Finite Group Databasebeta

← #11864435

Subgroups — #11864435

Order 1152.

1545 conjugacy classes of subgroups.

The subgroup lattice has 1013 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3C2×#63925C211yesmaximal, characteristic, complemented
4#10595064C211yesmaximal, characteristic, complemented
5#10592937C211yesmaximal, characteristic, complemented
6C3×#5238C211yesmaximal, characteristic, complemented
7#10591584C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10591557C211yesmaximal, characteristic, complemented
10#10591452C211yesmaximal, characteristic, complemented
11#10591450C211yesmaximal, characteristic, complemented
12#10591420C211yesmaximal, characteristic, complemented
13#10591174C211yesmaximal, characteristic, complemented
14#10591171C211yesmaximal, characteristic, complemented
15#10591145C211yesmaximal, characteristic, complemented
16#84113—31nomaximal
17#80086—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C3×#1010—24no—
20C3×#1010—24no—
21C2×C3×D3×Q8C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23C2×C3×#237—21no—
24C2×C3×#237—21no—
25C2×C3×#237C2211yescharacteristic
26C2×C3×#237C2211yescharacteristic, complemented
27C2×C3×#235—21no—
28C2×C3×#235C2211yescharacteristic
29C22×C3×Dic6—21no—
30C22×C3×Dic6C2211yescharacteristic, complemented
31C2×D3×D12C2211yescharacteristic
32C2×#3755C2211yescharacteristic
33C2×#3753C2211yescharacteristic
34#64139C2211yescharacteristic
35C2×C3×#215C2211yescharacteristic
36C2×C3×#213C2211yescharacteristic
37C3×#930C2211yescharacteristic
38#63983—21no—
39#63979—21no—
40D3×#215—24no—
41#63925—24no—
42#63922—21no—
43#63909C2211yescharacteristic
44#63908C2211yescharacteristic
45#63907—21no—
46#63841C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3715C2211yescharacteristic
50C2×#3715C2211yescharacteristic
51C2×#3711C2211yescharacteristic
52C2×D3×C3⋊C8C2211yescharacteristic
53#63662C2211yescharacteristic, complemented
54#63659C2211yescharacteristic, complemented
55#63657C2211yescharacteristic, complemented
56C3×#835C2211yescharacteristic, complemented
57C3×#832C2211yescharacteristic, complemented
58C3×#830C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63565C2211yescharacteristic, complemented
63(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×C3×2−1+4—31no—
66C2×#1010D311yescharacteristic, complemented
67#5830—31no—
68C2×#949—31no—
69C22×#215—31no—
70C2×D3×SD16—31no—
71C2×#911—31no—
72#5607—31no—
73C3×#449—31no—
74#5238—31no—
75#5238—31no—
76#5238—31no—
77#5238—31no—
78#5238—61no—
79#5238D311yescharacteristic, complemented
80#5234—31no—
81#5233—31no—
82#5227—31no—
83#5227—31no—
84#5227—31no—
85#5227—31no—
86#5225—31no—
87#5170—31no—
88#5158—31no—
89#5040—31no—
90#4806—31no—
91#4802—31no—
92#4781—31no—
93#4772—31no—
94#4738—31no—
95#4727—31no—
96C22×D32—21no—
97C32×#41—22no—
98C32×#41—22no—
99C2×C32×Q8C2311yescharacteristic
100C2×C32×D4—21no—
101C2×C32×D4C2311yescharacteristic
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×#67—21no—
109C2×C3×#67D411yescharacteristic
