Finite Group Databasebeta

← #11884004

Subgroups — #11884004

Order 1152.

1154 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2#10595069C211yesmaximal, characteristic, complemented
3#10594830C211yesmaximal, characteristic, complemented
4C2×#63796C211yesmaximal, characteristic, complemented
5#10592826C211yesmaximal, characteristic, complemented
6C3×#5134C211yesmaximal, characteristic, complemented
7#10591169C211yesmaximal, characteristic, complemented
8#10591161C211yesmaximal, characteristic, complemented
9#10590945C211yesmaximal, characteristic, complemented
10#10590887C211yesmaximal, characteristic, complemented
11#10590876C211yesmaximal, characteristic, complemented
12#10590844C211yesmaximal, characteristic, complemented
13#10590824C211yesmaximal, characteristic, complemented
14#10590779C211yesmaximal, characteristic, complemented
15#10590751C211yesmaximal, characteristic, complemented
16#83953—31nomaximal
17#80834—31nomaximal
18C2×C3×#235C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C2×D3×#67—21no—
21C2×#3802C2211yescharacteristic
22C2×#3797C2211yescharacteristic, complemented
23C2×C32×M16C2211yescharacteristic, complemented
24C4×#638C2211yescharacteristic
25C2×C8×C3⋊D3C2211yescharacteristic, complemented
26C3×#930C2211yescharacteristic
27C3×#924C2211yescharacteristic, complemented
28C3×#908—24no—
29C2×C3×D24C2211yescharacteristic
30C2×C3×D24C2211yescharacteristic, complemented
31C2×C3×#204C2211yescharacteristic
32C2×C3×#204C2211yescharacteristic, complemented
33C2×C3×#204C2211yescharacteristic, complemented
34#63976—21no—
35#63959—21no—
36#63958—21no—
37#63922—21no—
38#63916C2211yescharacteristic
39#63916C2211yescharacteristic, complemented
40#63914C2211yescharacteristic
41#63904—21no—
42#63898C2211yescharacteristic
43#63885—21no—
44#63863C2211yescharacteristic, complemented
45#63851—21no—
46#63843C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic
48C2×#3715C2211yescharacteristic, complemented
49C2×#3715C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51#63796—24no—
52#63657C2211yescharacteristic, complemented
53#63647C2211yescharacteristic, complemented
54#63642C2211yescharacteristic, complemented
55#63641C2211yescharacteristic, complemented
56C3×#821C2211yescharacteristic, complemented
57C3×#818C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63565C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#63562C2211yescharacteristic, complemented
62#63562C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5831—31no—
65D4×#67—31no—
66C2×D3×SD16—31no—
67C2×D3×SD16—31no—
68C2×#908D311yescharacteristic, complemented
69#5633—31no—
70#5609—31no—
71C3×#468—31no—
72#5238—31no—
73#5218—31no—
74#5176—31no—
75#5170—31no—
76#5164—31no—
77#5163—31no—
78#5157—31no—
79#5156—31no—
80#5154—31no—
81#5153—31no—
82#5134D311yescharacteristic, complemented
83#5127—31no—
84#5127—31no—
85#5127—61no—
86#5046—31no—
87#5037—31no—
88#4889—31no—
89#4883—31no—
90#4819—31no—
91#4806—31no—
92#4773—31no—
93#4762—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C2×#638D411yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×#235—22no—
102C3×#235—41no—
103C2×C3×D12—22no—
104C2×C3×D12—21no—
105C2×C3×D12—41no—
106C2×C3×D12C2311yescharacteristic
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113D3×#67—44no—
114C2×#627—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#625—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×#624—21no—
121C2×D3×Dic3—21no—
122#3802—22no—
123#3802—41no—
124#3797—22no—
125#3797—41no—
126C32×M16—22no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129#3757D411yescharacteristic
