Finite Group Databasebeta

← #11787641

Subgroups — #11787641

Order 1152.

751 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596293C211yesmaximal, characteristic
2C3×#5819C211yesmaximal, characteristic, complemented
3C3×#5233C211yesmaximal, characteristic, complemented
4#10591113C211yesmaximal, characteristic, complemented
5#10591073C211yesmaximal, characteristic, complemented
6#10589169C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72020—31nomaximal
9#70293—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×#3828C2211yescharacteristic
12#64160C412yescomplemented
13#64159—22no—
14#64158C412yescomplemented
15#64151—21no—
16#64141—21no—
17C2×#3748C2211yescharacteristic
18C3×#948—22no—
19C3×#948—22no—
20C3×#926C2211yescharacteristic
21C2×C3×#208—22no—
22C2×C3×#208C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#835—21no—
26C3×#832—21no—
27#63570—22no—
28#63557—22no—
29C3×#568—31no—
30#5822—31no—
31#5822—31no—
32#5822—61no—
33#5819D311yescharacteristic, complemented
34C3×#416—31no—
35#5233D311yescharacteristic, complemented
36#5139—31no—
37#5129—31no—
38#5110—31no—
39#5005—31no—
40#4558—31no—
41#4556—31no—
42#4552—31no—
43#4533—31no—
44C32×#41—21no—
45C32×#41—21no—
46C32×#41C2×C412yes—
47C32×#41D412yes—
48C2×C32×Q8D411yescharacteristic
49C2×C32×D4—21no—
50C2×C32×D4D411yescharacteristic
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C2×#638—21no—
54#3828—21no—
55#3828—21no—
56#3828—21no—
57#3828—21no—
58C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634C2×C411yescharacteristic
61#3756—22no—
62#3755—22no—
63#3754—22no—
64#3753—22no—
65#3748—21no—
66#3748C2×C412yes—
67C2×C3⋊(C3⋊C8)—21no—
68C3×#217—21no—
69C3×C4⋊Dic3—21no—
70C3×C4×Dic3—21no—
71C3×#208—24no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208—21no—
75C3×#208D412yes—
76C2×C3×C3⋊C8—24no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8D412yes—
82#1881—91noSylow
83C2×C3×#41—21no—
84C2×C3×#41C2×D311yescharacteristic
85C2×C3×#41C2×D311yescharacteristic
86C2×#235—31no—
87C2×#235—31no—
88C2×#235—61no—
89C3×#131—62no—
90C3×#131—62no—
91C2×C3×M16—31no—
92C2×C3×M16—31no—
93C2×C3×M16—62no—
94C22×C3×C8—31no—
95C3×#117—31no—
96#951—32no—
97#951—32no—
98#951—62no—
99#950—64no—
100#950—62no—
101#950—62no—
102#949—32no—
103#949—32no—
104#949—62no—
105#948—22no—
106#948—22no—
107#942—62no—
108#942—61no—
109#942—61no—
110#932—62no—
111#932—61no—
112#932—61no—
113#926C2×D311yescharacteristic
114C2×#208—22no—
115C2×#208—31no—
116C2×#208—31no—
117C2×#208—61no—
118C2×#208C2×D311yescharacteristic
119C2×#208C2×D311yescharacteristic
120C22×C3⋊C8C2×D311yescharacteristic
121C3×#103—61no—
122C3×#102—61no—
123#835—21no—
124#832—21no—
125#825—62no—
126(C2×D3)⋊C8—62no—
127(C2×D3)⋊C8—62no—
128#805—62no—
129C23×C32—21no—
130C23×C32#4111yescharacteristic
131C22×C3⋊D3—21no—
132C32×Q8—21no—
133C32×Q8C22⋊C412yes—
134C32×D4—22no—
135C32×D4—22no—
136C32×D4—21no—
137C32×D4C22⋊C412yes—
138C2×C32×C4—21no—
139C2×C32×C4—22no—
140C2×C32×C4—22no—
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4111yescharacteristic
147#638—41no—
148#638—41no—
149C2×C3⋊Dic3—21no—
150C4⋊(C3⋊D3)—21no—
151C4⋊(C3⋊D3)—21no—
152C4×C3⋊D3—41no—
153C4×C3⋊D3—41no—
154#634—21no—
155#634—21no—
156C2×C3×Dic3—41no—
157C3⋊(C3⋊C8)—22no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—22no—
160C3×C3⋊C8—41no—
161#575—91no—
162#568—31no—
163#421—91no—
164#416—31no—
165#408—91no—
166#344—91no—
167#341—91no—
168C3×#41—21no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—41no—
175C3×#41—41no—
176C3×#41C4×D312yes—
177C3×#41C4×D312yes—
178C3×#41D1212yes—
179C3×#41#6712yes—
180C2×C3×Q8—21no—
