Finite Group Databasebeta

← #11803875

Subgroups — #11803875

Order 1152.

1693 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic, complemented
4C3×#5221C211yesmaximal, characteristic, complemented
5#10591721C214yesmaximal, complemented
6#10591713C214yesmaximal, complemented
7#10591318C211yesmaximal, characteristic, complemented
8#10591224C211yesmaximal, characteristic, complemented
9#10591222C211yesmaximal, characteristic, complemented
10#83172—31nomaximal
11#76298—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C23×C3⋊Dic3C2212yes—
14C22×C3×#67C2214yes—
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3C2212yes—
17C2×#3757C2212yes—
18D4×C3⋊Dic3—24no—
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21C2×C3×#217C2214yes—
22C3×#940C418yescomplemented
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2214yes—
28#63898—24no—
29#63579C2212yes—
30#63579C2214yes—
31#63579C2212yes—
32C2×C3×#127—31no—
33C2×#940D311yescharacteristic
34C2×D4×Dic3—31no—
35C2×D4×Dic3—31no—
36C2×D4×Dic3—31no—
37C2×D4×Dic3—61no—
38C2×#893—31no—
39C3×#390—31no—
40#5221—31no—
41#5221D311yescharacteristic, complemented
42#5220—34no—
43#5220—34no—
44#4977—31no—
45#4958—34no—
46#4956—34no—
47#4939—31no—
48#4936—31no—
49#4932—31no—
50#4932—31no—
51C24×C32C2312yes—
52C23×C3×D3C2312yes—
53C2×C32×D4—22no—
54C2×C32×D4—22no—
55C2×C32×D4C2×C414yescomplemented
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—24no—
58C22×C3⋊Dic3—44no—
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C2×C3×#67—44no—
63C2×C3×#67—44no—
64C2×C3×#67C2×C4116yescomplemented
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12C2×C414yescomplemented
71C2×D3×Dic3—24no—
72C2×D3×Dic3—44no—
73#3757—24no—
74C4⋊(C3⋊Dic3)—22no—
75C4×C3⋊Dic3D414yescomplemented
76C3×#217—44no—
77C3×C4⋊Dic3—22no—
78C3×C4×Dic3—22no—
79C3×C4×Dic3C2×C414yescomplemented
80(C2×D3)⋊Dic3—24no—
81(C2×D3)⋊Dic3—44no—
82#2328—91noSylow
83C22×C3×D4—21no—
84C22×C3×D4—34no—
85C22×C3×D4—31no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C2×D311yescharacteristic
88C22×#67C2×D314yes—
89C23×Dic3—32no—
90C23×Dic3—32no—
91C23×Dic3—32no—
92C23×Dic3—62no—
93C22×D12C2×D311yescharacteristic
94C22×C4×D3—32no—
95C3×#127—38no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C22⋊C4—34no—
98C2×C3×C42—31no—
99C2×C3×C42—31no—
100C2×#217—32no—
101C2×#217—32no—
102C2×#217—32no—
103C2×#217—34no—
104C2×#217—62no—
105C2×#217C2×D314yes—
106#940Dic318yescomplemented
107D4×Dic3—64no—
108D4×Dic3—64no—
109D4×Dic3—64no—
110D4×Dic3—68no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—34no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4×Dic3—31no—
118C2×C4×Dic3—31no—
119C2×C4×Dic3—61no—
120C2×C4×Dic3C2×D311yescharacteristic
121C2×C4×Dic3C2×D311yescharacteristic
122#893—64no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—34no—
128C3⋊#95—34no—
129C23×C32—22no—
130C23×C32—22no—
131C23×C32—24no—
132C23×C32—24no—
133C23×C32C22×C414yes—
134C23×C32C2411yescharacteristic
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—24no—
138C22×C3×D3—24no—
139C22×C3×D3C22×C414yes—
140C32×D4—28no—
141C2×C32×C4C22×C412yes—
142C2×C32×C4C2×D412yes—
143C2×C32×C4#4112yes—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—24no—
148C2×C3⋊Dic3—48no—
149C2×C3⋊Dic3C2×D412yes—
150C2×C3⋊Dic3C2×D412yes—
151C3×#67—416no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—24no—
159C2×C3×Dic3C22×C414yes—
160C3×D12—28no—
161D3×Dic3—48no—
162C2×#127—31no—
163C2×C4×D4—91no—
164C2×C4×D4—91no—
165#390—31no—
166#390—91no—
167#386—94no—
168#386—94no—
169#382—91no—
170#376—91no—
171C24×C3—22no—
172C24×C3—32no—
173C24×C3C22×D312yes—
174C24×C3C22×D312yes—
175C23×D3C22×D312yes—
176C2×C3×D4—24no—
177C2×C3×D4—24no—
178C2×C3×D4—22no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—22no—
182C2×C3×D4—24no—
183C2×C3×D4—316no—
184C2×C3×D4—34no—
