Finite Group Databasebeta

← #11788786

Subgroups — #11788786

Order 1152.

801 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic, complemented
2#10595042C211yesmaximal, characteristic
3#10592704C211yesmaximal, characteristic, complemented
4#10591113C211yesmaximal, characteristic, complemented
5C2×#63558C211yesmaximal, characteristic, complemented
6C3×#4531C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#71652—31nomaximal
9#68705—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#893—22no—
18C3×D3×C22⋊C4—22no—
19C3×C4×D12—22no—
20#63977—22no—
21#63916—22no—
22#63911C412yescomplemented
23#63860C412yescomplemented
24#63632—22no—
25#63570—22no—
26#63558—22no—
27C3×#518—31no—
28#5805—31no—
29#5525—31no—
30#5521D311yescharacteristic, complemented
31C2×#833—31no—
32#5139—31no—
33C2×#823—31no—
34#5005—31no—
35#5005—31no—
36#5005—31no—
37#5005—61no—
38C3×H(3,ℤ/4)—31no—
39#4531—31no—
40#4531—31no—
41#4531D311yescharacteristic, complemented
42C23×C3×D3D412yes—
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
50C2×C4×C3⋊D3—21no—
51C2×#634C2×C411yescharacteristic, complemented
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12C2×C412yes—
57C2×C3×D12D412yes—
58C2×C3×C4×D3—24no—
59C2×#626—24no—
60C32×C4⋊C4—21no—
61C32×C22⋊C4—21no—
62C32×C42D412yescomplemented
63#3748—21no—
64#3748—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C3×#217—21no—
67C3×#217—21no—
68C3×(C2×D3)⋊C4—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3C2×C412yescomplemented
72C3×C4×Dic3D412yescomplemented
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8—21no—
76(C2×D3)⋊Dic3—24no—
77#1911—91noSylow
78C22×C3×D4—31no—
79C2×#235—31no—
80C2×#235—31no—
81C2×#235—61no—
82C22×D12C2×D311yescharacteristic
83C2×C3×M16—31no—
84C3×C4×D4—62no—
85C3×C4×D4—62no—
86C3×#117—21no—
87C3×#117—31no—
88C3×#117—31no—
89C3×#117C2×D311yescharacteristic
90C3×#117C2×D311yescharacteristic
91C2×C3×C22⋊C4—62no—
92#953—62no—
93#940—32no—
94#938—62no—
95#936—32no—
96#926C2×D311yescharacteristic
97#926C2×D311yescharacteristic
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208C2×D311yescharacteristic
102#895—62no—
103#893—22no—
104#882—62no—
105D3×C22⋊C4—22no—
106#875—32no—
107#874—32no—
108C4×D12—22no—
109#833—62no—
110#825—62no—
111#823—62no—
112#805—62no—
113#805—64no—
114#805—62no—
115#805—62no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3—21no—
118C22×C3×D3—22no—
119C22×C3×D3—22no—
120C22×C3×D3—82no—
121C22×C3×D3C22⋊C414yes—
122C2×C32×C4—22no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4#4111yescharacteristic
128C2×C32×C4#4111yescharacteristic
129#638—41no—
130#638—41no—
131C2×C3⋊Dic3—21no—
132C4⋊(C3⋊D3)—21no—
133C4⋊(C3⋊D3)—21no—
134C4×C3⋊D3—41no—
135C4×C3⋊D3—41no—
136#634—21no—
137#634—21no—
138C2×C3×Dic3—22no—
139C2×C3×Dic3—22no—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12—22no—
143C3×D12—22no—
144C3×C4×D3—84no—
145#626—84no—
146C3⋊(C3⋊C8)—41no—
147C3×C3⋊C8—41no—
148#535—91no—
149#518—31no—
150#421—91no—
151#421—91no—
152C2×#100—91no—
153H(3,ℤ/4)—31no—
154H(3,ℤ/4)—91no—
155C24×C3—32no—
156C23×D3#6712yes—
157C2×C3×D4—32no—
158C2×C3×D4—32no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C22×C3×C4—21no—
164C22×C3×C4—64no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—64no—
168C2×#67—61no—
169C2×#67—61no—
170C2×#67—121no—
171#235—62no—
172#235—62no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177#235—61no—
178#235—61no—
179#235—61no—
180#235—61no—
181#235—121no—
