Finite Group Databasebeta

← #11803877

Subgroups — #11803877

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C2×Dic3×D12C211yesmaximal, characteristic, complemented
4#10592920C211yesmaximal, characteristic, complemented
5#10591721C214yesmaximal, complemented
6#10591710C214yesmaximal, complemented
7#10591323C211yesmaximal, characteristic, complemented
8#10591224C211yesmaximal, characteristic, complemented
9#10591222C211yesmaximal, characteristic, complemented
10#83172—31nomaximal
11#82329—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67C2214yes—
14C23×C3×Dic3C2212yes—
15C22×C3×D12C2211yescharacteristic
16C22×D3×Dic3C2212yes—
17C2×#3757C2214yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#217C2212yes—
21C3×#940C418yescomplemented
22C3×D4×Dic3—24no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×(C2×D3)⋊Dic3C2212yes—
27C2×(C2×D3)⋊Dic3C2214yes—
28Dic3×D12—24no—
29#63579C2212yes—
30#63579C2214yes—
31#63579C2212yes—
32C2×C3×#127—31no—
33C2×C3×C4×D4—31no—
34C2×#940D311yescharacteristic
35C2×D4×Dic3—31no—
36C2×D4×Dic3D311yescharacteristic, complemented
37C2×C4×D12—31no—
38#5221—31no—
39#5221—31no—
40#5221—31no—
41#5221—61no—
42#5220—34no—
43#5220—34no—
44#5213—34no—
45#4988—31no—
46#4977—31no—
47#4956—34no—
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⋊Dic3C2312yes—
58C22×C3⋊Dic3C2312yes—
59C2×C3×#67—44no—
60C2×C3×#67—44no—
61C2×C3×#67C2×C4116yescomplemented
62C22×C3×Dic3—24no—
63C22×C3×Dic3—44no—
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2311yescharacteristic
67C22×C3×Dic3C2311yescharacteristic
68C2×C3×D12—22no—
69C2×C3×D12—22no—
70C2×C3×D12C2×C414yescomplemented
71C2×D3×Dic3—24no—
72C2×D3×Dic3—44no—
73#3757—44no—
74C4⋊(C3⋊Dic3)—22no—
75C4×C3⋊Dic3—22no—
76C3×#217—24no—
77C3×C4⋊Dic3—22no—
78C3×C4×Dic3C2×C414yescomplemented
79C3×C4×Dic3D414yescomplemented
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
88C23×C3×C4—32no—
89C22×#67C2×D314yes—
90C23×Dic3—32no—
91C23×Dic3C2×D312yes—
92C22×D12C2×D311yescharacteristic
93C22×C4×D3—32no—
94C3×#127—38no—
95C3×C4×D4—64no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C22⋊C4—32no—
98C2×C3×C42—31no—
99C2×C3×C42—31no—
100C2×#217—32no—
101C2×#217—34no—
102C2×#217—34no—
103C2×#217—34no—
104C2×#217—64no—
105C2×#217C2×D312yes—
106#940Dic318yescomplemented
107D4×Dic3—24no—
108D4×Dic3—64no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—34no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—61no—
114C2×C4⋊Dic3C2×D311yescharacteristic
115C2×C4×Dic3—31no—
116C2×C4×Dic3—31no—
117C2×C4×Dic3—61no—
118C2×C4×Dic3C2×D311yescharacteristic
119C2×C4×Dic3C2×D311yescharacteristic
120C4×D12—64no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95—34no—
126C3⋊#95—34no—
127C23×C32—22no—
128C23×C32—22no—
129C23×C32—24no—
130C23×C32—24no—
131C23×C32C22×C414yes—
132C23×C32C2411yescharacteristic
133C22×C3×D3—22no—
134C22×C3×D3—22no—
135C22×C3×D3—24no—
