Finite Group Databasebeta

← #11885744

Subgroups — #11885744

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic, complemented
2C3×D4×#67C211yesmaximal, characteristic, complemented
3C2×D3×#213C211yesmaximal, characteristic, complemented
4#10595074C211yesmaximal, characteristic, complemented
5C3×#5217C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591482C211yesmaximal, characteristic, complemented
8#10591481C211yesmaximal, characteristic, complemented
9#10591449C211yesmaximal, characteristic, complemented
10#10591448C211yesmaximal, characteristic, complemented
11#10591429C211yesmaximal, characteristic, complemented
12#10591400C211yesmaximal, characteristic, complemented
13#10591168C211yesmaximal, characteristic, complemented
14#10591166C211yesmaximal, characteristic, complemented
15#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
16D4×#213—31nomaximal
17#80024—31nomaximal
18C22×C32×D4C2211yescharacteristic, complemented
19C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C22×C3×#67—21no—
21C2×C3×D3×D4C2211yescharacteristic, complemented
22C2×#3811—21no—
23C2×D3×D12C2211yescharacteristic, complemented
24C2×#3753—24no—
25C2×#3753C2211yescharacteristic
26C2×#3753C2211yescharacteristic, complemented
27C2×#3753C2211yescharacteristic, complemented
28C2×#3753C2211yescharacteristic, complemented
29C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
30C3×#953—21no—
31C3×#940C2211yescharacteristic, complemented
32C3×#939—21no—
33C3×#938C2211yescharacteristic, complemented
34C3×#937—21no—
35C3×D4×Dic3C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic, complemented
37C2×C3×#213C2211yescharacteristic, complemented
38C3×#930C2211yescharacteristic, complemented
39C3×#930C2211yescharacteristic, complemented
40C3×C4×#67C2211yescharacteristic
41#63981—21no—
42D3×#213—24no—
43#63923—21no—
44#63911C2211yescharacteristic, complemented
45#63910—21no—
46#63909C2211yescharacteristic, complemented
47#63894C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63564C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63C3×D42—31no—
64D4×#67D311yescharacteristic, complemented
65C22×#213—31no—
66C22×#213—31no—
67C22×#213—31no—
68C22×#213—61no—
69C2×D3×D8—31no—
70#5609—31no—
71D4×D12—31no—
72C3×#447—31no—
73#5217—31no—
74#5217D311yescharacteristic, complemented
75#5156—31no—
76#5151—31no—
77#5150—31no—
78#5073—31no—
79#5072—31no—
80#5038—31no—
81#5038—31no—
82#5038—31no—
83#5036—31no—
84#5036—31no—
85#5015—31no—
86C4×#213—31no—
87D4×C3⋊C8—31no—
88#4786—31no—
89#4775—31no—
90#4773—31no—
91#4756—31no—
92#4732—31no—
93#67⋊C8—31no—
94C24×C32—21no—
95C23×C3⋊D3—21no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C2×C32×D4—22no—
99C2×C32×D4—21no—
100C2×C32×D4—41no—
101C2×C32×D4C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C2×C4⋊(C3⋊D3)—22no—
105C2×C4⋊(C3⋊D3)—21no—
106C2×C4⋊(C3⋊D3)—41no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4⋊(C3⋊D3)C2311yescharacteristic
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C2×C3×#67—21no—
114C2×C3×#67—21no—
115C2×C3×#67—44no—
116C2×C3×#67D411yescharacteristic
117C22×C3×Dic3—21no—
