Finite Group Databasebeta

← #11884006

Subgroups — #11884006

Order 1152.

1152 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
2D12×#67C211yesmaximal, characteristic, complemented
3#10594899C211yesmaximal, characteristic, complemented
4C2×D3×#204C211yesmaximal, characteristic, complemented
5#10592833C211yesmaximal, characteristic, complemented
6C3×#5127C211yesmaximal, characteristic, complemented
7#10591172C211yesmaximal, characteristic, complemented
8#10591163C211yesmaximal, characteristic, complemented
9#10590944C211yesmaximal, characteristic, complemented
10#10590883C211yesmaximal, characteristic, complemented
11#10590831C211yesmaximal, characteristic, complemented
12#10590822C211yesmaximal, characteristic, complemented
13#10590799C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15#10590755C211yesmaximal, characteristic, complemented
16#83953—31nomaximal
17#79494—31nomaximal
18C2×C3×#235C2211yescharacteristic, complemented
19C22×C3×D12C2211yescharacteristic
20C2×D3×#67—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic, complemented
23C2×C32×M16C2211yescharacteristic, complemented
24#64139C2211yescharacteristic
25#64133C2211yescharacteristic, complemented
26C2×#3744C2211yescharacteristic, complemented
27C3×C4×#67C2211yescharacteristic
28C3×#908—24no—
29C2×C3×D24C2211yescharacteristic
30C2×C3×D24C2211yescharacteristic, complemented
31C2×C3×#204C2211yescharacteristic
32C2×C3×#204C2211yescharacteristic, complemented
33C2×C3×D3×C8C2211yescharacteristic, complemented
34#63977—21no—
35#63970—21no—
36#63959—21no—
37#63922—21no—
38#63911C2211yescharacteristic
39#63908C2211yescharacteristic
40#63908C2211yescharacteristic, complemented
41Dic3×D12C2211yescharacteristic
42#63886—21no—
43#63879—21no—
44#63860C2211yescharacteristic, complemented
45#63851—21no—
46Dic3×Dic6C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3716C2211yescharacteristic
49C2×#3716C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51D3×#204—24no—
52#63648C2211yescharacteristic, complemented
53#63645C2211yescharacteristic, complemented
54#63643C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×#815C2211yescharacteristic, complemented
58C3×Dic3⋊C8C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#63563C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×C3×AGL(1,ℤ/8)—31no—
64#5831—31no—
65D4×#67—31no—
66C2×D3×SD16—31no—
67C2×#908D311yescharacteristic, complemented
68C22×#204—31no—
69#5552—31no—
70D4×D12—31no—
71C3×#435—31no—
72#5238—31no—
73#5218—31no—
74#5170—31no—
75#5164—31no—
76#5163—31no—
77#5157—31no—
78#5156—31no—
79#5154—31no—
80#5153—31no—
81#5134—31no—
82#5134—31no—
83#5134—61no—
84#5127D311yescharacteristic, complemented
85#5115—31no—
86#4848—31no—
87#4844—31no—
88#4738—31no—
89#4734—31no—
90#4732—31no—
91#4731—31no—
92#4712—31no—
93#4710—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C22×C32×C4C2311yescharacteristic
97C2×#638—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C3×#235—22no—
103C3×#235—41no—
104C2×C3×D12—22no—
105C2×C3×D12—21no—
106C2×C3×D12—41no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—21no—
111C2×C3×C4×D3C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113D3×#67—44no—
114C2×#627—21no—
115C2×#626—21no—
116C2×#626—21no—
117C2×#626—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121C2×D3×Dic3—21no—
122D3×D12—22no—
123D3×D12—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C32×M16—22no—
127C2×C32×C8C2311yescharacteristic
