Finite Group Databasebeta

← #11819076

Subgroups — #11819076

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64106C211yesmaximal, characteristic
2C2×C3×#888C211yesmaximal, characteristic, complemented
3C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
4#10591325C211yesmaximal, characteristic
5#10591310C212yesmaximal
6#10591289C212yesmaximal
7C4×#3722C211yesmaximal, characteristic
8#10591226C212yesmaximal, complemented
9#10591220C212yesmaximal, complemented
10#10591213C211yesmaximal, characteristic, complemented
11#10591213C211yesmaximal, characteristic, complemented
12#83258—31nomaximal
13#73789—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×#634C2211yescharacteristic
16C22×C3×Dic6C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3752C2212yes—
19C2×C4⋊(C3⋊Dic3)C2212yes—
20#64106—24no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2212yes—
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2212yes—
27C3×#888—24no—
28C2×#3722C2211yescharacteristic
29C2×#3722C2212yes—
30C2×#3722C2211yescharacteristic
31C3×C3⋊#95C2212yes—
32#63579C2211yescharacteristic
33#63579C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×C3×C4⋊Q8—31no—
40C2×#897—31no—
41C2×#897—31no—
42C2×#897—61no—
43C2×#888D311yescharacteristic, complemented
44C3×C4×C4⋊C4—31no—
45#5231—32no—
46#5229—32no—
47#4990—32no—
48#4987—31no—
49#4987—31no—
50#4986—32no—
51Dic3×C4⋊C4D311yescharacteristic, complemented
52#4973—31no—
53#4973—31no—
54#4940—32no—
55C4×(C2×D3)⋊C4—31no—
56C4×(C2×D3)⋊C4—31no—
57#4929—32no—
58#4929—31no—
59#4929—31no—
60#4673—32no—
61#4659—32no—
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3C2312yes—
66C22×C3⋊Dic3C2311yescharacteristic
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×#634—22no—
71C2×#634—22no—
72C2×#634—22no—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2311yescharacteristic
79C2×C3×Dic6—24no—
80C2×C3×Dic6—24no—
81C2×C3×Dic6—42no—
82C32×C4⋊C4D414yes—
83#3752—24no—
84C4⋊(C3⋊Dic3)—24no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3—22no—
87C3×Dic3⋊C4—24no—
88C3×C4×Dic3—22no—
89C3×C4×Dic3—22no—
90C3×C4×Dic3—42no—
91#3722—22no—
92#3722—42no—
93#3722Q814yescomplemented
94#2492—91noSylow
95C22×C3×Q8—32no—
96C22×C4×D3—31no—
97C22×C4×D3—31no—
98C22×C4×D3—61no—
99C22×Dic6—31no—
100C22×Dic6—31no—
101C22×Dic6—61no—
102C22×Dic6C2×D312yes—
103C3×C4⋊Q8—64no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—32no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—31no—
108C2×C3×C4⋊C4C2×D311yescharacteristic
109C2×C3×C4⋊C4C2×D311yescharacteristic
110C2×C3×C42—31no—
111C2×C3×C42—31no—
112C2×C3×C42—32no—
113C2×(C2×D3)⋊C4—31no—
114C2×(C2×D3)⋊C4—31no—
115C2×(C2×D3)⋊C4—32no—
116C2×(C2×D3)⋊C4—32no—
117C2×(C2×D3)⋊C4—31no—
118C2×(C2×D3)⋊C4—31no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—62no—
122C2×C4⋊Dic3—32no—
123C2×C4⋊Dic3—32no—
124C2×C4⋊Dic3—62no—
125C2×C4⋊Dic3C2×D311yescharacteristic
126C2×C4⋊Dic3C2×D311yescharacteristic
127C2×Dic3⋊C4C2×D312yes—
128C2×C4×Dic3C2×D311yescharacteristic
129C2×C4×Dic3C2×D311yescharacteristic
130C2×C4×Dic3C2×D312yes—
131#897—68no—
132#897—64no—
133#897—64no—
134#888—24no—
135C3×#95—32no—
136C3⋊#95—31no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95—32no—