118C3×D3×D4—22no—
119C3×D3×D4—41no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×C4×D3C2311yescharacteristic
123#3811—44no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—21no—
127C2×#626—21no—
128C2×#624—21no—
129D3×D12—22no—
130D3×D12—41no—
131#3753—22no—
132#3753—22no—
133#3753—22no—
134#3753D414yescomplemented
135C2×C3⋊(C3⋊C8)—22no—
136C2×C3⋊(C3⋊C8)C2311yescharacteristic
137C2×C3⋊(C3⋊C8)C2311yescharacteristic
138C3×#217—21no—
139C3×#217—21no—
140C3×#217D411yescharacteristic
141C3×#213—22no—
142C3×#213—41no—
143C3×(C2×D3)⋊C4—21no—
144C3×(C2×D3)⋊C4—21no—
145C3×(C2×D3)⋊C4D411yescharacteristic
146C3×C4⋊Dic3C2311yescharacteristic
147C3×C4⋊Dic3C2311yescharacteristic
148C3×Dic3⋊C4D411yescharacteristic
149C3×C4×Dic3C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152#3722—21no—
153#3722—21no—
154#3714—22no—
155#3714—41no—
156#3713—22no—
157D3×C3⋊C8—22no—
158D4×D8—91noSylow
159C22×C3×D4—21no—
160C22×C3×D4—31no—
161C22×C3×D4—61no—
162C22×C3×D4C2×D311yescharacteristic, complemented
163C22×C3×D4C2×D311yescharacteristic, complemented
164C22×#67—21no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×D3×D4—61no—
168C2×D3×D4C2×D311yescharacteristic, complemented
169C22×D12—31no—
170C22×D12—31no—
171C22×D12—31no—
172C22×D12—61no—
173C2×C3×D8—31no—
174C2×C3×D8—31no—
175C3×#127—31no—
176C3×#121—31no—
177C3×#121—31no—
178C3×#121—31no—
179C3×#121—61no—
180C3×#120—61no—
181C3×#120—61no—
182C3×C4×D4—31no—
183C3×C4×D4—31no—
184#953—21no—
185#940—31no—
186#940C2×D311yescharacteristic, complemented
187#939—21no—
188#938C2×D311yescharacteristic, complemented
189#937—21no—
190#937—61no—
191D4×Dic3C2×D311yescharacteristic, complemented
192C2×#213—31no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—61no—
205C2×#213—61no—
206C2×#213—61no—
207C2×#213—61no—
208C2×#213—64no—
209C2×#213—64no—
210C2×#213—64no—
211C2×#213—68no—
212C2×#213C2×D311yescharacteristic, complemented
213C2×#213C2×D311yescharacteristic, complemented
214#930—31no—
215#930C2×D311yescharacteristic, complemented
216#930C2×D311yescharacteristic, complemented
217C4×#67C2×D311yescharacteristic
218C22×C3⋊C8—31no—
219C22×C3⋊C8—31no—
220C22×C3⋊C8—31no—
221C22×C3⋊C8—61no—
222D3×D8—64no—
223C2×D24—31no—
224C2×D24—31no—
225C2×D3×C8—31no—
226#895—31no—
227#895—61no—
228#893—31no—
229#884—61no—
230#882—61no—
231#882—61no—
232#882—61no—
233#874—31no—
234C4×D12—31no—
235C3×#102—31no—
236C3×#102—31no—
237C3×C22⋊C8—31no—
238#832—31no—
239#832—31no—
240#832C2×D311yescharacteristic, complemented
241#832C2×D311yescharacteristic, complemented
242#830—31no—
243#830C2×D311yescharacteristic, complemented
244#821—31no—
245#821—31no—
246(C2×D3)⋊C8—31no—
247Dic3⋊C8—31no—
248C8×Dic3—31no—
249#809—31no—
250#809—31no—
251#809—31no—
252#809—31no—
253#807—31no—
254#807—31no—
255C4⋊(C3⋊C8)—31no—
256C4×C3⋊C8—31no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—42no—
260C23×C32—42no—
261C23×C32—81no—
262C23×C32C2×D411yescharacteristic
263C22×C3⋊D3—21no—
264C22×C3⋊D3—21no—
265C22×C3⋊D3—42no—
266C22×C3⋊D3—42no—
267C22×C3⋊D3—81no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—42no—
271C22×C3×D3—42no—
