Finite Group Databasebeta

← #11806052

Subgroups — #11806052

Order 1152.

1333 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C3×#5211C211yesmaximal, characteristic, complemented
3C3×C4×#217C211yesmaximal, characteristic, complemented
4#10591704C212yesmaximal
5#10591703C212yesmaximal, complemented
6#10591360C211yesmaximal, characteristic, complemented
7#10591260C211yesmaximal, characteristic, complemented
8#10591257C211yesmaximal, characteristic, complemented
9#10591243C212yesmaximal, complemented
10#10591219C211yesmaximal, characteristic, complemented
11#10591202C212yesmaximal, complemented
12#74061—31nomaximal
13#73463—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×#3757C2211yescharacteristic
18C4×#638C418yescomplemented
19C2×#3752C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×C4×Dic3C2212yes—
25C2×#3724C2212yes—
26C2×#3724C2212yes—
27C2×#3722C2212yes—
28C2×#3722C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36#63579C2212yes—
37#63579C2212yes—
38C2×C4×#67—31no—
39C2×C4×#67—31no—
40C2×C4×#67—61no—
41C3×#381—31no—
42C3×C4×C22⋊C4—31no—
43#5211D311yescharacteristic, complemented
44C4×#217D311yescharacteristic, complemented
45#4957—32no—
46#4957—32no—
47#4945—32no—
48#4944—32no—
49#4940—32no—
50C4×Dic3⋊C4—32no—
51#4669—32no—
52#4666—31no—
53#4666—31no—
54#4664—31no—
55#4664—31no—
56#4650—31no—
57#4650—31no—
58#4649—32no—
59#4649—31no—
60#4649—31no—
61C24×C32C2311yescharacteristic
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4—42no—
64C22×C32×C4C2×C414yes—
65C22×C32×C4C2311yescharacteristic
66C22×C32×C4C2311yescharacteristic
67C2×#638—22no—
68C2×#638—22no—
69C2×#638C2×C414yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4×C3⋊D3—42no—
74C2×C4×C3⋊D3C2×C414yes—
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79#3757C2×C414yes—
80#3752C2×C414yes—
81#3750C2×C414yes—
82C4×C3⋊Dic3C2×C414yes—
83C3×#217—24no—
84C3×#217—42no—
85C3×C4×Dic3—42no—
86#3724—24no—
87#3724—24no—
88#3722—24no—
89#3722—42no—
90Dic32—24no—
91Dic32—42no—
92#2357—91noSylow
93C23×C3×C4—21no—
94C23×C3×C4C2×D311yescharacteristic
95C23×C3×C4C2×D311yescharacteristic
96C22×#67—31no—
97C22×#67—31no—
98C22×#67—61no—
99C22×C4×D3—31no—
100C22×C4×D3—31no—
101C22×C4×D3—61no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C42—32no—
105C2×#217—31no—
106C2×#217—31no—
107C2×#217—61no—
108C2×#217C2×D312yes—
109C2×#217C2×D312yes—
110C4×#67—38no—
111C4×#67—38no—
112C4×#67—68no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—61no—
120C2×Dic3⋊C4—31no—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4—32no—
126C2×Dic3⋊C4—61no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—32no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—61no—
134C2×C4×Dic3C2×D312yes—
135C3×#95—31no—
136C3×#95—31no—
137C3×#95—32no—
138C3×#95—31no—
139C3×#95—31no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95C2×D311yescharacteristic
145C3⋊#95C2×D311yescharacteristic
146C3⋊#95C2×D311yescharacteristic
147C3⋊#95C2×D311yescharacteristic
148C3⋊#95C2×D312yes—
149C23×C32—21no—
150C23×C32—21no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32C22×C412yes—
154C23×C32C2411yescharacteristic
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3C22×C412yes—
160C2×C32×C4—22no—
161C2×C32×C4—22no—
162C2×C32×C4—44no—
163C2×C32×C4C22×C412yes—
164C2×C32×C4C22×C412yes—
165#638—28no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3C22×C412yes—
169C2×C3⋊Dic3C22×C412yes—
170C2×C3⋊Dic3C22×C412yes—
171C2×C3⋊Dic3#4112yes—
172C2×C3⋊Dic3#4112yes—
173C4×C3⋊D3—44no—
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#4114yes—
186C2×C4×D4—91no—
187#390—92no—
188#388—92no—
189#388—92no—
190#382—91no—
191#381—31no—
192#381—91no—
193C4×C4⋊C4—91no—
194C4×C4⋊C4—92no—
195C4×C22⋊C4—31no—
196C4×C22⋊C4—91no—