128C2×C32×C8C2311yescharacteristic
129#3757—21no—
130#3752—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132C4⋊(C3⋊Dic3)C2311yescharacteristic
133#3750—21no—
134#3744—22no—
135C3×#217D411yescharacteristic
136C3×(C2×D3)⋊C4D411yescharacteristic
137C3×Dic3⋊C4D411yescharacteristic
138C3×C4×Dic3C2311yescharacteristic
139C2×C3×C3⋊C8C2311yescharacteristic
140C2×C3×C3⋊C8C2311yescharacteristic
141C3×D24—22no—
142C3×D24—22no—
143C3×#204—22no—
144C3×#204D414yescomplemented
145C3×D3×C8—22no—
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#3717—22no—
154#3716—22no—
155#3716—41no—
156#3714—41no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×D3×Q8—31no—
162C2×D3×D4—31no—
163C2×D3×D4—61no—
164C2×#235C2×D311yescharacteristic, complemented
165C22×D12—31no—
166C22×D12C2×D311yescharacteristic
167C22×Dic6—31no—
168C3×AGL(1,ℤ/8)—64no—
169C2×C3×SD16—31no—
170C2×C3×SD16—31no—
171C2×C3×D8—31no—
172C2×C3×D8—31no—
173C2×C3×M16—21no—
174C2×C3×M16C2×D311yescharacteristic, complemented
175C2×C3×M16C2×D311yescharacteristic, complemented
176C22×C3×C8—31no—
177C3×C4×D4—31no—
178#953—61no—
179Q8×Dic3—31no—
180C2×#215—31no—
181#940—31no—
182#939—61no—
183#939—61no—
184#938—31no—
185#938—31no—
186#938—61no—
187#937—61no—
188#936—31no—
189#936—61no—
190D4×Dic3—31no—
191C2×#214—31no—
192C2×#214—31no—
193C2×#213—31no—
194#930—31no—
195#930—31no—
196#930—31no—
197#930—31no—
198#930—61no—
199C4×#67—61no—
200C4×#67C2×D311yescharacteristic
201#924—31no—
202#924—31no—
203#924—61no—
204#924—61no—
205D3×SD16—64no—
206#908—24no—
207C2×D24—31no—
208C2×D24C2×D311yescharacteristic
209C2×D24C2×D311yescharacteristic, complemented
210C2×#204—31no—
211C2×#204—31no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—61no—
216C2×#204—64no—
217C2×#204C2×D311yescharacteristic
218C2×#204C2×D311yescharacteristic, complemented
219C2×D3×C8C2×D311yescharacteristic, complemented
220#896—61no—
221#895—61no—
222#885—61no—
223#882—61no—
224#882—61no—
225#67⋊C4—61no—
226#875—31no—
227#874—31no—
228C4×D12—31no—
229C4×Dic6—31no—
230C3×C4⋊C8—31no—
231C3×C22⋊C8—31no—
232C3×C22⋊C8—31no—
233C3×#97—31no—
234#835—31no—
235#832—31no—
236#832—31no—
237#832—31no—
238#830C2×D311yescharacteristic, complemented
239#821—31no—
240#821—31no—
241#821—31no—
242#821—31no—
243#821—31no—
244#821—61no—
245(C2×D3)⋊C8C2×D311yescharacteristic, complemented
246#818—31no—
247#818—31no—
248#818—61no—
249#816—31no—
250#816—31no—
251#816—31no—
252#816—61no—
253#815C2×D311yescharacteristic, complemented
254Dic3⋊C8C2×D311yescharacteristic, complemented
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
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—42no—
272C2×C3⋊Dic3—21no—
273C2×C3⋊Dic3—21no—
274C2×C3⋊Dic3—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277#634—21no—
278#634—21no—
279C3×#67—22no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12C2×D412yes—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—42no—
295C3×Dic6—21no—
296C3×Dic6C2×D412yescomplemented
297#627—42no—
298#626—42no—
299#626—42no—
300#626—81no—
301#625—42no—
302#625—42no—
303D3×Dic3—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—91no—
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—31no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—31no—
335C2×C3×D4—62no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—121no—
339C22×C3×C4—21no—
340C22×C3×C4—31no—
341C22×C3×C4—61no—
