Finite Group Databasebeta

← #11785122

Subgroups — #11785122

Order 1152.

721 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Dic3×D12C211yesmaximal, characteristic
2C2×C3×#823C211yesmaximal, characteristic
3C3×#5118C211yesmaximal, characteristic, complemented
4#10591115C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic
6#10589420C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70527—31nomaximal
9#70063—31nomaximal
10C22×C3×D12C2211yescharacteristic
11C22×D3×Dic3C412yes—
12C2×C32×M16C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×(C2×D3)⋊Dic3C412yes—
19Dic3×D12—21no—
20Dic3×D12—21no—
21Dic3×D12—21no—
22Dic3×D12—21no—
23C3×#823—22no—
24C3×Dic3⋊C8—21no—
25C3×Dic3⋊C8—21no—
26Dic3⋊(C3⋊C8)—21no—
27Dic3⋊(C3⋊C8)—21no—
28#63558—22no—
29C2×D4×Dic3—31no—
30C2×C4×D12—31no—
31C3×#423—31no—
32C2×C3×#100—31no—
33C2×#833—31no—
34C2×#823—31no—
35C2×#823D311yescharacteristic
36#5118—31no—
37#5118D311yescharacteristic, complemented
38#4924—31no—
39#4554—31no—
40#4554—31no—
41#4554—31no—
42#4554—31no—
43#4554—61no—
44C23×C3×D3C2×C412yes—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3C2×C412yes—
47C22×C3×Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C2×C3×D12—21no—
50C2×C3×D12—21no—
51C2×C3×D12—21no—
52C2×C3×D12—21no—
53C2×C3×D12D412yes—
54C2×C3×D12Q812yes—
55C2×D3×Dic3—22no—
56C2×D3×Dic3—22no—
57C2×D3×Dic3—44no—
58C32×M16—21no—
59C32×M16—21no—
60C2×C32×C8—21no—
61C4⋊(C3⋊Dic3)—21no—
62C4⋊(C3⋊Dic3)—21no—
63#3748—21no—
64#3748—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×C4×Dic3D411yescharacteristic
67C3×C4×Dic3D411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×#208—21no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76(C2×D3)⋊Dic3—22no—
77(C2×D3)⋊Dic3—22no—
78#1800—91noSylow
79C22×C3×D4—31no—
80C23×Dic3—32no—
81C22×D12C2×D311yescharacteristic
82C22×C4×D3—32no—
83C2×C3×M16—21no—
84C2×C3×M16—31no—
85C2×C3×M16—31no—
86C2×C3×M16C2×D311yescharacteristic
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×C42—31no—
89C2×#217—32no—
90D4×Dic3—61no—
91D4×Dic3—61no—
92D4×Dic3—61no—
93D4×Dic3—61no—
94C2×(C2×D3)⋊C4—32no—
95C2×C4⋊Dic3—31no—
96C2×C4⋊Dic3—31no—
97C2×C4⋊Dic3—61no—
98C2×C4×Dic3C2×D311yescharacteristic
99C2×#208—31no—
100C2×#208—31no—
101C2×#208—61no—
102C2×#208C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104C4×D12—61no—
105C4×D12—61no—
106C4×D12—61no—
107C4×D12—61no—
108C3×C4⋊C8—61no—
109C3×C4⋊C8—61no—
110C3×#100—62no—
111#833—62no—
112#823—22no—
113#823—62no—
114Dic3⋊C8—21no—
115Dic3⋊C8—21no—
116Dic3⋊C8—61no—
117Dic3⋊C8—61no—
118C4⋊(C3⋊C8)—61no—
119C4⋊(C3⋊C8)—61no—
120C23×C32C22×C411yescharacteristic
121C22×C3×D3—22no—
122C22×C3×D3—22no—
123C22×C3×D3—42no—
124C22×C3×D3—42no—
125C22×C3×D3C4⋊C414yes—
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×Q811yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—42no—
134C2×C3×Dic3—22no—
135C2×C3×Dic3—41no—
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C2×C3×Dic3C22⋊C411yescharacteristic
140C3×D12—22no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12—22no—
144D3×Dic3—44no—
145D3×Dic3—44no—
146C32×C8—41no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—41no—
149C3×C3⋊C8—41no—
150C2×C4×D4—91no—
151#423—31no—
152#423—91no—
153C2×#100—31no—
154C2×#100—91no—
155#343—91no—
156#343—91no—
157C24×C3—32no—
158C23×D3C4×D312yes—
159C2×C3×D4—32no—
160C2×C3×D4—32no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C2×C3×D4—61no—
165C22×C3×C4—21no—
166C22×C3×C4—31no—
167C22×C3×C4—31no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C22×Dic3—32no—
171C22×Dic3—32no—
172C22×Dic3—62no—
173C22×Dic3—62no—
174C22×Dic3—62no—
175C22×Dic3—124no—