110C2×C3×#67D411yescharacteristic
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C22×C3×Dic3—21no—
114C3×D3×Q8—22no—
115C3×D3×Q8—22no—
116C3×D3×Q8—22no—
117C3×D3×Q8D414yescomplemented
118C3×#237—28no—
119C3×#237—28no—
120C3×#237—22no—
121C3×#237—22no—
122C3×#237—22no—
123C3×#237D414yescomplemented
124C3×#235—28no—
125C3×#235—22no—
126C3×#235—22no—
127C2×C3×D12D411yescharacteristic
128C2×C3×D12C2311yescharacteristic
129C2×C3×C4×D3—21no—
130C2×C3×C4×D3—21no—
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×Dic6—28no—
134C2×C3×Dic6—21no—
135C2×C3×Dic6—21no—
136C2×C3×Dic6—21no—
137C2×C3×Dic6—22no—
138C2×C3×Dic6—22no—
139C2×C3×Dic6D411yescharacteristic
140C2×C3×Dic6C2311yescharacteristic
141C2×C3×Dic6C2311yescharacteristic
142C2×#626—21no—
143C2×#626—21no—
144C2×#625—21no—
145D3×D12—22no—
146D3×D12—22no—
147#3755—22no—
148#3753—22no—
149#3752—21no—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C2×C3⋊(C3⋊C8)C2311yescharacteristic
152C2×C3⋊(C3⋊C8)C2311yescharacteristic
153C3×#215—22no—
154C3×#213—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#3717—22no—
165#3715—22no—
166#3715—22no—
167#3711—22no—
168D3×C3⋊C8—22no—
169#3010—91noSylow
170C3×2−1+4—64no—
171C3×2−1+4—64no—
172C2×C3×#41—21no—
173C2×C3×#41—31no—
174C2×C3×#41—31no—
175C2×C3×#41—31no—
176C2×C3×#41—61no—
177C2×C3×#41—61no—
178C2×C3×#41—61no—
179C2×C3×#41C2×D311yescharacteristic, complemented
180C2×C3×#41C2×D311yescharacteristic, complemented
181C22×C3×Q8—31no—
182C22×C3×Q8—31no—
183C22×C3×Q8—31no—
184C22×C3×Q8—61no—
185#1010—24no—
186#1010—24no—
187C2×D3×Q8C2×D311yescharacteristic
188C2×D3×Q8C2×D311yescharacteristic, complemented
189C2×#237—21no—
190C2×#237—21no—
191C2×#237C2×D311yescharacteristic
192C2×#237C2×D311yescharacteristic, complemented
193C2×D3×D4—31no—
194C2×#235—21no—
195C2×#235C2×D311yescharacteristic
196C22×D12—31no—
197C22×Dic6—21no—
198C22×Dic6C2×D311yescharacteristic, complemented
199C2×C3×SD16—31no—
200C2×C3×D8—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—64no—
212C2×#215C2×D311yescharacteristic
213#940—61no—
214#940—61no—
215#938—31no—
216#937—61no—
217#937—61no—
218#937—61no—
219C2×#214—31no—
220C2×#214—31no—
221C2×#213—31no—
222C2×#213—31no—
223C2×#213—61no—
224C2×#213C2×D311yescharacteristic
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—
234D3×SD16—64no—
235#911—64no—
236C2×#204—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×#102—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#835C2×D311yescharacteristic, complemented
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(C2×D3)⋊C8—31no—
266(C2×D3)⋊C8—31no—
267#816—31no—
268#816—31no—
269#810—31no—
270#810—31no—
271C23×C32—21no—
272C23×C32C2×D411yescharacteristic
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—21no—
281C32×Q8C2×D412yes—
282C32×D4—24no—
283C32×D4—21no—
284C32×D4C2×D412yes—
285C2×C32×C4—24no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4C2×D411yescharacteristic
290C2×C32×C4C2411yescharacteristic
291#638—81no—
292C2×C3⋊Dic3—21no—