181C2×C3×Q8D1211yescharacteristic
182C2×C3×Q8#6711yescharacteristic
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—41no—
187C2×C3×D4D1211yescharacteristic
188C2×C3×D4#6711yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—41no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—61no—
196C2×#67—61no—
197C2×#67—121no—
198#235—62no—
199#235—62no—
200#235—61no—
201#235—61no—
202#235—61no—
203#235—61no—
204#235—61no—
205#235—61no—
206#235—61no—
207#235—61no—
208#235—121no—
209#235—121no—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—121no—
216C2×Dic6—31no—
217C2×Dic6—31no—
218C2×Dic6—61no—
219C3×M16—32no—
220C3×M16—64no—
221C3×M16—61no—
222C3×M16—61no—
223C3×M16—61no—
224C2×C3×C8—32no—
225C2×C3×C8—64no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230C3×C4⋊C4—61no—
231C3×C22⋊C4—61no—
232C3×C42—61no—
233#217—21no—
234#216—64no—
235#216—62no—
236#216—62no—
237#215—64no—
238#215—62no—
239#215—62no—
240#214—64no—
241#214—62no—
242#214—62no—
243#213—64no—
244#213—62no—
245#213—62no—
246C4⋊Dic3—21no—
247C4×Dic3—21no—
248#208—24no—
249#208—21no—
250#208—21no—
251#208—21no—
252#208—32no—
253#208—32no—
254#208—62no—
255#208—62no—
256#208—61no—
257#208—61no—
258#208#6712yes—
259C2×C3⋊C8—24no—
260C2×C3⋊C8—21no—
261C2×C3⋊C8—21no—
262C2×C3⋊C8—21no—
263C2×C3⋊C8—21no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—61no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8#6712yes—
268C22×C32—22no—
269C22×C32—41no—
270C22×C32—81no—
271C22×C32C4×D411yescharacteristic
272C22×C32#12111yescharacteristic
273C22×C32#12311yescharacteristic
274C2×C3⋊D3—41no—
275C2×C3⋊D3—42no—
276C32×C4—22no—
277C32×C4C2×C22⋊C411yescharacteristic
278C32×C4C4×D411yescharacteristic
279C32×C4#12011yescharacteristic
280C32×C4#12111yescharacteristic
281C3⋊Dic3—41no—
282C3×Dic3—81no—
283C2×#41—91no—
284C2×#41D3211yescharacteristic
285#137—92no—
286#137—181no—
287AGL(1,ℤ/8)—92no—
288AGL(1,ℤ/8)—181no—
289#135—182no—
290#131—62no—
291#131—62no—
292C2×M16—31no—
293C2×M16—31no—
294C2×M16—62no—
295C2×M16—91no—
296C22×C8—31no—
297#117—31no—
298#104—182no—
299#103—61no—
300#102—61no—
301C22⋊C8—182no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—41no—
306C23×C3#23511yescharacteristic
307C23×C3#23711yescharacteristic
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—121no—
311C3×Q8—21no—
312C3×Q8—21no—
313C3×Q8—22no—
314C3×Q8—41no—
315C3×Q8(C2×D3)⋊C412yes—
316C3×Q8(C2×D3)⋊C412yes—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—22no—
320C3×D4—22no—
321C3×D4—21no—
322C3×D4—21no—
323C3×D4—22no—
324C3×D4—41no—
325C3×D4—42no—
326C3×D4—42no—
327C3×D4(C2×D3)⋊C412yes—
328C3×D4(C2×D3)⋊C412yes—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—42no—
342C2×C3×C4—42no—
343C2×C3×C4—41no—
344C2×C3×C4—121no—
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4C2×D1211yescharacteristic
349C2×C3×C4#23511yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4#23711yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6711yescharacteristic
357#67—122no—
358#67—122no—
359#67—121no—
360#67—121no—
361#67—121no—
362#67—121no—
363C2×Dic3—41no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—121no—
367D12—62no—
368D12—61no—
369D12—61no—
370D12—61no—
371D12—61no—
372D12—121no—
373C4×D3—122no—
374C4×D3—122no—
375C4×D3—121no—
376C4×D3—121no—
377C4×D3—121no—
378C4×D3—121no—
379Dic6—62no—
380Dic6—61no—
381Dic6—61no—
382Dic6—61no—
383Dic6—61no—
384Dic6—121no—
385C3×C8—62no—
386C3×C8—62no—
387C3×C8—121no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C3⋊C8—41no—
391C3⋊C8—64no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C2×C32—21no—
395C2×C32—21no—
396C2×C32—21no—
397C2×C32—42no—