272C22×C3×D3—81no—
273C22×C3×D3C2×D411yescharacteristic
274C2×D32—42no—
275C2×D32—42no—
276C2×D32—81no—
277C32×D4—21no—
278C32×D4—21no—
279C32×D4—21no—
280C32×D4—42no—
281C32×D4C2×D412yescomplemented
282C2×C32×C4—21no—
283C2×C32×C4—21no—
284C2×C32×C4C2×D411yescharacteristic
285C2×C32×C4C2411yescharacteristic
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)—21no—
288C4⋊(C3⋊D3)—21no—
289C4⋊(C3⋊D3)—42no—
290C4⋊(C3⋊D3)C2×D412yescomplemented
291C3×#67—42no—
292C3×#67—42no—
293C3×#67—42no—
294C3×#67—42no—
295C3×#67—42no—
296C3×#67—81no—
297C3×#67D814yescomplemented
298C2×C3×Dic3—21no—
299C2×C3×Dic3—21no—
300C2×C3×Dic3—42no—
301C2×C3×Dic3C2×D411yescharacteristic
302C2×C3×Dic3C2×D411yescharacteristic
303C2×C3×Dic3C2×D411yescharacteristic
304C3×D12—21no—
305C3×D12—21no—
306C3×D12—21no—
307C3×D12—21no—
308C3×C4×D3—21no—
309C3×C4×D3—21no—
310#626—42no—
311#626—42no—
312#626—42no—
313#626—81no—
314#624—42no—
315C3⋊(C3⋊C8)—21no—
316C3⋊(C3⋊C8)C2×D412yescomplemented
317C3×C3⋊C8—21no—
318C3×C3⋊C8—21no—
319C22×D8—91no—
320C22×D8—91no—
321D42—31no—
322D42—91no—
323#493—91no—
324#466—91no—
325#466—91no—
326#459—91no—
327#459—91no—
328#447—31no—
329#447—91no—
330#447—91no—
331#447—91no—
332C4×D8—91no—
333C8×D4—91no—
334C24×C3—21no—
335C24×C3—21no—
336C24×C3—41no—
337C24×C3—61no—
338C23×D3—21no—
339C23×D3—61no—
340C23×D3—61no—
341C23×D3—61no—
342C23×D3—61no—
343C23×D3—121no—
344C2×C3×D4—24no—
345C2×C3×D4—22no—
346C2×C3×D4—22no—
347C2×C3×D4—21no—
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—31no—
352C2×C3×D4—31no—
353C2×C3×D4—31no—
354C2×C3×D4—41no—
355C2×C3×D4—41no—
356C2×C3×D4—41no—
357C2×C3×D4—42no—
358C2×C3×D4—61no—
359C2×C3×D4—61no—
360C2×C3×D4—61no—
361C2×C3×D4—62no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—61no—
365C2×C3×D4—121no—
366C2×C3×D4—124no—
367C2×C3×D4C22×D311yescharacteristic
368C2×C3×D4C22×D311yescharacteristic
369C2×C3×D4C22×D311yescharacteristic
370C2×C3×D4C22×D311yescharacteristic
371C22×C3×C4—21no—
372C22×C3×C4—31no—
373C22×C3×C4—61no—
374C22×C3×C4C22×D311yescharacteristic
375C22×C3×C4C22×D311yescharacteristic
376C2×#67—21no—
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—21no—
380C2×#67—21no—
381C2×#67—21no—
382C2×#67—44no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67#6711yescharacteristic
388C22×Dic3—21no—
389D3×D4—22no—
390D3×D4—41no—
391D3×D4—62no—
392D3×D4—121no—
393D3×D4—124no—
394D3×D4—124no—
395C2×D12—31no—
396C2×D12—31no—
397C2×D12—31no—
398C2×D12—31no—
399C2×D12—61no—
400C2×D12—61no—
401C2×D12—62no—
402C2×D12—62no—
403C2×D12—62no—
404C2×D12—64no—
405C2×D12—61no—
406C2×D12—61no—
407C2×D12—61no—
408C2×D12—61no—
409C2×D12—61no—
410C2×D12—61no—
411C2×D12—121no—
412C2×D12—121no—
413C2×D12—121no—
414C2×D12—121no—
415C2×D12—122no—
416C2×D12C22×D311yescharacteristic
417C2×D12C22×D311yescharacteristic
418C2×C4×D3—61no—
419C2×C4×D3—61no—
420C2×C4×D3C22×D311yescharacteristic
421C3×D8—62no—
422C3×D8—121no—
423C2×C3×C8—31no—
424C2×C3×C8—31no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4—31no—
428C3×C22⋊C4—31no—
429C3×C22⋊C4—31no—
430C3×C22⋊C4—61no—
431C3×C22⋊C4—61no—
432C3×C22⋊C4—61no—
