Finite Group Databasebeta

← #11864430

Subgroups — #11864430

Order 1152.

1543 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10595064C211yesmaximal, characteristic, complemented
5#10592926C211yesmaximal, characteristic, complemented
6C3×#5227C211yesmaximal, characteristic, complemented
7#10591588C211yesmaximal, characteristic, complemented
8#10591586C211yesmaximal, characteristic, complemented
9#10591584C211yesmaximal, characteristic, complemented
10#10591583C211yesmaximal, characteristic, complemented
11#10591557C211yesmaximal, characteristic, complemented
12#10591556C211yesmaximal, characteristic, complemented
13#10591163C211yesmaximal, characteristic, complemented
14#10591161C211yesmaximal, characteristic, complemented
15#10591145C211yesmaximal, characteristic, complemented
16#84113—31nomaximal
17#80041—31nomaximal
18C22×C32×Q8C2211yescharacteristic, complemented
19C3×#1007—24no—
20C3×#1007—24no—
21C2×C3×#239—21no—
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2211yescharacteristic, complemented
24C2×C3×D3×Q8—21no—
25C2×C3×D3×Q8C2211yescharacteristic
26C2×C3×D3×Q8C2211yescharacteristic, complemented
27C2×C3×#235—21no—
28C2×C3×#235—21no—
29C2×C3×#235C2211yescharacteristic
30C2×C3×#235C2211yescharacteristic, complemented
31C2×D3×D12C2211yescharacteristic
32C2×#3755C2211yescharacteristic
33C2×#3755C2211yescharacteristic
34#64139C2211yescharacteristic
35C2×C3×#215C2211yescharacteristic
36C2×C3×#215C2211yescharacteristic
37C3×#930C2211yescharacteristic
38#63983—21no—
39#63979—21no—
40#63939—24no—
41D3×#215—24no—
42#63922—21no—
43#63909C2211yescharacteristic
44#63908C2211yescharacteristic
45#63907—21no—
46#63841C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3715C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3713C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52C2×D3×C3⋊C8C2211yescharacteristic
53#63662C2211yescharacteristic, complemented
54#63662C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#835C2211yescharacteristic, 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×C3×2−1+4—31no—
66C2×#1007D311yescharacteristic, complemented
67#5830—31no—
68C2×#949—31no—
69C22×#215—31no—
70C2×#914—31no—
71C2×D3×SD16—31no—
72#5607—31no—
73C3×#448—31no—
74#5238—31no—
75#5238—31no—
76#5238—31no—
77#5238—31no—
78#5234—31no—
79#5233—31no—
80#5227—31no—
81#5227—31no—
82#5227—31no—
83#5227—31no—
84#5227—61no—
85#5227D311yescharacteristic, complemented
86#5225—31no—
87#5172—31no—
88#5170—31no—
89#5037—31no—
90#4810—31no—
91#4806—31no—
92#4804—31no—
93#4802—31no—
94#4734—31no—
95#4727—31no—
96C22×D32—21no—
97C2×C32×Q8—22no—
98C2×C32×Q8—22no—
99C2×C32×Q8—21no—
100C2×C32×Q8C2311yescharacteristic
101C2×C32×Q8C2311yescharacteristic
102C22×C32×C4—21no—
103C22×C32×C4C2311yescharacteristic
104C2×#638—21no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C3×#67—21no—
107C2×C3×#67—21no—
