Finite Group Databasebeta

← #11864358

Subgroups — #11864358

Order 1152.

1580 conjugacy classes of subgroups.

The subgroup lattice has 1017 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2C2×#63943C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10594884C211yesmaximal, characteristic, complemented
5#10592938C211yesmaximal, characteristic, complemented
6C3×#5239C211yesmaximal, characteristic, complemented
7#10591599C211yesmaximal, characteristic, complemented
8#10591597C211yesmaximal, characteristic, complemented
9#10591556C211yesmaximal, characteristic, complemented
10#10591459C211yesmaximal, characteristic, complemented
11#10591458C211yesmaximal, characteristic, complemented
12#10591421C211yesmaximal, characteristic, complemented
13#10591172C211yesmaximal, characteristic, complemented
14#10591169C211yesmaximal, characteristic, complemented
15#10591145C211yesmaximal, characteristic, complemented
16#84105—31nomaximal
17#80229—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C3×#1009—24no—
20C3×#1009—24no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic
23C2×C3×D3×D4—21no—
24C2×C3×D3×D4—21no—
25C2×C3×D3×D4C2211yescharacteristic
26C2×C3×D3×D4C2211yescharacteristic
27C2×C3×#235—21no—
28C2×C3×#235C2211yescharacteristic
29C22×C3×D12—21no—
30C22×C3×D12C2211yescharacteristic
31C2×D3×Dic6C2211yescharacteristic, complemented
32C2×#3756C2211yescharacteristic, complemented
33C2×#3754C2211yescharacteristic, complemented
34#64133C2211yescharacteristic, complemented
35C2×C3×#216C2211yescharacteristic, complemented
36C2×C3×#214C2211yescharacteristic, complemented
37C3×#924C2211yescharacteristic, complemented
38#63969—21no—
39#63959—21no—
40#63943—24no—
41D3×#214—24no—
42#63884—21no—
43#63857C2211yescharacteristic, complemented
44#63856C2211yescharacteristic, complemented
45#63841C2211yescharacteristic, complemented
46#63839—21no—
47C2×#3716C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3711C2211yescharacteristic, complemented
52C2×D3×C3⋊C8C2211yescharacteristic, complemented
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63562C2211yescharacteristic, 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×#1009D311yescharacteristic
67#5825—31no—
68C2×#951—31no—
69C22×#214—31no—
70C2×#918—31no—
71C2×D3×SD16—31no—
72#5628—31no—
73C3×#452—31no—
74#5239—31no—
75#5239—31no—
76#5239—31no—
77#5239—31no—
78#5239—61no—
79#5239D311yescharacteristic, complemented
80#5234—31no—
81#5233—31no—
82#5218—31no—
83#5218—31no—
84#5218—31no—
85#5218—31no—
86#5215—31no—
87#5187—31no—
88#5169—31no—
89#5046—31no—
90#4808—31no—
91#4804—31no—
92#4776—31no—
93#4770—31no—
94#4731—31no—
95#4727—31no—
96C23×C3×D3—21no—
97C23×C3×D3—21no—
98C23×C3×D3—21no—
99C32×#41—22no—
100C32×#41—22no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4—21no—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4—21no—
105C22×C32×C4C2311yescharacteristic