293C4⋊(C3⋊D3)—21no—
294C4⋊(C3⋊D3)—21no—
295C3×#67—24no—
296C3×#67—22no—
297C3×#67—24no—
298C3×#67—22no—
299C3×#67—81no—
300C2×C3×Dic3—24no—
301C2×C3×Dic3—24no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—24no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3C2×D411yescharacteristic
307C2×C3×Dic3C2×D411yescharacteristic
308C3×D12—22no—
309C3×D12—21no—
310C3×D12—21no—
311C3×C4×D3—24no—
312C3×C4×D3—24no—
313C3×C4×D3—21no—
314C3×C4×D3—21no—
315C3×C4×D3C2×D412yes—
316C3×C4×D3C2×D412yes—
317C3×Dic6—24no—
318C3×Dic6—24no—
319C3×Dic6—21no—
320C3×Dic6—21no—
321C3×Dic6—22no—
322C3×Dic6—24no—
323C3×Dic6C2×D412yes—
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—31no—
337#449—91no—
338#449—91no—
339#449—91no—
340#448—91no—
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—22no—
350C3×#41—22no—
351C3×#41—22no—
352C3×#41—22no—
353C3×#41—34no—
354C3×#41—42no—
355C3×#41—42no—
356C3×#41—62no—
357C3×#41—62no—
358C3×#41—68no—
359C3×#41—62no—
360C3×#41—62no—
361C3×#41—68no—
362C3×#41—68no—
363C3×#41—62no—
364C2×C3×Q8—21no—
365C2×C3×Q8—31no—
366C2×C3×Q8—34no—
367C2×C3×Q8—31no—
368C2×C3×Q8—31no—
369C2×C3×Q8—61no—
370C2×C3×Q8—61no—
371C2×C3×Q8—62no—
372C2×C3×Q8—62no—
373C2×C3×Q8—68no—
374C2×C3×Q8—62no—
375C2×C3×Q8—62no—
376C2×C3×Q8—62no—
377C2×C3×Q8—61no—
378C2×C3×Q8C22×D311yescharacteristic
379C2×C3×Q8C22×D311yescharacteristic
380C2×C3×D4—21no—
381C2×C3×D4—21no—
382C2×C3×D4—21no—
383C2×C3×D4—31no—
384C2×C3×D4—31no—
385C2×C3×D4—31no—
386C2×C3×D4—31no—
387C2×C3×D4—41no—
388C2×C3×D4—61no—
389C2×C3×D4—61no—
390C2×C3×D4—61no—
391C2×C3×D4C22×D311yescharacteristic
392C2×C3×D4C22×D311yescharacteristic
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—21no—
409C2×#67—61no—
410C2×#67—61no—
411C2×#67—61no—
412C2×#67—61no—
413C2×#67—61no—
414C2×#67—61no—
415C2×#67—121no—
416C2×#67#6711yescharacteristic
417C2×#67#6711yescharacteristic
418C22×Dic3—21no—
419C22×Dic3—21no—
420C22×Dic3—21no—
421D3×Q8—22no—
422D3×Q8—22no—
423D3×Q8—22no—
424D3×Q8#6714yescomplemented
425#237—28no—
426#237—28no—
427#237—22no—
428#237—22no—
429#237—22no—
430#237#6714yescomplemented
431D3×D4—62no—
432D3×D4—62no—
433#235—28no—
434#235—22no—
435#235—22no—
436C2×D12—31no—
437C2×D12—31no—
438C2×D12—61no—
439C2×D12—62no—
440C2×D12—62no—
441C2×D12—61no—
442C2×D12—61no—
443C2×D12#6711yescharacteristic
444C2×D12C22×D311yescharacteristic
445C2×C4×D3—21no—
446C2×C4×D3—21no—
447C2×C4×D3C22×D311yescharacteristic
448C2×C4×D3C22×D311yescharacteristic
449C2×Dic6—28no—
450C2×Dic6—21no—
451C2×Dic6—21no—
452C2×Dic6—21no—
453C2×Dic6—22no—
454C2×Dic6—22no—
455C2×Dic6#6711yescharacteristic
456C2×Dic6C22×D311yescharacteristic
457C2×Dic6C22×D311yescharacteristic
458C3×SD16—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#215—22no—
467#215—62no—
468#215—62no—
469#215—62no—
470#215—62no—
471#215—62no—
472#215—62no—
473#215—122no—
474#214—62no—
475#214—62no—
476#213—22no—
477#213—62no—
478#213—62no—
479#213—122no—
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
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—41no—
