Finite Group Databasebeta

← #11895979

Subgroups — #11895979

Order 1152.

864 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5087C211yesmaximal, characteristic, complemented
5#10590554C212yesmaximal, complemented
6#10590553C212yesmaximal, complemented
7#10590473C212yesmaximal, complemented
8#10590461C212yesmaximal, complemented
9#10590377C211yesmaximal, characteristic, complemented
10C4×#3716C211yesmaximal, characteristic, complemented
11#10590296C211yesmaximal, characteristic, complemented
12#81590—31nomaximal
13#80995—31nomaximal
14C2×#3795—21no—
15C32×C4⋊Q8C2211yescharacteristic
16Q8×C3⋊Dic3—21no—
17#64153—21no—
18#64099C2212yes—
19#64098—22no—
20#64096C2212yes—
21C4×#634C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#874C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25#63914C2212yes—
26#63908—21no—
27#63898C2212yes—
28#63885—22no—
29C2×#3716C2211yescharacteristic
30C2×#3716C2212yes—
31C3×#809C2212yes—
32C3×#809C2212yes—
33C3×#809C2212yes—
34C3×#807C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63567C2211yescharacteristic
40#63563C2212yes—
41#63563C2211yescharacteristic
42#63555C2212yes—
43#5721—31no—
44#5721—31no—
45#5721—61no—
46#5718—31no—
47#5553—31no—
48C3×#486—31no—
49C3×#474—31no—
50#5088D311yescharacteristic, complemented
51#5087D311yescharacteristic, complemented
52#5075—31no—
53C4×#214—31no—
54#4891—32no—
55#4889—32no—
56#4848—31no—
57#4831—31no—
58#4764—32no—
59#4764—32no—
60#4763—32no—
61#4762—32no—
62#4762—32no—
63#4757—32no—
64C4×#204—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67C2×#634D411yescharacteristic
68C2×#634C2311yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×#625—22no—
75C2×#625—22no—
76C2×D3×Dic3—22no—
77#3795—44no—
78C32×C4⋊C4—21no—
79C32×C4⋊C4C2312yes—
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85#3750—22no—
86#3750—22no—
87#3750D412yes—
88C4×C3⋊Dic3—21no—
89C4×C3⋊Dic3—22no—
90C4×C3⋊Dic3C2312yes—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96(C2×D3)⋊Dic3—22no—
97#3716—22no—
98#3716—24no—
99#3368—91noSylow
100C2×#237—61no—
101C2×#235—61no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×#127—31no—
106C3×C4×D4—31no—
107Q8×Dic3—61no—
108Q8×Dic3—61no—
109Q8×Dic3—62no—
110#944—61no—
111#944—61no—
112#944—62no—
113#940—32no—
114#940—32no—
115#939—62no—
116#938—61no—
117D4×Dic3—32no—
118C2×#214—32no—
119C2×#214—31no—
120#930—61no—
121C2×#204—32no—
122C2×#204—31no—
123#893—32no—
124#890—32no—
125#890—32no—
126#890—62no—
127#889—62no—
128#889—62no—
129#889—64no—
130#887—32no—
131#887—32no—
132#887—62no—
133#884—62no—
134#874C2×D311yescharacteristic
135C4×D12C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—31no—
140C4×Dic6—61no—
141C4×Dic6—61no—
142C3×#107—32no—
143C3×C4⋊C8—31no—
144C3×#102—32no—
145C3×#102—32no—
146C3×#102—32no—
147C3×C4×C8—31no—
148#832—31no—
149#832—32no—
150#821—32no—
151#821—31no—
152#817—31no—
153#816—31no—
154#815—32no—
155#815—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158#810—31no—
159#809C2×D312yes—
160#809C2×D312yes—
161#809C2×D312yes—
162#808—31no—
163#807C2×D312yes—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C32×Q8—42no—
169C2×C32×C4—22no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3C2×D412yes—
177#634—21no—
178#634—22no—
179#634#4112yescomplemented
180C2×C3×Dic3—21no—
181C3×D12—22no—
182C3×D12—21no—
183C3×D12—21no—
184C3×D12—22no—
185C3×D12—42no—
186C3×D12—81no—
187C3×C4×D3—42no—
188#625—44no—
189#625—82no—
190D3×Dic3—44no—
191C3×C3⋊C8—22no—