106C2×#634C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67D411yescharacteristic
110C2×C3×#67D411yescharacteristic
111C3×#239—22no—
112C3×#239—22no—
113C3×#239—22no—
114C3×#239D414yes—
115C3×D3×D4—28no—
116C3×D3×D4—28no—
117C3×D3×D4—22no—
118C3×D3×D4—22no—
119C3×D3×D4—22no—
120C3×D3×D4D414yes—
121C3×#235—28no—
122C3×#235—22no—
123C3×#235—22no—
124C2×C3×D12—28no—
125C2×C3×D12—21no—
126C2×C3×D12—21no—
127C2×C3×D12—21no—
128C2×C3×D12—22no—
129C2×C3×D12—22no—
130C2×C3×D12D411yescharacteristic
131C2×C3×D12C2311yescharacteristic
132C2×C3×D12C2311yescharacteristic
133C2×C3×C4×D3—21no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×Dic6D411yescharacteristic
138C2×C3×Dic6C2311yescharacteristic
139C2×#627—21no—
140C2×D3×Dic3—21no—
141D3×Dic6—22no—
142D3×Dic6—22no—
143#3757—21no—
144#3756—22no—
145#3754—22no—
146C4⋊(C3⋊Dic3)C2311yescharacteristic
147#3750—21no—
148C2×C3⋊(C3⋊C8)C2311yescharacteristic
149C2×C3⋊(C3⋊C8)C2311yescharacteristic
150C3×#217—21no—
151C3×#216—22no—
152C3×#214—22no—
153C3×C4⋊Dic3C2311yescharacteristic
154C3×Dic3⋊C4—21no—
155C2×C3×C3⋊C8C2311yescharacteristic
156C2×C3×C3⋊C8C2311yescharacteristic
157#3724—21no—
158Dic3⋊Dic3—21no—
159(C2×D3)⋊Dic3—21no—
160(C2×D3)⋊Dic3—21no—
161(C2×D3)⋊Dic3—21no—
162Dic32—21no—
163#3716—22no—
164#3716—22no—
165#3715—22no—
166#3715—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3009—91noSylow
170C3×H(5,𝔽2)—64no—
171C3×H(5,𝔽2)—64no—
172C2×C3×#41—21no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C2×C3×#41C2×D311yescharacteristic
178C2×C3×#41C2×D311yescharacteristic
179C22×C3×D4—31no—
180C22×C3×D4—31no—
181C22×C3×D4—31no—
182C22×C3×D4—61no—
183C22×C3×D4—61no—
184C22×C3×D4—61no—
185#1009—24no—
186#1009—24no—
187C2×#239C2×D311yescharacteristic
188C2×#239C2×D311yescharacteristic
189C2×D3×Q8—31no—
190C2×D3×D4—21no—
191C2×D3×D4—21no—
192C2×D3×D4C2×D311yescharacteristic
193C2×D3×D4C2×D311yescharacteristic
194C2×#235—21no—
195C2×#235C2×D311yescharacteristic
196C22×D12—21no—
197C22×D12C2×D311yescharacteristic
198C22×Dic6—31no—
199C2×C3×Q16—31no—
200C2×C3×SD16—31no—
201C3×C22⋊Q8—31no—
202#951—64no—
203#946—31no—
204#944—61no—
205C2×#216—31no—
206C2×#216—31no—
207C2×#216—61no—
208C2×#216C2×D311yescharacteristic, complemented
209C2×#215—31no—
210C2×#215—31no—
211#936—61no—
212#935—61no—
213#935—61no—
214C2×#214—31no—
215C2×#214—31no—
216C2×#214—31no—
217C2×#214—31no—
218C2×#214—31no—
219C2×#214—31no—
220C2×#214—61no—
221C2×#214—64no—
222C2×#214C2×D311yescharacteristic, complemented
223#926—31no—
224#924—31no—
225#924—31no—
226#924—31no—
227#924—31no—
228#924—61no—
229#924C2×D311yescharacteristic, complemented
230C2×#208—31no—
231C22×C3⋊C8—31no—
232#918—64no—
233D3×SD16—64no—
234C2×#204—31no—
235C2×#204—31no—
236C2×ΓL(1,𝔽25)—31no—
237C2×D3×C8—31no—
238#897—31no—
239#894—61no—
240#892—31no—
241#888—61no—
242#885—61no—
243#883—61no—
244C3×#103—31no—
245C3×#102—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—61no—