140C3⋊#95—32no—
141C3⋊#95—31no—
142C3⋊#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—31no—
146C3⋊#95—31no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95—32no—
150C3⋊#95C2×D312yes—
151C23×C32C2411yescharacteristic
152C22×C3⋊D3—21no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3C2×Q812yes—
159C2×C32×C4—22no—
160C2×C32×C4—22no—
161C2×C32×C4C2×D414yes—
162C2×C32×C4C2×D412yes—
163C2×C32×C4#4112yes—
164C2×C32×C4#4112yes—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C4×C3⋊D3—44no—
172#634—44no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C2×C3×Dic3C2×Q812yes—
189C2×C3×Dic3C2×Q812yes—
190C2×C3×Dic3#4112yes—
191C3×Dic6—48no—
192C2×C4⋊Q8—31no—
193C2×C22⋊Q8—91no—
194#400—92no—
195#393—92no—
196#391—91no—
197#391—91no—
198#391—92no—
199#388—92no—
200#380—91no—
201C4×C4⋊C4—31no—
202C4×C22⋊C4—91no—
203C23×D3—31no—
204C23×D3—31no—
205C23×D3—61no—
206C2×C3×Q8—64no—
207C2×C3×Q8—64no—
208C2×C3×Q8—122no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—31no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—31no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4C22×D312yes—
218C22×C3×C4C22×D312yes—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—32no—
224C22×Dic3—32no—
225C22×Dic3—61no—
226C22×Dic3—62no—
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D312yes—
229C22×Dic3C22×D312yes—
230C22×Dic3C22×D311yescharacteristic
231C22×Dic3C22×D311yescharacteristic
232C22×Dic3C22×D311yescharacteristic
233C2×C4×D3—64no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C2×C4×D3—62no—
240C2×C4×D3—122no—
241C2×C4×D3—122no—
242C2×Dic6—24no—
243C2×Dic6—24no—
244C2×Dic6—42no—
245C2×Dic6—64no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—62no—
251C2×Dic6—62no—
252C2×Dic6—122no—
253C2×Dic6—122no—
254C3×C4⋊C4—24no—
255C3×C4⋊C4—64no—
256C3×C4⋊C4—62no—
257C3×C4⋊C4—62no—
258C3×C4⋊C4D1214yes—
259C3×C4⋊C4#6714yes—
260C3×C42—62no—
261C3×C42—62no—
262C3×C42—122no—
263(C2×D3)⋊C4—34no—
264(C2×D3)⋊C4—34no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—68no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—122no—
271(C2×D3)⋊C4—122no—
272C4⋊Dic3—22no—
273C4⋊Dic3—22no—
274C4⋊Dic3—68no—
275C4⋊Dic3—64no—
276C4⋊Dic3—64no—
277Dic3⋊C4—24no—
278C4×Dic3—22no—
279C4×Dic3—22no—
280C4×Dic3—42no—
281C22×C32C22×D411yescharacteristic
282C22×C32C22×Q811yescharacteristic
283C22×C32C2×#4111yescharacteristic
284C22×C32C2×#4111yescharacteristic
285C22×C32C2×#4111yescharacteristic
286C22×C32H(5,𝔽2)11yescharacteristic
287C22×C322−1+411yescharacteristic
288C2×C3⋊D3—22no—
289C2×C3⋊D3—22no—
290C2×C3⋊D3—22no—
291C2×C3⋊D3—41no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C32×C4—24no—
296C32×C4#12414yes—
297C3⋊Dic3—42no—
298C3⋊Dic3—41no—
299C3×Dic3—22no—
300C3×Dic3—22no—
301C3×Dic3—22no—
302C3×Dic3—42no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C22×Q8—32no—
306C22×Q8—91no—
307C23×C4—91no—
308C4⋊Q8—64no—
309C22⋊Q8—184no—
310C2×C4⋊C4—31no—
311C2×C4⋊C4—32no—
312C2×C4⋊C4—31no—
313C2×C4⋊C4—92no—
314C2×C4⋊C4D3211yescharacteristic
315C2×C22⋊C4—91no—
316C2×C22⋊C4—91no—
317C2×C22⋊C4—92no—
318C2×C22⋊C4—92no—
319C2×C42—31no—
320C2×C42—31no—
321C2×C42—32no—
322#95—32no—
323#95—91no—
