Finite Group Databasebeta

← #11787640

Subgroups — #11787640

Order 1152.

749 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596290C211yesmaximal, characteristic, complemented
2C3×#5822C211yesmaximal, characteristic
3C3×#5233C211yesmaximal, characteristic, complemented
4#10591111C211yesmaximal, characteristic, complemented
5#10591070C211yesmaximal, characteristic, complemented
6#10589170C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72116—31nomaximal
9#70293—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12#64157—22no—
13#64157—22no—
14C2×#3748—22no—
15C2×#3748C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#951C412yescomplemented
18C3×#950—22no—
19C3×#949C412yescomplemented
20C3×#942—21no—
21C3×#932—21no—
22C3×#926C2211yescharacteristic
23C2×C3×#208C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C3×#835—21no—
26C3×#832—21no—
27#63569—22no—
28(C2×D3)⋊(C3⋊C8)—22no—
29C3×#575—31no—
30#5822D311yescharacteristic
31#5819—31no—
32#5819—31no—
33#5819—61no—
34C3×#416—31no—
35#5236—31no—
36#5234—31no—
37#5233D311yescharacteristic, complemented
38#5110—31no—
39#5005—31no—
40#4559—31no—
41#4558—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×C3×#67—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C2×C3×D12C2×C411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×Dic6C2×C411yescharacteristic
61#3748—24no—
62#3748—21no—
63#3748—21no—
64#3748—21no—
65#3748D412yes—
66C2×C3⋊(C3⋊C8)—24no—
67C2×C3⋊(C3⋊C8)—21no—
68C2×C3⋊(C3⋊C8)D412yes—
69C3×#217—21no—
70C3×#216—22no—
71C3×#215—22no—
72C3×#214—22no—
73C3×#213—22no—
74C3×C4⋊Dic3—21no—
75C3×C4×Dic3—21no—
76C3×#208—21no—
77C3×#208C2×C412yes—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8—21no—
80C2×C3×C3⋊C8—21no—
81C2×C3×C3⋊C8—21no—
82#1881—91noSylow
83C2×C3×#41—21no—
84C2×C3×#41—31no—
85C2×C3×#41C2×D311yescharacteristic
86C2×C3×#41C2×D311yescharacteristic
87C2×#235C2×D311yescharacteristic
88C3×#137—32no—
89C3×#137—61no—
90C3×AGL(1,ℤ/8)—32no—
91C3×AGL(1,ℤ/8)—61no—
92C3×#135—62no—
93C2×C3×M16—31no—
94C22×C3×C8—31no—
95C3×#117—31no—
96#951Dic312yescomplemented
97#950—22no—
98#949Dic312yescomplemented
99#948—62no—
100#948—62no—
101#948—64no—
102#948—64no—
103#948—62no—
104#948—62no—
105#942—21no—
106#932—21no—
107#926C2×D311yescharacteristic
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113C2×#208—61no—
114C2×#208—62no—
115C2×#208—62no—
116C2×#208—64no—
117C2×#208C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119C3×#103—61no—
120C3×#102—61no—
121#837—62no—
122#835—21no—
123#832—21no—
124#830—62no—
125(C2×D3)⋊C8—62no—
126#805—62no—
127C23×C32—21no—
128C23×C32#4111yescharacteristic
129C22×C3×D3—21no—
130C32×Q8—21no—
131C32×Q8C22⋊C412yes—
132C32×D4—22no—
133C32×D4—22no—
134C32×D4—21no—
135C32×D4C22⋊C412yes—
136C2×C32×C4—21no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4#4111yescharacteristic
145C3×#67—41no—
146C3×#67—41no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—41no—
149C3×D12—21no—
150C3×D12—21no—
151C3×C4×D3—41no—
152C3×C4×D3—41no—
153C3×Dic6—21no—
154C3×Dic6—21no—
155C3⋊(C3⋊C8)—22no—
156C3⋊(C3⋊C8)—22no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8—41no—
159#575—31no—
160#568—91no—
161#421—91no—
162#416—31no—
163#408—91no—
164#344—91no—
165#341—91no—
166C3×#41—22no—
167C3×#41—22no—
168C3×#41—21no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—22no—
173C3×#41—22no—
174C3×#41—61no—
175C3×#41—61no—
176C3×#41—61no—
177C3×#41—61no—
178C3×#41C4×D312yes—
179C3×#41D1212yes—
180C3×#41C2×Dic312yes—
181C3×#41#6712yes—
