Finite Group Databasebeta

← #11800916

Subgroups — #11800916

Order 1152.

1773 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#638C211yesmaximal, characteristic
2C2×#63952C212yesmaximal
3C3×C4×#217C211yesmaximal, characteristic, complemented
4C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
5Dic3×#217C212yesmaximal, complemented
6#10591370C211yesmaximal, characteristic, complemented
7#10591260C211yesmaximal, characteristic, complemented
8#10591257C211yesmaximal, characteristic, complemented
9#10591252C211yesmaximal, characteristic, complemented
10#10591243C212yesmaximal, complemented
11#10591233C212yesmaximal, complemented
12#73436—31nomaximal
13#73322—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C22×#638C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C23×C3×Dic3C2212yes—
18C22×#624C2212yes—
19C2×#3757C2211yescharacteristic
20C4×#638C418yescomplemented
21C2×#3752C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2212yes—
25C2×C3×C4×Dic3C2212yes—
26C2×#3724C2212yes—
27C2×#3722C2212yes—
28C2×Dic32C2212yes—
29C2×Dic32C2212yes—
30C2×Dic32C2212yes—
31#63952C4116yescomplemented
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2211yescharacteristic
37#63579C2212yes—
38#63579C2212yes—
39C2×C4×#67—31no—
40C2×C4×#67—31no—
41C2×C4×#67—32no—
42C2×C4×#67—61no—
43C2×#67⋊C4—32no—
44C3×C4×C22⋊C4—31no—
45C2×C3×#95—31no—
46C4×#217—32no—
47C4×#217D311yescharacteristic, complemented
48C2×C3⋊#95D311yescharacteristic, complemented
49Dic3×C22⋊C4—32no—
50C4×(C2×D3)⋊C4—32no—
51C4×Dic3⋊C4—32no—
52#4666—32no—
53#4666—31no—
54#4666—31no—
55D3×#95—31no—
56D3×#95—31no—
57#4649—32no—
58#4649—31no—
59#4649—31no—
60#4648—31no—
61#4648—31no—
62C24×C32C2311yescharacteristic
63C23×C3⋊D3C2311yescharacteristic
64C22×C32×C4—42no—
65C22×C32×C4C2×C414yescomplemented
66C22×C32×C4C2311yescharacteristic
67C22×C32×C4C2311yescharacteristic
68C2×#638C2×C414yes—
69C2×#638C2×C418yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2311yescharacteristic
73C2×C4×C3⋊D3—42no—
74C2×C4×C3⋊D3C2×C414yescomplemented
75C22×C3×Dic3—42no—
76C22×C3×Dic3—42no—
77C22×C3×Dic3C2×C418yescomplemented
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×#624—42no—
83C2×#624—42no—
84C2×#624C2×C418yescomplemented
85#3757C2×C414yescomplemented
86#3752C2×C414yescomplemented
87#3750C2×C414yescomplemented
88C4×C3⋊Dic3C2×C414yescomplemented
89C3×#217C2×C418yescomplemented
90C3×C4×Dic3—42no—
91#3724C2×C418yescomplemented
92#3722C2×C418yescomplemented
93Dic32—42no—
94Dic32—42no—
95Dic32C2×C418yescomplemented
96#2275—91noSylow
97C23×C3×C4—21no—
98C23×C3×C4—32no—
99C23×C3×C4C2×D311yescharacteristic
100C23×C3×C4C2×D311yescharacteristic
101C22×#67—31no—
102C22×#67—31no—
103C22×#67—61no—
104C23×Dic3C2×D312yes—