324#95—91no—
325#95—92no—
326#95—92no—
327#95—92no—
328#95—92no—
329#95—92no—
330C23×C3—21no—
331C23×C3C23×D311yescharacteristic
332C23×C3C23×D311yescharacteristic
333C22×D3—32no—
334C22×D3—32no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—61no—
339C22×D3—61no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—61no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—61no—
346C22×D3—61no—
347C22×D3—61no—
348C22×D3—61no—
349C22×D3—61no—
350C22×D3—121no—
351C22×D3—121no—
352C22×D3—121no—
353C22×D3—121no—
354C3×Q8—128no—
355C2×C3×C4—22no—
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—24no—
363C2×C3×C4—32no—
364C2×C3×C4—32no—
365C2×C3×C4—32no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—61no—
369C2×C3×C4—61no—
370C2×C3×C4—61no—
371C2×C3×C4—61no—
372C2×C3×C4—61no—
373C2×C3×C4—61no—
374C2×C3×C4—62no—
375C2×C3×C4—61no—
376C2×C3×C4—62no—
377C2×C3×C4—62no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—61no—
381C2×C3×C4—62no—
382C2×C3×C4—62no—
383C2×C3×C4C2×D1214yes—
384C2×C3×C4C2×D1212yes—
385C2×C3×C4#23512yes—
386C2×C3×C4#23512yes—
387C2×C3×C4#23912yes—
388C2×C3×C4#23912yes—
389C2×C3×C4C2×#6714yes—
390C2×C3×C4C2×#6712yes—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—21no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—62no—
407C2×Dic3—64no—
408C2×Dic3—61no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—61no—
413C2×Dic3—61no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—62no—
420C2×Dic3—122no—
421C2×Dic3—122no—
422C2×Dic3—121no—
423C2×Dic3—121no—
424C2×Dic3#23712yes—
425C2×Dic3D3×Q812yes—
426C2×Dic3D3×Q812yes—
427C4×D3—128no—
428C4×D3—124no—
429C4×D3—124no—
430Dic6—48no—
431Dic6—128no—
432Dic6—124no—
433Dic6—124no—
434C2×C32C2×#12411yescharacteristic
435C2×C32#53311yescharacteristic
436C2×C32#54211yescharacteristic
437C2×C32#54611yescharacteristic
438C2×C32D4×Q811yescharacteristic
439C2×C32#55411yescharacteristic
440C2×C32#55611yescharacteristic
441C3⋊D3—42no—
442C24—91no—
443C2×Q8—64no—
444C2×Q8—64no—
445C2×Q8—122no—
446C2×Q8—182no—
447C2×Q8—182no—
448C2×Q8—182no—
449C22×C4—31no—
450C22×C4—31no—
451C22×C4—31no—
452C22×C4—31no—
453C22×C4—32no—
454C22×C4—32no—
455C22×C4—92no—
456C22×C4—91no—
457C22×C4—182no—
458C22×C4—182no—
459C22×C4—182no—
460C22×C4C2×D3212yes—
461C22×C4C2×D3211yescharacteristic
462C4⋊C4—62no—
463C4⋊C4—64no—
464C4⋊C4—62no—
465C4⋊C4—184no—
466C4⋊C4#62614yes—
467C22⋊C4—94no—
468C22⋊C4—182no—
469C22⋊C4—184no—
470C22⋊C4—362no—
471C42—62no—
472C42—62no—
473C42—122no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3C22×D1211yescharacteristic
482C22×C3C2×#23511yescharacteristic
483C22×C3C2×#23511yescharacteristic
484C22×C3C2×#23711yescharacteristic
485C22×C3#100411yescharacteristic
486C22×C3#100411yescharacteristic
487C22×C3C2×D3×Q811yescharacteristic
488C22×C3C2×D3×Q811yescharacteristic
489C22×C3C2×#23911yescharacteristic
490C22×C3C2×#23911yescharacteristic
491C22×C3#100711yescharacteristic
492C22×C3D3×#4111yescharacteristic
493C22×C3#101011yescharacteristic
494C22×C3C22×#6711yescharacteristic
495C2×D3—64no—
496C2×D3—62no—
497C2×D3—62no—
498C2×D3—62no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—122no—
503C2×D3—122no—
504C2×D3—122no—