398C2×C32#38611yescharacteristic
399C3⋊D3—81no—
400#41—21no—
401#41—21no—
402#41—181no—
403#41—181no—
404#41—181no—
405#41—181no—
406#41#62412yes—
407#41#62612yes—
408C2×Q8—91no—
409C2×Q8#62611yescharacteristic
410C2×D4—21no—
411C2×D4—91no—
412C2×D4—181no—
413C2×D4#62611yescharacteristic
414C22×C4—21no—
415C22×C4—181no—
416C22×C4C2×D3211yescharacteristic
417Q16—182no—
418SD16—182no—
419SD16—182no—
420D8—182no—
421M16—32no—
422M16—64no—
423M16—61no—
424M16—61no—
425M16—61no—
426M16—92no—
427M16—181no—
428C2×C8—32no—
429C2×C8—64no—
430C2×C8—61no—
431C2×C8—61no—
432C2×C8—61no—
433C2×C8—61no—
434C2×C8—181no—
435C4⋊C4—61no—
436C22⋊C4—61no—
437C42—61no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—42no—
444C22×C3—41no—
445C22×C3—41no—
446C22×C3—81no—
447C22×C3—81no—
448C22×C3—81no—
449C22×C3—82no—
450C22×C3#67⋊C411yescharacteristic
451C22×C3#88611yescharacteristic
452C22×C3C4×#6711yescharacteristic
453C22×C3#92911yescharacteristic
454C22×C3#93011yescharacteristic
455C22×C3#93911yescharacteristic
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—242no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—42no—
469C3×C4—241no—
470C3×C4#67⋊C411yescharacteristic
471C3×C4#88211yescharacteristic
472C3×C4C2×(C2×D3)⋊C411yescharacteristic
473C3×C4C2×(C2×D3)⋊C411yescharacteristic
474C3×C4C4×#6711yescharacteristic
475C3×C4#93011yescharacteristic
476C3×C4#93911yescharacteristic
477C3×C4#95311yescharacteristic
478Dic3—81no—
479Dic3—122no—
480Dic3—121no—
481Dic3—121no—
482C32#188111yescharacteristic, complemented, Sylow
483C23—21no—
484C23—181no—
485C23#380411yescharacteristic
486Q8—21no—
487Q8—181no—
488Q8—181no—
489Q8#372212yes—
490D4—22no—
491D4—22no—
492D4—21no—
493D4—181no—
494D4—181no—
495D4—361no—
496D4—361no—
497D4#372212yes—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—121no—
502C2×C4—181no—
503C2×C4—361no—
504C2×C4—361no—
505C2×C4#380411yescharacteristic
506C2×C4C2×#62411yescharacteristic
507C2×C4C2×#62611yescharacteristic
508C2×C4C2×#62611yescharacteristic
509C2×C4D3×#6711yescharacteristic
510C2×C4D3×#6711yescharacteristic
511C8—62no—
512C8—62no—
513C8—121no—
514C8—182no—
515C2×C3—21no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—41no—
523C2×C3—41no—
524C2×C3—41no—
525C2×C3—42no—
526C2×C3—42no—
527C2×C3—82no—
528C2×C3#495811yescharacteristic
529C2×C3#521311yescharacteristic
530D3—242no—
531D3—241no—
532D3—241no—
533C22—22no—
534C22—41no—
535C22—81no—
536C22—362no—
537C22—361no—
538C22#6395211yescharacteristic
539C22#6396611yescharacteristic
540C22#6397811yescharacteristic
541C4—22no—
542C4—241no—
543C4—361no—
544C4#6395211yescharacteristic
545C4C2×#372211yescharacteristic
546C4#6397711yescharacteristic
547C4#6397811yescharacteristic
548C3—21no—
549C3#7029311yescharacteristic, complemented
550C3#7202011yescharacteristic, complemented
551C2—21no—
552C2—21no—
553C2—21no—
554C2—42no—
555C2—721no—
556C2#1059171111yescharacteristic
subgroupG/H
centerC4#63977
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radical#10596293C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1881
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. C3×#5819C2semidirect
3. C3×#5233C2semidirect
4. #10591113C2semidirect
5. #10591073C2semidirect
6. #10589169C2semidirect
7. #10589166C2semidirect
12. #64160C4semidirect
14. #64158C4semidirect
33. #5819D3semidirect
35. #5233D3semidirect
482. C32#1881semidirect
549. C3#70293semidirect
550. C3#72020semidirect

Maximal subgroups

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

subgroupindex
#105962932
C3×#58192
C3×#52332
#105911132
#105910732
#105891692
#105891662
#720203
#702933