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—21no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—121no—
355C2×#67—124no—
356C2×#67D1211yescharacteristic
357C22×Dic3—61no—
358C22×Dic3—61no—
359D3×Q8—62no—
360D3×Q8—121no—
361D3×D4—62no—
362D3×D4—121no—
363D3×D4—124no—
364#235—22no—
365#235—41no—
366C2×D12—22no—
367C2×D12—21no—
368C2×D12—31no—
369C2×D12—31no—
370C2×D12—41no—
371C2×D12—61no—
372C2×D12—62no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×C4×D3—21no—
381C2×C4×D3—61no—
382C2×C4×D3—61no—
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6—61no—
389C2×Dic6—61no—
390C2×Dic6—121no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—34no—
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×C8—31no—
402C2×C3×C8—31no—
403C2×C3×C8—62no—
404C2×C3×C8C22×D311yescharacteristic
405C2×C3×C8C22×D311yescharacteristic
406C2×C3×C8C22×D311yescharacteristic
407C2×C3×C8C22×D311yescharacteristic
408C3×C4⋊C4—31no—
409C3×C22⋊C4—31no—
410C3×C22⋊C4—31no—
411C3×C42—31no—
412#217—61no—
413#217—61no—
414#217—61no—
415#217—61no—
416#217—61no—
417#217—61no—
418#217—61no—
419#217—121no—
420#217D1211yescharacteristic
421#215—62no—
422#214—62no—
423#214—121no—
424#213—121no—
425(C2×D3)⋊C4—61no—
426(C2×D3)⋊C4—61no—
427(C2×D3)⋊C4—61no—
428(C2×D3)⋊C4—61no—
429(C2×D3)⋊C4—61no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—121no—
433(C2×D3)⋊C4D1211yescharacteristic
434C4⋊Dic3—31no—
435C4⋊Dic3—31no—
436C4⋊Dic3—31no—
437C4⋊Dic3—31no—
438C4⋊Dic3—61no—
439C4⋊Dic3—61no—
440C4⋊Dic3—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—121no—
445Dic3⋊C4D1211yescharacteristic
446C4×Dic3—61no—
447C4×Dic3—61no—
448C4×Dic3C22×D311yescharacteristic
449C2×C3⋊C8C22×D311yescharacteristic
450C2×C3⋊C8C22×D311yescharacteristic
451D24—22no—
452D24—22no—
453D24—121no—
454#204—22no—
455#204—62no—
456#204—62no—
457#204—62no—
458#204—62no—
459#204—122no—
460#204—121no—
461#204#6714yescomplemented
462D3×C8—22no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
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—84no—
482C2×C3×D3AGL(1,ℤ/8)12yescomplemented
483D32—84no—
484C32×C4—21no—
485C32×C4C22×D411yescharacteristic
486C32×C4H(5,𝔽2)11yescharacteristic
487C3⋊Dic3—41no—
488C3⋊Dic3—41no—
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—21no—
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—91no—
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—31no—
512#127—91no—
513#124—91no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—91no—
518#121—91no—
519#121—91no—
520#121—181no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—91no—
525C4×D4—31no—
526C4×D4—91no—
527C4×D4—181no—
528#107—91no—
529C4⋊C8—31no—
530#103—91no—
531#103—91no—
532#102—91no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—31no—
538#97—31no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—122no—
545C23×C3—122no—
546C23×C3—241no—
547C23×C3C2×D1211yescharacteristic
548C23×C3D3×D411yescharacteristic
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—81no—
557C22×D3—121no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3C2×D1211yescharacteristic
565C3×Q8—32no—
566C3×Q8—61no—
567C3×D4—32no—
568C3×D4—62no—
569C3×D4—61no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—122no—
575C3×D4—122no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—31no—
585C2×C3×C4—41no—
586C2×C3×C4—41no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—122no—
591C2×C3×C4C2×D1211yescharacteristic
592C2×C3×C4D3×D411yescharacteristic