433C3×C22⋊C4—61no—
434C3×C42—31no—
435#217—21no—
436#217—21no—
437#217#6711yescharacteristic
438#213—22no—
439#213—34no—
440#213—34no—
441#213—41no—
442#213—64no—
443#213—62no—
444#213—62no—
445#213—62no—
446#213—62no—
447#213—62no—
448#213—62no—
449#213—62no—
450#213—64no—
451#213—64no—
452#213—64no—
453#213—62no—
454#213—62no—
455#213—121no—
456(C2×D3)⋊C4—21no—
457(C2×D3)⋊C4—21no—
458(C2×D3)⋊C4—61no—
459(C2×D3)⋊C4—61no—
460(C2×D3)⋊C4—61no—
461(C2×D3)⋊C4—61no—
462(C2×D3)⋊C4#6711yescharacteristic
463C4⋊Dic3C22×D311yescharacteristic
464C4⋊Dic3C22×D311yescharacteristic
465Dic3⋊C4#6711yescharacteristic
466C4×Dic3C22×D311yescharacteristic
467C2×C3⋊C8—31no—
468C2×C3⋊C8—31no—
469C2×C3⋊C8—31no—
470C2×C3⋊C8—31no—
471C2×C3⋊C8—61no—
472C2×C3⋊C8—61no—
473C2×C3⋊C8—62no—
474C2×C3⋊C8—62no—
475C2×C3⋊C8—62no—
476C2×C3⋊C8—64no—
477C2×C3⋊C8C22×D311yescharacteristic
478C2×C3⋊C8C22×D311yescharacteristic
479D24—62no—
480D24—121no—
481D3×C8—62no—
482C22×C32—21no—
483C22×C32—21no—
484C22×C32—22no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32—84no—
491C22×C32C2×D812yescomplemented
492C22×C32C22×D411yescharacteristic
493C2×C3⋊D3—22no—
494C2×C3⋊D3—41no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—41no—
498C2×C3⋊D3—41no—
499C2×C3⋊D3—84no—
500C2×C3×D3—21no—
501C2×C3×D3—21no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3—41no—
508C2×C3×D3—84no—
509C2×C3×D3C2×D812yescomplemented
510D32—84no—
511C32×C4—21no—
512C32×C4C22×D411yescharacteristic
513C32×C4H(5,𝔽2)11yescharacteristic
514C3×Dic3—21no—
515C3×Dic3—21no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C3×Dic3C2×D812yescomplemented
519C22×D4—31no—
520C22×D4—61no—
521C22×D4—91no—
522C22×D4—91no—
523C22×D4—181no—
524C22×D4D3211yescharacteristic, complemented
525C2×D8—31no—
526C2×D8—31no—
527C2×D8—91no—
528C2×D8—91no—
529C2×D8—91no—
530C2×D8—91no—
531C2×D8—91no—
532C2×D8—91no—
533C2×D8—91no—
534C2×D8—184no—
535C2×D8—184no—
536C22×C8—91no—
537C22×C8—91no—
538#127—31no—
539#127—91no—
540#121—31no—
541#121—31no—
542#121—31no—
543#121—61no—
544#121—91no—
545#121—181no—
546#120—61no—
547#120—61no—
548#120—181no—
549#120—181no—
550C4×D4—31no—
551C4×D4—31no—
552C4×D4—91no—
553#107—91no—
554C4⋊C8—91no—
555#102—31no—
556#102—31no—
557#102—91no—
558#102—91no—
559#102—91no—
560#102—91no—
561C22⋊C8—31no—
562C22⋊C8—91no—
563C4×C8—91no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—31no—
570C23×C3—41no—
571C23×C3—41no—
572C23×C3—42no—
573C23×C3—42no—
574C23×C3—44no—
575C23×C3—42no—
576C23×C3—42no—
577C23×C3—61no—
578C23×C3—61no—
579C23×C3—82no—
580C23×C3—81no—
581C23×C3—81no—
582C23×C3—82no—
583C23×C3—122no—
584C23×C3—122no—
585C23×C3—241no—
586C23×C3D3×D411yescharacteristic
587C23×C3C2×#6711yescharacteristic
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—42no—
591C22×D3—42no—
592C22×D3—61no—
593C22×D3—61no—
594C22×D3—61no—
595C22×D3—61no—
596C22×D3—81no—
597C22×D3—121no—
598C22×D3—121no—
599C22×D3—122no—
600C22×D3—122no—
601C22×D3—122no—
602C22×D3—122no—
603C22×D3—122no—
604C22×D3—124no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—242no—
609C22×D3—241no—
610C22×D3—241no—