108C2×C3×#67D411yescharacteristic
109C2×C3×#67D411yescharacteristic
110C3×#239—28no—
111C3×#239—22no—
112C3×#239—22no—
113C3×#239—22no—
114C3×#239D414yescomplemented
115C3×D3×Q8—28no—
116C3×D3×Q8—22no—
117C3×D3×Q8—22no—
118C3×D3×Q8—22no—
119C3×D3×Q8D414yescomplemented
120C3×#235—28no—
121C3×#235—28no—
122C3×#235—22no—
123C3×#235—22no—
124C3×#235—22no—
125C3×#235—22no—
126C2×C3×D12—21no—
127C2×C3×D12—21no—
128C2×C3×D12D411yescharacteristic
129C2×C3×D12C2311yescharacteristic
130C2×C3×D12C2311yescharacteristic
131C2×C3×C4×D3—21no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—21no—
134C2×C3×C4×D3—21no—
135C2×C3×C4×D3—21no—
136C2×C3×C4×D3C2311yescharacteristic
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6—21no—
139C2×C3×Dic6—21no—
140C2×C3×Dic6D411yescharacteristic
141C2×C3×Dic6C2311yescharacteristic
142C2×#626—21no—
143C2×#626—21no—
144C2×#625—21no—
145D3×D12—22no—
146D3×D12—22no—
147#3755—22no—
148#3755—22no—
149#3752—21no—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153C3×#215—22no—
154C3×#215—22no—
155C3×(C2×D3)⋊C4—21no—
156C3×C4⋊Dic3C2311yescharacteristic
157C2×C3×C3⋊C8C2311yescharacteristic
158C2×C3×C3⋊C8C2311yescharacteristic
159#3722—21no—
160(C2×D3)⋊Dic3—21no—
161(C2×D3)⋊Dic3—21no—
162Dic32—21no—
163#3717—22no—
164#3715—22no—
165#3714—22no—
166#3713—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3010—91noSylow
170C3×2−1+4—64no—
171C3×2−1+4—64no—
172C2×C3×#41—31no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C2×C3×#41—61no—
178C2×C3×#41—61no—
179C22×C3×Q8—21no—
180C22×C3×Q8—31no—
181C22×C3×Q8—31no—
182C22×C3×Q8—61no—
183C22×C3×Q8C2×D311yescharacteristic, complemented
184C22×C3×Q8C2×D311yescharacteristic, complemented
185#1007—24no—
186#1007—24no—
187C2×#239—21no—
188C2×#239C2×D311yescharacteristic
189C2×#239C2×D311yescharacteristic, complemented
190C2×D3×Q8—21no—
191C2×D3×Q8C2×D311yescharacteristic
192C2×D3×Q8C2×D311yescharacteristic, complemented
193C2×D3×D4—31no—
194C2×#235—21no—
195C2×#235—21no—
196C2×#235C2×D311yescharacteristic
197C2×#235C2×D311yescharacteristic, complemented
198C22×D12—31no—
199C2×C3×SD16—31no—
200C2×C3×SD16—31no—
201C3×#121—31no—
202#949—64no—
203#947—61no—
204C2×#215—31no—
205C2×#215—31no—
206C2×#215—31no—
207C2×#215—31no—
208C2×#215—31no—
209C2×#215—31no—
210C2×#215—61no—
211C2×#215—61no—
212C2×#215—64no—
213C2×#215C2×D311yescharacteristic
214C2×#215C2×D311yescharacteristic
215#940—61no—
216#940—61no—
217#938—31no—
218#937—61no—
219#937—61no—
220#937—61no—
221C2×#214—31no—
222C2×#213—31no—
223C2×#213—31no—
224C2×#213—31no—
225#930—31no—
226#930—31no—
227#930—31no—
228#930—31no—
229#930—61no—
230#930C2×D311yescharacteristic
231#926—31no—
232C2×#208—31no—
233C22×C3⋊C8—31no—
234#914—64no—
235D3×SD16—64no—
236C2×D24—31no—
237C2×#204—31no—
238C2×ΓL(1,𝔽25)—31no—
239C2×D3×C8—31no—
240#895—31no—
241#892—31no—
242#885—61no—
243#882—61no—