130#3752D411yescharacteristic
131#3750D411yescharacteristic
132C4×C3⋊Dic3C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C8×C3⋊D3—22no—
136C3×#217—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×D24—22no—
142C3×D24—22no—
143C3×#204—22no—
144C3×#204—22no—
145C3×#204D414yescomplemented
146Dic3⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151(C2×D3)⋊Dic3—21no—
152Dic32—21no—
153#3715—22no—
154#3715—22no—
155#3715—41no—
156#3713—41no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×D3×Q8—31no—
162C2×D3×Q8—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—61no—
166C2×#235C2×D311yescharacteristic, complemented
167C22×D12C2×D311yescharacteristic
168C3×AGL(1,ℤ/8)—64no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×SD16—31no—
172C2×C3×D8—31no—
173C2×C3×D8—31no—
174C2×C3×M16—21no—
175C2×C3×M16C2×D311yescharacteristic, complemented
176C2×C3×M16C2×D311yescharacteristic, complemented
177C3×C22⋊Q8—31no—
178C3×#121—31no—
179#953—61no—
180#947—31no—
181Q8×Dic3—31no—
182C2×#215—31no—
183C2×#215—31no—
184C2×#215—31no—
185#940—31no—
186#940—31no—
187#939—61no—
188#938—31no—
189#938—31no—
190#938—61no—
191#937—61no—
192#937—61no—
193#936—31no—
194#936—61no—
195D4×Dic3—31no—
196C2×#214—31no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#213—31no—
200C2×#213—31no—
201#930C2×D311yescharacteristic
202C4×#67—31no—
203C4×#67—31no—
204C4×#67—61no—
205C4×#67—61no—
206#924—61no—
207#924C2×D311yescharacteristic, complemented
208D3×SD16—64no—
209D3×SD16—64no—
210#908—24no—
211C2×D24C2×D311yescharacteristic
212C2×D24C2×D311yescharacteristic, complemented
213C2×#204C2×D311yescharacteristic
214C2×#204C2×D311yescharacteristic, complemented
215C2×#204C2×D311yescharacteristic, complemented
216C2×D3×C8—31no—
217C2×D3×C8—31no—
218C2×D3×C8—61no—
219#896—61no—
220#895—31no—
221#895—31no—
222#893—31no—
223#893—61no—
224#887—31no—
225#885—61no—
226#884—61no—
227#884—61no—
228#882—61no—
229C3×#107—31no—
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#830—31no—
237#830—31no—
238#830—61no—
239#821C2×D311yescharacteristic, complemented
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—61no—
243#818C2×D311yescharacteristic, complemented
244#816C2×D311yescharacteristic, complemented
245#815—31no—
246#815—31no—
247#815—61no—
248Dic3⋊C8—31no—
249Dic3⋊C8—31no—
250Dic3⋊C8—61no—
251#810—31no—
252#809—31no—
253#809—31no—
254#809—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3C2×D411yescharacteristic
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—81no—
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4C2×D411yescharacteristic
270C2×C32×C4C2411yescharacteristic
271#638—22no—
272C2×C3⋊Dic3C2×D411yescharacteristic
273C2×C3⋊Dic3C2×D411yescharacteristic
274C2×C3⋊Dic3C2×D411yescharacteristic
275C4×C3⋊D3—21no—
276C4×C3⋊D3—21no—
277C3×#67—42no—
278C3×#67—42no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12C2×D412yes—
292C3×C4×D3—42no—
293C3×Dic6—21no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6C2×D412yescomplemented
297#627—42no—
298#626—42no—
299#626—42no—
300#625—42no—
301#625—42no—
302#625—81no—
303#624—42no—
304D3×Dic3—42no—
305C32×C8—21no—
306C32×C8C2×D412yescomplemented
307C3⋊(C3⋊C8)—21no—
308C3⋊(C3⋊C8)—21no—
309C2×AGL(1,ℤ/8)—31no—
310C22×SD16—91no—
311#548—91no—
312D42—91no—
313#496—91no—
314#468—31no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—31no—
331C2×C3×Q8—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—31no—
336C2×C3×D4—62no—
337C2×C3×D4—61no—
338C2×C3×D4—61no—
339C2×C3×D4—61no—
340C2×C3×D4—121no—