250#835C2×D311yescharacteristic, complemented
251#832—31no—
252#832—31no—
253#832—31no—
254#832—31no—
255#832—31no—
256#832—31no—
257#832—61no—
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#821—31no—
267(C2×D3)⋊C8—31no—
268(C2×D3)⋊C8—31no—
269#809—31no—
270#809—31no—
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—24no—
276C22×C3×D3—24no—
277C22×C3×D3—24no—
278C22×C3×D3—81no—
279C22×C3×D3—81no—
280C22×C3×D3—81no—
281C22×C3×D3—81no—
282C22×C3×D3—81no—
283C22×C3×D3—81no—
284C22×C3×D3C2×D411yescharacteristic
285C22×C3×D3C2×D411yescharacteristic
286C32×Q8—21no—
287C32×Q8C2×D412yes—
288C32×D4—24no—
289C32×D4—21no—
290C32×D4C2×D412yes—
291C2×C32×C4—24no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4C2×D411yescharacteristic
296C2×C32×C4C2411yescharacteristic
297C2×C3⋊Dic3—21no—
298C2×C3⋊Dic3—21no—
299#634—21no—
300#634—21no—
301C3×#67—24no—
302C3×#67—22no—
303C3×#67—22no—
304C3×#67—24no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3C2×D411yescharacteristic
308C2×C3×Dic3C2×D411yescharacteristic
309C3×D12—24no—
310C3×D12—24no—
311C3×D12—22no—
312C3×D12—24no—
313C3×D12—21no—
314C3×D12—21no—
315C3×D12C2×D412yes—
316C3×D12C2×D412yes—
317C3×C4×D3—24no—
318C3×C4×D3—21no—
319C3×C4×D3—21no—
320C3×C4×D3—24no—
321C3×C4×D3C2×D412yes—
322C3×C4×D3C2×D412yes—
323C3×Dic6—22no—
324C3×Dic6—21no—
325C3×Dic6—21no—
326#627—42no—
327D3×Dic3—42no—
328C3⋊(C3⋊C8)—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C2×H(5,𝔽2)—31no—
333C2×#137—91no—
334C22×SD16—91no—
335#536—91no—
336#452—31no—
337#452—91no—
338#452—91no—
339#452—91no—
340#450—91no—
341#450—91no—
342#450—91no—
343#450—91no—
344#418—91no—
345#416—91no—
346#408—91no—
347C24×C3—61no—
348C24×C3—61no—
349C24×C3—61no—
350C23×D3—21no—
351C23×D3—21no—
352C23×D3—21no—
353C3×#41—22no—
354C3×#41—22no—
355C3×#41—22no—
356C3×#41—22no—
357C3×#41—34no—
358C3×#41—42no—
359C3×#41—42no—
360C3×#41—62no—
361C3×#41—62no—
362C3×#41—68no—
363C3×#41—62no—
364C3×#41—62no—
365C3×#41—62no—
366C2×C3×Q8—21no—
367C2×C3×Q8—31no—
368C2×C3×Q8—31no—
369C2×C3×Q8C22×D311yescharacteristic
370C2×C3×Q8C22×D311yescharacteristic
371C2×C3×D4—21no—
372C2×C3×D4—21no—
373C2×C3×D4—21no—
374C2×C3×D4—34no—
375C2×C3×D4—31no—
376C2×C3×D4—31no—
377C2×C3×D4—31no—
378C2×C3×D4—31no—
379C2×C3×D4—31no—
380C2×C3×D4—41no—
381C2×C3×D4—62no—
382C2×C3×D4—62no—
383C2×C3×D4—61no—
384C2×C3×D4—61no—
385C2×C3×D4—68no—
386C2×C3×D4—62no—
387C2×C3×D4—61no—
388C2×C3×D4—61no—
389C2×C3×D4—62no—
390C2×C3×D4—68no—
391C2×C3×D4—68no—
392C2×C3×D4—62no—
393C2×C3×D4—61no—
394C2×C3×D4C22×D311yescharacteristic
395C2×C3×D4C22×D311yescharacteristic
396C22×C3×C4—21no—
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4—31no—
400C22×C3×C4—31no—
401C22×C3×C4—41no—
402C22×C3×C4—61no—
403C22×C3×C4—61no—
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C2×#67—21no—
407C2×#67—21no—
408C2×#67#6711yescharacteristic
