Finite Group Databasebeta

← #11788754

Subgroups — #11788754

Order 1152.

817 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic, complemented
2#10595042C211yesmaximal, characteristic
3C3×#5131C211yesmaximal, characteristic, complemented
4#10591232C211yesmaximal, characteristic, complemented
5#10591085C211yesmaximal, characteristic, complemented
6C3×#4557C211yesmaximal, characteristic, complemented
7#10589157C211yesmaximal, characteristic, complemented
8#70330—31nomaximal
9#68713—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14#64116—22no—
15M16×C3⋊D3—22no—
16#64110—22no—
17C3×#926C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20#63977—22no—
21#63916—22no—
22#63911C412yescomplemented
23#63860C412yescomplemented
24C3×#821—22no—
25#63581—22no—
26#63562—22no—
27#5805—31no—
28#5745—31no—
29#5745—31no—
30#5745—61no—
31#5525—31no—
32C3×#418—31no—
33#5215—31no—
34#5131D311yescharacteristic, complemented
35#5006—31no—
36#5006—31no—
37#5001—31no—
38C3×H(3,ℤ/4)—31no—
39#4557D311yescharacteristic, complemented
40#4531—31no—
41#4531—31no—
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×M16—21no—
60C32×M16—21no—
61C2×C32×C8D412yescomplemented
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)D412yescomplemented
65#3743—24no—
66C8×C3⋊D3—24no—
67C3×#217—21no—
68C3×#217—21no—
69C3×#217—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3—21no—
73C3×C4×Dic3—21no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3C2×C412yes—
76(C2×D3)⋊Dic3—24no—
77#1910—91noSylow
78C22×C3×D4—31no—
79C2×#235—31no—
80C2×#235—31no—
81C2×#235—61no—
82C22×D12C2×D311yescharacteristic
83C2×C3×M16—21no—
84C2×C3×M16C2×D311yescharacteristic
85C2×C3×M16C2×D311yescharacteristic
86C3×#117—31no—
87C3×#117—31no—
88C3×#117—31no—
89#953—62no—
90#940—32no—
91#938—62no—
92#936—32no—
93#926C2×D311yescharacteristic
94#926C2×D311yescharacteristic
95#926C2×D311yescharacteristic
96C2×#208—31no—
97C2×#208—31no—
98C2×#208—61no—
99#907—62no—
100#907—62no—
101#907—64no—
102D3×M16—62no—
103D3×M16—62no—
104D3×M16—64no—
105#901—64no—
106#901—62no—
107#901—62no—
108#895—62no—
109#882—62no—
110#875—32no—
111#874—32no—
112C3×#102—62no—
113#832—62no—
114#821—22no—
115#809—62no—
116#806—62no—
117#806—62no—
118C23×C32C2×D411yescharacteristic
119C22×C3⋊D3C22⋊C412yes—
120C22×C3×D3—22no—
121C22×C3×D3—41no—
122C22×C3×D3—41no—
123C22×C3×D3—82no—
124C2×C32×C4C22×C411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4#4111yescharacteristic
129C2×C32×C4#4111yescharacteristic
130#638—22no—
131#638—22no—
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—
140C2×C3×Dic3—41no—
141C2×C3×Dic3—41no—
142C3×D12—22no—
143C3×D12—22no—
144C3×D12—41no—
145C3×D12—41no—
146#626—84no—
147C32×C8—22no—
148C3⋊(C3⋊C8)—22no—
149#568—91no—
150#535—91no—
151#418—31no—
152#418—91no—
153#410—91no—
154H(3,ℤ/4)—31no—
155H(3,ℤ/4)—91no—
156C24×C3—61no—
157C23×D3—21no—
158C2×C3×D4—32no—
159C2×C3×D4—61no—
160C2×C3×D4—61no—
161C2×C3×D4—61no—
162C2×C3×D4—61no—
163C2×C3×D4—61no—
164C22×C3×C4—21no—
165C22×C3×C4C22×D311yescharacteristic
166C22×C3×C4C22×D311yescharacteristic
167C2×#67—32no—
168C2×#67—32no—
169C2×#67—62no—
170C2×#67—64no—
171#235—62no—
172#235—62no—
173#235—62no—
174#235—62no—
175#235—61no—
176#235—61no—
177#235—61no—
178#235—61no—
179#235—61no—
180#235—61no—
181#235—61no—
182#235—61no—
183C2×D12—21no—
184C2×D12—21no—
185C2×D12—21no—
186C2×D12—21no—
187C2×D12—21no—
188C2×D12—31no—
189C2×D12—31no—
190C2×D12—61no—
191C2×D12—64no—
192C2×D12C4×D312yes—
193C2×C4×D3—32no—
194C2×C4×D3—32no—
195C2×C4×D3—62no—
196C2×Dic6—31no—