244C3×#103—31no—
245C3×#103—31no—
246C3×C22⋊C8—31no—
247#835—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#835—31no—
252#835—31no—
253#835—61no—
254#835—61no—
255#835C2×D311yescharacteristic, complemented
256#835C2×D311yescharacteristic, complemented
257#832—31no—
258#832—31no—
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×C32C2×D411yescharacteristic
272C22×C3⋊D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3C2×D411yescharacteristic
276C22×C3×D3C2×D411yescharacteristic
277C2×D32—42no—
278C2×D32—81no—
279C2×D32—81no—
280C32×Q8—24no—
281C32×Q8—21no—
282C32×Q8—21no—
283C32×Q8C2×D412yes—
284C32×Q8C2×D412yes—
285C2×C32×C4—24no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4C2×D411yescharacteristic
291C2×C32×C4C2411yescharacteristic
292#638—81no—
293C2×C3⋊Dic3—21no—
294C4⋊(C3⋊D3)—21no—
295C4⋊(C3⋊D3)—21no—
296C3×#67—24no—
297C3×#67—22no—
298C3×#67—22no—
299C3×#67—81no—
300C2×C3×Dic3—21no—
301C2×C3×Dic3—21no—
302C2×C3×Dic3C2×D411yescharacteristic
303C2×C3×Dic3C2×D411yescharacteristic
304C3×D12—24no—
305C3×D12—24no—
306C3×D12—22no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12C2×D412yes—
311C3×C4×D3—24no—
312C3×C4×D3—24no—
313C3×C4×D3—24no—
314C3×C4×D3—24no—
315C3×C4×D3—21no—
316C3×C4×D3—21no—
317C3×C4×D3—24no—
318C3×C4×D3C2×D412yes—
319C3×C4×D3C2×D412yes—
320C3×Dic6—24no—
321C3×Dic6—21no—
322C3×Dic6—24no—
323C3×Dic6—22no—
324C3×Dic6C2×D412yes—
325#626—42no—
326#626—81no—
327#625—81no—
328C3⋊(C3⋊C8)—21no—
329C3⋊(C3⋊C8)—21no—
330C3×C3⋊C8—21no—
331C3×C3⋊C8—21no—
332C2×2−1+4—31no—
333C2×AGL(1,ℤ/8)—91no—
334C22×SD16—91no—
335#535—91no—
336#449—91no—
337#449—91no—
338#449—91no—
339#449—91no—
340#448—31no—
341#448—91no—
342#448—91no—
343#448—91no—
344#419—91no—
345#416—91no—
346#408—91no—
347C23×D3—61no—
348C23×D3—61no—
349C3×#41—34no—
350C3×#41—62no—
351C3×#41—62no—
352C3×#41—62no—
353C3×#41—62no—
354C3×#41—68no—
355C3×#41—68no—
356C3×#41—62no—
357C3×#41—62no—
358C3×#41—68no—
359C3×#41—62no—
360C2×C3×Q8—22no—
361C2×C3×Q8—22no—
362C2×C3×Q8—22no—
363C2×C3×Q8—22no—
364C2×C3×Q8—21no—
365C2×C3×Q8—21no—
366C2×C3×Q8—21no—
367C2×C3×Q8—21no—
368C2×C3×Q8—31no—
369C2×C3×Q8—34no—
370C2×C3×Q8—31no—
371C2×C3×Q8—41no—
372C2×C3×Q8—42no—
373C2×C3×Q8—42no—
374C2×C3×Q8—61no—
375C2×C3×Q8—61no—
376C2×C3×Q8—62no—
377C2×C3×Q8—62no—
378C2×C3×Q8—68no—
379C2×C3×Q8—62no—
380C2×C3×Q8C22×D311yescharacteristic
381C2×C3×Q8C22×D311yescharacteristic
382C2×C3×Q8C22×D311yescharacteristic
383C2×C3×Q8C22×D311yescharacteristic
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—31no—
387C2×C3×D4—31no—
388C2×C3×D4—31no—
389C2×C3×D4—61no—
390C2×C3×D4—61no—
391C2×C3×D4—61no—
392C2×C3×D4—61no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—21no—
396C22×C3×C4—31no—
397C22×C3×C4—31no—
398C22×C3×C4—41no—
399C22×C3×C4—61no—
400C22×C3×C4—61no—
401C22×C3×C4—61no—
402C22×C3×C4—61no—
403C22×C3×C4—61no—
