Finite Group Databasebeta

← #11895975

Subgroups — #11895975

Order 1152.

811 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#10593906C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3#10592378C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×C4×#204C211yesmaximal, characteristic, complemented
6#10590888C212yesmaximal, complemented
7#10590876C212yesmaximal, complemented
8#10590782C212yesmaximal, complemented
9#10590743C212yesmaximal, complemented
10#10590364C211yesmaximal, characteristic, complemented
11#10590269C211yesmaximal, characteristic, complemented
12#81590—31nomaximal
13#79625—31nomaximal
14C2×#3795—21no—
15C4×#634C2211yescharacteristic
16C2×C3×#204C2211yescharacteristic
17C3×#874C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63914C2212yes—
22#63908—21no—
23#63898C2212yes—
24#63885—22no—
25#63872C2212yes—
26#63866—21no—
27#63846—22no—
28#63843C2212yes—
29Dic3×Dic6—21no—
30C2×#3715C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63642C2212yes—
33#63641C2212yes—
34C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
35C3×#821C2212yes—
36C3×#821C2211yescharacteristic
37C3×#821C2212yes—
38C3×#817C2211yescharacteristic
39C3×#816C2211yescharacteristic
40#63576C2212yes—
41#63562C2212yes—
42#63562C2212yes—
43#5721—31no—
44#5718—31no—
45#5570—31no—
46#5553—31no—
47C3×#486—31no—
48C3×C4×SD16—31no—
49#5163—32no—
50#5087—31no—
51#5075—31no—
52#5027—31no—
53#5007—31no—
54#4871—32no—
55#4817—32no—
56#4764—32no—
57#4764—32no—
58#4763—32no—
59#4762—32no—
60#4757—32no—
61#4694D311yescharacteristic, complemented
62C4×#204D311yescharacteristic, complemented
63#4679—31no—
64#4679—31no—
65#4679—61no—
66C2×#634D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2311yescharacteristic
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2311yescharacteristic
74C2×#625—22no—
75C2×#625—22no—
76C2×D3×Dic3—22no—
77#3795—44no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)D411yescharacteristic
82#3750D412yes—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C3×#204—22no—
93Dic3⋊Dic3—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3715—24no—
99#3368—91noSylow
100C2×#237—61no—
101C2×#235—61no—
102C2×C3×SD16—31no—
103C3×C4⋊Q8—31no—
104C3×#127—31no—
105C3×C4×Q8—31no—
106C3×C4×D4—31no—
107Q8×Dic3—32no—
108Q8×Dic3—61no—
109#944—61no—
110C2×#215—32no—
111#940—32no—
112#940—32no—
113#939—62no—
114#938—61no—
115D4×Dic3—32no—
116C2×#214—32no—
117#930—61no—
118C2×#204C2×D311yescharacteristic
119#893—32no—
120#890—32no—
121#890—32no—
122#890—62no—
123#889—62no—
124#887—32no—
125#884—62no—
126#874C2×D311yescharacteristic
127C4×D12C2×D311yescharacteristic
128#869—61no—
129#869C2×D311yescharacteristic
130C4×Dic6—31no—
131C4×Dic6—31no—
132C4×Dic6—61no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C3×#106—31no—
136C3×#103—31no—
137C3×#102—32no—
138C3×#102—32no—
139C3×#102—31no—
140C3×C4×C8—21no—
141C3×C4×C8C2×D311yescharacteristic
142C3×C4×C8C2×D311yescharacteristic
143#832—32no—
144#832—32no—
145#821C2×D312yes—
146#821C2×D311yescharacteristic
147#821C2×D312yes—
148#817C2×D311yescharacteristic
149#816C2×D311yescharacteristic
150#815—32no—
151#815—32no—
152#815—62no—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155Dic3⋊C8—62no—
156#809—32no—
157#809—32no—
158#807—32no—
159#807—32no—
160C4⋊(C3⋊C8)—31no—
161C4⋊(C3⋊C8)—31no—
162C4⋊(C3⋊C8)—61no—
163C22×C3×D3—22no—
164C22×C3×D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3C2×D412yes—
169C2×C3⋊Dic3C2×D412yes—