341C22×C3×C4—21no—
342C22×C3×C4—61no—
343C22×C3×C4C22×D311yescharacteristic
344C22×C3×C4C22×D311yescharacteristic
345C2×#67—21no—
346C2×#67—21no—
347C2×#67—31no—
348C2×#67—31no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—124no—
359C22×Dic3—61no—
360D3×Q8—62no—
361D3×Q8—62no—
362D3×Q8—121no—
363D3×Q8—121no—
364D3×D4—62no—
365D3×D4—62no—
366D3×D4—121no—
367D3×D4—121no—
368D3×D4—124no—
369#235—22no—
370#235—41no—
371C2×D12—22no—
372C2×D12—21no—
373C2×D12—41no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—31no—
382C2×C4×D3—31no—
383C2×C4×D3—61no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—61no—
387C2×Dic6—61no—
388C2×Dic6—61no—
389C2×Dic6C22×D311yescharacteristic
390C2×Dic6C22×D311yescharacteristic
391C3×SD16—34no—
392C3×SD16—62no—
393C3×SD16—62no—
394C3×D8—62no—
395C3×D8—62no—
396C3×M16—22no—
397C3×M16—22no—
398C3×M16—42no—
399C2×C3×C8—21no—
400C2×C3×C8—21no—
401C2×C3×C8C22×D311yescharacteristic
402C2×C3×C8C22×D311yescharacteristic
403C2×C3×C8C22×D311yescharacteristic
404C2×C3×C8C22×D311yescharacteristic
405C3×C4⋊C4—31no—
406C3×C4⋊C4—31no—
407C3×C4⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410#217—21no—
411#217—31no—
412#217—31no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—61no—
419#215—62no—
420#215—62no—
421#215—121no—
422#214—62no—
423#214—62no—
424#214—121no—
425#213—121no—
426#213—121no—
427(C2×D3)⋊C4—21no—
428(C2×D3)⋊C4—31no—
429(C2×D3)⋊C4—31no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436C4⋊Dic3—61no—
437C4⋊Dic3C22×D311yescharacteristic
438C4⋊Dic3C22×D311yescharacteristic
439Dic3⋊C4—21no—
440Dic3⋊C4—31no—
441Dic3⋊C4—31no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444C4×Dic3—31no—
445C4×Dic3—31no—
446C4×Dic3—61no—
447C4×Dic3—61no—
448C4×Dic3—61no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—61no—
455D24—22no—
456D24—22no—
457#204—22no—
458#204—22no—
459#204#6714yescomplemented
460D3×C8—62no—
461D3×C8—62no—
462D3×C8—122no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—21no—
468C2×C3⋊D3—21no—
469C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
470C2×C3×D3—22no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—41no—
482C2×C3×D3—84no—
483D32—84no—
484C32×C4—21no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—21no—
488C3⋊Dic3—21no—
489C3⋊Dic3—21no—
490C3×Dic3—22no—
491C3×Dic3—41no—
492C3×Dic3—41no—
493C3×Dic3—41no—
494C2×#41—31no—
495C22×Q8—91no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—64no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—31no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—31no—
508C2×D8—31no—
509C2×D8—91no—
510C2×M16D3211yescharacteristic, complemented
511C22×C8—91no—
512#127—91no—
513#124—91no—
514#124—181no—
515C22⋊Q8—31no—
516C22⋊Q8—181no—
517#121—31no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—91no—
526C4×D4—91no—
527C4×D4—181no—
528#107—31no—
529C4⋊C8—91no—
530#103—31no—
531#103—91no—
532#102—31no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—91no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—122no—
545C23×C3—122no—
546C23×C3—241no—
547C23×C3D3×D411yescharacteristic
548C23×C3D3×D411yescharacteristic
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—21no—
553C22×D3—31no—
554C22×D3—31no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—61no—
558C22×D3—81no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—122no—
563C22×D3—241no—
564C22×D3—241no—
565C3×Q8—32no—
566C3×Q8—61no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×D4—32no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—122no—
578C3×D4—122no—
