Finite Group Databasebeta

← #11803055

Subgroups — #11803055

Order 1152.

1349 conjugacy classes of subgroups.

The subgroup lattice has 623 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C3×C4×#217C211yesmaximal, characteristic, complemented
3C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
4#10591711C212yesmaximal
5#10591693C212yesmaximal, complemented
6#10591360C211yesmaximal, characteristic, complemented
7#10591355C211yesmaximal, characteristic, complemented
8#10591229C211yesmaximal, characteristic, complemented
9#10591219C211yesmaximal, characteristic, complemented
10#10591202C212yesmaximal, complemented
11#10591197C212yesmaximal, complemented
12#73568—31nomaximal
13#73367—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C2×#3757C2211yescharacteristic
19C4×#638C418yescomplemented
20C2×#3752C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×#217C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×#3724C2212yes—
26C2×#3724C2212yes—
27C2×#3722C2212yes—
28C2×#3722C2212yes—
29C3×C3⋊#95C2211yescharacteristic
30C3×C3⋊#95C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×#67—31no—
40C2×C4×#67—61no—
41C3×C4×C22⋊C4—31no—
42C2×C3×#95—31no—
43#5213—32no—
44#5210—32no—
45C4×#217D311yescharacteristic, complemented
46C2×C3⋊#95D311yescharacteristic, complemented
47#4958—32no—
48#4946—32no—
49#4940—32no—
50#4933—32no—
51#4669—32no—
52#4667—31no—
53#4667—31no—
54#4664—31no—
55#4664—31no—
56#4652—32no—
57#4651—31no—
58#4651—31no—
59#4650—31no—
60#4650—31no—
61C24×C32C2311yescharacteristic
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4—42no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C2×#638—24no—
68C2×#638C2×C414yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C2×C4×C3⋊D3—42no—
73C2×C4×C3⋊D3C2×C414yescomplemented
74C22×C3×Dic3—24no—
75C22×C3×Dic3—42no—
76C22×C3×Dic3—42no—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81#3757C2×C414yes—
82#3752C2×C414yescomplemented
83#3750C2×C414yescomplemented
84C4×C3⋊Dic3C2×C414yescomplemented
85C3×#217—24no—
86C3×C4×Dic3—42no—
87#3724—42no—
88#3724—42no—
89#3722—42no—
90#3722—42no—
91#2318—91noSylow
92C23×C3×C4—21no—
93C23×C3×C4—32no—
94C23×C3×C4C2×D311yescharacteristic
95C23×C3×C4C2×D311yescharacteristic
96C22×#67—31no—
97C22×#67—31no—
98C22×#67—61no—
99C23×Dic3C2×D312yes—
100C22×C4×D3—31no—
101C22×C4×D3—31no—
102C22×C4×D3—61no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C42—32no—
105C2×#217—31no—
106C2×#217—31no—
107C2×#217—61no—
108C2×#217C2×D312yes—
109C4×#67—38no—
110C4×#67—38no—
111C4×#67—68no—
112C2×(C2×D3)⋊C4—31no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—61no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—31no—
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—61no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—61no—
129C2×C4×Dic3C2×D312yes—
130C3×#95—31no—
131C3×#95—31no—
132C3×#95—31no—
133C3×#95—31no—
134C3×#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95C2×D311yescharacteristic
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D311yescharacteristic
146C3⋊#95C2×D311yescharacteristic
147C3⋊#95C2×D312yes—
148C23×C32—21no—
149C23×C32—22no—
150C23×C32—21no—
151C23×C32C22×C412yes—
152C23×C32#4114yes—
153C23×C32C2411yescharacteristic
154C22×C3⋊D3—22no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3C22×C412yes—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4—44no—
162C2×C32×C4C22×C412yes—
163C2×C32×C4C22×C412yes—
164#638—28no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3C22×C412yes—
170C2×C3⋊Dic3C22×C412yes—
171C2×C3⋊Dic3C22×C412yes—
172C4×C3⋊D3—44no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—48no—
186C2×C4×D4—91no—
187#388—92no—
188#387—92no—
189#386—92no—
190#385—92no—
191#383—91no—
192#382—91no—
193#381—91no—
194#380—91no—
195C4×C22⋊C4—31no—
196C2×#95—31no—
197C24×C3—21no—
198C24×C3C22×D311yescharacteristic
199C24×C3C22×D311yescharacteristic
200C23×D3—31no—