409C2×#67#6711yescharacteristic
410C22×Dic3—61no—
411#239—22no—
412#239—22no—
413#239—22no—
414#239#6714yes—
415D3×Q8—62no—
416D3×Q8—62no—
417D3×D4—28no—
418D3×D4—28no—
419D3×D4—22no—
420D3×D4—22no—
421D3×D4—22no—
422D3×D4#6714yes—
423#235—28no—
424#235—22no—
425#235—22no—
426C2×D12—28no—
427C2×D12—21no—
428C2×D12—21no—
429C2×D12—21no—
430C2×D12—22no—
431C2×D12—22no—
432C2×D12#6711yescharacteristic
433C2×D12C22×D311yescharacteristic
434C2×D12C22×D311yescharacteristic
435C2×C4×D3—21no—
436C2×C4×D3—21no—
437C2×C4×D3—61no—
438C2×C4×D3C22×D311yescharacteristic
439C2×C4×D3C22×D311yescharacteristic
440C2×Dic6—31no—
441C2×Dic6—31no—
442C2×Dic6—61no—
443C2×Dic6—62no—
444C2×Dic6—62no—
445C2×Dic6—61no—
446C2×Dic6—61no—
447C2×Dic6#6711yescharacteristic
448C2×Dic6C22×D311yescharacteristic
449C3×Q16—62no—
450C3×SD16—62no—
451C2×C3×C8—31no—
452C2×C3×C8—31no—
453C3×C4⋊C4—31no—
454C3×C4⋊C4—61no—
455C3×C22⋊C4—61no—
456#217—21no—
457#217—61no—
458#217—61no—
459#217—61no—
460#217—61no—
461#217—61no—
462#217—121no—
463#216—22no—
464#216—62no—
465#216—62no—
466#216—122no—
467#215—62no—
468#215—62no—
469#214—22no—
470#214—62no—
471#214—62no—
472#214—62no—
473#214—62no—
474#214—62no—
475#214—62no—
476#214—122no—
477(C2×D3)⋊C4—61no—
478(C2×D3)⋊C4—61no—
479(C2×D3)⋊C4—61no—
480C4⋊Dic3—31no—
481C4⋊Dic3—31no—
482C4⋊Dic3—61no—
483C4⋊Dic3—61no—
484C4⋊Dic3C22×D311yescharacteristic
485Dic3⋊C4—21no—
486Dic3⋊C4—61no—
487Dic3⋊C4—61no—
488Dic3⋊C4—61no—
489Dic3⋊C4—61no—
490Dic3⋊C4—61no—
491Dic3⋊C4—121no—
492C4×Dic3—61no—
493C4×Dic3—61no—
494#208—62no—
495C2×C3⋊C8—31no—
496C2×C3⋊C8—31no—
497C2×C3⋊C8—31no—
498C2×C3⋊C8—31no—
499C2×C3⋊C8—61no—
500C2×C3⋊C8—61no—
501C2×C3⋊C8—62no—
502C2×C3⋊C8C22×D311yescharacteristic
503C2×C3⋊C8C22×D311yescharacteristic
504#204—62no—
505#204—62no—
506ΓL(1,𝔽25)—62no—
507D3×C8—62no—
508C22×C32—21no—
509C22×C32—22no—
510C22×C32—21no—
511C22×C32—21no—
512C22×C32—41no—
513C22×C32—41no—
514C22×C32C22×D411yescharacteristic
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—84no—
527C2×C3×D3—84no—
528C2×C3×D3—84no—
529C2×C3×D3#12012yes—
530C32×C4—21no—
531C32×C4—22no—
532C32×C4C22×D411yescharacteristic
533C32×C4C22×D411yescharacteristic
534C3⋊Dic3—41no—
535C3⋊Dic3—41no—
536C3×Dic3—21no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C3×Dic3#12012yes—
540H(5,𝔽2)—64no—
541H(5,𝔽2)—64no—
542C2×#41—31no—
543C2×#41—31no—
544C2×#41—31no—
545C2×#41—61no—
546C2×#41D3211yescharacteristic
547C22×Q8—91no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4—31no—
551C22×D4—61no—
552C22×D4—61no—
553C22×D4—61no—
554#137—184no—
555C2×Q16—31no—
556C2×Q16—91no—
557C2×SD16—31no—
558C2×SD16—91no—
559C2×SD16—91no—
560C2×SD16—91no—
561C2×SD16—91no—
562C2×SD16—91no—
563C2×SD16—184no—
564C2×M16—91no—
565C22×C8—91no—
566C4⋊Q8—181no—
567#124—181no—
568#123—181no—
569#123—181no—
570C22⋊Q8—31no—
571C22⋊Q8—91no—
572C22⋊Q8—91no—
573C22⋊Q8—91no—
574#117—91no—
575#103—31no—
576#103—91no—