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×C4C4×D314yes—
214C22×C3×C4C4×D314yes—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C2×#67—34no—
220C2×#67—34no—
221C2×#67—64no—
222C2×#67—62no—
223C2×#67—62no—
224C2×#67—62no—
225C2×#67—62no—
226C2×#67—64no—
227C2×#67—64no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—31no—
233C22×Dic3—31no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3C22×D312yes—
238C22×Dic3C22×D312yes—
239C22×Dic3C22×D312yes—
240C22×Dic3C22×D312yes—
241C2×C4×D3—34no—
242C2×C4×D3—34no—
243C2×C4×D3—64no—
244C2×C4×D3—122no—
245C2×C4×D3—122no—
246C2×C4×D3—124no—
247C3×C22⋊C4—64no—
248C3×C22⋊C4—122no—
249C3×C42—122no—
250#217—24no—
251#217—34no—
252#217—34no—
253#217—42no—
254#217—64no—
255(C2×D3)⋊C4—34no—
256(C2×D3)⋊C4—34no—
257(C2×D3)⋊C4—64no—
258(C2×D3)⋊C4—64no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—122no—
261(C2×D3)⋊C4—122no—
262Dic3⋊C4—34no—
263Dic3⋊C4—34no—
264Dic3⋊C4—64no—
265Dic3⋊C4—64no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269C4×Dic3—34no—
270C4×Dic3—34no—
271C4×Dic3—42no—
272C4×Dic3—64no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C4×Dic3—122no—
276C4×Dic3—122no—
277C22×C32—22no—
278C22×C32—22no—
279C22×C32—22no—
280C22×C32—42no—
281C22×C32—42no—
282C22×C32C23×C411yescharacteristic
283C22×C32C2×#4112yes—
284C22×C32C2×#4111yescharacteristic
285C22×C32C2×#4111yescharacteristic
286C22×C32H(5,𝔽2)12yes—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—42no—
291C2×C3⋊D3—42no—
292C32×C4—22no—
293C32×C4—22no—
294C3⋊Dic3—22no—
295C3⋊Dic3—22no—
296C3⋊Dic3#11714yes—
297C3×Dic3—24no—
298C3×Dic3—42no—
299C3×Dic3—42no—
300C3×Dic3—42no—
301C22×D4—91no—
302C23×C4—91no—
303C23×C4D3211yescharacteristic
304C4×D4—98no—
305C2×C4⋊C4—91no—
306C2×C4⋊C4—92no—
307C2×C4⋊C4—92no—
308C2×C22⋊C4—32no—
309C2×C22⋊C4—32no—
310C2×C22⋊C4—91no—
311C2×C22⋊C4—91no—
312C2×C22⋊C4—92no—
313C2×C22⋊C4—92no—
314C2×C42—32no—
315C2×C42—91no—
316C2×C42—92no—
317C2×C42—92no—
318#95—31no—
319#95—31no—
320#95—31no—
321#95—31no—
322#95—32no—
323#95—92no—
324#95—92no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—22no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—22no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3C2×C4×D312yes—
340C23×C3C2×C4×D312yes—
341C23×C3C23×D311yescharacteristic
342C23×C3C23×D311yescharacteristic
343C22×D3—32no—
344C22×D3—32no—
345C22×D3—62no—
346C22×D3—62no—
347C22×D3—62no—
348C22×D3—62no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—61no—
353C22×D3—61no—
354C22×D3—61no—
355C22×D3—61no—
356C22×D3—122no—
357C22×D3—122no—
358C2×C3×C4—24no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—22no—
365C2×C3×C4—34no—
366C2×C3×C4—42no—
367C2×C3×C4—44no—
368C2×C3×C4—44no—
369C2×C3×C4—48no—
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—62no—
379C2×C3×C4—62no—
380C2×C3×C4—62no—
381C2×C3×C4C2×C4×D312yes—
382C2×C3×C4C2×C4×D312yes—
383C2×C3×C4C2×C4×D312yes—
384C2×C3×C4C2×C4×D312yes—
385#67—68no—
386#67—68no—
387#67—616no—
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—22no—
399C2×Dic3—32no—
400C2×Dic3—32no—
401C2×Dic3—32no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—32no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—32no—
408C2×Dic3—32no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—122no—
419C2×Dic3—122no—
420C2×Dic3#23514yes—
421C4×D3—124no—
422C4×D3—124no—
423C4×D3—128no—
424C2×C32—42no—
425C2×C32C2×#11711yescharacteristic
426C2×C32C4×#4111yescharacteristic
427C2×C32#51811yescharacteristic
428C2×C32#55312yes—
429C2×C32#55912yes—
430C3⋊D3—42no—
431C24—91no—
432C24C2×D3211yescharacteristic
433C2×D4—94no—
434C2×D4—182no—
435C2×D4—182no—
436C22×C4—32no—
437C22×C4—32no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—42no—
441C22×C4—91no—
442C22×C4—91no—
443C22×C4—91no—
444C22×C4—94no—
