Finite Group Databasebeta

← #11788751

Subgroups — #11788751

Order 1152.

767 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595042C211yesmaximal, characteristic
2#10594780C211yesmaximal, characteristic, complemented
3#10592705C211yesmaximal, characteristic, complemented
4C3×#5001C211yesmaximal, characteristic, complemented
5#10591086C211yesmaximal, characteristic, complemented
6C3×#4531C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70330—31nomaximal
9#68713—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63977—22no—
18#63916—22no—
19#63911C412yescomplemented
20#63860C412yescomplemented
21#63818—22no—
22#63817—22no—
23#63817—22no—
24#63633—22no—
25C3×#809—22no—
26#63563—22no—
27#5805—31no—
28#5745—31no—
29#5745—31no—
30#5525—31no—
31C3×#418—31no—
32#5215—31no—
33#5131—31no—
34#5006—31no—
35#5006—31no—
36#5006—61no—
37#5001D311yescharacteristic, complemented
38C3×H(3,ℤ/4)—31no—
39#4557—31no—
40#4531—31no—
41#4531D311yescharacteristic, complemented
42C23×C3×D3—21no—
43C22×C32×C4C2311yescharacteristic
44C2×#638D412yes—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
50C2×C4×C3⋊D3D412yes—
51C2×#634C2×C411yescharacteristic
52C2×C3×D12—21no—
53C2×C3×D12—21no—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12C2×C412yes—
58C2×#626—24no—
59C32×C4⋊C4—21no—
60C32×C22⋊C4—21no—
61C32×C42—21no—
62#3757—21no—
63C4⋊(C3⋊Dic3)—21no—
64C4×C3⋊Dic3—21no—
65C3×#217—21no—
66C3×C4⋊Dic3—21no—
67C3×C4×Dic3C2×C412yes—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8D412yescomplemented
73C2×C3×C3⋊C8D412yescomplemented
74(C2×D3)⋊Dic3—24no—
75#3712—24no—
76#3710—24no—
77#1910—91noSylow
78C22×C3×D4—31no—
79C2×#235—31no—
80C2×#235—31no—
81C2×#235—61no—
82C22×D12C2×D311yescharacteristic
83C2×C3×M16—31no—
84C2×C3×M16—31no—
85C3×#117—21no—
86C3×#117—31no—
87C3×#117C2×D311yescharacteristic
88C3×#117C2×D311yescharacteristic
89#953—62no—
90#940—32no—
91#938—62no—
92#936—32no—
93#926—31no—
94#926—31no—
95#926—61no—
96#926C2×D311yescharacteristic
97C2×#208C2×D311yescharacteristic
98C2×#208C2×D311yescharacteristic
99#907—62no—
100#907—62no—
101D3×M16—62no—
102D3×M16—62no—
103#901—62no—
104#901—62no—
105#895—62no—
106#882—62no—
107#875—32no—
108#874—32no—
109C3×#102—62no—
110#832—62no—
111#821—62no—
112#809—22no—
113#806—62no—
114#806—62no—
115#806—64no—
116C23×C32C2×D411yescharacteristic
117C22×C3⋊D3C22⋊C412yes—
118C22×C3×D3—22no—
119C22×C3×D3—41no—
120C22×C3×D3—41no—
121C22×C3×D3—82no—
122C2×C32×C4—41no—
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—22no—
130#638—22no—
131C2×C3⋊Dic3—41no—
132C2×C3⋊Dic3C22⋊C412yes—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)—21no—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137#634—21no—
138#634—21no—
139C2×C3×Dic3—22no—
140C3×D12—22no—
141C3×D12—22no—
142C3×D12—41no—
143C3×D12—41no—
144#626—84no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—22no—
147#568—91no—
148#535—91no—
149#418—31no—
150#418—91no—
151#410—91no—
152H(3,ℤ/4)—31no—
153H(3,ℤ/4)—91no—
154C24×C3—61no—
155C23×D3—21no—
156C2×C3×D4—32no—
157C2×C3×D4—61no—
158C2×C3×D4—61no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C22×C3×C4—21no—
163C22×C3×C4C22×D311yescharacteristic
164C22×C3×C4C22×D311yescharacteristic
165C2×#67—32no—
166C2×#67—32no—
167C2×#67—62no—
168C2×#67—64no—
169#235—61no—
170#235—61no—
171#235—61no—
172#235—61no—
173#235—61no—
174#235—61no—
175#235—61no—
176#235—61no—
177#235—121no—
178#235—121no—
179#235—121no—
180#235—121no—
181C2×D12—21no—
182C2×D12—21no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12—31no—