611C22×D3—241no—
612C22×D3—241no—
613C22×D3—242no—
614C22×D3C2×#6711yescharacteristic
615C3×D4—22no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—22no—
623C3×D4—34no—
624C3×D4—41no—
625C3×D4—41no—
626C3×D4—42no—
627C3×D4—42no—
628C3×D4—44no—
629C3×D4—61no—
630C3×D4—61no—
631C3×D4—61no—
632C3×D4—61no—
633C3×D4—122no—
634C3×D4—122no—
635C3×D4—122no—
636C3×D4—122no—
637C3×D4—122no—
638C3×D4—241no—
639C3×D4D3×D412yescomplemented
640C3×D4D3×D412yescomplemented
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—21no—
648C2×C3×C4—21no—
649C2×C3×C4—31no—
650C2×C3×C4—31no—
651C2×C3×C4—31no—
652C2×C3×C4—61no—
653C2×C3×C4—61no—
654C2×C3×C4—61no—
655C2×C3×C4—61no—
656C2×C3×C4—122no—
657C2×C3×C4D3×D411yescharacteristic
658C2×C3×C4C2×#6711yescharacteristic
659C2×C3×C4C23×D311yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661#67—42no—
662#67—42no—
663#67—42no—
664#67—42no—
665#67—42no—
666#67—81no—
667#67—122no—
668#67—122no—
669#67—122no—
670#67—241no—
671#67#21314yescomplemented
672C2×Dic3—21no—
673C2×Dic3—21no—
674C2×Dic3—42no—
675C2×Dic3C2×#6711yescharacteristic
676C2×Dic3C2×#6711yescharacteristic
677C2×Dic3C2×#6711yescharacteristic
678D12—21no—
679D12—21no—
680D12—21no—
681D12—21no—
682D12—32no—
683D12—32no—
684D12—62no—
685D12—62no—
686D12—61no—
687D12—61no—
688D12—61no—
689D12—61no—
690D12—61no—
691D12—61no—
692D12—121no—
693D12—121no—
694D12—122no—
695D12—122no—
696D12—124no—
697D12—122no—
698D12—122no—
699D12—122no—
700D12—241no—
701C4×D3—21no—
702C4×D3—21no—
703C4×D3—122no—
704C4×D3—122no—
705C3×C8—61no—
706C3×C8—61no—
707C3⋊C8—21no—
708C3⋊C8—21no—
709C3⋊C8—32no—
710C3⋊C8—32no—
711C3⋊C8—62no—
712C3⋊C8—62no—
713C3⋊C8—61no—
714C3⋊C8—61no—
715C2×C32—22no—
716C2×C32—42no—
717C2×C32—81no—
718C2×C32D4211yescharacteristic
719C2×C32C22×D811yescharacteristic
720C2×C32#57611yescharacteristic
721C3⋊D3—42no—
722C3⋊D3—81no—
723C3×D3—22no—
724C3×D3—81no—
725C3×D3—81no—
726C24—21no—
727C24—61no—
728C24—181no—
729C24—181no—
730C2×D4—22no—
731C2×D4—21no—
732C2×D4—31no—
733C2×D4—31no—
734C2×D4—31no—
735C2×D4—41no—
736C2×D4—61no—
737C2×D4—61no—
738C2×D4—61no—
739C2×D4—62no—
740C2×D4—61no—
741C2×D4—61no—
742C2×D4—61no—
743C2×D4—91no—
744C2×D4—91no—
745C2×D4—121no—
746C2×D4—124no—
747C2×D4—182no—
748C2×D4—181no—
749C2×D4—181no—
750C2×D4—181no—
751C2×D4—182no—
752C2×D4—181no—
753C2×D4—181no—
754C2×D4—361no—
755C2×D4—361no—
756C2×D4—364no—
757C2×D4C2×D3211yescharacteristic
758C2×D4C2×D3211yescharacteristic
759C22×C4—31no—
760C22×C4—61no—
761C22×C4—181no—
762C22×C4C2×D3211yescharacteristic
763D8—62no—
764D8—94no—
765D8—121no—
766D8—182no—
767D8—182no—
768D8—182no—
769D8—182no—
770D8—182no—
771D8—361no—
772C2×C8—31no—
773C2×C8—31no—
774C2×C8—91no—
775C2×C8—91no—
776C2×C8—182no—
777C2×C8—182no—
778C4⋊C4—31no—
779C4⋊C4—31no—
780C4⋊C4—31no—
781C22⋊C4—31no—
782C22⋊C4—31no—
783C22⋊C4—61no—
784C22⋊C4—61no—
785C22⋊C4—61no—
786C22⋊C4—61no—
787C22⋊C4—181no—
788C22⋊C4—181no—
789C42—31no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—21no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—21no—
799C22×C3—22no—
800C22×C3—32no—
801C22×C3—42no—
