Finite Group Databasebeta

← #11793995

Subgroups — #11793995

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594795C211yesmaximal, characteristic
2#10592701C211yesmaximal, characteristic, complemented
3C3×#5006C211yesmaximal, characteristic, complemented
4#10591232C211yesmaximal, characteristic, complemented
5#10591117C211yesmaximal, characteristic, complemented
6#10591083C211yesmaximal, characteristic, complemented
7C3×#4531C211yesmaximal, characteristic, complemented
8#70043—31nomaximal
9#68698—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C32×#117C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63833—21no—
18#63831—21no—
19#63830—21no—
20#63829—22no—
21#63825—21no—
22#63637—21no—
23#63636—21no—
24C3×#806—22no—
25#63581—22no—
26Dic3⋊(C3⋊C8)—22no—
27#63565—21no—
28#63562—21no—
29#5822—31no—
30#5748—31no—
31C3×#410—31no—
32#5233—31no—
33#5119—31no—
34#5006—31no—
35#5006—31no—
36#5006D311yescharacteristic, complemented
37#5002—31no—
38#5002—31no—
39#5002—31no—
40#5002—61no—
41#4999—31no—
42C3×H(3,ℤ/4)—31no—
43#4531D311yescharacteristic, complemented
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634D411yescharacteristic
53C2×C3×#67—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C2×C3×D12D411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×Dic6D411yescharacteristic
61C32×C4⋊C4—21no—
62C32×C22⋊C4—21no—
63C32×C42—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#217—21no—
68C3×#217D412yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8D412yes—
76#3719—22no—
77#3717—22no—
78#3716—22no—
79#3714—22no—
80#2053—91noSylow
81C2×C3×#41—31no—
82C2×#235—31no—
83C2×#235—31no—
84C2×#235—61no—
85C2×#235C2×D311yescharacteristic
86C2×C3×M16—31no—
87C3×#117—21no—
88C3×#117—31no—
89C3×#117—31no—
90C3×#117C2×D311yescharacteristic
91C3×#117C2×D311yescharacteristic
92#951—61no—
93#950—62no—
94#949—61no—
95#942—61no—
96#932—61no—
97#926C2×D311yescharacteristic
98#926C2×D311yescharacteristic
99C2×#208C2×D311yescharacteristic
100C22×C3⋊C8—31no—
101C22×C3⋊C8—31no—
102C22×C3⋊C8—61no—
103#909—61no—
104#909—61no—
105#908—61no—
106#908—61no—
107#904—62no—
108C3×#99—62no—
109#835—61no—
110#832—61no—
111Dic3⋊C8—62no—
112#810—61no—
113#810—61no—
114#810—62no—
115#810—61no—
116#809—61no—
117#809—61no—
118#809—62no—
119#809—61no—
120#806—22no—
121#806—62no—
122#806—62no—
123C4⋊(C3⋊C8)—62no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—21no—
126C22×C3×D3—21no—
127C2×C32×C4—41no—
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133C2×C32×C4#4111yescharacteristic
134#638—41no—
135#638—41no—
136C2×C3⋊Dic3—21no—
137C4⋊(C3⋊D3)—21no—
138C4⋊(C3⋊D3)—21no—
139C4×C3⋊D3—41no—
140C4×C3⋊D3—41no—
141#634—21no—
142#634—21no—
143C3×#67—41no—
144C3×#67—41no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—41no—
148C3×D12—21no—
149C3×D12—21no—
150C3×C4×D3—41no—
151C3×C4×D3—41no—
152C3×Dic6—21no—
153C3×Dic6—21no—
154C3⋊(C3⋊C8)—41no—
155C3×C3⋊C8—22no—
156#575—91no—
157#424—91no—
158#416—91no—
159#416—91no—
160#410—31no—
161#410—91no—
162H(3,ℤ/4)—31no—
163C3×#41—61no—
164C3×#41—61no—
165C3×#41—61no—
166C3×#41—61no—
167C2×C3×Q8—31no—
168C2×C3×D4—31no—
169C2×C3×D4—61no—
170C22×C3×C4—21no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C2×#67—21no—
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—121no—
178#235—21no—
179#235—21no—
180#235—21no—
181#235—21no—
182#235—62no—
183#235—62no—
184#235—61no—
185#235—61no—
186#235—61no—