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C2×#67—21no—
407C2×#67—21no—
408C2×#67—61no—
409C2×#67—61no—
410C2×#67—61no—
411C2×#67—61no—
412C2×#67—61no—
413C2×#67—61no—
414C2×#67—121no—
415C2×#67#6711yescharacteristic
416C2×#67#6711yescharacteristic
417#239—28no—
418#239—22no—
419#239—22no—
420#239—22no—
421#239#6714yescomplemented
422D3×Q8—28no—
423D3×Q8—22no—
424D3×Q8—22no—
425D3×Q8—22no—
426D3×Q8#6714yescomplemented
427D3×D4—62no—
428D3×D4—62no—
429#235—28no—
430#235—28no—
431#235—22no—
432#235—22no—
433#235—22no—
434#235—22no—
435C2×D12—21no—
436C2×D12—21no—
437C2×D12—31no—
438C2×D12—31no—
439C2×D12—61no—
440C2×D12—62no—
441C2×D12—62no—
442C2×D12—61no—
443C2×D12—61no—
444C2×D12#6711yescharacteristic
445C2×D12C22×D311yescharacteristic
446C2×D12C22×D311yescharacteristic
447C2×C4×D3—21no—
448C2×C4×D3—21no—
449C2×C4×D3—21no—
450C2×C4×D3—21no—
451C2×C4×D3—21no—
452C2×C4×D3C22×D311yescharacteristic
453C2×C4×D3C22×D311yescharacteristic
454C2×Dic6—21no—
455C2×Dic6—21no—
456C2×Dic6#6711yescharacteristic
457C2×Dic6C22×D311yescharacteristic
458C3×SD16—62no—
459C3×SD16—62no—
460C2×C3×C8—31no—
461C2×C3×C8—31no—
462C3×C4⋊C4—31no—
463C3×C22⋊C4—61no—
464#217—61no—
465#217—61no—
466#215—22no—
467#215—22no—
468#215—62no—
469#215—62no—
470#215—62no—
471#215—62no—
472#215—62no—
473#215—62no—
474#215—122no—
475#215—122no—
476#214—62no—
477#213—62no—
478#213—62no—
479#213—62no—
480(C2×D3)⋊C4—21no—
481(C2×D3)⋊C4—61no—
482(C2×D3)⋊C4—61no—
483(C2×D3)⋊C4—61no—
484(C2×D3)⋊C4—61no—
485(C2×D3)⋊C4—61no—
486(C2×D3)⋊C4—61no—
487(C2×D3)⋊C4—121no—
488C4⋊Dic3—31no—
489C4⋊Dic3—31no—
490C4⋊Dic3—61no—
491C4⋊Dic3C22×D311yescharacteristic
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
504D24—62no—
505#204—62no—
506ΓL(1,𝔽25)—62no—
507D3×C8—62no—
508C22×C32—21no—
509C22×C32—21no—
510C22×C32—21no—
511C22×C32C22×D411yescharacteristic
512C2×C3⋊D3—41no—
513C2×C3⋊D3—41no—
514C2×C3⋊D3—41no—
515C2×C3×D3—21no—
516C2×C3×D3—21no—
517C2×C3×D3—21no—
518C2×C3×D3—22no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527D32—84no—
528C32×C4—22no—
529C32×C4—22no—
530C32×C4—21no—
531C32×C4C22×D411yescharacteristic
532C32×C4C22×D411yescharacteristic
533C3⋊Dic3—41no—
534C3×Dic3—21no—
535C3×Dic3—22no—
536C3×Dic3—41no—
537C3×Dic3#12012yes—
5382−1+4—64no—
5392−1+4—64no—
540C2×#41—31no—
541C2×#41—31no—
542C2×#41—31no—
543C2×#41—31no—
544C2×#41—61no—
545C2×#41—61no—
546C2×#41—61no—
547C22×Q8—31no—
548C22×Q8—31no—
549C22×Q8—61no—
550C22×Q8D3211yescharacteristic, complemented
551C22×D4—91no—
552AGL(1,ℤ/8)—184no—
553C2×SD16—31no—
554C2×SD16—31no—
555C2×SD16—91no—
556C2×SD16—91no—
557C2×SD16—91no—
558C2×SD16—91no—
559C2×SD16—184no—
560C2×D8—91no—
561C2×D8—91no—
562C2×M16—91no—
563C22×C8—91no—
564#127—181no—
565#124—181no—
566#121—31no—
567#121—91no—
568#121—91no—
569#121—91no—
570#120—181no—
571#120—181no—
572#117—91no—
573#103—31no—
574#103—31no—
575#103—91no—