197C2×Dic6—31no—
198C2×Dic6—61no—
199C3×M16—22no—
200C3×M16—22no—
201C3×M16—21no—
202C3×M16—21no—
203C3×M16—21no—
204C3×M16—21no—
205C2×C3×C8—22no—
206C2×C3×C8D1212yescomplemented
207C2×C3×C8#6712yescomplemented
208C3×C4⋊C4—61no—
209C3×C4⋊C4—61no—
210C3×C4⋊C4—61no—
211C3×C22⋊C4—61no—
212C3×C22⋊C4—61no—
213C3×C22⋊C4—61no—
214C3×C42—32no—
215C3×C42—61no—
216C3×C42—61no—
217#217—21no—
218#217—21no—
219#217—21no—
220#217—64no—
221(C2×D3)⋊C4—64no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3—21no—
225C4×Dic3—21no—
226C4×Dic3—21no—
227C4×Dic3C4×D312yes—
228#208—62no—
229#208—62no—
230#208—61no—
231#208—61no—
232#208—61no—
233#208—61no—
234C2×C3⋊C8—32no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—62no—
237ΓL(1,𝔽25)—68no—
238ΓL(1,𝔽25)—64no—
239ΓL(1,𝔽25)—64no—
240D3×C8—68no—
241D3×C8—64no—
242D3×C8—64no—
243C22×C32—41no—
244C22×C32C2×C22⋊C411yescharacteristic
245C22×C32#12111yescharacteristic
246C22×C32#12111yescharacteristic
247C2×C3⋊D3—22no—
248C2×C3⋊D3—42no—
249C2×C3×D3—44no—
250C2×C3×D3—42no—
251C2×C3×D3—82no—
252C2×C3×D3—82no—
253C32×C4C4×D411yescharacteristic
254C32×C4C4×D411yescharacteristic
255C32×C4#12011yescharacteristic
256C32×C4#12311yescharacteristic
257C3⋊Dic3—22no—
258C3×Dic3—42no—
259C3×Dic3—81no—
260C3×Dic3—81no—
261C2×#41—91no—
262C22×D4—31no—
263#131—182no—
264#131—182no—
265C2×M16—91no—
266C2×M16—182no—
267C2×M16D3211yescharacteristic
268#127—92no—
269#124—92no—
270#121—182no—
271#120—182no—
272#117—31no—
273#117—31no—
274#117—31no—
275#102—62no—
276#102—182no—
277#99—182no—
278C23×C3—21no—
279C23×C3—62no—
280C23×C3—121no—
281C23×C3—121no—
282C23×C3—242no—
283C23×C3D3×D411yescharacteristic
284C23×C3D3×D411yescharacteristic
285C22×D3—22no—
286C22×D3—32no—
287C22×D3—32no—
288C22×D3—41no—
289C22×D3—41no—
290C22×D3—62no—
291C22×D3—82no—
292C3×D4—62no—
293C3×D4—62no—
294C3×D4—121no—
295C3×D4—121no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—21no—
299C2×C3×C4—21no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—62no—
303C2×C3×C4—121no—
304C2×C3×C4—121no—
305C2×C3×C4C2×C4×D311yescharacteristic
306C2×C3×C4C2×C4×D311yescharacteristic
307C2×C3×C4C2×D1211yescharacteristic
308C2×C3×C4#23511yescharacteristic
309C2×C3×C4#23511yescharacteristic
310C2×C3×C4D3×D411yescharacteristic
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4D3×D411yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4#23711yescharacteristic
315C2×C3×C4#23911yescharacteristic
316C2×C3×C4C2×#6711yescharacteristic
317#67—64no—
318#67—64no—
319#67—62no—
320#67—62no—
321#67—62no—
322#67—62no—
323#67—244no—
324C2×Dic3—22no—
325C2×Dic3—32no—
326C2×Dic3—32no—
327C2×Dic3—41no—
328C2×Dic3—41no—
329C2×Dic3—62no—
330D12—22no—
331D12—22no—
332D12—41no—
333D12—41no—
334D12—62no—
335D12—62no—
336D12—61no—
337D12—61no—
338D12—61no—
339D12—61no—
340D12—244no—
341C4×D3—64no—
342C4×D3—64no—
343C4×D3—62no—
344C4×D3—62no—
345C4×D3—62no—
346C4×D3—62no—
347Dic6—62no—
348Dic6—62no—
349Dic6—61no—
350Dic6—61no—
351Dic6—61no—
352Dic6—61no—
353C3×C8—24no—
354C3×C8—22no—
355C3×C8—22no—
356C3⋊C8—64no—
357C3⋊C8—62no—
358C3⋊C8—62no—
359C2×C32—21no—
360C2×C32—21no—
361C2×C32—21no—
362C2×C32#38611yescharacteristic
363C3⋊D3—42no—
364C3×D3—82no—
365C24—61no—
366#41—181no—
367#41—181no—
368#41—181no—
369#41—181no—
370C2×Q8—91no—
371C2×D4—32no—
372C2×D4—61no—
373C2×D4—61no—
374C2×D4—61no—
375C2×D4—61no—
376C2×D4—61no—
377C2×D4—92no—
378C2×D4—91no—
379C2×D4—184no—
380C22×C4—92no—
381C22×C4C2×D3211yescharacteristic
382M16—21no—
383M16—21no—
384M16—184no—
385M16—181no—
386M16—181no—