136C22×C3×D3—24no—
137C22×C3×D3C22×C414yes—
138C32×D4—28no—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C2×D412yes—
141C2×C32×C4#4112yes—
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—22no—
145C2×C3⋊Dic3—22no—
146C2×C3⋊Dic3—24no—
147C3×#67—416no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—24no—
154C2×C3×Dic3—48no—
155C2×C3×Dic3C22×C414yes—
156C2×C3×Dic3C2×D412yes—
157C2×C3×Dic3C2×D412yes—
158C3×D12—28no—
159D3×Dic3—48no—
160C2×#127—31no—
161C2×C4×D4—31no—
162C2×C4×D4—91no—
163#390—91no—
164#390—91no—
165#386—94no—
166#386—94no—
167#382—91no—
168#376—91no—
169C24×C3—22no—
170C24×C3—32no—
171C24×C3C22×D312yes—
172C24×C3C22×D312yes—
173C23×D3C22×D312yes—
174C2×C3×D4—22no—
175C2×C3×D4—22no—
176C2×C3×D4—22no—
177C2×C3×D4—22no—
178C2×C3×D4—24no—
179C2×C3×D4—316no—
180C2×C3×D4—34no—
181C2×C3×D4—42no—
182C2×C3×D4—42no—
183C2×C3×D4—62no—
184C2×C3×D4—62no—
185C2×C3×D4—124no—
186C2×C3×D4—124no—
187C2×C3×D4C4×D314yescomplemented
188C2×C3×D4C2×Dic314yescomplemented
189C22×C3×C4—21no—
190C22×C3×C4—32no—
191C22×C3×C4—31no—
192C22×C3×C4—31no—
193C22×C3×C4—32no—
194C22×C3×C4—64no—
195C22×C3×C4—124no—
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C2×#67—44no—
199C2×#67—44no—
200C2×#67C2×Dic3116yescomplemented
201C22×Dic3—24no—
202C22×Dic3—32no—
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—32no—
206C22×Dic3—44no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209C22×Dic3—64no—
210C22×Dic3—124no—
211C22×Dic3C22×D312yes—
212C22×Dic3C22×D312yes—
213C22×Dic3C22×D311yescharacteristic
214C22×Dic3C22×D311yescharacteristic
215C2×D12—22no—
216C2×D12—22no—
217C2×D12C2×Dic314yescomplemented
218C2×C4×D3—64no—
219C2×C4×D3—124no—
220C3×C4⋊C4—62no—
221C3×C22⋊C4—64no—
222C3×C42—34no—
223C3×C42—34no—
224#217—24no—
225#217—64no—
226#217—124no—
227#217—124no—
228#217—124no—
229#217—128no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—124no—
232C4⋊Dic3—22no—
233C4⋊Dic3—62no—
234C4⋊Dic3—62no—
235C4⋊Dic3—122no—
236C4×Dic3—62no—
237C4×Dic3—62no—
238C4×Dic3—122no—
239C4×Dic3C2×Dic314yescomplemented
240C4×Dic3#6714yescomplemented
241C22×C32—24no—
242C22×C32—28no—
243C22×C32—42no—
244C22×C32—42no—
245C22×C32—44no—
246C22×C32C23×C411yescharacteristic
247C22×C32C22×D411yescharacteristic
248C22×C32C2×#4111yescharacteristic
249C22×C32H(5,𝔽2)12yes—
250C22×C32H(5,𝔽2)12yes—
251C2×C3×D3—24no—
252C2×C3×D3—28no—
253C2×C3×D3—42no—
254C2×C3×D3—42no—
255C2×C3×D3—44no—
256C32×C4C4×D414yes—
257C3⋊Dic3—42no—
258C3⋊Dic3—42no—
259C3×Dic3—24no—
260C3×Dic3—22no—
261C3×Dic3—22no—
262C3×Dic3—42no—
263C22×D4—34no—
264C22×D4—31no—
265C22×D4D3211yescharacteristic
266C23×C4—32no—
267C23×C4—92no—
268#127—38no—
269C4×D4—64no—
270C4×D4—184no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—91no—
273C2×C22⋊C4—32no—
274C2×C22⋊C4—92no—
275C2×C22⋊C4—94no—
276C2×C22⋊C4—94no—
277C2×C42—31no—
278C2×C42—31no—
279C2×C42—91no—