577#102—31no—
578#102—91no—
579#102—91no—
580#102—91no—
581#102—91no—
582#102—91no—
583C22⋊C8—31no—
584C22⋊C8—91no—
585C22⋊C8—91no—
586C22⋊C8—91no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—31no—
591C23×C3—31no—
592C23×C3—41no—
593C23×C3—64no—
594C23×C3—64no—
595C23×C3—64no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—241no—
599C23×C3—241no—
600C23×C3—241no—
601C23×C3—241no—
602C23×C3—241no—
603C23×C3—241no—
604C23×C3D3×D411yescharacteristic
605C23×C3C2×#6711yescharacteristic
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—24no—
609C22×D3—24no—
610C22×D3—24no—
611C22×D3—81no—
612C22×D3—81no—
613C22×D3—81no—
614C22×D3—81no—
615C22×D3—81no—
616C22×D3—81no—
617C22×D3C2×#6711yescharacteristic
618C22×D3C2×#6711yescharacteristic
619C3×Q8—21no—
620C3×Q8—21no—
621C3×Q8—22no—
622C3×Q8—41no—
623C3×Q8—62no—
624C3×Q8—61no—
625C3×Q8—61no—
626C3×Q8D3×D412yes—
627C3×Q8C2×#6712yes—
628C3×D4—24no—
629C3×D4—24no—
630C3×D4—21no—
631C3×D4—21no—
632C3×D4—22no—
633C3×D4—32no—
634C3×D4—32no—
635C3×D4—41no—
636C3×D4—44no—
637C3×D4—62no—
638C3×D4—64no—
639C3×D4—64no—
640C3×D4—64no—
641C3×D4—62no—
642C3×D4—64no—
643C3×D4—62no—
644C3×D4—64no—
645C3×D4—61no—
646C3×D4—61no—
647C3×D4D3×D412yes—
648C3×D4C2×#6712yes—
649C2×C3×C4—24no—
650C2×C3×C4—24no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—31no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—31no—
663C2×C3×C4—41no—
664C2×C3×C4—41no—
665C2×C3×C4—41no—
666C2×C3×C4—44no—
667C2×C3×C4—64no—
668C2×C3×C4—64no—
669C2×C3×C4—61no—
670C2×C3×C4—61no—
671C2×C3×C4—61no—
672C2×C3×C4—61no—
673C2×C3×C4D3×D411yescharacteristic
674C2×C3×C4C2×#6711yescharacteristic
675C2×C3×C4C23×D311yescharacteristic
676C2×C3×C4C23×D311yescharacteristic
677#67—24no—
678#67—22no—
679#67—22no—
680#67—24no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—61no—
686C2×Dic3—61no—
687C2×Dic3—121no—
688C2×Dic3—121no—
689C2×Dic3—122no—
690C2×Dic3C2×#6711yescharacteristic
691C2×Dic3C2×#6711yescharacteristic
692D12—24no—
693D12—24no—
694D12—22no—
695D12—24no—
696D12—21no—
697D12—21no—
698D12C2×#6712yes—
699D12C2×#6712yes—
700C4×D3—24no—
701C4×D3—21no—
702C4×D3—21no—
703C4×D3—24no—
704C4×D3—122no—
705C4×D3C2×#6712yes—
706C4×D3C2×#6712yes—
707Dic6—22no—
708Dic6—21no—
709Dic6—21no—
710Dic6—61no—
711Dic6—61no—
712Dic6—61no—
713Dic6—61no—
714Dic6—121no—
715Dic6—121no—
716Dic6—122no—
717Dic6—122no—
718C3×C8—61no—
719C3×C8—61no—
720C3⋊C8—21no—
721C3⋊C8—21no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8—61no—
726C3⋊C8—121no—
727C3⋊C8—121no—
728C2×C32—41no—
729C2×C32—42no—
730C2×C32C2×#12011yescharacteristic
731C2×C32#57711yescharacteristic
732C2×C32#57711yescharacteristic
733C3×D3—22no—
734C3×D3—41no—
735C3×D3—42no—
736C3×D3—42no—
737C24—61no—
738C24—61no—
739C24—61no—
740#41—22no—
741#41—22no—
742#41—34no—
743#41—62no—
744#41—62no—
745#41—68no—
746#41—62no—
747#41—62no—
748#41—62no—
749C2×Q8—31no—
750C2×Q8—31no—