576#103—91no—
577#103—91no—
578#103—91no—
579#102—91no—
580#102—91no—
581C22⋊C8—31no—
582C22⋊C8—91no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C23×C3—21no—
586C23×C3—31no—
587C23×C3—31no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3D3×D411yescharacteristic
591C23×C3C2×#6711yescharacteristic
592C22×D3—21no—
593C22×D3—21no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—121no—
597C22×D3—122no—
598C22×D3—122no—
599C22×D3—241no—
600C22×D3—241no—
601C22×D3—241no—
602C22×D3—241no—
603C22×D3C2×#6711yescharacteristic
604C22×D3C2×#6711yescharacteristic
605C3×Q8—24no—
606C3×Q8—24no—
607C3×Q8—21no—
608C3×Q8—21no—
609C3×Q8—21no—
610C3×Q8—21no—
611C3×Q8—22no—
612C3×Q8—22no—
613C3×Q8—32no—
614C3×Q8—41no—
615C3×Q8—41no—
616C3×Q8—44no—
617C3×Q8—64no—
618C3×Q8—62no—
619C3×Q8—64no—
620C3×Q8—61no—
621C3×Q8D3×D412yes—
622C3×Q8D3×D412yes—
623C3×Q8C2×#6712yes—
624C3×Q8C2×#6712yes—
625C3×D4—32no—
626C3×D4—62no—
627C3×D4—64no—
628C3×D4—64no—
629C3×D4—62no—
630C3×D4—62no—
631C3×D4—64no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—61no—
635C3×D4—241no—
636C2×C3×C4—24no—
637C2×C3×C4—24no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—21no—
642C2×C3×C4—21no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—31no—
649C2×C3×C4—32no—
650C2×C3×C4—32no—
651C2×C3×C4—31no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—41no—
655C2×C3×C4—41no—
656C2×C3×C4—44no—
657C2×C3×C4—64no—
658C2×C3×C4—64no—
659C2×C3×C4—64no—
660C2×C3×C4—64no—
661C2×C3×C4—64no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4—61no—
666C2×C3×C4D3×D411yescharacteristic
667C2×C3×C4C2×#6711yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669C2×C3×C4C23×D311yescharacteristic
670#67—24no—
671#67—22no—
672#67—22no—
673#67—81no—
674#67—122no—
675#67—241no—
676#67—241no—
677#67—241no—
678#67—241no—
679#67—241no—
680#67—242no—
681C2×Dic3—21no—
682C2×Dic3—21no—
683C2×Dic3—61no—
684C2×Dic3—61no—
685C2×Dic3—121no—
686C2×Dic3C2×#6711yescharacteristic
687C2×Dic3C2×#6711yescharacteristic
688D12—24no—
689D12—24no—
690D12—22no—
691D12—21no—
692D12—21no—
693D12—21no—
694D12—61no—
695D12—61no—
696D12—61no—
697D12—61no—
698D12—121no—
699D12—121no—
700D12—122no—
701D12—241no—
702D12C2×#6712yes—
703C4×D3—24no—
704C4×D3—24no—
705C4×D3—24no—
706C4×D3—24no—
707C4×D3—21no—
708C4×D3—21no—
709C4×D3—24no—
710C4×D3C2×#6712yes—
711C4×D3C2×#6712yes—
712Dic6—24no—
713Dic6—21no—
714Dic6—24no—
715Dic6—22no—
716Dic6C2×#6712yes—
717C3×C8—61no—
718C3×C8—61no—
719C3⋊C8—21no—
720C3⋊C8—21no—
721C3⋊C8—61no—
722C3⋊C8—61no—
723C3⋊C8—61no—
724C3⋊C8—61no—
725C3⋊C8—121no—
726C3⋊C8—121no—
727C2×C32—41no—
728C2×C32C2×#12011yescharacteristic
729C2×C32#57711yescharacteristic
730C2×C32#57711yescharacteristic
731C3⋊D3—81no—
732C3×D3—22no—
733C3×D3—41no—
734C3×D3—42no—
735C3×D3—81no—
736C24—181no—
737#41—34no—
738#41—62no—
739#41—62no—
740#41—62no—
741#41—62no—