280#95—92no—
281#95—92no—
282#95—94no—
283C23×C3—22no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—24no—
287C23×C3—24no—
288C23×C3—24no—
289C23×C3—24no—
290C23×C3—22no—
291C23×C3—21no—
292C23×C3—24no—
293C23×C3—34no—
294C23×C3—44no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—44no—
298C23×C3—62no—
299C23×C3—64no—
300C23×C3—64no—
301C23×C3—62no—
302C23×C3C2×C4×D314yes—
303C23×C3C22×Dic314yes—
304C23×C3C23×D311yescharacteristic
305C23×C3C23×D311yescharacteristic
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—24no—
309C22×D3—24no—
310C22×D3C22×Dic314yes—
311C3×D4—28no—
312C3×D4—28no—
313C3×D4—48no—
314C3×D4—68no—
315C3×D4—1216no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—34no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—62no—
323C2×C3×C4—62no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—64no—
328C2×C3×C4—128no—
329C2×C3×C4C2×C4×D312yes—
330C2×C3×C4#23512yes—
331C2×C3×C4D3×D412yes—
332C2×C3×C4#23712yes—
333C2×C3×C4C22×Dic312yes—
334C2×C3×C4C2×#6712yes—
335#67—416no—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—24no—
341C2×Dic3—22no—
342C2×Dic3—48no—
343C2×Dic3—64no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—64no—
351C2×Dic3—62no—
352C2×Dic3—64no—
353C2×Dic3—62no—
354C2×Dic3—122no—
355C2×Dic3—122no—
356C2×Dic3—122no—
357C2×Dic3—124no—
358C2×Dic3—128no—
359C2×Dic3C22×Dic314yes—
360C2×Dic3C2×#6712yes—
361C2×Dic3C2×#6712yes—
362D12—28no—
363C4×D3—128no—
364C2×C32—44no—
365C2×C32C2×C4×D411yescharacteristic
366C2×C32#51812yes—
367C2×C32#53511yescharacteristic
368C2×C32#53511yescharacteristic
369C2×C32#54012yes—
370C3×D3—44no—
371C24—32no—
372C24C2×D3212yes—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—316no—
376C2×D4—34no—
377C2×D4—62no—
378C2×D4—62no—
379C2×D4—124no—
380C2×D4—124no—
381C2×D4D3×Dic314yescomplemented
382C22×C4—32no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—32no—
386C22×C4—64no—
387C22×C4—92no—
388C22×C4—92no—
389C22×C4—124no—
390C22×C4—184no—
391C22×C4—364no—
392C22×C4C2×D3211yescharacteristic
393C4⋊C4—62no—
394C4⋊C4—182no—
395C22⋊C4—64no—
396C22⋊C4—184no—
397C22⋊C4—364no—
398C22⋊C4—364no—
399C42—34no—
400C42—34no—
401C42—182no—
402C22×C3—24no—
403C22×C3—24no—
404C22×C3—28no—
405C22×C3—28no—
406C22×C3—22no—
407C22×C3—22no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—44no—
412C22×C3—48no—
413C22×C3—42no—
414C22×C3—42no—
415C22×C3—44no—
416C22×C3—42no—
417C22×C3—44no—
418C22×C3—42no—
419C22×C3—64no—
420C22×C3—68no—
421C22×C3—84no—
422C22×C3—82no—
423C22×C3—82no—
424C22×C3—122no—
425C22×C3—124no—
426C22×C3—122no—
427C22×C3C22×C4×D311yescharacteristic
428C22×C3C2×#23511yescharacteristic
429C22×C3C2×D3×D411yescharacteristic
430C22×C3C2×#23711yescharacteristic
431C22×C3#100412yes—
432C22×C3#100412yes—
433C22×C3#100412yes—
434C22×C3#100912yes—
435C22×C3C23×Dic311yescharacteristic
436C22×C3C22×#6711yescharacteristic