187C2×D12—31no—
188C2×D12—61no—
189C2×D12—64no—
190C2×D12C4×D312yes—
191C2×C4×D3—32no—
192C2×C4×D3—32no—
193C2×C4×D3—62no—
194C2×Dic6—31no—
195C2×Dic6—31no—
196C2×Dic6—61no—
197C3×M16—61no—
198C3×M16—61no—
199C3×M16—61no—
200C3×M16—61no—
201C2×C3×C8—32no—
202C2×C3×C8—32no—
203C3×C4⋊C4—21no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—41no—
206C3×C4⋊C4—61no—
207C3×C22⋊C4—22no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—61no—
211C3×C42—21no—
212C3×C42—21no—
213C3×C42—32no—
214C3×C42—41no—
215#217—21no—
216#217—64no—
217#217—62no—
218#217—61no—
219#217—61no—
220(C2×D3)⋊C4—64no—
221C4⋊Dic3—21no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—121no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—121no—
228C4×Dic3C4×D312yes—
229#208—21no—
230#208—21no—
231#208—21no—
232#208—21no—
233C2×C3⋊C8D1212yescomplemented
234C2×C3⋊C8#6712yescomplemented
235ΓL(1,𝔽25)—64no—
236ΓL(1,𝔽25)—64no—
237D3×C8—64no—
238D3×C8—64no—
239C22×C32—41no—
240C22×C32C2×C22⋊C411yescharacteristic
241C22×C32#12111yescharacteristic
242C22×C32#12111yescharacteristic
243C2×C3⋊D3—22no—
244C2×C3⋊D3—42no—
245C2×C3×D3—44no—
246C2×C3×D3—42no—
247C2×C3×D3—82no—
248C2×C3×D3—82no—
249C32×C4—81no—
250C32×C4C4×D411yescharacteristic
251C32×C4C4×D411yescharacteristic
252C32×C4#12011yescharacteristic
253C32×C4#12311yescharacteristic
254C3⋊Dic3—22no—
255C3⋊Dic3—81no—
256C3×Dic3—42no—
257C2×#41—91no—
258C22×D4—31no—
259#131—182no—
260#131—182no—
261C2×M16—31no—
262C2×M16—31no—
263C2×M16—182no—
264#127—92no—
265#124—92no—
266#121—182no—
267#120—182no—
268#117—31no—
269#117—91no—
270#117D3211yescharacteristic
271#102—62no—
272#102—182no—
273#99—182no—
274C23×C3—21no—
275C23×C3—62no—
276C23×C3—121no—
277C23×C3—121no—
278C23×C3—242no—
279C23×C3D3×D411yescharacteristic
280C23×C3D3×D411yescharacteristic
281C22×D3—22no—
282C22×D3—32no—
283C22×D3—32no—
284C22×D3—41no—
285C22×D3—41no—
286C22×D3—62no—
287C22×D3—82no—
288C3×D4—62no—
289C3×D4—62no—
290C3×D4—121no—
291C3×D4—121no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—42no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4—62no—
302C2×C3×C4C2×C4×D311yescharacteristic
303C2×C3×C4C2×C4×D311yescharacteristic
304C2×C3×C4C2×D1211yescharacteristic
305C2×C3×C4#23511yescharacteristic
306C2×C3×C4#23511yescharacteristic
307C2×C3×C4D3×D411yescharacteristic
308C2×C3×C4D3×D411yescharacteristic
309C2×C3×C4D3×D411yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4#23711yescharacteristic
312C2×C3×C4#23911yescharacteristic
313C2×C3×C4C2×#6711yescharacteristic
314#67—62no—
315#67—62no—
316#67—62no—
317#67—62no—
318#67—122no—
319#67—122no—
320#67—244no—
321C2×Dic3—22no—
322C2×Dic3—32no—
323C2×Dic3—32no—
324C2×Dic3—62no—
325C2×Dic3—122no—
326C2×Dic3—121no—
327C2×Dic3—121no—
328D12—22no—
329D12—22no—
330D12—41no—
331D12—41no—
332D12—61no—
333D12—61no—
334D12—61no—
335D12—61no—
336D12—121no—
337D12—121no—
338D12—244no—
339C4×D3—62no—
340C4×D3—62no—
341C4×D3—62no—
342C4×D3—62no—
343C4×D3—122no—
344C4×D3—122no—
345Dic6—61no—
346Dic6—61no—
347Dic6—61no—
348Dic6—61no—
349Dic6—121no—
350Dic6—121no—
351C3×C8—62no—
352C3×C8—62no—
353C3⋊C8—22no—
354C3⋊C8—22no—
355C2×C32—21no—
356C2×C32—21no—
357C2×C32—21no—
358C2×C32#38611yescharacteristic
359C3⋊D3—42no—
360C3×D3—82no—
361C24—61no—
362#41—181no—
363#41—181no—
364#41—181no—
365#41—181no—
366C2×Q8—91no—
367C2×D4—32no—
368C2×D4—61no—
369C2×D4—61no—
370C2×D4—61no—
371C2×D4—61no—
372C2×D4—61no—
373C2×D4—92no—
374C2×D4—91no—
375C2×D4—184no—
376C22×C4—92no—
377C22×C4C2×D3211yescharacteristic