742#41—68no—
743#41—68no—
744#41—62no—
745#41—62no—
746#41—68no—
747#41—62no—
748C2×Q8—22no—
749C2×Q8—22no—
750C2×Q8—21no—
751C2×Q8—31no—
752C2×Q8—34no—
753C2×Q8—31no—
754C2×Q8—61no—
755C2×Q8—61no—
756C2×Q8—62no—
757C2×Q8—62no—
758C2×Q8—68no—
759C2×Q8—62no—
760C2×Q8C2×D3211yescharacteristic
761C2×Q8C2×D3211yescharacteristic
762C2×D4—31no—
763C2×D4—31no—
764C2×D4—31no—
765C2×D4—31no—
766C2×D4—31no—
767C2×D4—61no—
768C2×D4—61no—
769C2×D4—61no—
770C2×D4—61no—
771C2×D4—91no—
772C2×D4—182no—
773C2×D4—182no—
774C2×D4—181no—
775C2×D4—181no—
776C2×D4—181no—
777C2×D4—181no—
778C22×C4—21no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4C2×D3211yescharacteristic
787SD16—62no—
788SD16—62no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792SD16—182no—
793D8—182no—
794D8—182no—
795M16—182no—
796C2×C8—31no—
797C2×C8—31no—
798C2×C8—91no—
799C2×C8—91no—
800C2×C8—182no—
801C4⋊C4—31no—
802C4⋊C4—91no—
803C22⋊C4—61no—
804C22⋊C4—181no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C42—181no—
809C22×C3—22no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—21no—
815C22×C3—21no—
816C22×C3—21no—
817C22×C3—32no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—61no—
821C22×C3—61no—
822C22×C3—61no—
823C22×C3—61no—
824C22×C3—62no—
825C22×C3—61no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3C2×D3×D411yescharacteristic
832C22×C3C22×#6711yescharacteristic
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—21no—
836C2×D3—21no—
837C2×D3—21no—
838C2×D3—22no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—41no—
842C2×D3—41no—
843C2×D3—41no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—241no—
851C2×D3—241no—
852C2×D3—241no—
853C2×D3—244no—
854C2×D3—244no—
855C2×D3#95312yes—
856C3×C4—22no—
857C3×C4—22no—
858C3×C4—21no—
859C3×C4—22no—
860C3×C4—22no—
861C3×C4—21no—
862C3×C4—21no—
863C3×C4—21no—
864C3×C4—32no—
865C3×C4—41no—
866C3×C4—42no—
867C3×C4—42no—
868C3×C4—61no—
869C3×C4—62no—
870C3×C4—121no—
871C3×C4C2×D3×D411yescharacteristic
872C3×C4C2×D3×D411yescharacteristic
873C3×C4C22×#6711yescharacteristic
874C3×C4C22×#6711yescharacteristic
875Dic3—21no—
876Dic3—22no—
877Dic3—41no—
878Dic3—121no—
879Dic3—121no—
880Dic3—241no—
881Dic3#95312yes—
882C32#301011yescharacteristic, complemented, Sylow
883C23—31no—
884C23—31no—
885C23—61no—
886C23—61no—
887C23—181no—
888C23—362no—
889C23—721no—
890C23—721no—
891C23D3×#6711yescharacteristic
892Q8—24no—
893Q8—21no—
894Q8—21no—
895Q8—32no—
896Q8—64no—
897Q8—62no—
898Q8—64no—
899Q8—61no—
900Q8D3×#6712yes—
901Q8D3×#6712yes—
902D4—32no—
903D4—62no—
904D4—64no—
905D4—64no—
906D4—62no—
907D4—62no—
908D4—64no—
909D4—61no—
910D4—61no—
911D4—61no—
912D4—181no—
913D4—181no—
914D4—241no—
915D4—362no—
916D4—721no—
917D4—721no—
918D4—721no—
919C2×C4—24no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—31no—
925C2×C4—32no—
926C2×C4—32no—
927C2×C4—31no—