176C22×Dic3C4×D311yescharacteristic
177C22×Dic3C4×D311yescharacteristic
178C2×D12—21no—
179C2×D12—21no—
180C2×D12—21no—
181C2×D12—21no—
182C2×D12Dic612yes—
183C2×D12#6712yes—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—124no—
187C3×M16—22no—
188C3×M16—21no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16—21no—
192C3×M16—41no—
193C3×M16—61no—
194C3×M16—61no—
195C3×M16—61no—
196C3×M16—61no—
197C2×C3×C8—21no—
198C2×C3×C8—21no—
199C2×C3×C8—41no—
200C2×C3×C8—61no—
201C2×C3×C8—61no—
202C3×C42—31no—
203C3×C42—31no—
204C3×C42—31no—
205C3×C42—31no—
206#217—62no—
207#217—62no—
208(C2×D3)⋊C4—62no—
209(C2×D3)⋊C4—62no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—61no—
213C4⋊Dic3—61no—
214C4⋊Dic3—121no—
215C4⋊Dic3—121no—
216C4×Dic3D1211yescharacteristic
217C4×Dic3D1211yescharacteristic
218C4×Dic3#6711yescharacteristic
219C4×Dic3#6711yescharacteristic
220#208—21no—
221#208—21no—
222#208—21no—
223#208—21no—
224#208—62no—
225#208—61no—
226#208—61no—
227#208—61no—
228#208—61no—
229#208—121no—
230C2×C3⋊C8—21no—
231C2×C3⋊C8—21no—
232C2×C3⋊C8—61no—
233C2×C3⋊C8—61no—
234C2×C3⋊C8—121no—
235C22×C32—21no—
236C22×C32—21no—
237C22×C32C2×C22⋊C411yescharacteristic
238C22×C32C2×C4⋊C411yescharacteristic
239C22×C32#11711yescharacteristic
240C2×C3×D3—24no—
241C2×C3×D3—44no—
242C2×C3×D3—42no—
243C2×C3×D3—42no—
244C2×C3×D3—44no—
245C32×C4#12111yescharacteristic
246C32×C4#12111yescharacteristic
247C32×C4C22⋊Q811yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C3⋊Dic3—42no—
250C3×Dic3—21no—
251C3×Dic3—21no—
252C3×Dic3—21no—
253C3×Dic3#10012yescomplemented
254C22×D4—31no—
255C23×C4—92no—
256C2×M16—31no—
257C2×M16—31no—
258C2×M16—91no—
259C2×M16D3211yescharacteristic
260C4×D4—181no—
261C4×D4—181no—
262C4×D4—181no—
263C4×D4—181no—
264C2×C4⋊C4—91no—
265C2×C22⋊C4—92no—
266C2×C42—31no—
267C4⋊C8—61no—
268C4⋊C8—61no—
269C4⋊C8—181no—
270C4⋊C8—181no—
271#100—62no—
272#100—182no—
273C23×C3—21no—
274C23×C3—34no—
275C23×C3—62no—
276C23×C3—62no—
277C23×C3—122no—
278C23×C3—122no—
279C23×C3C2×C4×D311yescharacteristic
280C23×C3C2×C4×D311yescharacteristic
281C22×D3—22no—
282C22×D3—22no—
283C22×D3—42no—
284C22×D3—42no—
285C22×D3Dic3⋊C414yes—
286C3×D4—62no—
287C3×D4—62no—
288C3×D4—62no—
289C3×D4—62no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—31no—
297C2×C3×C4—31no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—62no—
301C2×C3×C4—121no—
302C2×C3×C4C2×Dic611yescharacteristic
303C2×C3×C4C2×D1211yescharacteristic
304C2×C3×C4D3×D411yescharacteristic
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4#23711yescharacteristic
308C2×C3×C4#23711yescharacteristic
309C2×C3×C4#23711yescharacteristic
310C2×C3×C4D3×Q811yescharacteristic
311C2×C3×C4#23911yescharacteristic
312C2×C3×C4C2×#6711yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314C2×Dic3—22no—
315C2×Dic3—41no—
316C2×Dic3—62no—
317C2×Dic3—62no—
318C2×Dic3—122no—
319C2×Dic3—124no—
320C2×Dic3—124no—
321C2×Dic3—122no—
322C2×Dic3—122no—
323C2×Dic3—242no—
324C2×Dic3(C2×D3)⋊C411yescharacteristic
325C2×Dic3(C2×D3)⋊C411yescharacteristic
326C2×Dic3(C2×D3)⋊C411yescharacteristic
327C2×Dic3(C2×D3)⋊C411yescharacteristic
328D12—22no—
329D12—22no—
330D12—22no—
331D12—22no—
332C4×D3—124no—
333C4×D3—124no—
334C3×C8—42no—
335C3×C8—41no—
336C3×C8—41no—
337C3×C8—121no—
338C3×C8—121no—
339C3⋊C8—41no—
340C3⋊C8—41no—
341C3⋊C8—122no—
342C3⋊C8—121no—
343C3⋊C8—121no—
344C2×C32—21no—
345C2×C32—21no—
346C2×C32#38011yescharacteristic
347C2×C32C2×#10011yescharacteristic
348C2×C32#41311yescharacteristic
349C3×D3—44no—
350C24—32no—
351C2×D4—32no—
352C2×D4—32no—
353C2×D4—61no—
354C2×D4—61no—
355C2×D4—61no—
356C2×D4—61no—
357C22×C4—31no—
