Finite Group Databasebeta

← #11808791

Subgroups — #11808791

Order 1152.

1285 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64096C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic
3C3×#4991C211yesmaximal, characteristic
4C3×#4986C211yesmaximal, characteristic, complemented
5#10591368C212yesmaximal, complemented
6#10591368C212yesmaximal, complemented
7#10591322C212yesmaximal, complemented
8#10591302C211yesmaximal, characteristic
9#10591298C212yesmaximal, complemented
10#10591252C211yesmaximal, characteristic, complemented
11#10591227C211yesmaximal, characteristic, complemented
12#78131—31nomaximal
13#76893—31nomaximal
14C22×#634C2211yescharacteristic
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23#64096—24no—
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×(C2×D3)⋊C4C2212yes—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×(C2×D3)⋊Dic3C2212yes—
28C2×(C2×D3)⋊Dic3C2212yes—
29C2×(C2×D3)⋊Dic3C2212yes—
30C2×Dic32C2212yes—
31#63898—24no—
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2211yescharacteristic
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38#63579C2212yes—
39C2×D4×Dic3—31no—
40C2×#893—31no—
41C2×#887—31no—
42C2×#887—31no—
43C2×#887—61no—
44C3×#400—31no—
45C3×#394—31no—
46#5222—31no—
47#4991D311yescharacteristic
48#4986D311yescharacteristic, complemented
49#4985—31no—
50#4952—32no—
51#4947—32no—
52Dic3×C22⋊C4—32no—
53Dic3×C22⋊C4—32no—
54#4675—32no—
55#4673—32no—
56#4672—31no—
57#4666—32no—
58#4666—32no—
59#4659—31no—
60#4648—31no—
61#4648—31no—
62C23×C3×D3C2312yes—
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C22×C3⋊Dic3C2311yescharacteristic
70C2×#634—22no—
71C2×#634—22no—
72C2×#634—22no—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×D12—24no—
77C2×C3×D12—22no—
78C2×D3×Dic3—24no—
79C2×D3×Dic3—24no—
80C2×D3×Dic3—24no—
81C32×C4⋊C4—22no—
82#3750—22no—
83#3750—22no—
84C4×C3⋊Dic3—22no—
85C4×C3⋊Dic3—22no—
86C4×C3⋊Dic3D414yes—
87C3×(C2×D3)⋊C4—24no—
88C3×(C2×D3)⋊C4—24no—
89C3×C4⋊Dic3—22no—
90(C2×D3)⋊Dic3—24no—
91(C2×D3)⋊Dic3—24no—
92(C2×D3)⋊Dic3—24no—
93Dic32—24no—
94#2398—91noSylow
95C22×C3×D4—31no—
96C23×Dic3—32no—
97C22×D12C2×D311yescharacteristic
98C22×C4×D3—32no—
99C22×Dic6—31no—
100C22×Dic6—31no—
101C22×Dic6—61no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—31no—
104C2×C3×C4⋊C4C2×D311yescharacteristic
105C2×C3×C4⋊C4C2×D311yescharacteristic
106C2×C3×C22⋊C4—32no—
107C2×C3×C22⋊C4—32no—
108C2×#217—32no—
109C2×#217—32no—
110C2×#217—32no—
111D4×Dic3—64no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—32no—
114C2×(C2×D3)⋊C4—32no—
115C2×(C2×D3)⋊C4C2×D312yes—
116C2×(C2×D3)⋊C4C2×D312yes—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×Dic3⋊C4—31no—
119C2×Dic3⋊C4—31no—
120C2×Dic3⋊C4—31no—
121C2×Dic3⋊C4—31no—
122C2×Dic3⋊C4—61no—
123C2×Dic3⋊C4—61no—
124C2×C4×Dic3—31no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—31no—
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—61no—
133C2×C4×Dic3—61no—
134C2×C4×Dic3—61no—
135#893—64no—
136#887—64no—
137#887—64no—
138#887—68no—
139C3×#95—31no—
140C3×#95—31no—
141C3×#95—32no—
142C3×#95—32no—
143C3⋊#95—32no—
144C3⋊#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95—32no—
148C3⋊#95—32no—
149C3⋊#95C2×D311yescharacteristic
150C3⋊#95C2×D311yescharacteristic
151C3⋊#95C2×D312yes—
152C3⋊#95C2×D312yes—
153C23×C32C2411yescharacteristic
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3—22no—
160C22×C3×D3#4114yes—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4#4112yes—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3C2×D412yes—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3#4112yes—
177C2×C3⋊Dic3#4114yes—
