Finite Group Databasebeta

← #11808717

Subgroups — #11808717

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64101C211yesmaximal, characteristic
2C2×#63843C211yesmaximal, characteristic, complemented
3C3×#4986C211yesmaximal, characteristic, complemented
4C3×#4979C211yesmaximal, characteristic, complemented
5#10591351C212yesmaximal, complemented
6#10591350C211yesmaximal, characteristic
7#10591347C212yesmaximal
8#10591310C211yesmaximal, characteristic
9#10591260C212yesmaximal
10#10591257C211yesmaximal, characteristic, complemented
11#10591241C212yesmaximal, complemented
12#78130—31nomaximal
13#77170—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×#3752C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64101—24no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×Dic3⋊C4C2212yes—
25C2×#3724C2212yes—
26C2×Dic3⋊Dic3C2212yes—
27C2×Dic3⋊Dic3C2212yes—
28C2×#3722C2212yes—
29C2×#3722C2212yes—
30C2×Dic32C2212yes—
31C2×Dic32C2212yes—
32#63843—24no—
33C3×C3⋊#95C2212yes—
34C3×C3⋊#95C2211yescharacteristic
35C3×C3⋊#95C2211yescharacteristic
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39C2×Q8×Dic3—31no—
40C2×#892—31no—
41C2×#892—31no—
42C2×#892—61no—
43C2×#887—31no—
44C3×#400—31no—
45C3×#395—31no—
46#5231—31no—
47#4994—32no—
48#4993—31no—
49#4986D311yescharacteristic, complemented
50#4979D311yescharacteristic, complemented
51Dic3×C4⋊C4—32no—
52#4677—31no—
53#4676—32no—
54#4673—31no—
55#4666—32no—
56#4666—32no—
57#4661—32no—
58#4657—32no—
59#4649—32no—
60#4649—31no—
61#4649—31no—
62C23×C3⋊D3C2311yescharacteristic
63C22×C32×C4C2311yescharacteristic
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C22×C3⋊Dic3C2311yescharacteristic
68C22×C3⋊Dic3C2311yescharacteristic
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3—22no—
71C2×C4×C3⋊D3Q814yescomplemented
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2312yes—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—24no—
78C32×C4⋊C4—22no—
79#3752—22no—
80#3752—22no—
81C4⋊(C3⋊Dic3)—22no—
82C4×C3⋊Dic3—22no—
83C4×C3⋊Dic3D414yes—
84C3×C4⋊Dic3—22no—
85C3×Dic3⋊C4—24no—
86#3724—24no—
87Dic3⋊Dic3—24no—
88Dic3⋊Dic3—24no—
89#3722—24no—
90#3722—24no—
91Dic32—24no—
92Dic32—24no—
93#2396—91noSylow
94C22×C3×Q8—31no—
95C22×C4×D3—31no—
96C22×C4×D3—31no—
97C22×C4×D3—61no—
98C22×Dic6C2×D311yescharacteristic
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—31no—
102C2×C3×C4⋊C4C2×D311yescharacteristic
103C2×C3×C4⋊C4C2×D311yescharacteristic
104Q8×Dic3—64no—
105C2×(C2×D3)⋊C4—31no—
106C2×(C2×D3)⋊C4—31no—
107C2×(C2×D3)⋊C4—31no—
108C2×(C2×D3)⋊C4—31no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—32no—
118C2×C4⋊Dic3—32no—
119C2×C4⋊Dic3—61no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×Dic3⋊C4—32no—
122C2×Dic3⋊C4—32no—
123C2×Dic3⋊C4—32no—
124C2×Dic3⋊C4—32no—
125C2×Dic3⋊C4C2×D312yes—
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—32no—
133C2×C4×Dic3—32no—
134C2×C4×Dic3—61no—
135C2×C4×Dic3—61no—
136#892—64no—
137#892—64no—
138#892—68no—
139#887—64no—
140C3×#95—31no—
141C3×#95—32no—
142C3×#95—31no—
143C3×#95—32no—
144C3×#95—32no—
145C3⋊#95—32no—
146C3⋊#95—32no—
147C3⋊#95C2×D311yescharacteristic
148C3⋊#95C2×D311yescharacteristic
149C3⋊#95C2×D312yes—
150C3⋊#95C2×D312yes—
151C3⋊#95C2×D312yes—
152C23×C32C2411yescharacteristic
153C22×C3⋊D3—21no—
154C22×C3⋊D3—21no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3C2×Q812yes—
158C2×C32×C4—21no—
159C2×C32×C4—21no—
160C2×C32×C4—21no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×Q812yes—
165C2×C3⋊Dic3—21no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3C2×D412yes—
169C2×C3⋊Dic3C2×D412yes—
170C2×C3⋊Dic3C2×Q812yes—