802C22×C3—42no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—41no—
810C22×C3—41no—
811C22×C3—41no—
812C22×C3—41no—
813C22×C3—61no—
814C22×C3—61no—
815C22×C3—81no—
816C22×C3—81no—
817C22×C3—81no—
818C22×C3—81no—
819C22×C3—84no—
820C22×C3—84no—
821C22×C3—88no—
822C22×C3—121no—
823C22×C3—121no—
824C22×C3—121no—
825C22×C3—121no—
826C22×C3—121no—
827C22×C3—121no—
828C22×C3—244no—
829C22×C3D3×D812yescomplemented
830C22×C3C2×#21312yescomplemented
831C22×C3C2×D3×D411yescharacteristic
832C22×C3C22×#6711yescharacteristic
833C2×D3—21no—
834C2×D3—21no—
835C2×D3—41no—
836C2×D3—41no—
837C2×D3—41no—
838C2×D3—41no—
839C2×D3—41no—
840C2×D3—41no—
841C2×D3—62no—
842C2×D3—62no—
843C2×D3—84no—
844C2×D3—122no—
845C2×D3—121no—
846C2×D3—121no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—122no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—121no—
854C2×D3—121no—
855C2×D3—121no—
856C2×D3—241no—
857C2×D3—241no—
858C2×D3—241no—
859C2×D3—241no—
860C2×D3—244no—
861C2×D3—244no—
862C2×D3—244no—
863C2×D3—244no—
864C2×D3—248no—
865C2×D3C2×#21312yescomplemented
866C3×C4—22no—
867C3×C4—21no—
868C3×C4—21no—
869C3×C4—21no—
870C3×C4—21no—
871C3×C4—32no—
872C3×C4—61no—
873C3×C4—61no—
874C3×C4—121no—
875C3×C4—121no—
876C3×C4C2×D3×D411yescharacteristic
877C3×C4C2×D3×D411yescharacteristic
878C3×C4#100411yescharacteristic
879C3×C4#100411yescharacteristic
880Dic3—21no—
881Dic3—21no—
882Dic3—41no—
883Dic3—41no—
884Dic3C2×#21312yescomplemented
885C32D4×D811yescharacteristic, complemented, Sylow
886C23—21no—
887C23—21no—
888C23—31no—
889C23—42no—
890C23—42no—
891C23—61no—
892C23—61no—
893C23—81no—
894C23—122no—
895C23—122no—
896C23—181no—
897C23—181no—
898C23—241no—
899C23—362no—
900C23—362no—
901C23—362no—
902C23—362no—
903C23—721no—
904C23—721no—
905C23D3×#6711yescharacteristic
906D4—21no—
907D4—21no—
908D4—21no—
909D4—34no—
910D4—42no—
911D4—61no—
912D4—61no—
913D4—61no—
914D4—61no—
915D4—92no—
916D4—122no—
917D4—122no—
918D4—122no—
919D4—122no—
920D4—122no—
921D4—181no—
922D4—181no—
923D4—181no—
924D4—241no—
925D4—362no—
926D4—362no—
927D4—362no—
928D4—362no—
929D4—721no—
930D4#381112yescomplemented
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—31no—
934C2×C4—31no—
935C2×C4—31no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—61no—
939C2×C4—61no—
940C2×C4—122no—
941C2×C4—362no—
942C2×C4D3×#6711yescharacteristic
943C2×C4C22×D3211yescharacteristic
944C8—61no—
945C8—61no—
946C8—92no—
947C8—181no—
948C2×C3—24no—
949C2×C3—22no—
950C2×C3—22no—
951C2×C3—21no—
952C2×C3—21no—
953C2×C3—21no—
954C2×C3—42no—
955C2×C3—42no—
956C2×C3—62no—
957C2×C3—82no—
958C2×C3—82no—
959C2×C3—81no—
960C2×C3—81no—
961C2×C3—241no—
962C2×C3—241no—
963C2×C3#559011yescharacteristic
964C2×C3C2×D3×D811yescharacteristic
965C2×C3#577411yescharacteristic
966C2×C3C22×#21311yescharacteristic
967C2×C3D4×#6711yescharacteristic
968C2×C3#583511yescharacteristic
969D3—22no—
970D3—81no—
971D3—81no—
972D3—122no—
973D3—122no—
974D3—242no—
975D3—242no—
976D3—241no—
977D3—241no—
978C22—21no—
979C22—21no—
980C22—22no—
981C22—32no—
982C22—41no—
983C22—41no—
984C22—41no—
985C22—41no—
986C22—41no—
