Finite Group Databasebeta

← #11788787

Subgroups — #11788787

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 529 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic, complemented
2#10595045C211yesmaximal, characteristic
3C3×#5005C211yesmaximal, characteristic, complemented
4#10591110C211yesmaximal, characteristic, complemented
5C2×#63559C211yesmaximal, characteristic, complemented
6C3×#4531C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70408—31nomaximal
9#68705—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14#64102—22no—
15C22⋊C4×C3⋊D3—22no—
16C4×C4⋊(C3⋊D3)—22no—
17C3×#926C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20#63981—22no—
21#63911C412yescomplemented
22#63909—22no—
23#63864C412yescomplemented
24C3×#805—22no—
25#63568—22no—
26#63559—22no—
27#5830—31no—
28#5525—31no—
29#5521—31no—
30#5521—31no—
31#5521—61no—
32C3×#421—31no—
33#5236—31no—
34#5139—31no—
35C2×#823—31no—
36C2×#823—31no—
37#5005D311yescharacteristic, complemented
38C3×H(3,ℤ/4)—31no—
39#4557—31no—
40#4531—31no—
41#4531D311yescharacteristic, complemented
42C23×C3⋊D3D412yes—
43C22×C32×C4C2311yescharacteristic
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)C2×C412yes—
49C2×C4⋊(C3⋊D3)D412yes—
50C2×C4×C3⋊D3—24no—
51C2×C3×#67—21no—
52C3×#235—21no—
53C3×#235—21no—
54C3×#235—21no—
55C3×#235—21no—
56C2×C3×D12C2×C411yescharacteristic, complemented
57C2×C3×C4×D3—21no—
58C2×C3×Dic6C2×C411yescharacteristic, complemented
59C2×#626—24no—
60C32×C4⋊C4—21no—
61C32×C22⋊C4—21no—
62C32×C42D412yescomplemented
63#3757—21no—
64#3752—24no—
65C4⋊(C3⋊Dic3)—21no—
66C4×C3⋊Dic3D412yescomplemented
67C3×#217—21no—
68C3×C4⋊Dic3—21no—
69C3×C4×Dic3C2×C412yescomplemented
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76#3722—24no—
77#1911—91noSylow
78C2×C3×#41—31no—
79C2×#235C2×D311yescharacteristic
80C22×D12—31no—
81C22×D12—31no—
82C22×D12—61no—
83C2×C3×M16—31no—
84C2×C3×M16—31no—
85C3×#117—21no—
86C3×#117—31no—
87C3×#117C2×D311yescharacteristic
88C3×#117C2×D311yescharacteristic
89#947—32no—
90#940—32no—
91#937—62no—
92#930—62no—
93#926—31no—
94#926—31no—
95#926—61no—
96#926C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99#895—62no—
100#893—62no—
101#893—62no—
102#893—64no—
103#882—62no—
104D3×C22⋊C4—62no—
105D3×C22⋊C4—62no—
106D3×C22⋊C4—64no—
107#875—32no—
108#874—32no—
109C4×D12—64no—
110C4×D12—62no—
111C4×D12—62no—
112C3×#104—62no—
113#837—62no—
114#825—62no—
115#823—62no—
116#823—62no—
117#805—22no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3—22no—
120C22×C3⋊D3—22no—
121C22×C3⋊D3—82no—
122C22×C3⋊D3C22⋊C414yes—
123C22×C3×D3—21no—
124C2×C32×C4—22no—
125C2×C32×C4C22×C411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4#4111yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C3⋊Dic3—22no—
132C4⋊(C3⋊D3)—22no—
133C4⋊(C3⋊D3)—22no—
134C4⋊(C3⋊D3)—22no—
135C4⋊(C3⋊D3)—22no—
136C4×C3⋊D3—84no—
137C3×#67—41no—
138C3×#67—41no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3—22no—
141C3×D12—21no—
142C3×D12—21no—
143C3×C4×D3—41no—
144C3×C4×D3—41no—
145C3×Dic6—21no—
146C3×Dic6—21no—
147#626—84no—
148C3×C3⋊C8—41no—
149C3×C3⋊C8—41no—
150#535—91no—
151#518—91no—
152#421—31no—
153#421—91no—
154C2×#100—91no—
155H(3,ℤ/4)—31no—
156H(3,ℤ/4)—91no—
157C23×D3—32no—
158C23×D3—32no—
159C23×D3—62no—
160C3×#41—61no—
161C3×#41—61no—
162C3×#41—61no—
163C3×#41—61no—
164C2×C3×Q8—31no—
165C2×C3×D4—31no—
166C2×C3×D4—61no—
167C22×C3×C4—21no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C2×#67—21no—
172C2×#67—64no—
173#235—21no—
174#235—21no—
175#235—21no—
176#235—21no—
177C2×D12—32no—
178C2×D12—32no—
179C2×D12—32no—
180C2×D12—32no—
181C2×D12—62no—
182C2×D12—62no—