105C22×C4×D3—31no—
106C22×C4×D3—31no—
107C22×C4×D3—32no—
108C22×C4×D3—32no—
109C22×C4×D3—61no—
110C2×C3×C22⋊C4—32no—
111C2×C3×C42—32no—
112C2×#217—31no—
113C2×#217—31no—
114C2×#217—61no—
115C2×#217C2×D312yes—
116C4×#67—38no—
117C4×#67—38no—
118C4×#67—316no—
119C4×#67—68no—
120C2×(C2×D3)⋊C4—31no—
121C2×(C2×D3)⋊C4—31no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—61no—
125C2×Dic3⋊C4—31no—
126C2×Dic3⋊C4—31no—
127C2×Dic3⋊C4—32no—
128C2×Dic3⋊C4—32no—
129C2×Dic3⋊C4—61no—
130C2×C4×Dic3—31no—
131C2×C4×Dic3—31no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—32no—
135C2×C4×Dic3—32no—
136C2×C4×Dic3—32no—
137C2×C4×Dic3—32no—
138C2×C4×Dic3—61no—
139C2×C4×Dic3C2×D312yes—
140#67⋊C4—316no—
141C3×#95—31no—
142C3×#95—31no—
143C3×#95—31no—
144C3×#95—32no—
145C3×#95—31no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95C2×D311yescharacteristic
151C3⋊#95C2×D311yescharacteristic
152C3⋊#95C2×D311yescharacteristic
153C3⋊#95C2×D311yescharacteristic
154C3⋊#95C2×D312yes—
155C23×C32—21no—
156C23×C32—22no—
157C23×C32—21no—
158C23×C32C22×C414yes—
159C23×C32C22×C412yes—
160C23×C32C2411yescharacteristic
161C22×C3⋊D3—21no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—21no—
164C22×C3⋊D3C22×C414yes—
165C22×C3⋊D3C22×C412yes—
166C2×C32×C4—22no—
167C2×C32×C4—22no—
168C2×C32×C4—44no—
169C2×C32×C4C22×C412yes—
170C2×C32×C4C22×C412yes—
171#638C42116yescomplemented
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C22×C412yes—
176C2×C3⋊Dic3C22×C412yes—
177C2×C3⋊Dic3C22×C414yes—
178C2×C3⋊Dic3C22×C412yes—
179C4×C3⋊D3—44no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—48no—
189C2×C3×Dic3C22×C414yes—
190C2×C3×Dic3C22×C414yes—
191C2×C3×Dic3C22×C414yes—
192C2×C3×Dic3C22×C414yes—
193#624—48no—
194C2×C4×D4—92no—
195C2×C4×D4—91no—
196C4×C4⋊C4—91no—
197C4×C4⋊C4—92no—
198C4×C22⋊C4—31no—
199C4×C22⋊C4—91no—
200C4×C22⋊C4—92no—
201C4×C22⋊C4—92no—
202#376—91no—
203C2×#95—31no—
204C2×#95—91no—
205C24×C3—21no—
206C24×C3C22×D311yescharacteristic
207C24×C3C22×D311yescharacteristic
208C23×D3—31no—
209C23×D3—31no—
210C23×D3—61no—
211C22×C3×C4—24no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4—32no—
218C22×C3×C4—38no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4—44no—
222C22×C3×C4—122no—
223C22×C3×C4—122no—
224C22×C3×C4C4×D314yescomplemented
225C22×C3×C4C4×D314yescomplemented
226C22×C3×C4C22×D311yescharacteristic
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—38no—
231C2×#67—38no—
232C2×#67—34no—
233C2×#67—34no—
234C2×#67—64no—
235C2×#67—68no—
236C22×Dic3—31no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—31no—
242C22×Dic3—42no—
243C22×Dic3—42no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—61no—
247C22×Dic3C4×D318yescomplemented