378M16—61no—
379M16—61no—
380M16—61no—
381M16—61no—
382M16—184no—
383C2×C8—32no—
384C2×C8—32no—
385C2×C8—184no—
386C4⋊C4—21no—
387C4⋊C4—61no—
388C4⋊C4—181no—
389C22⋊C4—21no—
390C22⋊C4—61no—
391C22⋊C4—184no—
392C22⋊C4—181no—
393C42—21no—
394C42—32no—
395C42—181no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—21no—
399C22×C3—41no—
400C22×C3—41no—
401C22×C3—81no—
402C22×C3—124no—
403C22×C3—122no—
404C22×C3—242no—
405C22×C3—242no—
406C22×C3D3×C22⋊C411yescharacteristic
407C22×C3D3×C22⋊C411yescharacteristic
408C22×C3#88411yescharacteristic
409C22×C3#88411yescharacteristic
410C22×C3#89511yescharacteristic
411C22×C3#93811yescharacteristic
412C2×D3—44no—
413C2×D3—42no—
414C2×D3—62no—
415C2×D3—62no—
416C2×D3—82no—
417C2×D3—82no—
418C2×D3—122no—
419C2×D3—122no—
420C2×D3—122no—
421C2×D3—242no—
422C3×C4—21no—
423C3×C4—21no—
424C3×C4—21no—
425C3×C4—21no—
426C3×C4—81no—
427C3×C4—81no—
428C3×C4—82no—
429C3×C4—122no—
430C3×C4C4×D1211yescharacteristic
431C3×C4#67⋊C411yescharacteristic
432C3×C4#88211yescharacteristic
433C3×C4#88311yescharacteristic
434C3×C4#89311yescharacteristic
435C3×C4#89411yescharacteristic
436C3×C4C4×#6711yescharacteristic
437C3×C4#93711yescharacteristic
438Dic3—42no—
439Dic3—62no—
440Dic3—62no—
441Dic3—122no—
442Dic3—241no—
443Dic3—241no—
444Dic3—242no—
445C32#191011yescharacteristic, complemented, Sylow
446C23—62no—
447C23—92no—
448C23—121no—
449C23—121no—
450C23—242no—
451C23#381111yescharacteristic
452Q8—181no—
453Q8—181no—
454D4—62no—
455D4—62no—
456D4—121no—
457D4—121no—
458D4—182no—
459D4—182no—
460D4—181no—
461D4—181no—
462D4—724no—
463C2×C4—41no—
464C2×C4—62no—
465C2×C4—92no—
466C2×C4—182no—
467C2×C4—182no—
468C2×C4—361no—
469C2×C4#379911yescharacteristic
470C2×C4C4×D3211yescharacteristic
471C2×C4D3×D1211yescharacteristic
472C2×C4#380211yescharacteristic
473C2×C4#380411yescharacteristic
474C2×C4D3×#6711yescharacteristic
475C8—62no—
476C8—62no—
477C2×C3—21no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—41no—
485C2×C3—41no—
486C2×C3—41no—
487C2×C3—242no—
488C2×C3#466511yescharacteristic
489C2×C3#495611yescharacteristic
490D3—82no—
491D3—122no—
492D3—122no—
493D3—242no—
494C22—41no—
495C22—124no—
496C22—122no—
497C22—182no—
498C22—242no—
499C22—242no—
500C22—362no—
501C22#6391011yescharacteristic
502C22#6392111yescharacteristic
503C22#6395811yescharacteristic
504C4—81no—
505C4—122no—
506C4—182no—
507C4—721no—
508C4#6385411yescharacteristic
509C4#6388011yescharacteristic
510C4#6390411yescharacteristic
511C4#6392211yescharacteristic
512C3—21no—
513C3#6871311yescharacteristic, complemented
514C3#7033011yescharacteristic, complemented
515C2—21no—
516C2—21no—
517C2—21no—
518C2—242no—
519C2—362no—
520C2#1059127511yescharacteristic
subgroupG/H
centerC2#10591275
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radical#10595042C2
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1910
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
2. #10594780C2semidirect
3. #10592705C2semidirect
4. C3×#5001C2semidirect
5. #10591086C2semidirect
6. C3×#4531C2semidirect
7. #10589158C2semidirect
19. #63911C4semidirect
20. #63860C4semidirect
37. #5001D3semidirect
41. #4531D3semidirect
72. C2×C3×C3⋊C8D4semidirect
73. C2×C3×C3⋊C8D4semidirect
233. C2×C3⋊C8D12semidirect
234. C2×C3⋊C8#67semidirect
445. C32#1910semidirect
513. C3#68713semidirect
514. C3#70330semidirect

Maximal subgroups

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

subgroupindex
#105950422
#105947802
#105927052
C3×#50012
#105910862
C3×#45312
#105891582
#703303
#687133