445C22×C4—362no—
446C22×C4#62414yes—
447C22×C4C2×D3211yescharacteristic
448C22×C4C2×D3211yescharacteristic
449C4⋊C4—94no—
450C4⋊C4—184no—
451C4⋊C4—184no—
452C22⋊C4—64no—
453C22⋊C4—94no—
454C22⋊C4—94no—
455C22⋊C4—122no—
456C22⋊C4—184no—
457C22⋊C4—362no—
458C42—94no—
459C42—122no—
460C42—184no—
461C42—362no—
462C22×C3—24no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—22no—
469C22×C3—22no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—22no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—44no—
477C22×C3—44no—
478C22×C3—42no—
479C22×C3—42no—
480C22×C3—42no—
481C22×C3—42no—
482C22×C3C22×C4×D311yescharacteristic
483C22×C3C22×C4×D311yescharacteristic
484C22×C3C2×#23512yes—
485C22×C3#100412yes—
486C22×C3#100412yes—
487C22×C3D3×#4112yes—
488C22×C3D3×#4111yescharacteristic
489C22×C3D3×#4111yescharacteristic
490C22×C3D3×#4111yescharacteristic
491C22×C3D3×#4111yescharacteristic
492C2×D3—64no—
493C2×D3—62no—
494C2×D3—62no—
495C2×D3—62no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—122no—
500C2×D3—122no—
501C2×D3—124no—
502C2×D3—124no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C3×C4—24no—
508C3×C4—22no—
509C3×C4—22no—
510C3×C4—22no—
511C3×C4—22no—
512C3×C4—42no—
513C3×C4—64no—
514C3×C4—122no—
515C3×C4—122no—
516C3×C4—122no—
517Dic3—24no—
518Dic3—34no—
519Dic3—34no—
520Dic3—42no—
521Dic3—42no—
522Dic3—42no—
523Dic3—64no—
524Dic3—62no—
525Dic3—62no—
526Dic3—62no—
527Dic3—62no—
528Dic3—122no—
529Dic3—122no—
530C32#235711yescharacteristic, complemented, Sylow
531C23—22no—
532C23—21no—
533C23—21no—
534C23—22no—
535C23—92no—
536C23—182no—
537C23—181no—
538C23—181no—
539C23—182no—
540C23C2×#62412yes—
541C23C22×D3211yescharacteristic
542D4—188no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—34no—
546C2×C4—44no—
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—62no—
557C2×C4—62no—
558C2×C4—92no—
559C2×C4—92no—
560C2×C4—92no—
561C2×C4—92no—
562C2×C4—92no—
563C2×C4—182no—
564C2×C4—182no—
565C2×C4—364no—
566C2×C4C2×#62412yes—
567C2×C4C2×#62412yes—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—22no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—44no—
574C2×C3—42no—
575C2×C3—42no—
576C2×C3C4×#23511yescharacteristic
577C2×C3#548611yescharacteristic
578C2×C3#548611yescharacteristic
579C2×C3D3×#11711yescharacteristic
580C2×C3D3×#11711yescharacteristic
581C2×C3#552211yescharacteristic
582C2×C3#554012yes—
583C2×C3#555912yes—
584C2×C3#566112yes—
585C2×C3#566412yes—
586D3—124no—
587D3—122no—
588D3—122no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—42no—
593C22—42no—
594C22—182no—
595C22—182no—
596C22—182no—
597C22—362no—
598C22—362no—
599C22D3×#23512yes—
600C22#6430611yescharacteristic
601C22#6430611yescharacteristic
602C22C22×#62411yescharacteristic
603C22#6433012yes—
604C4—22no—
605C4—22no—
606C4—64no—
607C4—94no—
608C4—122no—
609C4—122no—
610C4—122no—
611C4—182no—
612C4—182no—
613C3—21no—
614C3#7346311yescharacteristic, complemented
615C3#7406111yescharacteristic, complemented
616C2—42no—
617C2—362no—
618C2#1059494412yes—
619C2#1059495411yescharacteristic
620C2#1059495712yes—
621C2#1059496911yescharacteristic
622C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2357
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×#5211C2semidirect
3. C3×C4×#217C2semidirect
5. #10591703C2semidirect
6. #10591360C2semidirect
7. #10591260C2semidirect
8. #10591257C2semidirect
9. #10591243C2semidirect
10. #10591219C2semidirect
11. #10591202C2semidirect
18. C4×#638C4semidirect
43. #5211D3semidirect
44. C4×#217D3semidirect
530. C32#2357semidirect
614. C3#73463semidirect
615. C3#74061semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C3×#52112
C3×C4×#2172
#105917042
#105917032
#105913602
#105912602
#105912572
#105912432
#105912192
#105912022
#740613
#734633