Finite Group Databasebeta

← #11787785

Subgroups — #11787785

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5832C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic, complemented
3#10592935C211yesmaximal, characteristic, complemented
4C3×#5236C211yesmaximal, characteristic, complemented
5#10591231C211yesmaximal, characteristic, complemented
6#10589162C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71817—31nomaximal
9#70417—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#947C411yescharacteristic, complemented
15C3×#944C411yescharacteristic, complemented
16C3×#940C411yescharacteristic, complemented
17C3×#939—22no—
18C3×#936C411yescharacteristic, complemented
19C3×C4×#67—22no—
20C3×#926C2211yescharacteristic
21C2×C3×C4×Dic3C2211yescharacteristic
22C2×C3×#208C2211yescharacteristic
23#63815—22no—
24#63814—22no—
25D3×#208—22no—
26#63664—22no—
27C3×#837—22no—
28#63580—22no—
29C3×#532—31no—
30#5832D311yescharacteristic
31#5819—31no—
32#5745—31no—
33C3×#421—31no—
34#5240—31no—
35#5236—31no—
36#5236—31no—
37#5236—61no—
38#5236D311yescharacteristic, complemented
39#5006—31no—
40#4555—31no—
41#4532—31no—
42#4523—31no—
43#4523—31no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41—21no—
47C32×#41—21no—
48C2×C32×Q8C2×C411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4C2×C411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×C3×#67—22no—
54C2×C3×#67D412yes—
55C22×C3×Dic3—21no—
56C3×#235—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C2×C3×D12C2×C411yescharacteristic
61C2×C3×C4×D3D412yes—
62C2×C3×Dic6C2×C411yescharacteristic
63#3757—21no—
64C4⋊(C3⋊Dic3)—21no—
65C4×C3⋊Dic3—21no—
66#3748—21no—
67#3748D412yescomplemented
68C2×C3⋊(C3⋊C8)—21no—
69C3×#217—22no—
70C3×#217—21no—
71C3×(C2×D3)⋊C4—22no—
72C3×C4⋊Dic3—21no—
73C3×Dic3⋊C4—22no—
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3C2×C411yescharacteristic
77C3×C4×Dic3C2×C411yescharacteristic
78C3×#208—21no—
79C3×#208D412yescomplemented
80C2×C3×C3⋊C8—21no—
81#3711—24no—
82D3×C3⋊C8—24no—
83#1884—91noSylow
84C2×C3×#41—21no—
85C2×C3×#41—31no—
86C2×C3×#41C2×D311yescharacteristic
87C2×C3×#41C2×D311yescharacteristic
88C2×#235C2×D311yescharacteristic
89C2×C3×M16—31no—
90C3×C4⋊Q8—31no—
91C3×#127—31no—
92C3×#124—31no—
93C3×#124—31no—
94C3×#121—62no—
95C3×C4×D4—62no—
96C3×#117—31no—
97C2×C3×C42—31no—
98#948—62no—
99#948—62no—
100#947Dic311yescharacteristic, complemented
101#944Dic311yescharacteristic, complemented
102#940Dic311yescharacteristic, complemented
103#939—22no—
104#936Dic311yescharacteristic, complemented
105C4×#67—22no—
106#926—31no—
107#926—31no—
108#926—61no—
109#926C2×D311yescharacteristic
110C2×C4×Dic3C2×D311yescharacteristic
111C2×#208—31no—
112C2×#208—31no—
113C2×#208—61no—
114C2×#208—62no—
115C2×#208C2×D311yescharacteristic
116#907—62no—
117D3×M16—62no—
118#901—62no—
119C3×#104—62no—
120#837—22no—
121#837—62no—
122#837—62no—
123#837—64no—
124#834—62no—
125#806—62no—
126C23×C32—21no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3C22⋊C412yes—
129C32×Q8—21no—
130C32×Q8—21no—
131C32×D4—21no—
132C32×D4—21no—
133C32×D4—41no—
134C32×D4—41no—
135C2×C32×C4—21no—
136C2×C32×C4—41no—
137C2×C32×C4—41no—
138C2×C32×C4C22×C411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C3⋊Dic3—41no—
145C3×#67—22no—
146C3×#67—22no—
147C3×#67—44no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—21no—
150C2×C3×Dic3—42no—
151C2×C3×Dic3—41no—
152C2×C3×Dic3C22⋊C412yes—
153C3×D12—21no—
154C3×D12—21no—
155C3×C4×D3—22no—
156C3×C4×D3—22no—
157C3×Dic6—21no—
158C3×Dic6—21no—
159C3⋊(C3⋊C8)—22no—
160C3×C3⋊C8—22no—
161#568—91no—
162#532—31no—
163#421—31no—
164#421—91no—
165#410—91no—
166#339—91no—
167#339—91no—
168C3×#41—22no—
169C3×#41—22no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—21no—
175C3×#41—21no—
176C3×#41—21no—
177C3×#41—21no—
178C3×#41—41no—