516C2×C3⋊D3—41no—
517C2×C3⋊D3—41no—
518C2×C3×D3—21no—
519C2×C3×D3—21no—
520C2×C3×D3—21no—
521C2×C3×D3—21no—
522C2×C3×D3—21no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3#12012yes—
527D32—84no—
528C32×C4—21no—
529C32×C4—22no—
530C32×C4C22×D411yescharacteristic
531C32×C4C22×D411yescharacteristic
532C3⋊Dic3—41no—
533C3×Dic3—21no—
534C3×Dic3—22no—
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—61no—
544C2×#41—61no—
545C2×#41—61no—
546C2×#41D3211yescharacteristic, complemented
547C22×Q8—31no—
548C22×Q8—31no—
549C22×Q8—31no—
550C22×Q8—61no—
551C22×D4—91no—
552AGL(1,ℤ/8)—184no—
553C2×SD16—31no—
554C2×SD16—91no—
555C2×SD16—91no—
556C2×SD16—91no—
557C2×SD16—91no—
558C2×SD16—91no—
559C2×SD16—184no—
560C2×D8—31no—
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—91no—
575#103—91no—
576#103—91no—
577#103—91no—
578#103—91no—
579#102—31no—
580#102—91no—
581C22⋊C8—31no—
582C22⋊C8—91no—
583C22⋊C8—91no—
584C22⋊C8—91no—
585C23×C3—21no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—31no—
589C23×C3—31no—
590C23×C3—41no—
591C23×C3—61no—
592C23×C3D3×D411yescharacteristic
593C23×C3C2×#6711yescharacteristic
594C22×D3—21no—
595C22×D3—61no—
596C22×D3—61no—
597C22×D3—121no—
598C22×D3—122no—
599C22×D3—122no—
600C22×D3—241no—
601C22×D3—241no—
602C22×D3—241no—
603C22×D3—241no—
604C22×D3C2×#6711yescharacteristic
605C22×D3C2×#6711yescharacteristic
606C3×Q8—21no—
607C3×Q8—21no—
608C3×Q8—22no—
609C3×Q8—32no—
610C3×Q8—32no—
611C3×Q8—41no—
612C3×Q8—62no—
613C3×Q8—64no—
614C3×Q8—64no—
615C3×Q8—64no—
616C3×Q8—61no—
617C3×Q8—61no—
618C3×Q8D3×D412yes—
619C3×Q8C2×#6712yes—
620C3×D4—24no—
621C3×D4—24no—
622C3×D4—21no—
623C3×D4—21no—
624C3×D4—22no—
625C3×D4—41no—
626C3×D4—44no—
627C3×D4—62no—
628C3×D4—62no—
629C3×D4—62no—
630C3×D4—64no—
631C3×D4—64no—
632C3×D4—61no—
633C3×D4—61no—
634C3×D4—241no—
635C3×D4D3×D412yes—
636C3×D4C2×#6712yes—
637C2×C3×C4—24no—
638C2×C3×C4—24no—
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—31no—
648C2×C3×C4—32no—
649C2×C3×C4—32no—
650C2×C3×C4—31no—
651C2×C3×C4—41no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—44no—
655C2×C3×C4—64no—
656C2×C3×C4—64no—
657C2×C3×C4—64no—
658C2×C3×C4—64no—
659C2×C3×C4—64no—
660C2×C3×C4—61no—
661C2×C3×C4—61no—
662C2×C3×C4—61no—
663C2×C3×C4—61no—
664C2×C3×C4—61no—
665C2×C3×C4D3×D411yescharacteristic
666C2×C3×C4C2×#6711yescharacteristic
667C2×C3×C4C23×D311yescharacteristic
668C2×C3×C4C23×D311yescharacteristic
669#67—24no—
670#67—22no—
671#67—24no—
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—24no—
682C2×Dic3—24no—
683C2×Dic3—21no—
684C2×Dic3—21no—
685C2×Dic3—24no—
686C2×Dic3—21no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—121no—
690C2×Dic3C2×#6711yescharacteristic
691C2×Dic3C2×#6711yescharacteristic
692D12—22no—
693D12—21no—
694D12—21no—
695D12—61no—
696D12—61no—
697D12—61no—
698D12—61no—
699D12—121no—
700D12—121no—
701D12—122no—
702D12—241no—
703C4×D3—24no—
704C4×D3—24no—
705C4×D3—21no—
706C4×D3—21no—
707C4×D3C2×#6712yes—
708C4×D3C2×#6712yes—