182#235—121no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—31no—
188C2×D12—31no—
189C2×D12—61no—
190C2×D12—64no—
191C2×D12C4×D312yes—
192C2×D12D1212yes—
193C2×C4×D3—24no—
194C2×C4×D3—61no—
195C2×C4×D3—61no—
196C2×C4×D3—121no—
197C2×Dic6—31no—
198C2×Dic6—31no—
199C2×Dic6—61no—
200C3×M16—61no—
201C3×M16—61no—
202C2×C3×C8—61no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—41no—
206C3×C4⋊C4—61no—
207C3×C4⋊C4—61no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—41no—
211C3×C22⋊C4—64no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C42—22no—
215C3×C42—32no—
216C3×C42—32no—
217C3×C42D1212yescomplemented
218C3×C42#6712yescomplemented
219#217—21no—
220#217—21no—
221#217—64no—
222(C2×D3)⋊C4—24no—
223(C2×D3)⋊C4—64no—
224C4⋊Dic3—21no—
225C4⋊Dic3—21no—
226C4×Dic3C4×D312yescomplemented
227C4×Dic3#6712yescomplemented
228#208—21no—
229#208—21no—
230#208—62no—
231#208—61no—
232#208—61no—
233#208—61no—
234#208—61no—
235#208—121no—
236C2×C3⋊C8—21no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—121no—
240C22×C32—41no—
241C22×C32C2×C22⋊C411yescharacteristic
242C22×C32#12011yescharacteristic
243C22×C32#12311yescharacteristic
244C2×C3⋊D3—41no—
245C2×C3⋊D3—42no—
246C2×C3×D3—24no—
247C2×C3×D3—44no—
248C2×C3×D3—44no—
249C2×C3×D3—82no—
250C32×C4—42no—
251C32×C4C4×D411yescharacteristic
252C32×C4C4×D411yescharacteristic
253C32×C4#12111yescharacteristic
254C32×C4#12111yescharacteristic
255C3⋊Dic3—41no—
256C3×Dic3—42no—
257C3×Dic3—42no—
258C2×#41—91no—
259C22×D4—31no—
260C2×M16—31no—
261C2×M16—91no—
262#127—92no—
263#124—92no—
264#121—182no—
265#120—182no—
266C4×D4—62no—
267C4×D4—62no—
268#117—31no—
269#117—31no—
270#117D3211yescharacteristic
271C2×C22⋊C4—62no—
272#104—182no—
273#104—182no—
274#100—182no—
275C23×C3—21no—
276C23×C3—34no—
277C23×C3—62no—
278C23×C3—62no—
279C23×C3—242no—
280C23×C3D3×D411yescharacteristic
281C23×C3C2×#6711yescharacteristic
282C22×D3—22no—
283C22×D3—22no—
284C22×D3—61no—
285C22×D3—61no—
286C22×D3—82no—
287C22×D3—121no—
288C22×D3(C2×D3)⋊C414yes—
289C3×D4—62no—
290C3×D4—62no—
291C3×D4—62no—
292C3×D4—62no—
293C2×C3×C4—22no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—42no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—244no—
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×D1211yescharacteristic
308C2×C3×C4C2×D1211yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4#23911yescharacteristic
315C2×C3×C4C2×#6711yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317#67—122no—
318#67—122no—
319#67—121no—
320#67—121no—
321#67—121no—
322#67—121no—
323#67—244no—
324C2×Dic3—22no—
325C2×Dic3—22no—
326C2×Dic3—61no—
327C2×Dic3—61no—
328C2×Dic3—121no—
329D12—22no—
330D12—22no—
331D12—22no—
332D12—22no—
333D12—62no—
334D12—61no—
335D12—61no—
336D12—61no—
337D12—61no—
338D12—121no—
339D12—244no—
340C4×D3—84no—
341C4×D3—122no—
342C4×D3—122no—
343C4×D3—121no—
344C4×D3—121no—
345C4×D3—121no—
346C4×D3—121no—
347Dic6—62no—
348Dic6—61no—
349Dic6—61no—
350Dic6—61no—
351Dic6—61no—
352Dic6—121no—
353C3×C8—121no—
354C3⋊C8—41no—
355C3⋊C8—122no—
356C3⋊C8—121no—
357C3⋊C8—121no—
358C2×C32—21no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32#38611yescharacteristic
362C3⋊D3—81no—
363C3×D3—44no—
364C24—32no—
365#41—181no—
366#41—181no—
367#41—181no—
368#41—181no—
369C2×Q8—91no—
370C2×D4—32no—
371C2×D4—32no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—91no—
377C2×D4—184no—
378C2×D4—181no—
379C22×C4—64no—
380C22×C4—181no—
381C22×C4C2×D3211yescharacteristic
382M16—61no—
383M16—61no—