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D311yescharacteristic
595#67—22no—
596#67—42no—
597#67—122no—
598#67—122no—
599#67—122no—
600#67—122no—
601#67—122no—
602#67—122no—
603#67—122no—
604#67—122no—
605#67—242no—
606#67—241no—
607C2×Dic3—21no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—121no—
617C2×Dic3—122no—
618C2×Dic3—122no—
619C2×Dic3C2×D1211yescharacteristic
620C2×Dic3C2×D1211yescharacteristic
621C2×Dic3C2×D1211yescharacteristic
622D12—21no—
623D12—21no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—42no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—61no—
632D12—121no—
633D12—121no—
634D12—122no—
635D12—122no—
636D12—241no—
637D12C2×#6712yes—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—42no—
641C4×D3—122no—
642C4×D3—122no—
643Dic6—21no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—121no—
649Dic6—121no—
650Dic6—122no—
651Dic6—122no—
652Dic6C2×#6712yescomplemented
653C3×C8—21no—
654C3×C8—21no—
655C3×C8—22no—
656C3×C8—41no—
657C3×C8—61no—
658C3×C8—61no—
659C3×C8D3×D412yescomplemented
660C3×C8C2×#6712yescomplemented
661C3⋊C8—21no—
662C3⋊C8—21no—
663C2×C32—41no—
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—81no—
668C3×D3—22no—
669C3×D3—42no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—181no—
674#41—62no—
675#41—121no—
676C2×Q8—31no—
677C2×Q8—91no—
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—91no—
689C2×D4—121no—
690C2×D4—181no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—182no—
694C2×D4—181no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—361no—
698C2×D4—364no—
699C22×C4—31no—
700C22×C4—61no—
701C22×C4—181no—
702C22×C4—181no—
703C22×C4C2×D3211yescharacteristic
704SD16—34no—
705SD16—62no—
706SD16—182no—
707SD16—182no—
708SD16—182no—
709SD16—361no—
710D8—62no—
711D8—62no—
712D8—361no—
713M16—22no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—62no—
717C2×C8C2×D3211yescharacteristic
718C2×C8C2×D3211yescharacteristic
719C4⋊C4—31no—
720C4⋊C4—91no—
721C4⋊C4—91no—
722C4⋊C4—181no—
723C4⋊C4—181no—
724C22⋊C4—31no—
725C22⋊C4—31no—
726C22⋊C4—181no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—31no—
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—32no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—62no—
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×C3C22×D1211yescharacteristic
759C22×C3C2×D3×D411yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—22no—
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—84no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3#90812yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—41no—
789C3×C4—61no—
790C3×C4—61no—
791C3×C4—61no—
792C3×C4—62no—
793C3×C4C2×D3×D411yescharacteristic
794C3×C4#100411yescharacteristic
795C3×C4#100911yescharacteristic
796C3×C4C22×#6711yescharacteristic
797Dic3—21no—
798Dic3—21no—
799Dic3—22no—
800Dic3—21no—
801Dic3—121no—
802Dic3—121no—
803Dic3—121no—
804Dic3—121no—
805Dic3—121no—
806Dic3—121no—
807Dic3—241no—
808Dic3—241no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—31no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—122no—
816C23—122no—
817C23—181no—
818C23—241no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23D3×D1211yescharacteristic
823Q8—32no—
824Q8—61no—
825Q8—181no—
826Q8—181no—
827Q8—362no—
828D4—32no—
829D4—62no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—122no—
836D4—122no—
837D4—181no—
838D4—181no—