170#634—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C3×D12—22no—
176C3×D12—21no—
177C3×D12—21no—
178C3×D12—22no—
179C3×D12—42no—
180C3×D12—81no—
181C3×C4×D3—42no—
182C3×Dic6—21no—
183C3×Dic6—42no—
184C3×Dic6#4112yescomplemented
185#625—44no—
186#625—82no—
187D3×Dic3—44no—
188C32×C8—21no—
189C32×C8—21no—
190C3⋊(C3⋊C8)—22no—
191#557—91no—
192#550—91no—
193#490—92no—
194#486—31no—
195#478—92no—
196#474—91no—
197#460—92no—
198#460—91no—
199#446—91no—
200#440—92no—
201C4×SD16—31no—
202C2×C3×Q8—31no—
203C2×C3×Q8—61no—
204C2×C3×D4—31no—
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C22×C3×C4—61no—
209C2×#67—62no—
210C2×#67—62no—
211C2×#67—62no—
212C2×#67—62no—
213C22×Dic3—62no—
214#237—124no—
215#235—124no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12C22×D311yescharacteristic
219C2×D12C22×D312yes—
220C2×C4×D3—21no—
221C2×C4×D3—62no—
222C2×Dic6—21no—
223C2×Dic6—31no—
224C2×Dic6—31no—
225C2×Dic6—61no—
226C2×Dic6C22×D311yescharacteristic
227C3×SD16—62no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C22×D311yescharacteristic
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C22⋊C4—61no—
240C3×C42—21no—
241C3×C42—61no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—62no—
245#215—64no—
246#214—64no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—21no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3C22×D311yescharacteristic
257C4⋊Dic3C22×D312yes—
258C4⋊Dic3C22×D311yescharacteristic
259Dic3⋊C4—21no—
260Dic3⋊C4—32no—
261Dic3⋊C4—32no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266C4×Dic3—21no—
267C4×Dic3—32no—
268C4×Dic3—32no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C4×Dic3—62no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—62no—
275#204—22no—
276C22×C32C22×D411yescharacteristic
277C2×C3×D3—42no—
278C2×C3×D3—41no—
279C2×C3×D3—42no—
280C2×C3×D3—41no—
281C2×C3×D3—41no—
282C2×C3×D3—42no—
283C32×C4—21no—
284C32×C4AGL(1,ℤ/8)12yes—
285C32×C4C2×#4111yescharacteristic
286C32×C42−1+411yescharacteristic
287C3⋊Dic3—22no—
288C3⋊Dic3—22no—
289C3×Dic3—22no—
290C3×Dic3—41no—
291C3×Dic3—42no—
292C3×Dic3—41no—
293C2×#41—181no—
294C2×SD16—31no—
295C2×SD16—92no—
296C4⋊Q8—31no—
297C4⋊Q8—181no—
298#127—31no—
299#127—92no—
300#125—92no—
301#125—182no—
302#121—182no—
303#121—181no—
304C4×Q8—31no—
305C4×Q8—91no—
306C4×Q8—92no—
307C4×Q8—181no—
308C4×D4—31no—
309C4×D4—92no—
310#107—92no—
311#106—31no—
312C4⋊C8—92no—
313C4⋊C8—91no—
314#103—31no—
315#102—31no—
316#102—32no—
317#102—32no—
318#102—92no—
319#102—92no—
320#97—92no—
321C4×C8D3211yescharacteristic
322C23×C3—62no—
323C23×C3—61no—
324C22×D3—21no—
325C22×D3—22no—
326C3×Q8—32no—
327C3×Q8—61no—
328C3×Q8—122no—
329C3×D4—62no—
330C3×D4—61no—
331C3×D4—61no—
332C3×D4—62no—
333C3×D4—122no—
334C3×D4—241no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—61no—
339C2×C3×C4—62no—
340C2×C3×C4—61no—
341C2×C3×C4—61no—
342C2×C3×C4—122no—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349#67—124no—
350#67—124no—
351#67—242no—
352#67—242no—
353C2×Dic3—21no—
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—21no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—124no—
364D12—21no—
365D12—22no—
366D12—22no—
367D12—21no—
368D12—42no—
369D12—81no—
370C4×D3—42no—
371C4×D3—124no—
372Dic6—21no—
373Dic6—42no—
374Dic6—62no—
375Dic6—62no—
376Dic6—122no—
377Dic6#23512yescomplemented
378C3×C8—22no—
379C3×C8—21no—
380C3×C8—21no—
381C3×C8—21no—
382C3×C8—21no—
383C3×C8—41no—
384C3⋊C8—62no—
385C3⋊C8—62no—
