Finite Group Databasebeta

← #11895972

Subgroups — #11895972

Order 1152.

920 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596189C211yesmaximal, characteristic
2#10593861C211yesmaximal, characteristic, complemented
3C3×#5075C211yesmaximal, characteristic, complemented
4C3×#5070C211yesmaximal, characteristic, complemented
5#10591480C212yesmaximal, complemented
6#10591479C212yesmaximal, complemented
7#10591446C212yesmaximal, complemented
8#10591444C212yesmaximal, complemented
9C4×#3717C211yesmaximal, characteristic, complemented
10#10590313C211yesmaximal, characteristic, complemented
11#10590296C211yesmaximal, characteristic, complemented
12#81590—31nomaximal
13#80371—31nomaximal
14C2×#3830—21no—
15C32×#127C2211yescharacteristic
16#64149C2212yes—
17#64148—22no—
18#64147—21no—
19D4×C3⋊Dic3C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2212yes—
23C3×#869C2211yescharacteristic
24C3×C4×Dic6C2211yescharacteristic
25#63872C2212yes—
26#63866—21no—
27#63846—22no—
28#63843C2212yes—
29Dic3×Dic6—21no—
30C2×#3717C2211yescharacteristic
31C3×#832C2212yes—
32C3×#832C2212yes—
33C3×#832C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2212yes—
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63566C2211yescharacteristic
40#63564C2212yes—
41#63564C2211yescharacteristic
42#63555C2212yes—
43#5721—31no—
44#5718—31no—
45#5718—31no—
46#5718—61no—
47#5570—31no—
48C3×#486—31no—
49C3×#460—31no—
50#5164—32no—
51#5163—32no—
52#5087—31no—
53#5075D311yescharacteristic, complemented
54#5070D311yescharacteristic, complemented
55C4×#215—31no—
56#4846—31no—
57#4831—31no—
58#4766—32no—
59#4764—32no—
60#4764—32no—
61#4763—32no—
62#4762—32no—
63#4757—32no—
64C4×#204—31no—
65#4679—31no—
66C2×C32×D4—21no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C2×#638—22no—
70C2×#638—22no—
71C22×C3⋊Dic3—22no—
72#3830—44no—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3—21no—
75C2×#634D411yescharacteristic
76C2×C3×Dic6—21no—
77C2×C3×Dic6C2311yescharacteristic
78C32×C42C2311yescharacteristic
79#3757—22no—
80#3752—21no—
81C4⋊(C3⋊Dic3)D411yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C3×#214—24no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×Dic3⋊C4—21no—
90C3×C4×Dic3—21no—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96Dic3⋊Dic3—22no—
97Dic32—22no—
98#3717—22no—
99#3368—91noSylow
100C2×#237—61no—
101C2×#237—61no—
102C2×#237—62no—
103C2×C3×SD16—32no—
104C3×C4⋊Q8—31no—
105C3×#127—21no—
106C3×#127C2×D311yescharacteristic
107C3×#127C2×D311yescharacteristic
108C3×C4×Q8—31no—
109Q8×Dic3—32no—
110Q8×Dic3—61no—
111#944—61no—
112C2×#215—31no—
113#940—32no—
114#940—32no—
115#940—62no—
116#939—62no—
117#939—62no—
118#939—64no—
119#938—61no—
120#938—61no—
121#938—62no—
122D4×Dic3—32no—
123D4×Dic3—32no—
124D4×Dic3—62no—
125C2×#214C2×D312yes—
126C2×#204—31no—
127#890—32no—
128#890—32no—
129#890—62no—
130#889—62no—
131#887—32no—
132C4×D12—31no—
133C4×D12—31no—
134C4×D12—61no—
135#869—61no—
136#869C2×D311yescharacteristic
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6—61no—
141C4×Dic6C2×D311yescharacteristic
142C3×C4⋊C8—31no—
143C3×#102—32no—
144C3×#102—32no—
145C3×#102—32no—
146C3×C4×C8—31no—
147#835—31no—
148#832C2×D312yes—
149#832C2×D312yes—
150#832C2×D312yes—
151#821—32no—
152#821—31no—
153#818—32no—
154#817—31no—
155#816—31no—
156#815—32no—
157#815—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160#809—32no—
161#809—31no—
162#808—31no—
163#807—32no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—22no—
167C22×C3⋊D3—21no—
168C32×D4—22no—
169C32×D4—22no—
170C32×D4—42no—
171C32×D4—81no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175#638—44no—
176#638—82no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—44no—
179C2×C3⋊Dic3C2×D412yes—
180C2×C3⋊Dic3C2×D412yes—