201C23×D3—31no—
202C23×D3—61no—
203C22×C3×C4—24no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—42no—
211C22×C3×C4—42no—
212C22×C3×C4—44no—
213C22×C3×C4—64no—
214C22×C3×C4—122no—
215C22×C3×C4—122no—
216C22×C3×C4C4×D314yes—
217C22×C3×C4C4×D314yes—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C2×#67—34no—
223C2×#67—34no—
224C2×#67—64no—
225C2×#67—68no—
226C2×#67—64no—
227C2×#67—64no—
228C22×Dic3—24no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—31no—
235C22×Dic3—42no—
236C22×Dic3—42no—
237C22×Dic3—61no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3C22×D312yes—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C2×C4×D3—34no—
245C2×C4×D3—34no—
246C2×C4×D3—64no—
247C2×C4×D3—122no—
248C2×C4×D3—122no—
249C2×C4×D3—124no—
250C3×C22⋊C4—64no—
251C3×C42—122no—
252#217—24no—
253#217—34no—
254#217—34no—
255#217—64no—
256(C2×D3)⋊C4—34no—
257(C2×D3)⋊C4—34no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—122no—
260(C2×D3)⋊C4—122no—
261(C2×D3)⋊C4—122no—
262(C2×D3)⋊C4—122no—
263Dic3⋊C4—34no—
264Dic3⋊C4—34no—
265Dic3⋊C4—64no—
266Dic3⋊C4—122no—
267Dic3⋊C4—122no—
268Dic3⋊C4—122no—
269Dic3⋊C4—122no—
270C4×Dic3—34no—
271C4×Dic3—34no—
272C4×Dic3—42no—
273C4×Dic3—64no—
274C22×C32—22no—
275C22×C32—22no—
276C22×C32—24no—
277C22×C32—24no—
278C22×C32#11714yes—
279C22×C32C23×C411yescharacteristic
280C22×C32C2×#4112yes—
281C22×C32H(5,𝔽2)12yes—
282C22×C32H(5,𝔽2)11yescharacteristic
283C22×C322−1+411yescharacteristic
284C2×C3⋊D3—22no—
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—42no—
288C2×C3⋊D3—42no—
289C32×C4—22no—
290C32×C4—22no—
291C3⋊Dic3—22no—
292C3⋊Dic3—22no—
293C3⋊Dic3—22no—
294C3×Dic3—42no—
295C3×Dic3—42no—
296C3×Dic3—42no—
297C3×Dic3—42no—
298C22×D4—91no—
299C23×C4—32no—
300C23×C4—91no—
301C23×C4D3211yescharacteristic
302C4×D4—98no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—92no—
305C2×C4⋊C4—92no—
306C2×C22⋊C4—32no—
307C2×C22⋊C4—91no—
308C2×C22⋊C4—91no—
309C2×C22⋊C4—92no—
310C2×C22⋊C4—92no—
311C2×C42—32no—
312C2×C42—91no—
313#95—31no—
314#95—31no—
315#95—32no—
316#95—31no—
317#95—31no—
318#95—92no—
319#95—92no—
320#95—92no—
321#95—92no—
322C23×C3—21no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—24no—
330C23×C3—22no—
331C23×C3—42no—
332C23×C3—41no—
333C23×C3—41no—
334C23×C3C2×C4×D312yes—
335C23×C3C2×C4×D312yes—
336C23×C3#23514yes—
337C23×C3#23514yes—
338C23×C3C23×D311yescharacteristic
339C23×C3C23×D311yescharacteristic
340C22×D3—32no—
341C22×D3—32no—
342C22×D3—62no—
343C22×D3—64no—
344C22×D3—62no—
345C22×D3—62no—
346C22×D3—61no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—61no—
350C22×D3—61no—
351C22×D3—61no—
352C22×D3—122no—
353C22×D3—121no—
354C22×D3—121no—
355C2×C3×C4—24no—
356C2×C3×C4—22no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—42no—
363C2×C3×C4—44no—
364C2×C3×C4—44no—
365C2×C3×C4—48no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—62no—
371C2×C3×C4—62no—
372C2×C3×C4—62no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—128no—
379C2×C3×C4C2×C4×D312yes—
380C2×C3×C4C2×C4×D312yes—
381C2×C3×C4C2×C4×D312yes—
382C2×C3×C4C2×C4×D312yes—
383#67—616no—
384#67—68no—
385#67—68no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—32no—
399C2×Dic3—32no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—48no—
405C2×Dic3—62no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—64no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—61no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—122no—
418C2×Dic3—121no—
419C2×Dic3—121no—
420C4×D3—124no—
421C4×D3—124no—
422C4×D3—128no—
423C2×C32—24no—
424C2×C32C2×#11711yescharacteristic
425C2×C32#51811yescharacteristic
426C2×C32#52011yescharacteristic
427C2×C32#53812yes—
428C2×C32#53912yes—
429C3⋊D3—42no—
430C24—91no—
431C24C2×D3211yescharacteristic
432C2×D4—94no—
433C2×D4—184no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—32no—
437C22×C4—32no—
438C22×C4—42no—
439C22×C4—64no—
440C22×C4—91no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—94no—