178#634—28no—
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—22no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C3×D12—28no—
189D3×Dic3—48no—
190C2×C4×Q8—91no—
191C2×C4×D4—91no—
192#400—31no—
193#400—91no—
194#397—92no—
195#394—31no—
196#394—91no—
197#393—92no—
198C4×C22⋊C4—92no—
199C4×C22⋊C4—92no—
200#376—91no—
201C24×C3—32no—
202C23×D3C22×D312yes—
203C2×C3×D4—64no—
204C2×C3×D4—62no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—32no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—31no—
222C22×Dic3—31no—
223C22×Dic3—31no—
224C22×Dic3—31no—
225C22×Dic3—61no—
226C22×Dic3—61no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—64no—
230C22×Dic3—64no—
231C22×Dic3—64no—
232C22×Dic3C22×D312yes—
233C22×Dic3C22×D312yes—
234C22×Dic3C22×D312yes—
235C2×D12—24no—
236C2×D12—22no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—64no—
240C2×Dic6—62no—
241C2×Dic6—62no—
242C2×Dic6—62no—
243C2×Dic6—62no—
244C2×Dic6—64no—
245C2×Dic6—64no—
246C2×Dic6—64no—
247C2×Dic6—62no—
248C2×Dic6—62no—
249C3×C4⋊C4—24no—
250C3×C4⋊C4—22no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—62no—
253C3×C22⋊C4—64no—
254C3×C22⋊C4—64no—
255#217—64no—
256#217—64no—
257#217—64no—
258(C2×D3)⋊C4—24no—
259(C2×D3)⋊C4—24no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—22no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—64no—
267Dic3⋊C4—64no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270C4×Dic3—34no—
271C4×Dic3—34no—
272C4×Dic3—64no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—64no—
280C4×Dic3—64no—
281C22×C32C22×D411yescharacteristic
282C22×C32C2×#4111yescharacteristic
283C22×C32C2×#4112yes—
284C22×C32C2×#4111yescharacteristic
285C22×C32C2×#4112yes—
286C2×C3×D3—24no—
287C2×C3×D3—24no—
288C2×C3×D3—24no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C32×C4—22no—
294C32×C4—22no—
295C32×C4—41no—
296C3⋊Dic3—22no—
297C3⋊Dic3—22no—
298C3⋊Dic3—41no—
299C3⋊Dic3#12414yes—
300C3×Dic3—42no—
301C3×Dic3—42no—
302C3×Dic3—42no—
303C22×Q8—91no—
304C22×D4—31no—
305C23×C4—92no—
306C4×Q8—184no—
307C4×D4—184no—
308C2×C4⋊C4—31no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C4⋊C4D3211yescharacteristic
312C2×C22⋊C4—32no—
313C2×C22⋊C4—32no—
314C2×C22⋊C4—92no—
315C2×C22⋊C4—92no—
316C2×C22⋊C4—92no—
317C2×C42—91no—
318C2×C42—92no—
319C2×C42—91no—
320C2×C42—91no—
321#95—31no—
322#95—31no—
323#95—32no—
324#95—32no—
325#95—92no—
326#95—92no—
327#95—92no—
328C23×C3—21no—
329C23×C3—34no—
330C23×C3—62no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3—62no—
336C23×C3C23×D311yescharacteristic
337C23×C3C23×D311yescharacteristic
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—22no—
343C22×D3—22no—
344C22×D3#23714yes—
345C3×D4—68no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
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×C4D3×D412yes—
373C2×C3×C4D3×D412yes—
374C2×C3×C4#23712yes—
375C2×C3×C4#23912yes—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—32no—
386C2×Dic3—32no—
387C2×Dic3—34no—
388C2×Dic3—34no—
389C2×Dic3—32no—
390C2×Dic3—32no—
391C2×Dic3—32no—
392C2×Dic3—32no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—64no—
397C2×Dic3—62no—
398C2×Dic3—62no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—61no—
402C2×Dic3—61no—
403C2×Dic3—61no—
404C2×Dic3—61no—
405C2×Dic3—61no—
406C2×Dic3—61no—
407C2×Dic3—61no—
408C2×Dic3—61no—
409C2×Dic3—62no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—122no—
415C2×Dic3—128no—
416D12—28no—
417C4×D3—128no—
418Dic6—616no—
419Dic6—68no—
420Dic6—68no—
421C2×C32#52511yescharacteristic
422C2×C32#52511yescharacteristic
423C2×C32C2×#12411yescharacteristic
424C2×C32#52912yes—