181C4⋊(C3⋊D3)—21no—
182C4⋊(C3⋊D3)—21no—
183C4×C3⋊D3—42no—
184#634—22no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—21no—
188C3×Dic6—21no—
189C3×Dic6—42no—
190C3×Dic6#4112yescomplemented
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8—21no—
194#557—91no—
195#550—91no—
196#490—92no—
197#486—31no—
198#478—92no—
199#474—91no—
200#460—31no—
201#460—92no—
202#446—91no—
203#440—92no—
204C4×SD16—91no—
205C2×C3×Q8—31no—
206C2×C3×Q8—61no—
207C2×C3×D4—22no—
208C2×C3×D4—22no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—22no—
214C2×C3×D4C22×D312yes—
215C2×C3×D4C22×D312yes—
216C2×#67—62no—
217C2×#67—62no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—64no—
221C2×#67—64no—
222C22×Dic3—62no—
223C22×Dic3—62no—
224C22×Dic3—64no—
225#237—128no—
226#237—124no—
227#237—124no—
228C2×D12—31no—
229C2×D12—31no—
230C2×D12—61no—
231C2×C4×D3—62no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×Dic6—21no—
235C2×Dic6—31no—
236C2×Dic6—31no—
237C2×Dic6—61no—
238C2×Dic6C22×D311yescharacteristic
239C3×SD16—64no—
240C2×C3×C8—31no—
241C2×C3×C8—32no—
242C2×C3×C8—31no—
243C3×C4⋊C4—32no—
244C3×C4⋊C4—31no—
245C3×C4⋊C4—61no—
246C3×C4⋊C4—61no—
247C3×C42—21no—
248C3×C42—61no—
249C3×C42C22×D311yescharacteristic
250C3×C42C22×D311yescharacteristic
251#217—62no—
252#217—62no—
253#217—64no—
254#215—62no—
255#214—24no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—61no—
258(C2×D3)⋊C4—61no—
259C4⋊Dic3—21no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—31no—
264C4⋊Dic3—61no—
265C4⋊Dic3—61no—
266C4⋊Dic3—62no—
267C4⋊Dic3—62no—
268C4⋊Dic3—62no—
269C4⋊Dic3C22×D311yescharacteristic
270C4⋊Dic3C22×D312yes—
271Dic3⋊C4—21no—
272Dic3⋊C4—32no—
273Dic3⋊C4—32no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277Dic3⋊C4—62no—
278C4×Dic3—21no—
279C4×Dic3—32no—
280C4×Dic3—32no—
281C4×Dic3—62no—
282C4×Dic3—62no—
283C4×Dic3—62no—
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D312yes—
287#204—62no—
288C22×C32—42no—
289C22×C32—42no—
290C22×C32—42no—
291C22×C32C22×D411yescharacteristic
292C2×C3⋊D3—41no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C32×C4—21no—
296C32×C4AGL(1,ℤ/8)12yes—
297C32×C4C2×#4111yescharacteristic
298C32×C42−1+411yescharacteristic
299C3⋊Dic3—22no—
300C3⋊Dic3—22no—
301C3⋊Dic3—41no—
302C3×Dic3—22no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C2×#41—181no—
306C2×SD16—32no—
307C2×SD16—91no—
308C4⋊Q8—31no—
309C4⋊Q8—181no—
310#127—92no—
311#127D3211yescharacteristic
312#125—92no—
313#125—182no—
314#121—181no—
315#121—182no—
316C4×Q8—31no—
317C4×Q8—91no—
318C4×Q8—92no—
319C4×Q8—181no—
320C4×D4—92no—
321C4×D4—91no—
322#107—92no—
323#106—91no—
324C4⋊C8—31no—
325C4⋊C8—92no—
326#103—91no—
327#102—32no—
328#102—32no—
329#102—32no—
330#102—91no—
331#102—92no—
332#97—92no—
333C4×C8—31no—
334C23×C3—24no—
335C23×C3—22no—
336C23×C3—22no—
337C22×D3—62no—
338C22×D3—61no—
339C22×D3—61no—
340C3×Q8—32no—
341C3×Q8—61no—
342C3×Q8—122no—
343C3×D4—22no—
344C3×D4—22no—
345C3×D4—22no—
346C3×D4—22no—
347C3×D4—42no—
348C3×D4—42no—
349C3×D4—44no—
350C3×D4—42no—
351C3×D4—42no—
352C3×D4—81no—
353C3×D4—81no—
354C3×D4—82no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—61no—
359C2×C3×C4—62no—
360C2×C3×C4—61no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—128no—
368#67—124no—
369#67—124no—
370#67—242no—
371#67—242no—
372#67—244no—
373C2×Dic3—21no—
374C2×Dic3—21no—
375C2×Dic3—22no—
376C2×Dic3—32no—
377C2×Dic3—32no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—61no—
384C2×Dic3—61no—
385C2×Dic3—128no—
386C2×Dic3—124no—
387C2×Dic3—124no—
388D12—61no—
389D12—61no—
390D12—61no—
391D12—61no—
392D12—121no—
393D12—121no—
394C4×D3—124no—
395C4×D3—122no—
396C4×D3—122no—
397Dic6—21no—
398Dic6—42no—
399Dic6—64no—
400Dic6—62no—
401Dic6—62no—
402Dic6#23712yescomplemented