358C22×C4—31no—
359C22×C4—92no—
360C22×C4—182no—
361C22×C4—182no—
362C22×C4—364no—
363C22×C4C2×D3211yescharacteristic
364M16—21no—
365M16—21no—
366M16—61no—
367M16—61no—
368M16—61no—
369M16—61no—
370M16—181no—
371M16—181no—
372C2×C8—21no—
373C2×C8—61no—
374C2×C8—61no—
375C2×C8—181no—
376C4⋊C4—181no—
377C4⋊C4—181no—
378C22⋊C4—182no—
379C22⋊C4—182no—
380C42—31no—
381C42—31no—
382C42—31no—
383C42—31no—
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—21no—
387C22×C3—21no—
388C22×C3—21no—
389C22×C3—21no—
390C22×C3—21no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—64no—
394C22×C3—124no—
395C22×C3—124no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3#87711yescharacteristic
399C22×C3D3×C22⋊C411yescharacteristic
400C22×C3D3×C4⋊C411yescharacteristic
401C22×C3#89211yescharacteristic
402C22×C3C2×Dic3⋊C411yescharacteristic
403C22×C3C2×(C2×D3)⋊C411yescharacteristic
404C2×D3—24no—
405C2×D3—44no—
406C2×D3—42no—
407C2×D3—42no—
408C2×D3—44no—
409C3×C4—21no—
410C3×C4—21no—
411C3×C4—21no—
412C3×C4—21no—
413C3×C4—32no—
414C3×C4—61no—
415C3×C4—61no—
416C3×C4—61no—
417C3×C4#87811yescharacteristic
418C3×C4#87811yescharacteristic
419C3×C4#89511yescharacteristic
420C3×C4#89711yescharacteristic
421C3×C4#93811yescharacteristic
422C3×C4#93911yescharacteristic
423C3×C4#93911yescharacteristic
424C3×C4#94611yescharacteristic
425Dic3—21no—
426Dic3—21no—
427Dic3—21no—
428Dic3—122no—
429Dic3—122no—
430Dic3—242no—
431Dic3#82312yescomplemented
432C32#180011yescharacteristic, complemented, Sylow
433C23—34no—
434C23—62no—
435C23—62no—
436C23—122no—
437C23—122no—
438C23C4×D3211yescharacteristic
439D4—62no—
440D4—62no—
441D4—62no—
442D4—62no—
443C2×C4—31no—
444C2×C4—31no—
445C2×C4—31no—
446C2×C4—31no—
447C2×C4—62no—
448C2×C4—121no—
449C2×C4—182no—
450C2×C4—364no—
451C2×C4—364no—
452C2×C4—362no—
453C2×C4D3×Dic611yescharacteristic
454C2×C4#379611yescharacteristic
455C2×C4D3×D1211yescharacteristic
456C2×C4#380511yescharacteristic
457C2×C4D3×#6711yescharacteristic
458C2×C4D3×#6711yescharacteristic
459C8—41no—
460C8—121no—
461C8—121no—
462C8—361no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—21no—
467C2×C3—21no—
468C2×C3—21no—
469C2×C3—21no—
470C2×C3—41no—
471C2×C3—41no—
472C2×C3—124no—
473C2×C3D3×#10011yescharacteristic
474C2×C3#474511yescharacteristic
475C2×C3#494211yescharacteristic
476C2×C3#498711yescharacteristic
477C2×C3C2×#82311yescharacteristic
478C2×C3#513211yescharacteristic
479D3—44no—
480C22—21no—
481C22—21no—
482C22—64no—
483C22—124no—
484C22—124no—
485C22—122no—
486C22—122no—
487C22D3×Dic3⋊C411yescharacteristic
488C22#6387811yescharacteristic
489C22D3×(C2×D3)⋊C411yescharacteristic
490C4—32no—
491C4—61no—
492C4—61no—
493C4—61no—
494C4—362no—
495C4#6388611yescharacteristic
496C4#6388711yescharacteristic
497C4#6389311yescharacteristic
498C4#6397011yescharacteristic
499C3—21no—
500C3#7006311yescharacteristic, complemented
501C3#7052711yescharacteristic, complemented
502C2—21no—
503C2—21no—
504C2—124no—
505C2D3×#82311yescharacteristic
506C2#1059100611yescharacteristic
507C2#1059136611yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D12C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1800
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5118C2semidirect
4. #10591115C2semidirect
6. #10589420C2semidirect
7. #10589168C2semidirect
37. #5118D3semidirect
253. C3×Dic3#100semidirect
431. Dic3#823semidirect
432. C32#1800semidirect
500. C3#70063semidirect
501. C3#70527semidirect

Maximal subgroups

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

subgroupindex
C2×Dic3×D122
C2×C3×#8232
C3×#51182
#105911152
C2×#635582
#105894202
#105891682
#705273
#700633