183C2×D12—62no—
184C2×D12—62no—
185C2×D12—62no—
186C2×D12—62no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—61no—
190C2×D12—61no—
191C2×D12—61no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—64no—
196C2×D12C4×D311yescharacteristic, complemented
197C2×C4×D3—21no—
198C2×C4×D3—68no—
199C2×C4×D3—64no—
200C2×C4×D3—64no—
201C2×Dic6C4×D311yescharacteristic, complemented
202C3×M16—61no—
203C3×M16—61no—
204C3×M16—61no—
205C3×M16—61no—
206C2×C3×C8—61no—
207C2×C3×C8—61no—
208C3×C4⋊C4—22no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—61no—
212C3×C22⋊C4—22no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—21no—
215C3×C22⋊C4—61no—
216C3×C42—22no—
217C3×C42—32no—
218C3×C42D1212yescomplemented
219C3×C42#6712yescomplemented
220#217—21no—
221#217—62no—
222#217—61no—
223#217—61no—
224(C2×D3)⋊C4—64no—
225(C2×D3)⋊C4—64no—
226(C2×D3)⋊C4—68no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
229C4⋊Dic3—21no—
230C4⋊Dic3—62no—
231C4⋊Dic3—61no—
232C4⋊Dic3—61no—
233C4×Dic3—32no—
234C4×Dic3—32no—
235C4×Dic3—62no—
236C4×Dic3C4×D312yescomplemented
237#208—21no—
238#208—21no—
239#208—21no—
240#208—21no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—21no—
243C22×C32—41no—
244C22×C32C2×C22⋊C411yescharacteristic
245C22×C32#12011yescharacteristic
246C22×C32#12311yescharacteristic
247C2×C3⋊D3—24no—
248C2×C3⋊D3—44no—
249C2×C3⋊D3—44no—
250C2×C3⋊D3—82no—
251C2×C3×D3—42no—
252C2×C3×D3—41no—
253C32×C4—42no—
254C32×C4C4×D411yescharacteristic
255C32×C4C4×D411yescharacteristic
256C32×C4#12111yescharacteristic
257C32×C4#12111yescharacteristic
258C3⋊Dic3—42no—
259C3×Dic3—42no—
260C3×Dic3—41no—
261C2×#41—31no—
262C22×D4—91no—
263C2×M16—31no—
264C2×M16—31no—
265#127—92no—
266#124—92no—
267#121—182no—
268#120—182no—
269C4×D4—182no—
270C4×D4—182no—
271#117—31no—
272#117—91no—
273#117D3211yescharacteristic
274C2×C22⋊C4—182no—
275#104—62no—
276#104—182no—
277#100—182no—
278C23×C3—21no—
279C23×C3—61no—
280C23×C3D3×D411yescharacteristic
281C23×C3D3×D411yescharacteristic
282C22×D3—21no—
283C22×D3—34no—
284C22×D3—34no—
285C22×D3—64no—
286C22×D3—64no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—64no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—242no—
293C22×D3—242no—
294C22×D3—244no—
295C3×Q8—61no—
296C3×Q8—61no—
297C3×D4—61no—
298C3×D4—61no—
299C3×D4—121no—
300C3×D4—121no—
301C2×C3×C4—24no—
302C2×C3×C4—22no—
303C2×C3×C4—22no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—61no—
311C2×C3×C4—62no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×C4×D311yescharacteristic
316C2×C3×C4C2×D1211yescharacteristic
317C2×C3×C4#23511yescharacteristic
318C2×C3×C4#23511yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4#23911yescharacteristic
325C2×C3×C4C2×#6711yescharacteristic
326#67—41no—
327#67—41no—
328#67—244no—
329C2×Dic3—22no—
330C2×Dic3—21no—
331C2×Dic3—64no—
332C2×Dic3—62no—
333C2×Dic3—62no—
334D12—21no—
335D12—21no—
336D12—64no—
337D12—64no—
338D12—64no—
339D12—64no—
340D12—62no—
341D12—62no—
342D12—62no—
343D12—62no—
344D12—62no—
345D12—62no—
346D12—62no—
347D12—62no—
348D12—244no—
349C4×D3—41no—
350C4×D3—41no—
351C4×D3—248no—
352C4×D3—244no—
353C4×D3—244no—
354Dic6—21no—
355Dic6—21no—
356C3×C8—121no—
357C3×C8—121no—
358C3⋊C8—41no—
359C3⋊C8—41no—
360C2×C32—21no—
361C2×C32—21no—
362C2×C32—21no—
363C2×C32#38611yescharacteristic
364C3⋊D3—44no—
365C3×D3—81no—
366C24—92no—
367#41—61no—
368#41—61no—
369#41—61no—
370#41—61no—
371C2×Q8—31no—
372C2×D4—31no—
373C2×D4—61no—
374C2×D4—92no—
375C2×D4—92no—
376C2×D4—184no—
377C2×D4—181no—
378C2×D4—181no—
379C2×D4—181no—
380C2×D4—181no—
381C22×C4—61no—
382C22×C4—184no—
383C22×C4C2×D3211yescharacteristic
384M16—61no—