192C3×C3⋊C8—21no—
193C3×C3⋊C8—21no—
194#557—91no—
195#550—91no—
196#490—92no—
197#486—31no—
198#478—92no—
199#474—31no—
200#460—92no—
201#460—91no—
202#446—91no—
203#440—92no—
204C4×SD16—91no—
205C2×C3×Q8—22no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×D4—32no—
209C2×C3×D4—31no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C22×C3×C4—61no—
213C2×#67—62no—
214C2×#67—62no—
215C2×#67—62no—
216C2×#67—62no—
217C22×Dic3—62no—
218#237—124no—
219#235—124no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12C22×D311yescharacteristic
223C2×D12C22×D312yes—
224C2×C4×D3—21no—
225C2×C4×D3—62no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—31no—
229C2×Dic6—31no—
230C2×Dic6—61no—
231C2×Dic6—61no—
232C2×C3×C8—31no—
233C2×C3×C8—32no—
234C2×C3×C8—31no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4C22×D312yes—
241C3×C4⋊C4C22×D312yes—
242C3×C22⋊C4—61no—
243C3×C42—21no—
244C3×C42C22×D311yescharacteristic
245C3×C42C22×D311yescharacteristic
246#217—62no—
247#214—62no—
248#214—64no—
249(C2×D3)⋊C4—21no—
250(C2×D3)⋊C4—62no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—62no—
258C4⋊Dic3—62no—
259C4⋊Dic3—64no—
260C4⋊Dic3C22×D311yescharacteristic
261Dic3⋊C4—32no—
262Dic3⋊C4—32no—
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—64no—
270Dic3⋊C4—64no—
271Dic3⋊C4—61no—
272Dic3⋊C4—61no—
273C4×Dic3—32no—
274C4×Dic3—32no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—64no—
280C4×Dic3—61no—
281C4×Dic3—61no—
282C2×C3⋊C8C22×D311yescharacteristic
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D312yes—
285#204—64no—
286#204—62no—
287C22×C32C22×D411yescharacteristic
288C2×C3×D3—41no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—41no—
292C2×C3×D3—41no—
293C2×C3×D3—42no—
294C32×C4—21no—
295C32×C4—42no—
296C32×C4AGL(1,ℤ/8)12yes—
297C32×C4C2×#4111yescharacteristic
298C32×C42−1+411yescharacteristic
299C3⋊Dic3—22no—
300C3⋊Dic3—22no—
301C3⋊Dic3—22no—
302C3⋊Dic3—41no—
303C3×Dic3—41no—
304C2×#41—181no—
305C2×SD16—91no—
306C2×SD16—92no—
307C4⋊Q8—181no—
308C4⋊Q8D3211yescharacteristic
309#127—31no—
310#127—92no—
311#125—92no—
312#125—182no—
313#121—182no—
314#121—181no—
315C4×Q8—91no—
316C4×Q8—92no—
317C4×Q8—91no—
318C4×Q8—181no—
319C4×D4—31no—
320C4×D4—92no—
321#107—32no—
322#106—91no—
323C4⋊C8—31no—
324C4⋊C8—92no—
325#103—91no—
326#102—32no—
327#102—32no—
328#102—32no—
329#102—91no—
330#102—92no—
331#97—92no—
332C4×C8—31no—
333C23×C3—62no—
334C23×C3—61no—
335C22×D3—21no—
336C22×D3—22no—
337C3×Q8—44no—
338C3×Q8—42no—
339C3×Q8—42no—
340C3×D4—62no—
341C3×D4—62no—
342C3×D4—61no—
343C3×D4—61no—
344C3×D4—122no—
345C3×D4—241no—
346C2×C3×C4—24no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—61no—
353C2×C3×C4—122no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360#67—124no—
361#67—124no—
362#67—242no—
363#67—242no—
364C2×Dic3—21no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—32no—
368C2×Dic3—32no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—61no—
373C2×Dic3—61no—
374C2×Dic3—62no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—124no—
378D12—21no—
379D12—21no—
380D12—22no—
381D12—22no—
382D12—42no—
383D12—81no—
384C4×D3—42no—
385C4×D3—124no—
386Dic6—32no—
387Dic6—32no—
388Dic6—62no—
389Dic6—62no—
390Dic6—62no—
391Dic6—62no—
392Dic6—61no—
393Dic6—61no—
394Dic6—122no—
395C3×C8—61no—
396C3×C8—61no—
397C3×C8—62no—
398C3⋊C8—22no—
399C3⋊C8—21no—
400C3⋊C8—21no—
401C2×C32#54811yescharacteristic
402C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