928C2×C4—64no—
929C2×C4—64no—
930C2×C4—64no—
931C2×C4—64no—
932C2×C4—64no—
933C2×C4—61no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—181no—
938C2×C4D3×#6711yescharacteristic
939C2×C4C22×D3211yescharacteristic
940C8—61no—
941C8—61no—
942C8—181no—
943C8—181no—
944C2×C3—21no—
945C2×C3—21no—
946C2×C3—21no—
947C2×C3—42no—
948C2×C3—41no—
949C2×C3—41no—
950C2×C3—62no—
951C2×C3—121no—
952C2×C3—122no—
953C2×C3—241no—
954C2×C3D3×#12011yescharacteristic
955C2×C3#576211yescharacteristic
956C2×C3#577811yescharacteristic
957C2×C3#583711yescharacteristic
958C2×C3#583711yescharacteristic
959C2×C3C2×#95311yescharacteristic
960D3—22no—
961D3—41no—
962D3—42no—
963D3—81no—
964D3—241no—
965D3—241no—
966D3—481no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—32no—
971C22—61no—
972C22—61no—
973C22—62no—
974C22—61no—
975C22—61no—
976C22—61no—
977C22—121no—
978C22—121no—
979C22—121no—
980C22—121no—
981C22—121no—
982C22—361no—
983C22—361no—
984C22—361no—
985C22—724no—
986C22C2×D3×#6711yescharacteristic
987C4—22no—
988C4—22no—
989C4—21no—
990C4—32no—
991C4—61no—
992C4—62no—
993C4—121no—
994C4—361no—
995C4C2×D3×#6711yescharacteristic
996C4C2×D3×#6711yescharacteristic
997C3—21no—
998C3#8004111yescharacteristic, complemented
999C3#8411311yescharacteristic, complemented
1000C2—41no—
1001C2—62no—
1002C2—121no—
1003C2—122no—
1004C2—241no—
1005C2—721no—
1006C2#1059531811yescharacteristic
1007C2#1059531911yescharacteristic
1008C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32#3010
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×#63939C2semidirect
3. C2×D3×#215C2semidirect
4. #10595064C2semidirect
5. #10592926C2semidirect
6. C3×#5227C2semidirect
7. #10591588C2semidirect
8. #10591586C2semidirect
9. #10591584C2semidirect
10. #10591583C2semidirect
11. #10591557C2semidirect
12. #10591556C2semidirect
13. #10591163C2semidirect
14. #10591161C2semidirect
15. #10591145C2semidirect
18. C22×C32×Q8C22semidirect
23. C2×C3×#239C22semidirect
26. C2×C3×D3×Q8C22semidirect
30. C2×C3×#235C22semidirect
53. #63662C22semidirect
54. #63662C22semidirect
55. #63657C22semidirect
56. C3×#835C22semidirect
57. C3×#835C22semidirect
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×#1007D3semidirect
85. #5227D3semidirect
114. C3×#239D4semidirect
119. C3×D3×Q8D4semidirect
183. C22×C3×Q8C2×D3semidirect
184. C22×C3×Q8C2×D3semidirect
189. C2×#239C2×D3semidirect
192. C2×D3×Q8C2×D3semidirect
197. C2×#235C2×D3semidirect
255. #835C2×D3semidirect
256. #835C2×D3semidirect
264. #830C2×D3semidirect
421. #239#67semidirect
426. D3×Q8#67semidirect
550. C22×Q8D32semidirect
882. C32#3010semidirect
998. C3#80041semidirect
999. C3#84113semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×#639392
C2×D3×#2152
#105950642
#105929262
C3×#52272
#105915882
#105915862
#105915842
#105915832
#105915572
#105915562
#105911632
#105911612
#105911452
#841133
#800413