751C2×Q8—91no—
752C2×Q8—181no—
753C2×Q8—182no—
754C2×Q8—182no—
755C2×Q8C2×D3211yescharacteristic
756C2×D4—21no—
757C2×D4—34no—
758C2×D4—31no—
759C2×D4—31no—
760C2×D4—31no—
761C2×D4—31no—
762C2×D4—31no—
763C2×D4—62no—
764C2×D4—62no—
765C2×D4—61no—
766C2×D4—61no—
767C2×D4—68no—
768C2×D4—62no—
769C2×D4—61no—
770C2×D4—61no—
771C2×D4—62no—
772C2×D4—68no—
773C2×D4—68no—
774C2×D4—62no—
775C2×D4—61no—
776C2×D4C2×D3211yescharacteristic
777C22×C4—21no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—181no—
783C22×C4C2×D3211yescharacteristic
784Q16—62no—
785Q16—182no—
786SD16—62no—
787SD16—182no—
788SD16—182no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792M16—182no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—91no—
796C2×C8—91no—
797C2×C8—182no—
798C4⋊C4—31no—
799C4⋊C4—61no—
800C4⋊C4—91no—
801C4⋊C4—181no—
802C4⋊C4—181no—
803C4⋊C4—181no—
804C22⋊C4—61no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C22⋊C4—181no—
809C42—181no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—22no—
816C22×C3—21no—
817C22×C3—22no—
818C22×C3—21no—
819C22×C3—32no—
820C22×C3—42no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—61no—
829C22×C3—61no—
830C22×C3—61no—
831C22×C3—61no—
832C22×C3—62no—
833C22×C3—62no—
834C22×C3—61no—
835C22×C3—81no—
836C22×C3—81no—
837C22×C3—121no—
838C22×C3—121no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—244no—
842C22×C3—244no—
843C22×C3—244no—
844C22×C3C2×D3×D411yescharacteristic
845C22×C3C22×#6711yescharacteristic
846C2×D3—21no—
847C2×D3—21no—
848C2×D3—21no—
849C2×D3—21no—
850C2×D3—21no—
851C2×D3—22no—
852C2×D3—22no—
853C2×D3—41no—
854C2×D3—41no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—84no—
858C2×D3—84no—
859C2×D3—84no—
860C2×D3#95312yes—
861C3×C4—21no—
862C3×C4—22no—
863C3×C4—21no—
864C3×C4—22no—
865C3×C4—21no—
866C3×C4—21no—
867C3×C4—32no—
868C3×C4—41no—
869C3×C4—42no—
870C3×C4—61no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875C3×C4C22×#6711yescharacteristic
876C3×C4C22×#6711yescharacteristic
877Dic3—21no—
878Dic3—41no—
879Dic3—41no—
880Dic3—121no—
881Dic3—121no—
882Dic3—121no—
883Dic3—121no—
884Dic3—241no—
885Dic3—241no—
886Dic3#95312yes—
887C32#300911yescharacteristic, complemented, Sylow
888C23—21no—
889C23—31no—
890C23—31no—
891C23—64no—
892C23—64no—
893C23—64no—
894C23—61no—
895C23—61no—
896C23—241no—
897C23—241no—
898C23—241no—
899C23—241no—
900C23—241no—
901C23—241no—
902C23D3×#6711yescharacteristic
903Q8—21no—
904Q8—62no—
905Q8—61no—
906Q8—61no—
907Q8—181no—
908Q8—181no—
909Q8—362no—
910Q8D3×#6712yes—
911D4—24no—
912D4—21no—
913D4—32no—
914D4—32no—
915D4—62no—
916D4—64no—
917D4—64no—
918D4—64no—
919D4—62no—
920D4—64no—
921D4—62no—
922D4—64no—
923D4—61no—
924D4—61no—
925D4D3×#6712yes—
926C2×C4—24no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—31no—
931C2×C4—32no—
932C2×C4—32no—
933C2×C4—31no—
934C2×C4—64no—
935C2×C4—64no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—181no—