185C2×C3×D4—62no—
186C2×C3×D4—62no—
187C2×C3×D4—124no—
188C2×C3×D4—124no—
189C2×C3×D4C4×D314yescomplemented
190C2×C3×D4C2×Dic314yescomplemented
191C22×C3×C4—21no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—32no—
195C22×C3×C4C22×D311yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C2×#67—44no—
198C2×#67—44no—
199C2×#67C2×Dic3116yescomplemented
200C22×Dic3—31no—
201C22×Dic3—31no—
202C22×Dic3—31no—
203C22×Dic3—31no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3—62no—
209C22×Dic3—64no—
210C22×Dic3—64no—
211C22×Dic3—64no—
212C22×Dic3—68no—
213C22×Dic3—124no—
214C22×Dic3—124no—
215C22×Dic3—124no—
216C22×Dic3—128no—
217C22×Dic3C22×D312yes—
218C22×Dic3C22×D312yes—
219C22×Dic3C22×D312yes—
220C2×D12—22no—
221C2×D12—22no—
222C2×D12C2×Dic314yescomplemented
223C2×C4×D3—64no—
224C2×C4×D3—124no—
225C3×C4⋊C4—62no—
226C3×C22⋊C4—124no—
227C3×C42—34no—
228C3×C42—62no—
229#217—44no—
230#217—64no—
231#217—64no—
232#217—64no—
233#217—68no—
234#217—124no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—124no—
237C4⋊Dic3—22no—
238C4⋊Dic3—64no—
239C4⋊Dic3—62no—
240C4⋊Dic3—62no—
241C4×Dic3—22no—
242C4×Dic3—34no—
243C4×Dic3—34no—
244C4×Dic3—64no—
245C4×Dic3C2×Dic314yescomplemented
246C22×C32—24no—
247C22×C32—28no—
248C22×C32—42no—
249C22×C32—42no—
250C22×C32—44no—
251C22×C32C23×C411yescharacteristic
252C22×C32C22×D411yescharacteristic
253C22×C32C2×#4111yescharacteristic
254C22×C32H(5,𝔽2)12yes—
255C22×C32H(5,𝔽2)12yes—
256C2×C3×D3—24no—
257C2×C3×D3—28no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—44no—
261C32×C4C4×D414yes—
262C3⋊Dic3—22no—
263C3⋊Dic3—22no—
264C3⋊Dic3—42no—
265C3×Dic3—24no—
266C3×Dic3—42no—
267C3×Dic3—42no—
268C22×D4—34no—
269C22×D4—31no—
270C22×D4D3211yescharacteristic
271C23×C4—92no—
272C23×C4—92no—
273#127—38no—
274C4×D4—184no—
275C4×D4—184no—
276C2×C4⋊C4—31no—
277C2×C4⋊C4—91no—
278C2×C22⋊C4—34no—
279C2×C22⋊C4—92no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—94no—
282C2×C42—31no—
283C2×C42—31no—
284C2×C42—91no—
285#95—92no—
286#95—92no—
287#95—94no—
288C23×C3—24no—
289C23×C3—24no—
290C23×C3—22no—
291C23×C3—22no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—24no—
295C23×C3—24no—
296C23×C3—24no—
297C23×C3—24no—
298C23×C3—21no—
299C23×C3—24no—
300C23×C3—34no—
301C23×C3—44no—
302C23×C3—44no—
303C23×C3—62no—
304C23×C3—62no—
305C23×C3—64no—
306C23×C3—64no—
307C23×C3C2×C4×D314yes—
308C23×C3C22×Dic314yes—
309C23×C3C23×D311yescharacteristic
310C23×C3C23×D311yescharacteristic
311C22×D3—22no—
312C22×D3—22no—
313C22×D3—24no—
314C22×D3—24no—
315C22×D3C22×Dic314yes—
316C3×D4—216no—
317C3×D4—28no—
318C3×D4—28no—
319C3×D4—68no—
320C3×D4—1216no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—34no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—64no—
332C2×C3×C4C2×C4×D312yes—
333C2×C3×C4D3×D412yes—
334C2×C3×C4D3×D412yes—
335C2×C3×C4#23712yes—
336C2×C3×C4#23712yes—
337C2×C3×C4C22×Dic312yes—
338#67—416no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—24no—
345C2×Dic3—22no—
346C2×Dic3—32no—
347C2×Dic3—32no—
348C2×Dic3—32no—
349C2×Dic3—32no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—64no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—64no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—122no—
363C2×Dic3—124no—
364C2×Dic3—128no—
365C2×Dic3—1216no—
366C2×Dic3—128no—
367C2×Dic3—128no—
368C2×Dic3C22×Dic314yes—
369D12—28no—
370C4×D3—128no—
371C2×C32—44no—
372C2×C32C2×C4×D411yescharacteristic
373C2×C32#51812yes—
374C2×C32#53511yescharacteristic
375C2×C32#53511yescharacteristic
376C2×C32#54012yes—
377C3×D3—44no—
378C24—32no—
379C24C2×D3212yes—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—316no—
383C2×D4—34no—
384C2×D4—62no—
385C2×D4—62no—
386C2×D4—124no—
387C2×D4—124no—
388C2×D4D3×Dic314yescomplemented
389C22×C4—32no—
390C22×C4—32no—
391C22×C4—32no—
392C22×C4—91no—
