#3754C22semidirect
34. #64133C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×#213C22semidirect
37. C3×#930C22semidirect
42. #63908C22semidirect
43. D3×C4⋊Dic3C22semidirect
46. #63857C22semidirect
47. C2×#3719C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3713C22semidirect
51. C2×#3711C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63659C22semidirect
54. #63659C22semidirect
55. #63657C22semidirect
56. C3×#832C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. #63566C22semidirect
60. #63565C22semidirect
61. #63563C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#1004D3semidirect
85. #5217D3semidirect
122. C3×#237D4semidirect
127. C3×D3×D4D4semidirect
223. C2×#213C2×D3semidirect
224. C2×#213C2×D3semidirect
226. #930C2×D3semidirect
257. #832C2×D3semidirect
258. #832C2×D3semidirect
264. #830C2×D3semidirect
433. #237#67semidirect
438. D3×D4#67semidirect
908. C32#3012semidirect
1034. C3#80005semidirect
1035. C3#84102semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C2×#639332
C2×#639322
#105950042
#105929172
C3×#52172
#105914632
#105914592
#105914502
#105914472
#105914142
D3×#8322
#105911732
#105911612
#105911452
#841023
#800053