386C3⋊C8—122no—
387C2×C32#54811yescharacteristic
388C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
389C2×C32#57711yescharacteristic
390C3×D3—81no—
391C3×D3—82no—
392#41—364no—
393C2×Q8—31no—
394C2×Q8—61no—
395C2×Q8—91no—
396C2×D4—32no—
397C2×D4—31no—
398C2×D4—61no—
399C2×D4—61no—
400C2×D4—182no—
401C2×D4—182no—
402C22×C4—61no—
403C22×C4—182no—
404SD16—62no—
405SD16—184no—
406C2×C8—92no—
407C2×C8C2×D3211yescharacteristic
408C2×C8C2×D3211yescharacteristic
409C4⋊C4—32no—
410C4⋊C4—31no—
411C4⋊C4—31no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C4⋊C4—91no—
415C4⋊C4—92no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C22⋊C4—61no—
420C22⋊C4—182no—
421C42—61no—
422C42—92no—
423C42—182no—
424C42C2×D3211yescharacteristic
425C22×C3—21no—
426C22×C3—121no—
427C22×C3—121no—
428C22×C3—122no—
429C22×C3—121no—
430C22×C3—122no—
431C22×C3—122no—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—41no—
437C2×D3—42no—
438C2×D3—41no—
439C2×D3—41no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—41no—
446C3×C4—62no—
447C3×C4—121no—
448C3×C4—122no—
449C3×C4—121no—
450C3×C4#91112yes—
451C3×C4#91412yes—
452C3×C4C2×#23511yescharacteristic
453C3×C4D3×#4111yescharacteristic
454C3×C4#101011yescharacteristic
455C3×C4#101011yescharacteristic
456Dic3—22no—
457Dic3—42no—
458Dic3—41no—
459Dic3—41no—
460Dic3—62no—
461Dic3—62no—
462Dic3—62no—
463Dic3—62no—
464Dic3—122no—
465Dic3—122no—
466C32#336811yescharacteristic, complemented, Sylow
467C23—61no—
468C23—62no—
469Q8—32no—
470Q8—61no—
471Q8—122no—
472Q8—182no—
473D4—62no—
474D4—61no—
475D4—61no—
476D4—62no—
477D4—122no—
478D4—241no—
479D4—364no—
480D4—722no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—92no—
486C2×C4—92no—
487C2×C4—122no—
488C2×C4—364no—
489C2×C4#380211yescharacteristic
490C2×C4#380211yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—21no—
493C8—21no—
494C8—182no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—242no—
499C2×C3—241no—
500C2×C3#555211yescharacteristic
501C2×C3#567711yescharacteristic
502C2×C3C2×#91111yescharacteristic
503C2×C3C2×#91411yescharacteristic
504C2×C3#576211yescharacteristic
505C2×C3#577011yescharacteristic
506D3—81no—
507D3—82no—
508C22—121no—
509C22—122no—
510C22—121no—
511C22—122no—
512C22—122no—
513C22—121no—
514C22C2×#380211yescharacteristic
515C4—21no—
516C4—62no—
517C4—121no—
518C4—122no—
519C4—121no—
520C4—182no—
521C4—182no—
522C4#6379812yes—
523C4#6429811yescharacteristic
524C4D3×#23511yescharacteristic
525C3—21no—
526C3#7962511yescharacteristic, complemented
527C3#8159011yescharacteristic, complemented
528C2—241no—
529C2—242no—
530C2#1059390511yescharacteristic
531C2C2×#6379811yescharacteristic
532C2#1059468611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593906C2
hypercenterC4×C8D32
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593861C2semidirect
3. #10592378C2semidirect
4. C3×#4694C2semidirect
5. C3×C4×#204C2semidirect
6. #10590888C2semidirect
7. #10590876C2semidirect
8. #10590782C2semidirect
9. #10590743C2semidirect
10. #10590364C2semidirect
11. #10590269C2semidirect
61. #4694D3semidirect
62. C4×#204D3semidirect
184. C3×Dic6#41semidirect
377. Dic6#235semidirect
466. C32#3368semidirect
526. C3#79625semidirect
527. C3#81590semidirect

Maximal subgroups

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

subgroupindex
#105939062
#105938612
#105923782
C3×#46942
C3×C4×#2042
#105908882
#105908762
#105907822
#105907432
#105903642
#105902692
#815903
#796253