941C2×C4—181no—
942C2×C4—362no—
943C2×C4D3×#6711yescharacteristic
944C2×C4C22×D3211yescharacteristic
945C8—61no—
946C8—61no—
947C8—181no—
948C8—181no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—21no—
952C2×C3—41no—
953C2×C3—42no—
954C2×C3—41no—
955C2×C3—42no—
956C2×C3—62no—
957C2×C3—81no—
958C2×C3—82no—
959C2×C3—121no—
960C2×C3—122no—
961C2×C3—122no—
962C2×C3D3×#12011yescharacteristic
963C2×C3#577011yescharacteristic
964C2×C3#577811yescharacteristic
965C2×C3#583611yescharacteristic
966C2×C3#583611yescharacteristic
967C2×C3C2×#95311yescharacteristic
968D3—22no—
969D3—41no—
970D3—42no—
971D3—42no—
972C22—21no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—32no—
977C22—41no—
978C22—41no—
979C22—61no—
980C22—61no—
981C22—61no—
982C22—61no—
983C22—62no—
984C22—62no—
985C22—61no—
986C22—121no—
987C22—121no—
988C22—121no—
989C22—121no—
990C22—244no—
991C22—244no—
992C22—244no—
993C22C2×D3×#6711yescharacteristic
994C4—21no—
995C4—22no—
996C4—32no—
997C4—61no—
998C4—121no—
999C4—121no—
1000C4—361no—
1001C4—361no—
1002C4C2×D3×#6711yescharacteristic
1003C4C2×D3×#6711yescharacteristic
1004C3—21no—
1005C3#8022911yescharacteristic, complemented
1006C3#8410511yescharacteristic, complemented
1007C2—41no—
1008C2—42no—
1009C2—62no—
1010C2—121no—
1011C2—122no—
1012C2—122no—
1013C2#1059546411yescharacteristic
1014C2#1059546611yescharacteristic
1015C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC2×C3×#1009C2
hypercenterC2×#41D32
hypocenterC32#3009
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63943C2semidirect
3. C2×D3×#214C2semidirect
4. #10594884C2semidirect
5. #10592938C2semidirect
6. C3×#5239C2semidirect
7. #10591599C2semidirect
8. #10591597C2semidirect
9. #10591556C2semidirect
10. #10591459C2semidirect
11. #10591458C2semidirect
12. #10591421C2semidirect
13. #10591172C2semidirect
14. #10591169C2semidirect
15. #10591145C2semidirect
31. C2×D3×Dic6C22semidirect
32. C2×#3756C22semidirect
33. C2×#3754C22semidirect
34. #64133C22semidirect
35. C2×C3×#216C22semidirect
36. C2×C3×#214C22semidirect
37. C3×#924C22semidirect
43. #63857C22semidirect
44. #63856C22semidirect
45. #63841C22semidirect
47. C2×#3716C22semidirect
48. C2×#3716C22semidirect
49. C2×#3715C22semidirect
50. C2×#3715C22semidirect
51. C2×#3711C22semidirect
52. C2×D3×C3⋊C8C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63657C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
79. #5239D3semidirect
208. C2×#216C2×D3semidirect
222. C2×#214C2×D3semidirect
229. #924C2×D3semidirect
250. #835C2×D3semidirect
258. #832C2×D3semidirect
264. #830C2×D3semidirect
887. C32#3009semidirect
1005. C3#80229semidirect
1006. C3#84105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
C2×#639432
C2×D3×#2142
#105948842
#105929382
C3×#52392
#105915992
#105915972
#105915562
#105914592
#105914582
#105914212
#105911722
#105911692
#105911452
#841053
#802293