187#235—61no—
188#235—61no—
189#235—61no—
190#235—61no—
191#235—61no—
192#235—121no—
193#235—121no—
194C2×D12—31no—
195C2×D12—31no—
196C2×D12—61no—
197C2×D12D1211yescharacteristic
198C2×C4×D3—21no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—121no—
202C2×Dic6—31no—
203C2×Dic6—31no—
204C2×Dic6—61no—
205C2×Dic6D1211yescharacteristic
206C3×M16—61no—
207C3×M16—61no—
208C2×C3×C8—32no—
209C3×C4⋊C4—22no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—61no—
213C3×C4⋊C4—61no—
214C3×C22⋊C4—21no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—32no—
217C3×C22⋊C4—41no—
218C3×C22⋊C4—61no—
219C3×C42—21no—
220C3×C42—21no—
221C3×C42—41no—
222C3×C42—61no—
223C3×C42—61no—
224#217—21no—
225#217#6712yes—
226#216—62no—
227#215—62no—
228#214—62no—
229#213—62no—
230C4⋊Dic3—21no—
231C4⋊Dic3—21no—
232C4×Dic3—21no—
233C4×Dic3—21no—
234#208—21no—
235#208—21no—
236C2×C3⋊C8—62no—
237C2×C3⋊C8—61no—
238C2×C3⋊C8—61no—
239C2×C3⋊C8—61no—
240C2×C3⋊C8—61no—
241C2×C3⋊C8—61no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—121no—
244C2×C3⋊C8—121no—
245C2×C3⋊C8D1212yes—
246Dic12—62no—
247D24—62no—
248#204—62no—
249#204—62no—
250C22×C32—41no—
251C22×C32#12111yescharacteristic
252C22×C32#12111yescharacteristic
253C22×C32#12111yescharacteristic
254C2×C3⋊D3—41no—
255C2×C3⋊D3—81no—
256C2×C3×D3—41no—
257C2×C3×D3—81no—
258C32×C4—81no—
259C32×C4#12011yescharacteristic
260C32×C4#12311yescharacteristic
261C32×C4#12311yescharacteristic
262C32×C4#12411yescharacteristic
263C3⋊Dic3—41no—
264C3×Dic3—42no—
265C3×Dic3—41no—
266C3×Dic3—81no—
267C2×#41—31no—
268C2×#41—91no—
269#137—181no—
270#137—181no—
271AGL(1,ℤ/8)—181no—
272AGL(1,ℤ/8)—181no—
273#135—182no—
274C2×M16—31no—
275C22×C8—91no—
276#117—31no—
277#117—31no—
278#117D3211yescharacteristic
279C4⋊C8—182no—
280#103—181no—
281#103—181no—
282#102—181no—
283#102—181no—
284#99—62no—
285#99—182no—
286C23×C3—21no—
287C23×C3—61no—
288C23×C3D3×D411yescharacteristic
289C23×C3C2×#6711yescharacteristic
290C22×D3—21no—
291C22×D3—61no—
292C22×D3—61no—
293C22×D3—121no—
294C3×Q8—61no—
295C3×Q8—61no—
296C3×D4—61no—
297C3×D4—61no—
298C3×D4—121no—
299C3×D4—121no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—42no—
307C2×C3×C4—41no—
308C2×C3×C4—41no—
309C2×C3×C4—61no—
310C2×C3×C4—62no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4—121no—
314C2×C3×C4C2×D1211yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4#23511yescharacteristic
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#23711yescharacteristic
325C2×C3×C4#23911yescharacteristic
326#67—41no—
327#67—41no—
328#67—122no—
329#67—122no—
330#67—121no—
331#67—121no—
332#67—121no—
333#67—121no—
334C2×Dic3—21no—
335C2×Dic3—22no—
336C2×Dic3—41no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—121no—
340D12—21no—
341D12—21no—
342D12—62no—
343D12—61no—
344D12—61no—
345D12—61no—
346D12—61no—
347D12—121no—
348C4×D3—41no—
349C4×D3—41no—
350C4×D3—122no—
351C4×D3—122no—
352C4×D3—121no—
353C4×D3—121no—
354C4×D3—121no—
355C4×D3—121no—
356Dic6—21no—
357Dic6—21no—
358Dic6—62no—
359Dic6—61no—
360Dic6—61no—
361Dic6—61no—
362Dic6—61no—
363Dic6—121no—
364C3×C8—62no—
365C3⋊C8—22no—
366C3⋊C8—122no—
367C3⋊C8—121no—
368C3⋊C8—121no—
369C2×C32—21no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32#39411yescharacteristic
373C3⋊D3—81no—
374C3×D3—81no—
375#41—61no—
376#41—61no—
377#41—61no—
378#41—61no—
379#41—181no—
380#41—181no—
381#41—181no—
382#41—181no—