444C22×C4—122no—
445C22×C4—122no—
446C22×C4—362no—
447C22×C4#62414yes—
448C22×C4C2×D3211yescharacteristic
449C22×C4C2×D3211yescharacteristic
450C4⋊C4—94no—
451C4⋊C4—362no—
452C4⋊C4—362no—
453C22⋊C4—64no—
454C22⋊C4—94no—
455C22⋊C4—94no—
456C22⋊C4—362no—
457C22⋊C4—362no—
458C42—94no—
459C42—122no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—24no—
463C22×C3—22no—
464C22×C3—24no—
465C22×C3—22no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—21no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—22no—
473C22×C3—24no—
474C22×C3—42no—
475C22×C3—44no—
476C22×C3—42no—
477C22×C3—44no—
478C22×C3#87214yes—
479C22×C3#87214yes—
480C22×C3C22×C4×D311yescharacteristic
481C22×C3C22×C4×D311yescharacteristic
482C22×C3C2×#23512yes—
483C22×C3C2×#23512yes—
484C22×C3#100411yescharacteristic
485C22×C3#100412yes—
486C22×C3#100412yes—
487C22×C3#100711yescharacteristic
488C22×C3#100911yescharacteristic
489C22×C3#101011yescharacteristic
490C2×D3—64no—
491C2×D3—62no—
492C2×D3—62no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—124no—
500C2×D3—124no—
501C2×D3—122no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C3×C4—24no—
506C3×C4—22no—
507C3×C4—22no—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—42no—
511C3×C4—122no—
512C3×C4—122no—
513C3×C4—122no—
514C3×C4—122no—
515Dic3—42no—
516Dic3—42no—
517Dic3—42no—
518Dic3—42no—
519Dic3—64no—
520Dic3—62no—
521Dic3—62no—
522Dic3—62no—
523Dic3—62no—
524Dic3—62no—
525Dic3—62no—
526Dic3—122no—
527Dic3—122no—
528C32#231811yescharacteristic, complemented, Sylow
529C23—21no—
530C23—21no—
531C23—22no—
532C23—92no—
533C23—181no—
534C23—182no—
535C23—181no—
536C23—182no—
537C23#379814yes—
538C23C2×#62412yes—
539C23C22×D3211yescharacteristic
540D4—188no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—44no—
544C2×C4—62no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—62no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—92no—
557C2×C4—92no—
558C2×C4—92no—
559C2×C4—128no—
560C2×C4—181no—
561C2×C4—182no—
562C2×C4—181no—
563C2×C4—182no—
564C2×C4—364no—
565C2×C4C2×#62412yes—
566C2×C4C2×#62412yes—
567C2×C3—24no—
568C2×C3—24no—
569C2×C3—22no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—22no—
574C2×C3—44no—
575C2×C3C2×#87211yescharacteristic
576C2×C3C2×#87211yescharacteristic
577C2×C3#548611yescharacteristic
578C2×C3#548611yescharacteristic
579C2×C3#549412yes—
580C2×C3#550411yescharacteristic
581C2×C3#551512yes—
582C2×C3#552311yescharacteristic
583C2×C3#556012yes—
584C2×C3#556412yes—
585D3—124no—
586D3—122no—
587D3—122no—
588C22—24no—
589C22—22no—
590C22—22no—
591C22—24no—
592C22—182no—
593C22—182no—
594C22—182no—
595C22—362no—
596C22—362no—
597C22#6387414yes—
598C22#6429711yescharacteristic
599C22C2×#379812yes—
600C22#6430711yescharacteristic
601C22C22×#62411yescharacteristic
602C22#6433012yes—
603C4—22no—
604C4—22no—
605C4—122no—
606C4—122no—
607C4—122no—
608C4—122no—
609C4—182no—
610C4—182no—
611C4—182no—
612C3—21no—
613C3#7336711yescharacteristic, complemented
614C3#7356811yescharacteristic, complemented
615C2—24no—
616C2—362no—
617C2#1059484212yes—
618C2C2×#6387411yescharacteristic
619C2#1059499011yescharacteristic
620C2#1059503612yes—
621C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×#217C2semidirect
3. C2×C3×C3⋊#95C2semidirect
5. #10591693C2semidirect
6. #10591360C2semidirect
7. #10591355C2semidirect
8. #10591229C2semidirect
9. #10591219C2semidirect
10. #10591202C2semidirect
11. #10591197C2semidirect
19. C4×#638C4semidirect
45. C4×#217D3semidirect
46. C2×C3⋊#95D3semidirect
73. C2×C4×C3⋊D3C2×C4semidirect
82. #3752C2×C4semidirect
83. #3750C2×C4semidirect
84. C4×C3⋊Dic3C2×C4semidirect
528. C32#2318semidirect
613. C3#73367semidirect
614. C3#73568semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C3×C4×#2172
C2×C3×C3⋊#952
#105917112
#105916932
#105913602
#105913552
#105912292
#105912192
#105912022
#105911972
#735683
#733673