393C22×C4—91no—
394C22×C4—92no—
395C22×C4—184no—
396C22×C4—184no—
397C22×C4—364no—
398C22×C4—364no—
399C22×C4C2×D3211yescharacteristic
400C4⋊C4—62no—
401C4⋊C4—182no—
402C22⋊C4—124no—
403C22⋊C4—184no—
404C22⋊C4—184no—
405C22⋊C4—364no—
406C42—34no—
407C42—62no—
408C42—94no—
409C22×C3—28no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3—28no—
413C22×C3—28no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—48no—
420C22×C3—44no—
421C22×C3—48no—
422C22×C3—44no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—42no—
427C22×C3—44no—
428C22×C3—44no—
429C22×C3—64no—
430C22×C3—68no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3—124no—
434C22×C3C22×C4×D311yescharacteristic
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C22×C3C2×#23711yescharacteristic
438C22×C3C2×#23711yescharacteristic
439C22×C3#100412yes—
440C22×C3#100412yes—
441C22×C3#100412yes—
442C22×C3#100912yes—
443C22×C3C23×Dic311yescharacteristic
444C2×D3—24no—
445C2×D3—28no—
446C2×D3—42no—
447C2×D3—42no—
448C2×D3—44no—
449C3×C4—24no—
450C3×C4—64no—
451C3×C4—122no—
452C3×C4—122no—
453C3×C4#67⋊C414yes—
454C3×C4D4×Dic314yes—
455Dic3—24no—
456Dic3—42no—
457Dic3—42no—
458Dic3—64no—
459Dic3—62no—
460Dic3—62no—
461Dic3—62no—
462Dic3—62no—
463Dic3—122no—
464Dic3—124no—
465Dic3—122no—
466Dic3—122no—
467C32#232811yescharacteristic, complemented, Sylow
468C23—24no—
469C23—24no—
470C23—22no—
471C23—22no—
472C23—34no—
473C23—64no—
474C23—64no—
475C23—62no—
476C23—62no—
477C23C2×D3×Dic314yes—
478C23C22×D3211yescharacteristic
479D4—28no—
480D4—68no—
481D4—1216no—
482C2×C4—34no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—64no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—182no—
493C2×C4—182no—
494C2×C4—184no—
495C2×C4—182no—
496C2×C4—368no—
497C2×C4—368no—
498C2×C4C2×D3×Dic312yes—
499C2×C4#380512yes—
500C2×C4#381112yes—
501C2×C3—21no—
502C2×C3—22no—
503C2×C3—22no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—48no—
507C2×C3—44no—
508C2×C3—44no—
509C2×C3—124no—
510C2×C3C2×#67⋊C411yescharacteristic
511C2×C3#554512yes—
512C2×C3#561912yes—
513C2×C3#567411yescharacteristic
514C2×C3#571511yescharacteristic
515C2×C3#571511yescharacteristic
516C2×C3#571511yescharacteristic
517C2×C3#571912yes—
518C2×C3C2×D4×Dic311yescharacteristic
519C2×C3#579812yes—
520D3—44no—
521C22—28no—
522C22—24no—
523C22—42no—
524C22—44no—
525C22—42no—
526C22—68no—
527C22—64no—
528C22—122no—
529C22—124no—
530C22—122no—
531C22#6431312yes—
532C22#6431412yes—
533C22C22×D3×Dic311yescharacteristic
534C22C2×#380511yescharacteristic
535C22C2×#381111yescharacteristic
536C4—64no—
537C4—122no—
538C4—122no—
539C4—182no—
540C4—182no—
541C4—362no—
542C4#67⋊Dic314yes—
543C3—21no—
544C3#7629811yescharacteristic, complemented
545C3#8317211yescharacteristic, complemented
546C2—44no—
547C2—124no—
548C2#1059516811yescharacteristic
549C2#1059521512yes—
550C2#1059521712yes—
551C2#1059530911yescharacteristic
552C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32#2328
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
3. C2×#63898C2semidirect
4. C3×#5221C2semidirect
5. #10591721C2semidirect
6. #10591713C2semidirect
7. #10591318C2semidirect
8. #10591224C2semidirect
9. #10591222C2semidirect
22. C3×#940C4semidirect
41. #5221D3semidirect
55. C2×C32×D4C2×C4semidirect
64. C2×C3×#67C2×C4semidirect
70. C2×C3×D12C2×C4semidirect
75. C4×C3⋊Dic3D4semidirect
79. C3×C4×Dic3C2×C4semidirect
106. #940Dic3semidirect
189. C2×C3×D4C4×D3semidirect
190. C2×C3×D4C2×Dic3semidirect
199. C2×#67C2×Dic3semidirect
222. C2×D12C2×Dic3semidirect
245. C4×Dic3C2×Dic3semidirect
388. C2×D4D3×Dic3semidirect
467. C32#2328semidirect
544. C3#76298semidirect
545. C3#83172semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C3×#9402
C2×#638982
C3×#52212
#105917212
#105917132
#105913182
#105912242
#105912222
#831723
#762983