425C2×C32#52912yes—
426C3×D3—44no—
427C24—32no—
428C2×Q8—182no—
429C2×Q8—182no—
430C2×Q8—182no—
431C2×D4—64no—
432C2×D4—62no—
433C22×C4—32no—
434C22×C4—32no—
435C22×C4—32no—
436C22×C4—91no—
437C22×C4—91no—
438C22×C4—91no—
439C22×C4—91no—
440C22×C4—184no—
441C22×C4—184no—
442C22×C4—184no—
443C22×C4C2×D3211yescharacteristic
444C22×C4C2×D3211yescharacteristic
445C22×C4C2×D3211yescharacteristic
446C4⋊C4—22no—
447C4⋊C4—62no—
448C4⋊C4—182no—
449C4⋊C4—182no—
450C22⋊C4—64no—
451C22⋊C4—64no—
452C22⋊C4—184no—
453C22⋊C4—184no—
454C22⋊C4—184no—
455C42—94no—
456C42—182no—
457C42—182no—
458C42—184no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—21no—
464C22×C3—64no—
465C22×C3—64no—
466C22×C3—64no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—122no—
470C22×C3—122no—
471C22×C3C2×D3×D411yescharacteristic
472C22×C3C2×D3×D411yescharacteristic
473C22×C3C2×#23711yescharacteristic
474C22×C3C2×#23712yes—
475C22×C3C2×#23911yescharacteristic
476C22×C3D3×#4111yescharacteristic
477C22×C3D3×#4111yescharacteristic
478C22×C3D3×#4112yes—
479C22×C3D3×#4112yes—
480C22×C3D3×#4112yes—
481C2×D3—24no—
482C2×D3—24no—
483C2×D3—24no—
484C2×D3—42no—
485C2×D3—42no—
486C2×D3—42no—
487C2×D3—42no—
488C3×C4—24no—
489C3×C4—22no—
490C3×C4—22no—
491C3×C4—22no—
492C3×C4—22no—
493C3×C4—42no—
494C3×C4—42no—
495C3×C4—41no—
496C3×C4—41no—
497C3×C4—122no—
498C3×C4—122no—
499C3×C4—122no—
500Dic3—34no—
501Dic3—34no—
502Dic3—42no—
503Dic3—42no—
504Dic3—42no—
505Dic3—64no—
506Dic3—64no—
507Dic3—64no—
508Dic3—62no—
509Dic3—62no—
510Dic3—62no—
511Dic3—62no—
512Dic3—122no—
513Dic3—121no—
514Dic3—121no—
515C32#239811yescharacteristic, complemented, Sylow
516C23—34no—
517C23—62no—
518C23—62no—
519C23—62no—
520C23—62no—
521C23—62no—
522C23—62no—
523C23C22×D3211yescharacteristic
524Q8—188no—
525D4—68no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—22no—
530C2×C4—21no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—94no—
541C2×C4—92no—
542C2×C4—92no—
543C2×C4—92no—
544C2×C4—181no—
545C2×C4—181no—
546C2×C4—181no—
547C2×C4—181no—
548C2×C4—182no—
549C2×C4—181no—
550C2×C4—368no—
551C2×C4#379612yes—
552C2×C4#381112yes—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—22no—
557C2×C3—22no—
558C2×C3—124no—
559C2×C3#558611yescharacteristic
560C2×C3#560012yes—
561C2×C3#560611yescharacteristic
562C2×C3#562711yescharacteristic
563C2×C3#564912yes—
564C2×C3#565611yescharacteristic
565C2×C3D3×#12411yescharacteristic
566C2×C3D3×#12411yescharacteristic
567C2×C3#569112yes—
568C2×C3#570612yes—
569D3—44no—
570C22—64no—
571C22—64no—
572C22—64no—
573C22—122no—
574C22—122no—
575C22—122no—
576C22—122no—
577C22C2×#379611yescharacteristic
578C22#6430611yescharacteristic
579C22D3×#23712yes—
580C22#6431912yes—
581C22C2×#381111yescharacteristic
582C4—22no—
583C4—22no—
584C4—41no—
585C4—94no—
586C4—122no—
587C4—122no—
588C4—122no—
589C4—182no—
590C4—182no—
591C4—361no—
592C3—21no—
593C3#7689311yescharacteristic, complemented
594C3#7813111yescharacteristic, complemented
595C2—124no—
596C2#1059442712yes—
597C2#1059443512yes—
598C2#1059492211yescharacteristic
599C2#1059516011yescharacteristic
600C2#1059543211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64096C2semidirect
4. C3×#4986C2semidirect
5. #10591368C2semidirect
6. #10591368C2semidirect
7. #10591322C2semidirect
9. #10591298C2semidirect
10. #10591252C2semidirect
11. #10591227C2semidirect
48. #4986D3semidirect
515. C32#2398semidirect
593. C3#76893semidirect
594. C3#78131semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
C2×#638982
C3×#49912
C3×#49862
#105913682
#105913222
#105913022
#105912982
#105912522
#105912272
#781313
#768933