709Dic6—24no—
710Dic6—24no—
711Dic6—21no—
712Dic6—21no—
713Dic6—22no—
714Dic6—24no—
715Dic6C2×#6712yes—
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×C32—42no—
729C2×C32C2×#12011yescharacteristic
730C2×C32#57711yescharacteristic
731C2×C32#57711yescharacteristic
732C3⋊D3—81no—
733C3×D3—22no—
734C3×D3—41no—
735C3×D3—81no—
736C24—181no—
737#41—22no—
738#41—22no—
739#41—34no—
740#41—62no—
741#41—62no—
742#41—68no—
743#41—62no—
744#41—62no—
745#41—68no—
746#41—68no—
747#41—62no—
748C2×Q8—31no—
749C2×Q8—34no—
750C2×Q8—31no—
751C2×Q8—31no—
752C2×Q8—61no—
753C2×Q8—61no—
754C2×Q8—62no—
755C2×Q8—62no—
756C2×Q8—68no—
757C2×Q8—62no—
758C2×Q8—62no—
759C2×Q8—62no—
760C2×Q8—61no—
761C2×Q8C2×D3211yescharacteristic
762C2×D4—21no—
763C2×D4—31no—
764C2×D4—31no—
765C2×D4—31no—
766C2×D4—31no—
767C2×D4—61no—
768C2×D4—61no—
769C2×D4—61no—
770C2×D4—91no—
771C2×D4—182no—
772C2×D4—182no—
773C2×D4—181no—
774C2×D4—181no—
775C2×D4—181no—
776C2×D4—181no—
777C2×D4C2×D3211yescharacteristic
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—182no—
789SD16—182no—
790SD16—182no—
791SD16—182no—
792SD16—182no—
793D8—62no—
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—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—21no—
814C22×C3—22no—
815C22×C3—21no—
816C22×C3—22no—
817C22×C3—21no—
818C22×C3—32no—
819C22×C3—41no—
820C22×C3—42no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—61no—
828C22×C3—61no—
829C22×C3—61no—
830C22×C3—61no—
831C22×C3—61no—
832C22×C3—81no—
833C22×C3—81no—
834C22×C3—121no—
835C22×C3—121no—
836C22×C3—121no—
837C22×C3C2×D3×D411yescharacteristic
838C22×C3C22×#6711yescharacteristic
839C2×D3—21no—
840C2×D3—21no—
841C2×D3—21no—
842C2×D3—21no—
843C2×D3—21no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—241no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3—244no—
857C2×D3—244no—
858C2×D3#95312yes—
859C3×C4—21no—
860C3×C4—22no—
861C3×C4—21no—
862C3×C4—22no—
863C3×C4—21no—
864C3×C4—21no—
865C3×C4—32no—
866C3×C4—41no—
867C3×C4—42no—
868C3×C4—61no—
869C3×C4—62no—
870C3×C4—62no—
871C3×C4—121no—
872C3×C4C2×D3×D411yescharacteristic
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C22×#6711yescharacteristic
875C3×C4C22×#6711yescharacteristic
876Dic3—21no—
877Dic3—22no—
878Dic3—22no—
879Dic3—41no—
880Dic3—121no—
881Dic3—121no—
882Dic3—241no—
883Dic3#95312yes—
884C32#301011yescharacteristic, complemented, Sylow
885C23—21no—
886C23—31no—
887C23—31no—
888C23—61no—
889C23—181no—
890C23—362no—
891C23—721no—
892C23—721no—
893C23D3×#6711yescharacteristic
894Q8—21no—
895Q8—32no—
896Q8—32no—
897Q8—62no—
898Q8—64no—
899Q8—64no—
900Q8—64no—
901Q8—61no—
902Q8—61no—
903Q8D3×#6712yes—
904D4—24no—
905D4—21no—
906D4—62no—
907D4—62no—
908D4—62no—
909D4—64no—
910D4—64no—
911D4—61no—
912D4—61no—
913D4—181no—
914D4—181no—
915D4—241no—
916D4—362no—
917D4—721no—
918D4—721no—
919D4—721no—
920D4D3×#6712yes—
921C2×C4—24no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—31no—
926C2×C4—32no—
927C2×C4—32no—
928C2×C4—31no—
929C2×C4—64no—
930C2×C4—64no—
931C2×C4—64no—