387C2×C8—92no—
388C2×C8—184no—
389C2×C8#62612yescomplemented
390C4⋊C4—61no—
391C4⋊C4—61no—
392C4⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4—61no—
395C22⋊C4—61no—
396C22⋊C4—184no—
397C42—32no—
398C42—61no—
399C42—61no—
400C22×C3—21no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—41no—
404C22×C3—41no—
405C22×C3—81no—
406C22×C3—124no—
407C22×C3—122no—
408C22×C3—242no—
409C22×C3—242no—
410C22×C3D3×C22⋊C411yescharacteristic
411C22×C3D3×C22⋊C411yescharacteristic
412C22×C3#88411yescharacteristic
413C22×C3#88411yescharacteristic
414C22×C3#89511yescharacteristic
415C22×C3#93811yescharacteristic
416C2×D3—44no—
417C2×D3—42no—
418C2×D3—64no—
419C2×D3—62no—
420C2×D3—62no—
421C2×D3—82no—
422C2×D3—82no—
423C2×D3—122no—
424C2×D3—122no—
425C2×D3—242no—
426C3×C4—21no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—122no—
431C3×C4—241no—
432C3×C4—241no—
433C3×C4C4×D1211yescharacteristic
434C3×C4#67⋊C411yescharacteristic
435C3×C4#88211yescharacteristic
436C3×C4#88311yescharacteristic
437C3×C4#89311yescharacteristic
438C3×C4#89411yescharacteristic
439C3×C4C4×#6711yescharacteristic
440C3×C4#93711yescharacteristic
441Dic3—42no—
442Dic3—64no—
443Dic3—62no—
444Dic3—62no—
445Dic3—81no—
446Dic3—81no—
447C32#191011yescharacteristic, complemented, Sylow
448C23—62no—
449C23—92no—
450C23—121no—
451C23—121no—
452C23—242no—
453C23#380211yescharacteristic
454Q8—181no—
455Q8—181no—
456D4—62no—
457D4—62no—
458D4—121no—
459D4—121no—
460D4—182no—
461D4—182no—
462D4—181no—
463D4—181no—
464D4—724no—
465C2×C4—62no—
466C2×C4—92no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—182no—
470C2×C4—182no—
471C2×C4#379611yescharacteristic
472C2×C4#379811yescharacteristic
473C2×C4C4×D3211yescharacteristic
474C2×C4C2×#62611yescharacteristic
475C2×C4#381111yescharacteristic
476C2×C4#381111yescharacteristic
477C8—22no—
478C8—182no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3—21no—
483C2×C3—21no—
484C2×C3—21no—
485C2×C3—21no—
486C2×C3—41no—
487C2×C3—41no—
488C2×C3—41no—
489C2×C3—242no—
490C2×C3#466511yescharacteristic
491C2×C3#495611yescharacteristic
492D3—82no—
493D3—124no—
494D3—122no—
495D3—122no—
496C22—41no—
497C22—124no—
498C22—122no—
499C22—182no—
500C22—242no—
501C22—242no—
502C22—362no—
503C22#6391211yescharacteristic
504C22#6391611yescharacteristic
505C22#6392111yescharacteristic
506C4—122no—
507C4—182no—
508C4—241no—
509C4—241no—
510C4#6385311yescharacteristic
511C4#6388111yescharacteristic
512C4C4×#62611yescharacteristic
513C4#6398111yescharacteristic
514C3—21no—
515C3#6871311yescharacteristic, complemented
516C3#7033011yescharacteristic, complemented
517C2—21no—
518C2—21no—
519C2—21no—
520C2—242no—
521C2—362no—
522C2#1059138711yescharacteristic
subgroupG/H
centerC2#10591387
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radical#10595042C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1910
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10596216C2semidirect
3. C3×#5131C2semidirect
4. #10591232C2semidirect
5. #10591085C2semidirect
6. C3×#4557C2semidirect
7. #10589157C2semidirect
22. #63911C4semidirect
23. #63860C4semidirect
34. #5131D3semidirect
39. #4557D3semidirect
61. C2×C32×C8D4semidirect
64. C2×C3⋊(C3⋊C8)D4semidirect
206. C2×C3×C8D12semidirect
207. C2×C3×C8#67semidirect
389. C2×C8#626semidirect
447. C32#1910semidirect
515. C3#68713semidirect
516. C3#70330semidirect

Maximal subgroups

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

subgroupindex
#105962162
#105950422
C3×#51312
#105912322
#105910852
C3×#45572
#105891572
#703303
#687133