384M16—181no—
385M16—181no—
386C2×C8—61no—
387C2×C8—181no—
388C4⋊C4—21no—
389C4⋊C4—61no—
390C4⋊C4—61no—
391C22⋊C4—21no—
392C22⋊C4—64no—
393C22⋊C4—61no—
394C22⋊C4—61no—
395C22⋊C4—184no—
396C42—32no—
397C42—32no—
398C42#62612yescomplemented
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—64no—
405C22×C3—81no—
406C22×C3—124no—
407C22×C3—124no—
408C22×C3—242no—
409C22×C3D3×C22⋊C411yescharacteristic
410C22×C3#88211yescharacteristic
411C22×C3#89411yescharacteristic
412C22×C3C2×(C2×D3)⋊C411yescharacteristic
413C22×C3#92911yescharacteristic
414C22×C3#95311yescharacteristic
415C2×D3—24no—
416C2×D3—44no—
417C2×D3—44no—
418C2×D3—82no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—122no—
422C2×D3—121no—
423C2×D3—121no—
424C2×D3—242no—
425C3×C4—21no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—42no—
430C3×C4—42no—
431C3×C4—82no—
432C3×C4—122no—
433C3×C4—122no—
434C3×C4C4×D1211yescharacteristic
435C3×C4#88411yescharacteristic
436C3×C4#89311yescharacteristic
437C3×C4#89511yescharacteristic
438C3×C4C4×#6711yescharacteristic
439C3×C4C4×#6711yescharacteristic
440C3×C4#93011yescharacteristic
441C3×C4#93011yescharacteristic
442Dic3—42no—
443Dic3—42no—
444Dic3—122no—
445Dic3—121no—
446Dic3—121no—
447C32#191111yescharacteristic, complemented, Sylow
448C23—34no—
449C23—62no—
450C23—62no—
451C23—181no—
452C23—242no—
453C23D3×#6711yescharacteristic
454Q8—181no—
455Q8—181no—
456D4—62no—
457D4—62no—
458D4—62no—
459D4—62no—
460D4—181no—
461D4—181no—
462D4—361no—
463D4—361no—
464D4—724no—
465C2×C4—22no—
466C2×C4—62no—
467C2×C4—62no—
468C2×C4—181no—
469C2×C4—244no—
470C2×C4—361no—
471C2×C4—361no—
472C2×C4#379811yescharacteristic
473C2×C4#379911yescharacteristic
474C2×C4C4×D3211yescharacteristic
475C2×C4D3×D1211yescharacteristic
476C2×C4C2×#62611yescharacteristic
477C2×C4D3×#6711yescharacteristic
478C8—121no—
479C8—361no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—41no—
490C2×C3—124no—
491C2×C3#466511yescharacteristic
492C2×C3#521311yescharacteristic
493D3—44no—
494D3—242no—
495D3—241no—
496D3—241no—
497C22—41no—
498C22—64no—
499C22—124no—
500C22—124no—
501C22—242no—
502C22—362no—
503C22—361no—
504C22#6385011yescharacteristic
505C22D3×(C2×D3)⋊C411yescharacteristic
506C22#6397711yescharacteristic
507C4—42no—
508C4—122no—
509C4—122no—
510C4—361no—
511C4C4×#62611yescharacteristic
512C4#6390411yescharacteristic
513C4#6390611yescharacteristic
514C4#6390911yescharacteristic
515C3—21no—
516C3#6870511yescharacteristic, complemented
517C3#7165211yescharacteristic, complemented
518C2—21no—
519C2—21no—
520C2—21no—
521C2—124no—
522C2—721no—
523C2#1059138211yescharacteristic
subgroupG/H
centerC2#10591382
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radical#10595042C2
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. C3×#5521C2semidirect
3. #10592704C2semidirect
4. #10591113C2semidirect
5. C2×#63558C2semidirect
6. C3×#4531C2semidirect
7. #10589157C2semidirect
22. #63911C4semidirect
23. #63860C4semidirect
30. #5521D3semidirect
41. #4531D3semidirect
49. C2×C4⋊(C3⋊D3)C2×C4semidirect
51. C2×#634C2×C4semidirect
62. C32×C42D4semidirect
71. C3×C4×Dic3C2×C4semidirect
72. C3×C4×Dic3D4semidirect
217. C3×C42D12semidirect
218. C3×C42#67semidirect
226. C4×Dic3C4×D3semidirect
227. C4×Dic3#67semidirect
398. C42#626semidirect
447. C32#1911semidirect
516. C3#68705semidirect
517. C3#71652semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105950422
#105927042
#105911132
C2×#635582
C3×#45312
#105891572
#716523
#687053