932C2×C4—64no—
933C2×C4—64no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—181no—
940C2×C4D3×#6711yescharacteristic
941C2×C4C22×D3211yescharacteristic
942C8—61no—
943C8—61no—
944C8—181no—
945C8—181no—
946C2×C3—21no—
947C2×C3—21no—
948C2×C3—21no—
949C2×C3—41no—
950C2×C3—42no—
951C2×C3—41no—
952C2×C3—42no—
953C2×C3—62no—
954C2×C3—81no—
955C2×C3—82no—
956C2×C3—121no—
957C2×C3—241no—
958C2×C3D3×#12011yescharacteristic
959C2×C3#577011yescharacteristic
960C2×C3#577511yescharacteristic
961C2×C3#583711yescharacteristic
962C2×C3#583711yescharacteristic
963C2×C3C2×#95311yescharacteristic
964D3—22no—
965D3—41no—
966D3—81no—
967D3—241no—
968D3—241no—
969D3—481no—
970C22—21no—
971C22—21no—
972C22—21no—
973C22—22no—
974C22—32no—
975C22—41no—
976C22—41no—
977C22—61no—
978C22—61no—
979C22—61no—
980C22—61no—
981C22—61no—
982C22—121no—
983C22—121no—
984C22—121no—
985C22—361no—
986C22—361no—
987C22—361no—
988C22—724no—
989C22C2×D3×#6711yescharacteristic
990C4—21no—
991C4—22no—
992C4—32no—
993C4—61no—
994C4—62no—
995C4—62no—
996C4—121no—
997C4—361no—
998C4C2×D3×#6711yescharacteristic
999C4C2×D3×#6711yescharacteristic
1000C3—21no—
1001C3#8008611yescharacteristic, complemented
1002C3#8411311yescharacteristic, complemented
1003C2—41no—
1004C2—42no—
1005C2—62no—
1006C2—121no—
1007C2—241no—
1008C2—721no—
1009C2#1059545511yescharacteristic
1010C2#1059545711yescharacteristic
1011C2D3×#95311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3010
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
1. C2×C3×#1010C2semidirect
2. C2×D3×#215C2semidirect
3. C2×#63925C2semidirect
4. #10595064C2semidirect
5. #10592937C2semidirect
6. C3×#5238C2semidirect
7. #10591584C2semidirect
8. #10591583C2semidirect
9. #10591557C2semidirect
10. #10591452C2semidirect
11. #10591450C2semidirect
12. #10591420C2semidirect
13. #10591174C2semidirect
14. #10591171C2semidirect
15. #10591145C2semidirect
18. C2×C32×#41C22semidirect
22. C2×C3×D3×Q8C22semidirect
26. C2×C3×#237C22semidirect
30. C22×C3×Dic6C22semidirect
53. #63662C22semidirect
54. #63659C22semidirect
55. #63657C22semidirect
56. C3×#835C22semidirect
57. C3×#832C22semidirect
58. C3×#830C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
61. #63565C22semidirect
62. #63565C22semidirect
63. (C2×D3)⋊(C3⋊C8)C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
66. C2×#1010D3semidirect
79. #5238D3semidirect
117. C3×D3×Q8D4semidirect
123. C3×#237D4semidirect
179. C2×C3×#41C2×D3semidirect
180. C2×C3×#41C2×D3semidirect
188. C2×D3×Q8C2×D3semidirect
192. C2×#237C2×D3semidirect
198. C22×Dic6C2×D3semidirect
254. #835C2×D3semidirect
258. #832C2×D3semidirect
264. #830C2×D3semidirect
424. D3×Q8#67semidirect
430. #237#67semidirect
546. C2×#41D32semidirect
884. C32#3010semidirect
1001. C3#80086semidirect
1002. C3#84113semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
C2×D3×#2152
C2×#639252
#105950642
#105929372
C3×#52382
#105915842
#105915832
#105915572
#105914522
#105914502
#105914202
#105911742
#105911712
#105911452
#841133
#800863