385M16—61no—
386M16—61no—
387M16—61no—
388C2×C8—61no—
389C2×C8—61no—
390C4⋊C4—21no—
391C4⋊C4—61no—
392C4⋊C4—181no—
393C22⋊C4—21no—
394C22⋊C4—61no—
395C22⋊C4—184no—
396C22⋊C4—184no—
397C22⋊C4—181no—
398C42—32no—
399C42—92no—
400C42#62612yescomplemented
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—41no—
405C22×C3—41no—
406C22×C3—42no—
407C22×C3—122no—
408C22×C3—121no—
409C22×C3D3×C22⋊C411yescharacteristic
410C22×C3D3×C22⋊C411yescharacteristic
411C22×C3#88211yescharacteristic
412C22×C3#88311yescharacteristic
413C22×C3#89411yescharacteristic
414C22×C3#93711yescharacteristic
415C2×D3—42no—
416C2×D3—41no—
417C2×D3—68no—
418C2×D3—64no—
419C2×D3—64no—
420C2×D3—128no—
421C2×D3—124no—
422C2×D3—124no—
423C2×D3—124no—
424C2×D3—124no—
425C2×D3—244no—
426C2×D3—242no—
427C2×D3—242no—
428C2×D3—244no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—44no—
434C3×C4—42no—
435C3×C4—42no—
436C3×C4—122no—
437C3×C4—121no—
438C3×C4C4×D1211yescharacteristic
439C3×C4#67⋊C411yescharacteristic
440C3×C4#88411yescharacteristic
441C3×C4#88411yescharacteristic
442C3×C4#89311yescharacteristic
443C3×C4#89511yescharacteristic
444C3×C4C4×#6711yescharacteristic
445C3×C4#93811yescharacteristic
446Dic3—42no—
447Dic3—41no—
448Dic3—124no—
449Dic3—122no—
450Dic3—122no—
451C32#191111yescharacteristic, complemented, Sylow
452C23—61no—
453C23—94no—
454C23—182no—
455C23—182no—
456C23—722no—
457C23#381111yescharacteristic
458Q8—61no—
459Q8—61no—
460D4—61no—
461D4—61no—
462D4—121no—
463D4—121no—
464D4—182no—
465D4—182no—
466D4—182no—
467D4—182no—
468D4—724no—
469C2×C4—22no—
470C2×C4—62no—
471C2×C4—61no—
472C2×C4—121no—
473C2×C4—121no—
474C2×C4—182no—
475C2×C4—724no—
476C2×C4#379611yescharacteristic
477C2×C4#379811yescharacteristic
478C2×C4C4×D3211yescharacteristic
479C2×C4#380211yescharacteristic
480C2×C4C2×#62611yescharacteristic
481C2×C4#381111yescharacteristic
482C8—121no—
483C8—121no—
484C2×C3—22no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—41no—
493C2×C3—41no—
494C2×C3—241no—
495C2×C3#466511yescharacteristic
496C2×C3#495611yescharacteristic
497D3—81no—
498D3—128no—
499D3—124no—
500D3—124no—
501C22—41no—
502C22—122no—
503C22—121no—
504C22—184no—
505C22—364no—
506C22—364no—
507C22—722no—
508C22#6385311yescharacteristic
509C22#6392111yescharacteristic
510C22#6398111yescharacteristic
511C4—42no—
512C4—122no—
513C4—121no—
514C4—362no—
515C4#6388111yescharacteristic
516C4C4×#62611yescharacteristic
517C4#6391211yescharacteristic
518C4#6391611yescharacteristic
519C3—21no—
520C3#6870511yescharacteristic, complemented
521C3#7040811yescharacteristic, complemented
522C2—21no—
523C2—21no—
524C2—21no—
525C2—241no—
526C2—364no—
527C2#1059138711yescharacteristic
subgroupG/H
centerC2#10591387
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radical#10595045C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1911
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595992C2semidirect
3. C3×#5005C2semidirect
4. #10591110C2semidirect
5. C2×#63559C2semidirect
6. C3×#4531C2semidirect
7. #10589158C2semidirect
21. #63911C4semidirect
23. #63864C4semidirect
37. #5005D3semidirect
41. #4531D3semidirect
56. C2×C3×D12C2×C4semidirect
58. C2×C3×Dic6C2×C4semidirect
62. C32×C42D4semidirect
66. C4×C3⋊Dic3D4semidirect
69. C3×C4×Dic3C2×C4semidirect
196. C2×D12C4×D3semidirect
201. C2×Dic6C4×D3semidirect
218. C3×C42D12semidirect
219. C3×C42#67semidirect
236. C4×Dic3C4×D3semidirect
400. C42#626semidirect
451. C32#1911semidirect
520. C3#68705semidirect
521. C3#70408semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105950452
C3×#50052
#105911102
C2×#635592
C3×#45312
#105891582
#704083
#687053