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D312yes—
252C2×C4×D3—34no—
253C2×C4×D3—34no—
254C2×C4×D3—38no—
255C2×C4×D3—38no—
256C2×C4×D3—64no—
257C2×C4×D3—122no—
258C2×C4×D3—122no—
259C2×C4×D3—122no—
260C2×C4×D3—122no—
261C2×C4×D3—122no—
262C2×C4×D3—122no—
263C2×C4×D3—124no—
264C3×C22⋊C4—38no—
265C3×C42—122no—
266#217—34no—
267#217—34no—
268#217—64no—
269#217C4×D318yescomplemented
270(C2×D3)⋊C4—34no—
271(C2×D3)⋊C4—34no—
272(C2×D3)⋊C4—38no—
273(C2×D3)⋊C4—38no—
274(C2×D3)⋊C4—64no—
275Dic3⋊C4—34no—
276Dic3⋊C4—34no—
277Dic3⋊C4—38no—
278Dic3⋊C4—38no—
279Dic3⋊C4—64no—
280C4×Dic3—34no—
281C4×Dic3—34no—
282C4×Dic3—38no—
283C4×Dic3—38no—
284C4×Dic3—42no—
285C4×Dic3—64no—
286C4×Dic3—122no—
287C4×Dic3—122no—
288C4×Dic3—122no—
289C4×Dic3—122no—
290C22×C32—24no—
291C22×C32—22no—
292C22×C32—22no—
293C22×C32—24no—
294C22×C32C2×C4214yes—
295C22×C32C23×C412yes—
296C22×C32C23×C411yescharacteristic
297C22×C32H(5,𝔽2)12yes—
298C22×C32H(5,𝔽2)11yescharacteristic
299C22×C322−1+411yescharacteristic
300C2×C3⋊D3—24no—
301C2×C3⋊D3—22no—
302C2×C3⋊D3—22no—
303C2×C3⋊D3—24no—
304C2×C3⋊D3C2×C4214yes—
305C32×C4—22no—
306C32×C4—22no—
307C3⋊Dic3—22no—
308C3⋊Dic3—22no—
309C3⋊Dic3C2×C4214yes—
310C3×Dic3—24no—
311C3×Dic3—24no—
312C3×Dic3—24no—
313C3×Dic3—24no—
314C22×D4—91no—
315C23×C4—32no—
316C23×C4—92no—
317C23×C4—91no—
318C23×C4D3211yescharacteristic
319C4×D4—916no—
320C4×D4—98no—
321C2×C4⋊C4—92no—
322C2×C4⋊C4—91no—
323C2×C22⋊C4—32no—
324C2×C22⋊C4—92no—
325C2×C22⋊C4—91no—
326C2×C22⋊C4—91no—
327C2×C42—32no—
328C2×C42—92no—
329C2×C42—91no—
330C2×C42—92no—
331C2×C42—92no—
332#95—31no—
333#95—32no—
334#95—31no—
335#95—31no—
336#95—31no—
337#95—92no—
338#95—92no—
339C23×C3—21no—
340C23×C3—22no—
341C23×C3—22no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—24no—
347C23×C3—22no—
348C23×C3—42no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3C2×C4×D314yes—
352C23×C3C2×C4×D314yes—
353C23×C3C2×C4×D312yes—
354C23×C3C2×C4×D312yes—
355C23×C3C23×D311yescharacteristic
356C23×C3C23×D311yescharacteristic
357C22×D3—34no—
358C22×D3—34no—
359C22×D3—32no—
360C22×D3—32no—
361C22×D3—62no—
362C22×D3—64no—
363C22×D3—61no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—61no—
367C22×D3—61no—
368C22×D3—61no—
369C22×D3—122no—
370C22×D3—121no—
371C22×D3—121no—
372C2×C3×C4—24no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—34no—
380C2×C3×C4—34no—
381C2×C3×C4—34no—
382C2×C3×C4—34no—
383C2×C3×C4—42no—
384C2×C3×C4—44no—
385C2×C3×C4—44no—
386C2×C3×C4—48no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—128no—
396C2×C3×C4C2×C4×D312yes—
397C2×C3×C4C2×C4×D312yes—
398C2×C3×C4C2×C4×D312yes—
399C2×C3×C4C2×C4×D312yes—
400#67—316no—
401#67—316no—
402#67—616no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—32no—