179C3×#41—41no—
180C3×#41—61no—
181C3×#41—61no—
182C3×#41—61no—
183C3×#41—61no—
184C2×C3×Q8—21no—
185C2×C3×Q8—31no—
186C2×C3×Q8C4×D311yescharacteristic
187C2×C3×Q8C2×Dic311yescharacteristic
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—32no—
192C2×C3×D4—31no—
193C2×C3×D4—41no—
194C2×C3×D4—62no—
195C2×C3×D4C4×D311yescharacteristic
196C2×C3×D4C2×Dic311yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—32no—
201C22×C3×C4—41no—
202C22×C3×C4—61no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C2×#67—22no—
206C2×#67#6712yes—
207C22×Dic3—21no—
208#235—21no—
209#235—21no—
210#235—21no—
211#235—21no—
212C2×D12C2×Dic311yescharacteristic
213C2×C4×D3#6712yes—
214C2×Dic6C2×Dic311yescharacteristic
215C3×M16—32no—
216C3×M16—61no—
217C2×C3×C8—61no—
218C3×C4⋊C4—62no—
219C3×C4⋊C4—61no—
220C3×C22⋊C4—62no—
221C3×C22⋊C4—62no—
222C3×C22⋊C4—61no—
223C3×C42—31no—
224C3×C42—31no—
225C3×C42—61no—
226C3×C42—61no—
227#217—22no—
228#217—21no—
229#217—61no—
230#217—61no—
231#217—121no—
232(C2×D3)⋊C4—22no—
233C4⋊Dic3—21no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—121no—
237Dic3⋊C4—22no—
238C4×Dic3—21no—
239C4×Dic3—21no—
240C4×Dic3—62no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3C2×Dic311yescharacteristic
244C4×Dic3C2×Dic311yescharacteristic
245#208—21no—
246#208—32no—
247#208—32no—
248#208—62no—
249#208—64no—
250#208—61no—
251#208—61no—
252#208—121no—
253#208#6712yescomplemented
254C2×C3⋊C8—21no—
255C2×C3⋊C8—64no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—121no—
259ΓL(1,𝔽25)—64no—
260D3×C8—64no—
261C22×C32—41no—
262C22×C32—41no—
263C22×C32—42no—
264C22×C32C2×C22⋊C411yescharacteristic
265C22×C32#12111yescharacteristic
266C22×C32#12111yescharacteristic
267C2×C3×D3—22no—
268C2×C3×D3—42no—
269C32×C4—41no—
270C32×C4C4×D411yescharacteristic
271C32×C4C4×D411yescharacteristic
272C32×C4#12011yescharacteristic
273C32×C4#12311yescharacteristic
274C3⋊Dic3—81no—
275C3×Dic3—22no—
276C3×Dic3—22no—
277C3×Dic3—41no—
278C3×Dic3—81no—
279C2×#41—31no—
280C2×#41D3211yescharacteristic
281#131—182no—
282#131—182no—
283C2×M16—31no—
284C2×M16—91no—
285C2×M16—182no—
286C4⋊Q8—31no—
287#127—31no—
288#124—31no—
289#124—31no—
290#121—62no—
291C4×D4—62no—
292#117—31no—
293#117—91no—
294C2×C42—31no—
295#104—62no—
296#104—182no—
297#99—182no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—21no—
301C23×C3—32no—
302C23×C3—41no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3#21712yes—
306C3×Q8—22no—
307C3×Q8—21no—
308C3×Q8—21no—
309C3×Q8—21no—
310C3×Q8—21no—
311C3×Q8—41no—
312C3×Q8—61no—
313C3×Q8—61no—
314C3×D4—22no—
315C3×D4—21no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—21no—
319C3×D4—41no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—61no—
329C3×D4—61no—
330C3×D4—124no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—32no—
340C2×C3×C4—41no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—41no—
345C2×C3×C4—41no—
346C2×C3×C4—41no—
347C2×C3×C4—61no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—61no—
351C2×C3×C4—122no—
352C2×C3×C4—121no—
353C2×C3×C4C2×C4×D311yescharacteristic
354C2×C3×C4#23511yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4#23711yescharacteristic
360C2×C3×C4#23711yescharacteristic
361C2×C3×C4#23711yescharacteristic
362C2×C3×C4C22×Dic311yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365#67—22no—
366#67—22no—
367#67—44no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—42no—
371C2×Dic3—41no—
372C2×Dic3—122no—
373C2×Dic3—121no—
374C2×Dic3—121no—
375C2×Dic3#21712yes—
376D12—21no—
377D12—21no—
378C4×D3—22no—
379C4×D3—22no—
380Dic6—21no—
381Dic6—21no—
382C3×C8—62no—
383C3⋊C8—22no—
384C3⋊C8—62no—
385C3⋊C8—62no—
386C3⋊C8—122no—
387C2×C32—21no—
388C2×C32—21no—
389C2×C32—21no—
390C2×C32—81no—
391C2×C32#38611yescharacteristic
392C3×D3—42no—
393#41—21no—
394#41—21no—
395#41—21no—
396#41—21no—