579C3×D4—122no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—41no—
587C2×C3×C4—41no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—122no—
593C2×C3×C4D3×D411yescharacteristic
594C2×C3×C4D3×D411yescharacteristic
595C2×C3×C4C23×D311yescharacteristic
596C2×C3×C4C23×D311yescharacteristic
597#67—42no—
598#67—42no—
599#67—62no—
600#67—62no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—122no—
606#67—122no—
607#67—122no—
608#67—241no—
609#67—241no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—21no—
614C2×Dic3—31no—
615C2×Dic3—31no—
616C2×Dic3—31no—
617C2×Dic3—31no—
618C2×Dic3—31no—
619C2×Dic3—31no—
620C2×Dic3—61no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—122no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—21no—
628D12—21no—
629D12—21no—
630D12—21no—
631D12—42no—
632D12—122no—
633D12—122no—
634D12C2×#6712yes—
635C4×D3—42no—
636C4×D3—61no—
637C4×D3—61no—
638C4×D3—61no—
639C4×D3—61no—
640C4×D3—121no—
641C4×D3—121no—
642C4×D3—122no—
643C4×D3—122no—
644C4×D3—122no—
645Dic6—21no—
646Dic6—21no—
647Dic6—21no—
648Dic6—122no—
649Dic6—122no—
650Dic6C2×#6712yescomplemented
651C3×C8—21no—
652C3×C8—21no—
653C3×C8—22no—
654C3×C8—41no—
655C3×C8D3×D412yescomplemented
656C3×C8C2×#6712yescomplemented
657C3⋊C8—61no—
658C3⋊C8—61no—
659C3⋊C8—61no—
660C3⋊C8—61no—
661C3⋊C8—121no—
662C3⋊C8—121no—
663C2×C32—41no—
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—22no—
668C3×D3—42no—
669C3×D3—81no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—181no—
674#41—62no—
675#41—121no—
676C2×Q8—31no—
677C2×Q8—31no—
678C2×Q8—181no—
679C2×Q8—182no—
680C2×Q8—361no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—62no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—91no—
690C2×D4—121no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—182no—
697C2×D4—361no—
698C2×D4—364no—
699C22×C4—61no—
700C22×C4—91no—
701C22×C4—181no—
702C22×C4—181no—
703C22×C4C2×D3211yescharacteristic
704SD16—34no—
705SD16—62no—
706SD16—62no—
707SD16—182no—
708SD16—182no—
709SD16—361no—
710D8—62no—
711D8—62no—
712D8—361no—
713M16—22no—
714C2×C8—91no—
715C2×C8—91no—
716C2×C8—182no—
717C2×C8C2×D3211yescharacteristic
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—31no—
720C4⋊C4—31no—
721C4⋊C4—61no—
722C4⋊C4—91no—
723C4⋊C4—181no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—91no—
727C22⋊C4—91no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—91no—
734C42—181no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—62no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—244no—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C2×D3—22no—
761C2×D3—32no—
762C2×D3—32no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—62no—
775C2×D3—61no—
776C2×D3—61no—
777C2×D3—61no—
778C2×D3—61no—
779C2×D3—84no—
780C2×D3—121no—
781C2×D3—121no—
782C2×D3—244no—
783C2×D3—244no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—41no—
789C3×C4—62no—
790C3×C4—121no—
791C3×C4—121no—
792C3×C4—121no—
793C3×C4C2×D3×D411yescharacteristic
794C3×C4#100411yescharacteristic
795C3×C4#100911yescharacteristic
796C3×C4C22×#6711yescharacteristic
797Dic3—22no—
798Dic3—41no—
799Dic3—41no—
800Dic3—41no—
801Dic3—61no—
802Dic3—61no—
803Dic3—61no—
804Dic3—61no—
805Dic3—61no—
806Dic3—61no—
807Dic3—121no—
808Dic3—121no—
809Dic3—121no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—61no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—91no—
816C23—122no—
817C23—122no—
818C23—241no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23#380211yescharacteristic
823Q8—32no—
824Q8—61no—
825Q8—61no—
826Q8—61no—