414C2×Dic3—32no—
415C2×Dic3—32no—
416C2×Dic3—32no—
417C2×Dic3—32no—
418C2×Dic3—32no—
419C2×Dic3—48no—
420C2×Dic3—62no—
421C2×Dic3—64no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—61no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—61no—
428C2×Dic3—61no—
429C2×Dic3—61no—
430C2×Dic3—122no—
431C2×Dic3—121no—
432C2×Dic3—121no—
433C2×Dic3C2×C4×D314yes—
434C2×Dic3C2×C4×D314yes—
435C2×Dic3C2×C4×D314yes—
436C2×Dic3C2×C4×D314yes—
437C4×D3—128no—
438C4×D3—128no—
439C4×D3—124no—
440C4×D3—124no—
441C4×D3—128no—
442C2×C32—24no—
443C2×C32C22×C4211yescharacteristic
444C2×C32#51811yescharacteristic
445C2×C32#51812yes—
446C2×C32#52011yescharacteristic
447C2×C32#52012yes—
448C3⋊D3—24no—
449C24—91no—
450C24C2×D3211yescharacteristic
451C2×D4—98no—
452C2×D4—94no—
453C22×C4—32no—
454C22×C4—32no—
455C22×C4—32no—
456C22×C4—32no—
457C22×C4—38no—
458C22×C4—42no—
459C22×C4—98no—
460C22×C4—91no—
461C22×C4—91no—
462C22×C4—91no—
463C22×C4—94no—
464C22×C4—122no—
465C22×C4—122no—
466C22×C4—362no—
467C22×C4—362no—
468C22×C4—362no—
469C22×C4#62414yescomplemented
470C22×C4C2×D3211yescharacteristic
471C22×C4C2×D3211yescharacteristic
472C4⋊C4—98no—
473C4⋊C4—94no—
474C22⋊C4—38no—
475C22⋊C4—98no—
476C22⋊C4—94no—
477C22⋊C4—94no—
478C42—98no—
479C42—94no—
480C42—122no—
481C42—362no—
482C42—362no—
483C22×C3—24no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—24no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—24no—
490C22×C3—24no—
491C22×C3—21no—
492C22×C3—22no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—22no—
496C22×C3—24no—
497C22×C3—42no—
498C22×C3—44no—
499C22×C3—42no—
500C22×C3—44no—
501C22×C3C42×D314yes—
502C22×C3C42×D314yes—
503C22×C3C22×C4×D312yes—
504C22×C3C22×C4×D312yes—
505C22×C3C22×C4×D311yescharacteristic
506C22×C3C22×C4×D311yescharacteristic
507C22×C3#100411yescharacteristic
508C22×C3#100412yes—
509C22×C3#100412yes—
510C22×C3#100711yescharacteristic
511C22×C3#100911yescharacteristic
512C22×C3#101011yescharacteristic
513C2×D3—34no—
514C2×D3—34no—
515C2×D3—64no—
516C2×D3—62no—
517C2×D3—62no—
518C2×D3—64no—
519C2×D3—64no—
520C2×D3—62no—
521C2×D3—62no—
522C2×D3—64no—
523C2×D3—64no—
524C2×D3—122no—
525C2×D3—124no—
526C2×D3—122no—
527C2×D3—124no—
528C3×C4—24no—
529C3×C4—22no—
530C3×C4—22no—
531C3×C4—22no—
532C3×C4—22no—
533C3×C4—42no—
534C3×C4—64no—
535C3×C4—64no—
536C3×C4—64no—
537C3×C4—64no—
538Dic3—24no—
539Dic3—24no—
540Dic3—24no—
541Dic3—24no—
542Dic3—34no—
543Dic3—34no—
544Dic3—64no—
545Dic3—62no—
546Dic3—62no—
547Dic3—62no—
548Dic3—62no—
549Dic3—122no—
550Dic3—122no—
551C32#227511yescharacteristic, complemented, Sylow
552C23—21no—
553C23—21no—
554C23—22no—
555C23—94no—
556C23—92no—
557C23—181no—
558C23—181no—
559C23—182no—
560C23C4×D3214yes—