182C2×C3×Q8—21no—
183C2×C3×Q8—31no—
184C2×C3×Q8#6711yescharacteristic
185C2×C3×Q8#6711yescharacteristic
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—31no—
191C2×C3×D4—61no—
192C2×C3×D4#6711yescharacteristic
193C2×C3×D4#6711yescharacteristic
194C22×C3×C4—22no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—61no—
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—21no—
202#235—21no—
203#235—21no—
204#235—21no—
205#235—21no—
206C2×D12C2×Dic311yescharacteristic
207C2×C4×D3—21no—
208C2×Dic6C2×Dic311yescharacteristic
209C3×Q16—62no—
210C3×SD16—62no—
211C3×SD16—62no—
212C3×D8—62no—
213C3×M16—32no—
214C3×M16—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C2×C3×C8—61no—
219C3×C4⋊C4—61no—
220C3×C22⋊C4—61no—
221C3×C42—61no—
222#217—21no—
223#216—22no—
224#215—22no—
225#214—22no—
226#213—22no—
227C4⋊Dic3—21no—
228C4×Dic3—21no—
229#208—21no—
230#208—32no—
231#208—32no—
232#208—62no—
233#208—62no—
234#208—68no—
235#208—64no—
236#208—64no—
237#208—62no—
238#208—62no—
239#208—61no—
240#208—61no—
241#208—61no—
242#208—61no—
243#208—61no—
244#208—61no—
245#208C2×Dic312yes—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—21no—
249C2×C3⋊C8—21no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—68no—
254C2×C3⋊C8—64no—
255C2×C3⋊C8—64no—
256C2×C3⋊C8—62no—
257C2×C3⋊C8—61no—
258C2×C3⋊C8—61no—
259C22×C32—22no—
260C22×C32—41no—
261C22×C32—81no—
262C22×C32C4×D411yescharacteristic
263C22×C32#12111yescharacteristic
264C22×C32#12311yescharacteristic
265C2×C3×D3—42no—
266C2×C3×D3—41no—
267C32×C4—22no—
268C32×C4C2×C22⋊C411yescharacteristic
269C32×C4C4×D411yescharacteristic
270C32×C4#12011yescharacteristic
271C32×C4#12111yescharacteristic
272C3×Dic3—41no—
273C3×Dic3—81no—
274C2×#41—31no—
275C2×#41D3211yescharacteristic
276#137—32no—
277#137—61no—
278AGL(1,ℤ/8)—32no—
279AGL(1,ℤ/8)—61no—
280#135—62no—
281#131—182no—
282#131—182no—
283C2×M16—31no—
284C2×M16—91no—
285C2×M16—91no—
286C2×M16—182no—
287C22×C8—31no—
288#117—31no—
289#104—182no—
290#103—61no—
291#102—61no—
292C22⋊C8—182no—
293C23×C3—22no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3—21no—
297C23×C3—61no—
298C23×C3#23711yescharacteristic
299C23×C3#23711yescharacteristic
300C22×D3—21no—
301C3×Q8—22no—
302C3×Q8—21no—
303C3×Q8—21no—
304C3×Q8—22no—
305C3×Q8—61no—
306C3×Q8—61no—
307C3×Q8(C2×D3)⋊C412yes—
308C3×Q8#21712yes—
309C3×D4—24no—
310C3×D4—24no—
311C3×D4—22no—
312C3×D4—22no—
313C3×D4—22no—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—21no—
317C3×D4—21no—
318C3×D4—22no—
319C3×D4—61no—
320C3×D4—61no—
321C3×D4—121no—
322C3×D4—121no—
323C3×D4(C2×D3)⋊C412yes—
324C3×D4#21712yes—
325C2×C3×C4—24no—
326C2×C3×C4—22no—
327C2×C3×C4—24no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—21no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—61no—
341C2×C3×C4—121no—
342C2×C3×C4—121no—
343C2×C3×C4—121no—
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4#23711yescharacteristic
351C2×C3×C4#23711yescharacteristic
352C2×C3×C4C22×Dic311yescharacteristic
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356#67—41no—
357#67—41no—
358C2×Dic3—21no—
359C2×Dic3—41no—
360D12—21no—
361D12—21no—
362C4×D3—41no—
363C4×D3—41no—
364Dic6—21no—
365Dic6—21no—
366C3×C8—62no—
367C3×C8—121no—
368C3⋊C8—22no—
369C3⋊C8—41no—
370C3⋊C8—64no—
371C3⋊C8—64no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—62no—
375C3⋊C8—62no—
376C2×C32—21no—
377C2×C32—21no—
378C2×C32—21no—
379C2×C32—42no—
380C2×C32#38611yescharacteristic
381C3×D3—81no—
382#41—21no—
383#41—21no—
384#41—61no—
385#41—61no—