437C2×D3—24no—
438C2×D3—28no—
439C2×D3—42no—
440C2×D3—42no—
441C2×D3—44no—
442C3×C4—24no—
443C3×C4—62no—
444C3×C4—62no—
445C3×C4—64no—
446C3×C4—122no—
447C3×C4C4×#6714yes—
448C3×C4D4×Dic314yes—
449Dic3—24no—
450Dic3—22no—
451Dic3—22no—
452Dic3—42no—
453Dic3—124no—
454Dic3—122no—
455Dic3—122no—
456Dic3—122no—
457Dic3—122no—
458Dic3—242no—
459C32#232811yescharacteristic, complemented, Sylow
460C23—24no—
461C23—24no—
462C23—22no—
463C23—22no—
464C23—34no—
465C23—64no—
466C23—64no—
467C23—62no—
468C23—62no—
469C23C2×D3×Dic314yes—
470C23C22×D3211yescharacteristic
471D4—28no—
472D4—68no—
473D4—1216no—
474C2×C4—34no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—62no—
481C2×C4—64no—
482C2×C4—62no—
483C2×C4—128no—
484C2×C4—182no—
485C2×C4—182no—
486C2×C4—184no—
487C2×C4—182no—
488C2×C4—182no—
489C2×C4—368no—
490C2×C4C2×D3×Dic312yes—
491C2×C4#380412yes—
492C2×C4D3×#6712yes—
493C2×C3—22no—
494C2×C3—22no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—44no—
499C2×C3—44no—
500C2×C3—84no—
501C2×C3—124no—
502C2×C3#554512yes—
503C2×C3#556212yes—
504C2×C3#571511yescharacteristic
505C2×C3#571511yescharacteristic
506C2×C3#571912yes—
507C2×C3C2×C4×#6711yescharacteristic
508C2×C3C2×D4×Dic311yescharacteristic
509C2×C3#579812yes—
510C2×C3#580511yescharacteristic
511C2×C3#583011yescharacteristic
512D3—44no—
513C22—28no—
514C22—24no—
515C22—44no—
516C22—42no—
517C22—42no—
518C22—68no—
519C22—64no—
520C22—124no—
521C22—122no—
522C22—122no—
523C22#6431312yes—
524C22#6431412yes—
525C22C22×D3×Dic311yescharacteristic
526C22C2×#380411yescharacteristic
527C22C2×D3×#6711yescharacteristic
528C4—64no—
529C4—62no—
530C4—62no—
531C4—122no—
532C4—362no—
533C4—362no—
534C4Dic3×#6714yes—
535C3—21no—
536C3#8232911yescharacteristic, complemented
537C3#8317211yescharacteristic, complemented
538C2—44no—
539C2—124no—
540C2#1059521512yes—
541C2#1059521812yes—
542C2#1059523311yescharacteristic
543C2#1059530311yescharacteristic
544C2C2×Dic3×#6711yescharacteristic
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
2. C2×C3×D4×Dic3C2semidirect
3. C2×Dic3×D12C2semidirect
4. #10592920C2semidirect
5. #10591721C2semidirect
6. #10591710C2semidirect
7. #10591323C2semidirect
8. #10591224C2semidirect
9. #10591222C2semidirect
21. C3×#940C4semidirect
36. C2×D4×Dic3D3semidirect
55. C2×C32×D4C2×C4semidirect
61. C2×C3×#67C2×C4semidirect
70. C2×C3×D12C2×C4semidirect
78. C3×C4×Dic3C2×C4semidirect
79. C3×C4×Dic3D4semidirect
106. #940Dic3semidirect
187. C2×C3×D4C4×D3semidirect
188. C2×C3×D4C2×Dic3semidirect
200. C2×#67C2×Dic3semidirect
217. C2×D12C2×Dic3semidirect
239. C4×Dic3C2×Dic3semidirect
240. C4×Dic3#67semidirect
381. C2×D4D3×Dic3semidirect
459. C32#2328semidirect
536. C3#82329semidirect
537. C3#83172semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C2×C3×D4×Dic32
C2×Dic3×D122
#105929202
#105917212
#105917102
#105913232
#105912242
#105912222
#831723
#823293