403C3×C8—61no—
404C3×C8—62no—
405C3×C8—61no—
406C3⋊C8—22no—
407C3⋊C8—21no—
408C3⋊C8—21no—
409C2×C32—82no—
410C2×C32#54811yescharacteristic
411C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
412C2×C32#57711yescharacteristic
413C3⋊D3—81no—
414#41—364no—
415C2×Q8—31no—
416C2×Q8—61no—
417C2×Q8—91no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—91no—
421C2×D4—182no—
422C2×D4—182no—
423C2×D4C2×D3212yes—
424C22×C4—182no—
425C22×C4—181no—
426SD16—64no—
427SD16—182no—
428C2×C8—31no—
429C2×C8—31no—
430C2×C8—32no—
431C4⋊C4—31no—
432C4⋊C4—32no—
433C4⋊C4—61no—
434C4⋊C4—61no—
435C4⋊C4—91no—
436C4⋊C4—92no—
437C4⋊C4—91no—
438C4⋊C4—182no—
439C4⋊C4—182no—
440C4⋊C4—182no—
441C22⋊C4—182no—
442C22⋊C4—181no—
443C42—61no—
444C42—92no—
445C42—182no—
446C42C2×D3211yescharacteristic
447C22×C3—21no—
448C22×C3—44no—
449C22×C3—44no—
450C22×C3—44no—
451C22×C3—42no—
452C22×C3—42no—
453C22×C3—42no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—42no—
457C22×C3C2×D3×D411yescharacteristic
458C22×C3C2×D3×D411yescharacteristic
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—121no—
463C2×D3—121no—
464C2×D3—121no—
465C2×D3—121no—
466C2×D3—121no—
467C2×D3—121no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—41no—
474C3×C4—62no—
475C3×C4—122no—
476C3×C4—121no—
477C3×C4#91112yes—
478C3×C4#91412yes—
479C3×C4C2×#23711yescharacteristic
480C3×C4D3×#4111yescharacteristic
481C3×C4#101011yescharacteristic
482C3×C4#101011yescharacteristic
483Dic3—22no—
484Dic3—42no—
485Dic3—41no—
486Dic3—64no—
487Dic3—62no—
488Dic3—62no—
489Dic3—62no—
490Dic3—62no—
491Dic3—122no—
492Dic3—122no—
493Dic3—121no—
494Dic3—121no—
495C32#336811yescharacteristic, complemented, Sylow
496C23—22no—
497C23—181no—
498Q8—32no—
499Q8—61no—
500Q8—122no—
501Q8—182no—
502D4—22no—
503D4—22no—
504D4—42no—
505D4—81no—
506D4—181no—
507D4—181no—
508D4—364no—
509D4—722no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—92no—
514C2×C4—92no—
515C2×C4—181no—
516C2×C4—364no—
517C2×C4—362no—
518C2×C4#381111yescharacteristic
519C2×C4#381111yescharacteristic
520C2×C4C22×D3211yescharacteristic
521C8—61no—
522C8—62no—
523C8—61no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—84no—
528C2×C3—82no—
529C2×C3—82no—
530C2×C3#559811yescharacteristic
531C2×C3#567711yescharacteristic
532C2×C3C2×#91111yescharacteristic
533C2×C3C2×#91411yescharacteristic
534C2×C3#576211yescharacteristic
535C2×C3#577511yescharacteristic
536D3—242no—
537D3—241no—
538D3—241no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—361no—
543C22—361no—
544C22—361no—
545C22C2×#381111yescharacteristic
546C4—21no—
547C4—62no—
548C4—122no—
549C4—121no—
550C4—182no—
551C4—182no—
552C4—361no—
553C4#6393712yes—
554C4#6430911yescharacteristic
555C4D3×#23711yescharacteristic
556C3—21no—
557C3#8037111yescharacteristic, complemented
558C3#8159011yescharacteristic, complemented
559C2—82no—
560C2—721no—
561C2C2×#6393711yescharacteristic
562C2#1059511511yescharacteristic
563C2#1059516111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#127C22
socleC22×C32C22×D4
prime radical#10596189C2
hypercenter#127D32
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #10593861C2semidirect
3. C3×#5075C2semidirect
4. C3×#5070C2semidirect
5. #10591480C2semidirect
6. #10591479C2semidirect
7. #10591446C2semidirect
8. #10591444C2semidirect
9. C4×#3717C2semidirect
10. #10590313C2semidirect
11. #10590296C2semidirect
53. #5075D3semidirect
54. #5070D3semidirect
190. C3×Dic6#41semidirect
402. Dic6#237semidirect
495. C32#3368semidirect
557. C3#80371semidirect
558. C3#81590semidirect

Maximal subgroups

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

subgroupindex
#105961892
#105938612
C3×#50752
C3×#50702
#105914802
#105914792
#105914462
#105914442
C4×#37172
#105903132
#105902962
#815903
#803713