839D4—362no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—721no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—31no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—122no—
854C2×C4—181no—
855C2×C4—181no—
856C2×C4—181no—
857C2×C4—362no—
858C2×C4—362no—
859C2×C4D3×D1211yescharacteristic
860C2×C4C22×D3211yescharacteristic
861C8—21no—
862C8—61no—
863C8—61no—
864C8D3×#6712yescomplemented
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—41no—
869C2×C3—41no—
870C2×C3—62no—
871C2×C3—81no—
872C2×C3—122no—
873C2×C3—241no—
874C2×C3—241no—
875C2×C3D4×D1211yescharacteristic
876C2×C3C2×#90811yescharacteristic
877C2×C3#575111yescharacteristic
878C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
879C2×C3#577511yescharacteristic
880C2×C3D4×#6711yescharacteristic
881D3—22no—
882D3—42no—
883D3—81no—
884D3—81no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—32no—
892C22—61no—
893C22—61no—
894C22—62no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—244no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22—724no—
908C22C2×D3×D1211yescharacteristic
909C4—21no—
910C4—61no—
911C4—61no—
912C4—61no—
913C4—62no—
914C4—361no—
915C4—361no—
916C4—361no—
917C4#6430711yescharacteristic
918C4C2×D3×#6711yescharacteristic
919C3—21no—
920C3#7949411yescharacteristic, complemented
921C3#8395311yescharacteristic, complemented
922C2—41no—
923C2—62no—
924C2—122no—
925C2—241no—
926C2—241no—
927C2—721no—
928C2D3×#90811yescharacteristic
929C2#1059471311yescharacteristic
930C2D12×#6711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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. D12×#67C2semidirect
3. #10594899C2semidirect
4. C2×D3×#204C2semidirect
5. #10592833C2semidirect
6. C3×#5127C2semidirect
7. #10591172C2semidirect
8. #10591163C2semidirect
9. #10590944C2semidirect
10. #10590883C2semidirect
11. #10590831C2semidirect
12. #10590822C2semidirect
13. #10590799C2semidirect
14. #10590766C2semidirect
15. #10590755C2semidirect
18. C2×C3×#235C22semidirect
22. C2×D3×Dic6C22semidirect
23. C2×C32×M16C22semidirect
25. #64133C22semidirect
26. C2×#3744C22semidirect
30. C2×C3×D24C22semidirect
32. C2×C3×#204C22semidirect
33. C2×C3×D3×C8C22semidirect
40. #63908C22semidirect
44. #63860C22semidirect
46. Dic3×Dic6C22semidirect
47. C2×#3717C22semidirect
49. C2×#3716C22semidirect
50. C2×#3714C22semidirect
52. #63648C22semidirect
53. #63645C22semidirect
54. #63643C22semidirect
55. C3×#830C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×#815C22semidirect
58. C3×Dic3⋊C8C22semidirect
59. #63566C22semidirect
61. #63563C22semidirect
62. #63563C22semidirect
67. C2×#908D3semidirect
84. #5127D3semidirect
144. C3×#204D4semidirect
164. C2×#235C2×D3semidirect
174. C2×C3×M16C2×D3semidirect
175. C2×C3×M16C2×D3semidirect
209. C2×D24C2×D3semidirect
218. C2×#204C2×D3semidirect
219. C2×D3×C8C2×D3semidirect
238. #830C2×D3semidirect
245. (C2×D3)⋊C8C2×D3semidirect
253. #815C2×D3semidirect
254. Dic3⋊C8C2×D3semidirect
296. C3×Dic6C2×D4semidirect
306. C32×C8C2×D4semidirect
461. #204#67semidirect
482. C2×C3×D3AGL(1,ℤ/8)semidirect
510. C2×M16D32semidirect
652. Dic6C2×#67semidirect
659. C3×C8D3×D4semidirect
660. C3×C8C2×#67semidirect
783. C2×D3#908semidirect
810. C32#3265semidirect
864. C8D3×#67semidirect
920. C3#79494semidirect
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
D12×#672
#105948992
C2×D3×#2042
#105928332
C3×#51272
#105911722
#105911632
#105909442
#105908832
#105908312
#105908222
#105907992
#105907662
#105907552
#839533
#794943