383C2×Q8—31no—
384C2×Q8—91no—
385C2×D4—31no—
386C2×D4—61no—
387C2×D4—91no—
388C2×D4—181no—
389C22×C4—61no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392Q16—182no—
393SD16—182no—
394SD16—182no—
395D8—182no—
396M16—61no—
397M16—61no—
398C2×C8—32no—
399C2×C8—181no—
400C2×C8—181no—
401C2×C8—181no—
402C4⋊C4—21no—
403C4⋊C4—61no—
404C4⋊C4—61no—
405C22⋊C4—21no—
406C22⋊C4—32no—
407C22⋊C4—61no—
408C42—21no—
409C42—61no—
410C42—61no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—42no—
417C22×C3—121no—
418C22×C3—241no—
419C22×C3#88411yescharacteristic
420C22×C3#88411yescharacteristic
421C22×C3#89511yescharacteristic
422C22×C3#93011yescharacteristic
423C22×C3#93811yescharacteristic
424C22×C3#93911yescharacteristic
425C2×D3—41no—
426C2×D3—81no—
427C2×D3—122no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—242no—
431C2×D3—241no—
432C2×D3—241no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—82no—
438C3×C4—81no—
439C3×C4—81no—
440C3×C4—122no—
441C3×C4—121no—
442C3×C4—241no—
443C3×C4#87511yescharacteristic
444C3×C4#88211yescharacteristic
445C3×C4#88211yescharacteristic
446C3×C4#88311yescharacteristic
447C3×C4#88511yescharacteristic
448C3×C4#88611yescharacteristic
449C3×C4#89411yescharacteristic
450C3×C4#89411yescharacteristic
451Dic3—42no—
452Dic3—41no—
453Dic3—81no—
454Dic3—122no—
455Dic3—121no—
456Dic3—121no—
457C32#205311yescharacteristic, complemented, Sylow
458C23—61no—
459C23—181no—
460C23D3×#6711yescharacteristic
461Q8—61no—
462Q8—61no—
463Q8—181no—
464Q8—181no—
465D4—61no—
466D4—61no—
467D4—121no—
468D4—121no—
469D4—181no—
470D4—181no—
471D4—361no—
472D4—361no—
473C2×C4—41no—
474C2×C4—62no—
475C2×C4—61no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—121no—
479C2×C4—181no—
480C2×C4—361no—
481C2×C4—361no—
482C2×C4#379611yescharacteristic
483C2×C4#379811yescharacteristic
484C2×C4D3×D1211yescharacteristic
485C2×C4D3×D1211yescharacteristic
486C2×C4#380411yescharacteristic
487C2×C4#381111yescharacteristic
488C8—62no—
489C8—361no—
490C2×C3—22no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—41no—
499C2×C3—41no—
500C2×C3—241no—
501C2×C3#467211yescharacteristic
502C2×C3#496111yescharacteristic
503D3—81no—
504D3—242no—
505D3—241no—
506D3—241no—
507C22—41no—
508C22—121no—
509C22—241no—
510C22—361no—
511C22—721no—
512C22#6388611yescharacteristic
513C22#6390611yescharacteristic
514C22#6395811yescharacteristic
515C4—81no—
516C4—122no—
517C4—121no—
518C4—241no—
519C4—361no—
520C4#6385211yescharacteristic
521C4#6385311yescharacteristic
522C4#6389011yescharacteristic
523C4#6392311yescharacteristic
524C3—21no—
525C3#6869811yescharacteristic, complemented
526C3#7004311yescharacteristic, complemented
527C2—21no—
528C2—21no—
529C2—21no—
530C2—241no—
531C2—721no—
532C2#1059131211yescharacteristic
subgroupG/H
centerC4#63852
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#394
prime radical#10594795C2
hypercenter#117D32
hypocenterC32#2053
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10592701C2semidirect
3. C3×#5006C2semidirect
4. #10591232C2semidirect
5. #10591117C2semidirect
6. #10591083C2semidirect
7. C3×#4531C2semidirect
36. #5006D3semidirect
43. #4531D3semidirect
457. C32#2053semidirect
525. C3#68698semidirect
526. C3#70043semidirect

Maximal subgroups

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

subgroupindex
#105947952
#105927012
C3×#50062
#105912322
#105911172
#105910832
C3×#45312
#700433
#686983