171C2×C3⋊Dic3#4112yes—
172C4×C3⋊D3—28no—
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#4114yes—
184C2×C3×Dic3#4114yes—
185C3×Dic6—28no—
186C2×C4×Q8—91no—
187C2×#117—91no—
188#400—31no—
189#399—91no—
190#398—92no—
191#396—92no—
192#395—31no—
193#393—91no—
194C4×C4⋊C4—91no—
195C4×C4⋊C4—92no—
196C4×C22⋊C4—92no—
197C23×D3—31no—
198C23×D3—31no—
199C23×D3—61no—
200C2×C3×Q8—64no—
201C2×C3×Q8—62no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—32no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×C3×C4C22×D311yescharacteristic
215C22×Dic3—31no—
216C22×Dic3—31no—
217C22×Dic3—31no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—31no—
221C22×Dic3—61no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D312yes—
226C22×Dic3C22×D312yes—
227C22×Dic3C22×D312yes—
228C2×C4×D3—34no—
229C2×C4×D3—34no—
230C2×C4×D3—64no—
231C2×C4×D3—62no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×Dic6—22no—
238C2×Dic6—24no—
239C3×C4⋊C4—24no—
240C3×C4⋊C4—22no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—64no—
243C3×C4⋊C4—62no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—64no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254C4⋊Dic3—22no—
255C4⋊Dic3—64no—
256C4⋊Dic3—64no—
257C4⋊Dic3—62no—
258C4⋊Dic3—62no—
259C4⋊Dic3—64no—
260Dic3⋊C4—24no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265C4×Dic3—34no—
266C4×Dic3—34no—
267C4×Dic3—64no—
268C4×Dic3—64no—
269C4×Dic3—64no—
270C4×Dic3—64no—
271C4×Dic3—64no—
272C4×Dic3—62no—
273C4×Dic3—62no—
274C4×Dic3—64no—
275C22×C32C22×D411yescharacteristic
276C22×C32C22×Q811yescharacteristic
277C22×C32C2×#4112yes—
278C22×C32C2×#4112yes—
279C22×C32C2×#4111yescharacteristic
280C2×C3⋊D3—22no—
281C2×C3⋊D3—24no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—42no—
284C2×C3⋊D3—41no—
285C32×C4—22no—
286C32×C4—22no—
287C32×C4—41no—
288C3⋊Dic3—22no—
289C3⋊Dic3—41no—
290C3⋊Dic3C22⋊Q814yes—
291C3×Dic3—24no—
292C3×Dic3—24no—
293C3×Dic3—42no—
294C3×Dic3—42no—
295C22×Q8—31no—
296C23×C4—91no—
297C4×Q8—184no—
298#117—184no—
299C2×C4⋊C4—31no—
300C2×C4⋊C4—32no—
301C2×C4⋊C4—92no—
302C2×C4⋊C4—92no—
303C2×C4⋊C4—92no—
304C2×C4⋊C4—91no—
305C2×C4⋊C4D3211yescharacteristic
306C2×C22⋊C4—92no—
307C2×C22⋊C4—92no—
308C2×C22⋊C4—91no—
309C2×C22⋊C4—91no—
310C2×C42—91no—
311C2×C42—92no—
312C2×C42—92no—
313C2×C42—91no—
314#95—32no—
315#95—32no—
316#95—31no—
317#95—31no—
318#95—32no—
319#95—92no—
320C23×C3—21no—
321C23×C3C23×D311yescharacteristic
322C23×C3C23×D311yescharacteristic
323C22×D3—32no—
324C22×D3—32no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—61no—
335C22×D3—61no—
336C22×D3—122no—
337C22×D3—122no—
338C3×Q8—68no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—22no—
351C2×C3×C4—22no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—34no—
355C2×C3×C4—34no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—62no—
367C2×C3×C4—62no—
368C2×C3×C4D3×D412yes—
369C2×C3×C4D3×D412yes—
370C2×C3×C4D3×Q812yes—
371C2×C3×C4D3×Q812yes—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—22no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—32no—
386C2×Dic3—32no—
387C2×Dic3—32no—
388C2×Dic3—32no—
389C2×Dic3—32no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—62no—
397C2×Dic3—61no—
398C2×Dic3—61no—
399C2×Dic3—62no—
400C2×Dic3—62no—
401C2×Dic3—122no—
402C2×Dic3—122no—
403C2×Dic3#23714yes—
404C2×Dic3#23914yes—
405C4×D3—68no—
406C4×D3—68no—
407C4×D3—616no—
408Dic6—28no—
409C2×C32C2×C22⋊Q811yescharacteristic
410C2×C32#52511yescharacteristic
411C2×C32#52912yes—
412C2×C32#53211yescharacteristic
413C2×C32#53312yes—
414C3⋊D3—42no—
415C24—91no—
416C2×Q8—64no—
417C2×Q8—62no—