386#41—61no—
387#41—61no—
388#41D3×Dic312yes—
389#41#62612yes—
390C2×Q8—31no—
391C2×Q8#62511yescharacteristic
392C2×D4—21no—
393C2×D4—31no—
394C2×D4—61no—
395C2×D4#62511yescharacteristic
396C22×C4—21no—
397C22×C4—61no—
398C22×C4C2×D3211yescharacteristic
399Q16—62no—
400SD16—62no—
401SD16—62no—
402D8—62no—
403M16—32no—
404M16—61no—
405M16—92no—
406M16—184no—
407M16—181no—
408M16—181no—
409M16—181no—
410C2×C8—61no—
411C2×C8—61no—
412C2×C8—61no—
413C2×C8—61no—
414C2×C8—92no—
415C2×C8—184no—
416C2×C8—181no—
417C4⋊C4—61no—
418C22⋊C4—61no—
419C42—61no—
420C22×C3—24no—
421C22×C3—22no—
422C22×C3—22no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—41no—
427C22×C3—41no—
428C22×C3—81no—
429C22×C3—81no—
430C22×C3—81no—
431C22×C3—82no—
432C22×C3—122no—
433C22×C3—121no—
434C22×C3#67⋊C411yescharacteristic
435C22×C3#88611yescharacteristic
436C22×C3D4×Dic311yescharacteristic
437C22×C3#93511yescharacteristic
438C22×C3#93911yescharacteristic
439C22×C3#93911yescharacteristic
440C2×D3—42no—
441C2×D3—41no—
442C3×C4—24no—
443C3×C4—22no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—121no—
450C3×C4—241no—
451C3×C4#67⋊C411yescharacteristic
452C3×C4#88211yescharacteristic
453C3×C4C2×(C2×D3)⋊C411yescharacteristic
454C3×C4D4×Dic311yescharacteristic
455C3×C4#93711yescharacteristic
456C3×C4#93911yescharacteristic
457C3×C4#93911yescharacteristic
458C3×C4C2×#21711yescharacteristic
459Dic3—41no—
460Dic3—81no—
461C32#188111yescharacteristic, complemented, Sylow
462C23—21no—
463C23—61no—
464C23#380511yescharacteristic
465Q8—21no—
466Q8—61no—
467Q8—61no—
468Q8(C2×D3)⋊Dic312yes—
469D4—22no—
470D4—22no—
471D4—21no—
472D4—61no—
473D4—61no—
474D4—121no—
475D4—121no—
476D4(C2×D3)⋊Dic312yes—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—61no—
481C2×C4—121no—
482C2×C4—121no—
483C2×C4—121no—
484C2×C4C2×D3×Dic311yescharacteristic
485C2×C4#380511yescharacteristic
486C2×C4C2×#62511yescharacteristic
487C2×C4C2×#62611yescharacteristic
488C2×C4#381111yescharacteristic
489C2×C4#381111yescharacteristic
490C8—62no—
491C8—121no—
492C8—182no—
493C8—182no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—41no—
502C2×C3—41no—
503C2×C3—41no—
504C2×C3—44no—
505C2×C3—42no—
506C2×C3—42no—
507C2×C3—241no—
508C2×C3#495811yescharacteristic
509C2×C3#522011yescharacteristic
510D3—81no—
511C22—22no—
512C22—41no—
513C22—81no—
514C22—122no—
515C22—121no—
516C22#6396211yescharacteristic
517C22#67⋊Dic311yescharacteristic
518C22#6398011yescharacteristic
519C4—22no—
520C4—121no—
521C4—241no—
522C4C2×(C2×D3)⋊Dic311yescharacteristic
523C4#67⋊Dic311yescharacteristic
524C4#6398011yescharacteristic
525C4#6398111yescharacteristic
526C3—21no—
527C3#7029311yescharacteristic, complemented
528C3#7211611yescharacteristic, complemented
529C2—21no—
530C2—21no—
531C2—21no—
532C2—42no—
533C2—241no—
534C2#1059171311yescharacteristic
subgroupG/H
centerC4#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#386
prime radicalC3×#5822C2
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
1. #10596290C2semidirect
3. C3×#5233C2semidirect
4. #10591111C2semidirect
5. #10591070C2semidirect
6. #10589170C2semidirect
7. #10589166C2semidirect
17. C3×#951C4semidirect
19. C3×#949C4semidirect
37. #5233D3semidirect
96. #951Dic3semidirect
98. #949Dic3semidirect
461. C32#1881semidirect
527. C3#70293semidirect
528. C3#72116semidirect

Maximal subgroups

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

subgroupindex
#105962902
C3×#58222
C3×#52332
#105911112
#105910702
#105891702
#105891662
#721163
#702933