403C2×C32#57711yescharacteristic
404C3×D3—81no—
405C3×D3—82no—
406#41—364no—
407C2×Q8—21no—
408C2×Q8—91no—
409C2×Q8—91no—
410C2×D4—31no—
411C2×D4—32no—
412C2×D4—61no—
413C2×D4—61no—
414C2×D4—182no—
415C2×D4—182no—
416C22×C4—61no—
417C22×C4—182no—
418SD16—182no—
419SD16—184no—
420C2×C8—31no—
421C2×C8—31no—
422C2×C8—32no—
423C4⋊C4—21no—
424C4⋊C4—31no—
425C4⋊C4—91no—
426C4⋊C4—92no—
427C4⋊C4—91no—
428C4⋊C4—182no—
429C4⋊C4—182no—
430C4⋊C4—182no—
431C4⋊C4—181no—
432C4⋊C4C2×D3212yes—
433C22⋊C4—61no—
434C22⋊C4—182no—
435C42—92no—
436C42—182no—
437C42—181no—
438C42C2×D3211yescharacteristic
439C22×C3—21no—
440C22×C3—122no—
441C22×C3—121no—
442C22×C3—122no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3—122no—
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C2×D3×D411yescharacteristic
448C2×D3—41no—
449C2×D3—42no—
450C2×D3—41no—
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—41no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—22no—
459C3×C4—41no—
460C3×C4—44no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—121no—
464C3×C4#91112yes—
465C3×C4#91112yes—
466C3×C4#100711yescharacteristic
467C3×C4D3×#4111yescharacteristic
468C3×C4D3×#4111yescharacteristic
469C3×C4#101011yescharacteristic
470Dic3—41no—
471Dic3—64no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—62no—
476Dic3—62no—
477Dic3—62no—
478Dic3—122no—
479Dic3—122no—
480Dic3—122no—
481Dic3—121no—
482Dic3—121no—
483C32#336811yescharacteristic, complemented, Sylow
484C23—61no—
485C23—62no—
486Q8—42no—
487Q8—92no—
488Q8—181no—
489Q8—182no—
490D4—61no—
491D4—62no—
492D4—61no—
493D4—62no—
494D4—122no—
495D4—241no—
496D4—364no—
497D4—722no—
498C2×C4—22no—
499C2×C4—61no—
500C2×C4—92no—
501C2×C4—92no—
502C2×C4—122no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—364no—
506C2×C4#381111yescharacteristic
507C2×C4#381111yescharacteristic
508C2×C4C22×D3211yescharacteristic
509C8—61no—
510C8—61no—
511C8—62no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—242no—
516C2×C3—241no—
517C2×C3#563311yescharacteristic
518C2×C3#567711yescharacteristic
519C2×C3C2×#91111yescharacteristic
520C2×C3C2×#91111yescharacteristic
521C2×C3#576211yescharacteristic
522C2×C3#577811yescharacteristic
523D3—81no—
524D3—82no—
525C22—121no—
526C22—122no—
527C22—121no—
528C22—122no—
529C22—122no—
530C22—121no—
531C22C2×#381111yescharacteristic
532C4—21no—
533C4—42no—
534C4—121no—
535C4—182no—
536C4—182no—
537C4—182no—
538C4—361no—
539C4#6392712yes—
540C4#6431511yescharacteristic
541C4#6431911yescharacteristic
542C3—21no—
543C3#8099511yescharacteristic, complemented
544C3#8159011yescharacteristic, complemented
545C2—241no—
546C2—242no—
547C2C2×#6392711yescharacteristic
548C2#1059532411yescharacteristic
549C2#1059536211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10593906C2
hypercenterC4⋊Q8D32
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596192C2semidirect
3. C3×#5088C2semidirect
4. C3×#5087C2semidirect
5. #10590554C2semidirect
6. #10590553C2semidirect
7. #10590473C2semidirect
8. #10590461C2semidirect
9. #10590377C2semidirect
10. C4×#3716C2semidirect
11. #10590296C2semidirect
50. #5088D3semidirect
51. #5087D3semidirect
179. #634#41semidirect
483. C32#3368semidirect
543. C3#80995semidirect
544. C3#81590semidirect

Maximal subgroups

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

subgroupindex
#105961922
#105939062
C3×#50882
C3×#50872
#105905542
#105905532
#105904732
#105904612
#105903772
C4×#37162
#105902962
#815903
#809953