987C22—61no—
988C22—61no—
989C22—84no—
990C22—121no—
991C22—121no—
992C22—121no—
993C22—121no—
994C22—121no—
995C22—121no—
996C22—182no—
997C22—244no—
998C22—361no—
999C22—361no—
1000C22—361no—
1001C22—361no—
1002C22—361no—
1003C22—724no—
1004C22—724no—
1005C22D3×#21312yescomplemented
1006C22C2×D3×#6711yescharacteristic
1007C4—21no—
1008C4—32no—
1009C4—61no—
1010C4—61no—
1011C4—121no—
1012C4—121no—
1013C4C2×#381111yescharacteristic
1014C4#6433011yescharacteristic
1015C3—21no—
1016C3#8002411yescharacteristic, complemented
1017C3D4×#21311yescharacteristic, complemented
1018C2—22no—
1019C2—42no—
1020C2—62no—
1021C2—81no—
1022C2—241no—
1023C2—241no—
1024C2—362no—
1025C2—721no—
1026C2C2×D3×#21311yescharacteristic
1027C2#1059509711yescharacteristic
1028C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3753C2semidirect
2. C3×D4×#67C2semidirect
3. C2×D3×#213C2semidirect
4. #10595074C2semidirect
5. C3×#5217C2semidirect
6. #10591515C2semidirect
7. #10591482C2semidirect
8. #10591481C2semidirect
9. #10591449C2semidirect
10. #10591448C2semidirect
11. #10591429C2semidirect
12. #10591400C2semidirect
13. #10591168C2semidirect
14. #10591166C2semidirect
15. #67⋊(C3⋊C8)C2semidirect
18. C22×C32×D4C22semidirect
19. C22×C4⋊(C3⋊D3)C22semidirect
21. C2×C3×D3×D4C22semidirect
23. C2×D3×D12C22semidirect
26. C2×#3753C22semidirect
27. C2×#3753C22semidirect
28. C2×#3753C22semidirect
29. C22×C3⋊(C3⋊C8)C22semidirect
31. C3×#940C22semidirect
33. C3×#938C22semidirect
35. C3×D4×Dic3C22semidirect
36. C2×C3×#213C22semidirect
37. C2×C3×#213C22semidirect
38. C3×#930C22semidirect
39. C3×#930C22semidirect
44. #63911C22semidirect
46. #63909C22semidirect
47. #63894C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C3×#832C22semidirect
53. C3×#832C22semidirect
54. C3×#830C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63564C22semidirect
58. #63564C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. Dic3×C3⋊C8C22semidirect
64. D4×#67D3semidirect
74. #5217D3semidirect
134. #3753D4semidirect
162. C22×C3×D4C2×D3semidirect
163. C22×C3×D4C2×D3semidirect
168. C2×D3×D4C2×D3semidirect
186. #940C2×D3semidirect
188. #938C2×D3semidirect
191. D4×Dic3C2×D3semidirect
212. C2×#213C2×D3semidirect
213. C2×#213C2×D3semidirect
215. #930C2×D3semidirect
216. #930C2×D3semidirect
240. #832C2×D3semidirect
241. #832C2×D3semidirect
243. #830C2×D3semidirect
281. C32×D4C2×D4semidirect
290. C4⋊(C3⋊D3)C2×D4semidirect
297. C3×#67D8semidirect
316. C3⋊(C3⋊C8)C2×D4semidirect
491. C22×C32C2×D8semidirect
509. C2×C3×D3C2×D8semidirect
518. C3×Dic3C2×D8semidirect
524. C22×D4D32semidirect
639. C3×D4D3×D4semidirect
640. C3×D4D3×D4semidirect
671. #67#213semidirect
829. C22×C3D3×D8semidirect
830. C22×C3C2×#213semidirect
865. C2×D3C2×#213semidirect
884. Dic3C2×#213semidirect
885. C32D4×D8semidirect
930. D4#3811semidirect
1005. C22D3×#213semidirect
1016. C3#80024semidirect
1017. C3D4×#213semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C3×D4×#672
C2×D3×#2132
#105950742
C3×#52172
#105915152
#105914822
#105914812
#105914492
#105914482
#105914292
#105914002
#105911682
#105911662
#67⋊(C3⋊C8)2
D4×#2133
#800243