418C22×C4—32no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—32no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—94no—
425C22×C4—91no—
426C22×C4—182no—
427C22×C4—182no—
428C22×C4C2×D3211yescharacteristic
429C22×C4C2×D3211yescharacteristic
430C22×C4C2×D3211yescharacteristic
431C4⋊C4—22no—
432C4⋊C4—64no—
433C4⋊C4—62no—
434C4⋊C4—182no—
435C4⋊C4—184no—
436C4⋊C4—184no—
437C4⋊C4—184no—
438C22⋊C4—182no—
439C22⋊C4—184no—
440C22⋊C4—184no—
441C22⋊C4—182no—
442C42—94no—
443C42—182no—
444C42—184no—
445C42—184no—
446C22×C3—21no—
447C22×C3—21no—
448C22×C3—22no—
449C22×C3—22no—
450C22×C3—21no—
451C22×C3C2×D3×D411yescharacteristic
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C2×#23712yes—
454C22×C3C2×D3×Q811yescharacteristic
455C22×C3C2×D3×Q811yescharacteristic
456C22×C3C2×#23912yes—
457C22×C3D3×#4111yescharacteristic
458C22×C3D3×#4111yescharacteristic
459C22×C3D3×#4112yes—
460C22×C3D3×#4112yes—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—62no—
465C2×D3—62no—
466C2×D3—124no—
467C2×D3—122no—
468C2×D3—122no—
469C2×D3—124no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—122no—
473C2×D3—121no—
474C2×D3—121no—
475C2×D3—122no—
476C3×C4—24no—
477C3×C4—22no—
478C3×C4—22no—
479C3×C4—22no—
480C3×C4—22no—
481C3×C4—42no—
482C3×C4—42no—
483C3×C4—41no—
484C3×C4—41no—
485C3×C4—64no—
486C3×C4—64no—
487C3×C4—122no—
488C3×C4—122no—
489Dic3—24no—
490Dic3—24no—
491Dic3—34no—
492Dic3—34no—
493Dic3—42no—
494Dic3—42no—
495Dic3—64no—
496Dic3—62no—
497Dic3—62no—
498Dic3—122no—
499Dic3—122no—
500Dic3—121no—
501Dic3—121no—
502C32#239611yescharacteristic, complemented, Sylow
503C23—92no—
504C23—181no—
505C23—182no—
506C23—182no—
507C23—181no—
508C23C22×D3211yescharacteristic
509Q8—68no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—21no—
515C2×C4—34no—
516C2×C4—34no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—92no—
528C2×C4—92no—
529C2×C4—92no—
530C2×C4—92no—
531C2×C4—188no—
532C2×C4—182no—
533C2×C4—182no—
534C2×C4—181no—
535C2×C4#379712yes—
536C2×C4#381112yes—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—22no—
541C2×C3—22no—
542C2×C3#558611yescharacteristic
543C2×C3#562412yes—
544C2×C3D3×C22⋊Q811yescharacteristic
545C2×C3D3×C22⋊Q811yescharacteristic
546C2×C3#565611yescharacteristic
547C2×C3#566811yescharacteristic
548C2×C3#568812yes—
549C2×C3#570612yes—
550C2×C3#572511yescharacteristic
551C2×C3#572812yes—
552D3—124no—
553D3—122no—
554D3—122no—
555C22—182no—
556C22—184no—
557C22—361no—
558C22—361no—
559C22—362no—
560C22C2×#379711yescharacteristic
561C22#6430611yescharacteristic
562C22D3×#23712yes—
563C22D3×#23912yes—
564C22C2×#381111yescharacteristic
565C4—22no—
566C4—22no—
567C4—41no—
568C4—64no—
569C4—64no—
570C4—94no—
571C4—122no—
572C4—122no—
573C4—182no—
574C4—361no—
575C3—21no—
576C3#7717011yescharacteristic, complemented
577C3#7813011yescharacteristic, complemented
578C2—362no—
579C2#1059444212yes—
580C2#1059444812yes—
581C2#1059492511yescharacteristic
582C2#1059516011yescharacteristic
583C2#1059536311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2396
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×#63843C2semidirect
3. C3×#4986C2semidirect
4. C3×#4979C2semidirect
5. #10591351C2semidirect
10. #10591257C2semidirect
11. #10591241C2semidirect
49. #4986D3semidirect
50. #4979D3semidirect
71. C2×C4×C3⋊D3Q8semidirect
502. C32#2396semidirect
576. C3#77170semidirect
577. C3#78130semidirect

Maximal subgroups

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

subgroupindex
C2×#641012
C2×#638432
C3×#49862
C3×#49792
#105913512
#105913502
#105913472
#105913102
#105912602
#105912572
#105912412
#781303
#771703