561C23C2×#62412yes—
562C23C22×D3211yescharacteristic
563D4—916no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—34no—
567C2×C4—34no—
568C2×C4—34no—
569C2×C4—34no—
570C2×C4—44no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—94no—
580C2×C4—92no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—128no—
584C2×C4—181no—
585C2×C4—181no—
586C2×C4—182no—
587C2×C4—364no—
588C2×C4—368no—
589C2×C4C2×#62412yes—
590C2×C4C2×#62412yes—
591C2×C3—24no—
592C2×C3—24no—
593C2×C3—22no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3—22no—
598C2×C3—44no—
599C2×C3C2×C42×D311yescharacteristic
600C2×C3C2×C42×D311yescharacteristic
601C2×C3#548611yescharacteristic
602C2×C3#548611yescharacteristic
603C2×C3#548612yes—
604C2×C3#550412yes—
605C2×C3#550411yescharacteristic
606C2×C3#552311yescharacteristic
607C2×C3#554512yes—
608C2×C3#554612yes—
609D3—64no—
610D3—64no—
611D3—124no—
612C22—24no—
613C22—22no—
614C22—22no—
615C22—24no—
616C22—94no—
617C22—184no—
618C22—182no—
619C22—182no—
620C22—184no—
621C22C4×#62414yes—
622C22#6429711yescharacteristic
623C22C2×C4×D3212yes—
624C22#6430711yescharacteristic
625C22C22×#62411yescharacteristic
626C22#6433012yes—
627C4—22no—
628C4—22no—
629C4—64no—
630C4—64no—
631C4—64no—
632C4—64no—
633C4—94no—
634C4—182no—
635C4—182no—
636C3—21no—
637C3#7332211yescharacteristic, complemented
638C3#7343611yescharacteristic, complemented
639C2—24no—
640C2—184no—
641C2#1059487412yes—
642C2C2×C4×#62411yescharacteristic
643C2#1059499011yescharacteristic
644C2#1059505612yes—
645C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC23×C4D32
hypocenterC32#2275
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C3×C4×#217C2semidirect
4. C2×C3×C3⋊#95C2semidirect
5. Dic3×#217C2semidirect
6. #10591370C2semidirect
7. #10591260C2semidirect
8. #10591257C2semidirect
9. #10591252C2semidirect
10. #10591243C2semidirect
11. #10591233C2semidirect
20. C4×#638C4semidirect
31. #63952C4semidirect
47. C4×#217D3semidirect
48. C2×C3⋊#95D3semidirect
65. C22×C32×C4C2×C4semidirect
74. C2×C4×C3⋊D3C2×C4semidirect
77. C22×C3×Dic3C2×C4semidirect
84. C2×#624C2×C4semidirect
85. #3757C2×C4semidirect
86. #3752C2×C4semidirect
87. #3750C2×C4semidirect
88. C4×C3⋊Dic3C2×C4semidirect
89. C3×#217C2×C4semidirect
91. #3724C2×C4semidirect
92. #3722C2×C4semidirect
95. Dic32C2×C4semidirect
171. #638C42semidirect
224. C22×C3×C4C4×D3semidirect
225. C22×C3×C4C4×D3semidirect
247. C22×Dic3C4×D3semidirect
269. #217C4×D3semidirect
469. C22×C4#624semidirect
551. C32#2275semidirect
637. C3#73322semidirect
638. C3#73436semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
C2×#639522
C3×C4×#2172
C2×C3×C3⋊#952
Dic3×#2172
#105913702
#105912602
#105912572
#105912522
#105912432
#105912332
#734363
#733223