505C2×D3—122no—
506C2×D3—122no—
507C2×D3—122no—
508C2×D3—121no—
509C2×D3—121no—
510C2×D3—121no—
511C2×D3—121no—
512C2×D3—121no—
513C2×D3—121no—
514C2×D3—121no—
515C2×D3—121no—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4—24no—
519C3×C4—44no—
520C3×C4—62no—
521C3×C4—62no—
522C3×C4—62no—
523C3×C4—121no—
524C3×C4—122no—
525C3×C4—122no—
526C3×C4#87514yes—
527C3×C4#94714yes—
528Dic3—22no—
529Dic3—22no—
530Dic3—22no—
531Dic3—41no—
532Dic3—42no—
533Dic3—42no—
534Dic3—124no—
535Dic3—122no—
536Dic3—122no—
537Dic3—121no—
538Dic3—122no—
539Dic3—121no—
540C32#249211yescharacteristic, complemented, Sylow
541C23—92no—
542C23—181no—
543C23—181no—
544C23—181no—
545C23—181no—
546C23—181no—
547C23—181no—
548C23C22×D3211yescharacteristic
549Q8—128no—
550Q8—364no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—32no—
554C2×C4—32no—
555C2×C4—32no—
556C2×C4—61no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—61no—
561C2×C4—61no—
562C2×C4—61no—
563C2×C4—62no—
564C2×C4—61no—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—61no—
570C2×C4—62no—
571C2×C4—181no—
572C2×C4—181no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—181no—
577C2×C4—364no—
578C2×C4#379912yes—
579C2×C4#379912yes—
580C2×C4C2×#62614yes—
581C2×C4C2×#62612yes—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3C2×#87511yescharacteristic
590C2×C3#551111yescharacteristic
591C2×C3#553311yescharacteristic
592C2×C3#555411yescharacteristic
593C2×C3#556111yescharacteristic
594C2×C3Q8×D1211yescharacteristic
595C2×C3#557811yescharacteristic
596C2×C3#572811yescharacteristic
597C2×C3#573011yescharacteristic
598C2×C3#573211yescharacteristic
599C2×C3#573311yescharacteristic
600C2×C3#580611yescharacteristic
601C2×C3C2×#94711yescharacteristic
602C2×C3Q8×#6711yescharacteristic
603D3—124no—
604D3—122no—
605D3—122no—
606C22—182no—
607C22—182no—
608C22—182no—
609C22—361no—
610C22—361no—
611C22—361no—
612C22—361no—
613C22C2×#379911yescharacteristic
614C22C2×#379911yescharacteristic
615C22D3×#23711yescharacteristic
616C22#6431311yescharacteristic
617C22#6431511yescharacteristic
618C22D32×Q811yescharacteristic
619C22C22×#62611yescharacteristic
620C4—24no—
621C4—62no—
622C4—62no—
623C4—62no—
624C4—122no—
625C4—122no—
626C4—121no—
627C4—361no—
628C4—362no—
629C4#6386414yes—
630C3—21no—
631C3#7378911yescharacteristic, complemented
632C3#8325811yescharacteristic, complemented
633C2—362no—
634C2#1059434111yescharacteristic
635C2#1059439711yescharacteristic
636C2#1059453711yescharacteristic
637C2#1059455611yescharacteristic
638C2C2×#6386411yescharacteristic
639C2#1059524611yescharacteristic
640C2Q8×#62611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#888C2semidirect
3. C3×Dic3×C4⋊C4C2semidirect
8. #10591226C2semidirect
9. #10591220C2semidirect
10. #10591213C2semidirect
11. #10591213C2semidirect
43. C2×#888D3semidirect
51. Dic3×C4⋊C4D3semidirect
93. #3722Q8semidirect
540. C32#2492semidirect
631. C3#73789semidirect
632. C3#83258semidirect

Maximal subgroups

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

subgroupindex
C2×#641062
C2×C3×#8882
C3×Dic3×C4⋊C42
#105913252
#105913102
#105912892
C4×#37222
#105912262
#105912202
#105912132
#832583
#737893