397#41—61no—
398#41—61no—
399#41—61no—
400#41—61no—
401C2×Q8—31no—
402C2×Q8D3×Dic311yescharacteristic
403C2×D4—21no—
404C2×D4—32no—
405C2×D4—31no—
406C2×D4—62no—
407C2×D4D3×Dic311yescharacteristic
408C22×C4—21no—
409C22×C4—32no—
410C22×C4—61no—
411C22×C4C2×D3211yescharacteristic
412M16—32no—
413M16—61no—
414M16—92no—
415M16—184no—
416M16—181no—
417C2×C8—61no—
418C2×C8—184no—
419C2×C8—181no—
420C4⋊C4—62no—
421C4⋊C4—61no—
422C4⋊C4—181no—
423C22⋊C4—62no—
424C22⋊C4—62no—
425C22⋊C4—61no—
426C22⋊C4—181no—
427C42—31no—
428C42—31no—
429C42—61no—
430C42—61no—
431C42—181no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—42no—
438C22×C3—42no—
439C22×C3—42no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—62no—
443C22×C3—81no—
444C22×C3—82no—
445C22×C3—122no—
446C22×C3D3×C22⋊C411yescharacteristic
447C22×C3#88411yescharacteristic
448C22×C3#93811yescharacteristic
449C22×C3#93911yescharacteristic
450C22×C3#93911yescharacteristic
451C22×C3C2×#21711yescharacteristic
452C2×D3—22no—
453C2×D3—42no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—42no—
459C3×C4—41no—
460C3×C4—41no—
461C3×C4—62no—
462C3×C4—62no—
463C3×C4—121no—
464C3×C4—241no—
465C3×C4#67⋊C411yescharacteristic
466C3×C4#88311yescharacteristic
467C3×C4C4×#6711yescharacteristic
468C3×C4D4×Dic311yescharacteristic
469C3×C4D4×Dic311yescharacteristic
470C3×C4#93511yescharacteristic
471C3×C4#93711yescharacteristic
472C3×C4#93711yescharacteristic
473Dic3—22no—
474Dic3—22no—
475Dic3—41no—
476Dic3—81no—
477Dic3—241no—
478Dic3—241no—
479Dic3—242no—
480C32#188411yescharacteristic, complemented, Sylow
481C23—21no—
482C23—32no—
483C23D3×#6711yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—61no—
487Q8—61no—
488D4—21no—
489D4—21no—
490D4—41no—
491D4—41no—
492D4—62no—
493D4—62no—
494D4—61no—
495D4—61no—
496D4—124no—
497C2×C4—21no—
498C2×C4—32no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—61no—
502C2×C4—62no—
503C2×C4—62no—
504C2×C4—61no—
505C2×C4—122no—
506C2×C4—121no—
507C2×C4—361no—
508C2×C4C2×D3×Dic311yescharacteristic
509C2×C4#380411yescharacteristic
510C2×C4#380511yescharacteristic
511C2×C4D3×#6711yescharacteristic
512C2×C4D3×#6711yescharacteristic
513C2×C4#381111yescharacteristic
514C8—62no—
515C8—182no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—41no—
526C2×C3—82no—
527C2×C3—81no—
528C2×C3—81no—
529C2×C3—122no—
530C2×C3#495611yescharacteristic
531C2×C3#522011yescharacteristic
532D3—42no—
533C22—41no—
534C22—42no—
535C22—41no—
536C22—62no—
537C22—122no—
538C22D3×#21711yescharacteristic
539C22#6397011yescharacteristic
540C22#6397111yescharacteristic
541C4—41no—
542C4—62no—
543C4—62no—
544C4—121no—
545C4—241no—
546C4—721no—
547C4#6396911yescharacteristic
548C4Dic3×#6711yescharacteristic
549C4#67⋊Dic311yescharacteristic
550C4#6398311yescharacteristic
551C3—21no—
552C3#7041711yescharacteristic, complemented
553C3#7181711yescharacteristic, complemented
554C2—21no—
555C2—21no—
556C2—21no—
557C2—81no—
558C2—122no—
559C2#1059172111yescharacteristic
subgroupG/H
centerC4#63983
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radicalC3×#5832C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594776C2semidirect
3. #10592935C2semidirect
4. C3×#5236C2semidirect
5. #10591231C2semidirect
6. #10589162C2semidirect
7. #10589161C2semidirect
14. C3×#947C4semidirect
15. C3×#944C4semidirect
16. C3×#940C4semidirect
18. C3×#936C4semidirect
38. #5236D3semidirect
67. #3748D4semidirect
79. C3×#208D4semidirect
100. #947Dic3semidirect
101. #944Dic3semidirect
102. #940Dic3semidirect
104. #936Dic3semidirect
253. #208#67semidirect
480. C32#1884semidirect
552. C3#70417semidirect
553. C3#71817semidirect

Maximal subgroups

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

subgroupindex
C3×#58322
#105947762
#105929352
C3×#52362
#105912312
#105891622
#105891612
#718173
#704173