827Q8—362no—
828D4—32no—
829D4—61no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—61no—
836D4—122no—
837D4—122no—
838D4—122no—
839D4—182no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—721no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—91no—
852C2×C4—91no—
853C2×C4—91no—
854C2×C4—122no—
855C2×C4—181no—
856C2×C4—181no—
857C2×C4—362no—
858C2×C4—362no—
859C2×C4#380211yescharacteristic
860C2×C4C22×D3211yescharacteristic
861C8—21no—
862C8—181no—
863C8—181no—
864C8D3×#6712yescomplemented
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—41no—
869C2×C3—41no—
870C2×C3—81no—
871C2×C3—122no—
872C2×C3—241no—
873C2×C3—241no—
874C2×C3—241no—
875C2×C3#560911yescharacteristic
876C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
877C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
878C2×C3#577511yescharacteristic
879C2×C3#577811yescharacteristic
880C2×C3D4×#6711yescharacteristic
881D3—42no—
882D3—62no—
883D3—62no—
884D3—81no—
885D3—81no—
886D3—81no—
887D3—122no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—62no—
892C22—92no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—121no—
904C22—181no—
905C22—181no—
906C22—244no—
907C22—724no—
908C22C2×#380211yescharacteristic
909C4—21no—
910C4—62no—
911C4—121no—
912C4—121no—
913C4—121no—
914C4—181no—
915C4—181no—
916C4—181no—
917C4#6430711yescharacteristic
918C4C2×D3×#6711yescharacteristic
919C3—21no—
920C3#8083411yescharacteristic, complemented
921C3#8395311yescharacteristic, complemented
922C2—41no—
923C2—122no—
924C2—182no—
925C2—241no—
926C2—241no—
927C2—241no—
928C2#1059471611yescharacteristic
929C2#1059471911yescharacteristic
930C2#1059506911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#908C2semidirect
2. #10595069C2semidirect
3. #10594830C2semidirect
4. C2×#63796C2semidirect
5. #10592826C2semidirect
6. C3×#5134C2semidirect
7. #10591169C2semidirect
8. #10591161C2semidirect
9. #10590945C2semidirect
10. #10590887C2semidirect
11. #10590876C2semidirect
12. #10590844C2semidirect
13. #10590824C2semidirect
14. #10590779C2semidirect
15. #10590751C2semidirect
18. C2×C3×#235C22semidirect
22. C2×#3797C22semidirect
23. C2×C32×M16C22semidirect
25. C2×C8×C3⋊D3C22semidirect
27. C3×#924C22semidirect
30. C2×C3×D24C22semidirect
32. C2×C3×#204C22semidirect
33. C2×C3×#204C22semidirect
39. #63916C22semidirect
44. #63863C22semidirect
46. #63843C22semidirect
48. C2×#3715C22semidirect
49. C2×#3715C22semidirect
50. C2×#3713C22semidirect
52. #63657C22semidirect
53. #63647C22semidirect
54. #63642C22semidirect
55. #63641C22semidirect
56. C3×#821C22semidirect
57. C3×#818C22semidirect
58. C3×#816C22semidirect
59. #63565C22semidirect
61. #63562C22semidirect
62. #63562C22semidirect
68. C2×#908D3semidirect
82. #5134D3semidirect
145. C3×#204D4semidirect
166. C2×#235C2×D3semidirect
175. C2×C3×M16C2×D3semidirect
176. C2×C3×M16C2×D3semidirect
207. #924C2×D3semidirect
212. C2×D24C2×D3semidirect
214. C2×#204C2×D3semidirect
215. C2×#204C2×D3semidirect
239. #821C2×D3semidirect
243. #818C2×D3semidirect
244. #816C2×D3semidirect
296. C3×Dic6C2×D4semidirect
306. C32×C8C2×D4semidirect
459. #204#67semidirect
469. C2×C3⋊D3AGL(1,ℤ/8)semidirect
510. C2×M16D32semidirect
650. Dic6C2×#67semidirect
655. C3×C8D3×D4semidirect
656. C3×C8C2×#67semidirect
810. C32#3265semidirect
864. C8D3×#67semidirect
920. C3#80834semidirect
921. C3#83953semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
#105950692
#105948302
C2×#637962
#105928262
C3×#51342
#105911692
#105911612
#105909452
#105908872
#105908762
#105908442
#105908242
#105907792
#105907512
#839533
#808343