Finite Group Databasebeta

← #11787642

Subgroups — #11787642

Order 1152.

697 conjugacy classes of subgroups.

The subgroup lattice has 533 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5822C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic, complemented
3#10592935C211yesmaximal, characteristic, complemented
4C3×#5234C211yesmaximal, characteristic, complemented
5#10591084C211yesmaximal, characteristic, complemented
6#10589171C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72116—31nomaximal
9#70012—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C3×#951—21no—
15C3×#950—22no—
16C3×#949—21no—
17C3×#942C412yescomplemented
18C3×#932C412yescomplemented
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63815—22no—
23#63814—22no—
24D3×#208—22no—
25#63664—22no—
26C3×#830—22no—
27#63566—21no—
28#63563—21no—
29C3×#575—31no—
30#5822D311yescharacteristic
31#5819—31no—
32#5745—31no—
33C3×#408—31no—
34#5236—31no—
35#5236—31no—
36#5236—61no—
37#5234D311yescharacteristic, complemented
38#5233—31no—
39#5113—31no—
40#4559—31no—
41#4558—31no—
42#4556—31no—
43#4552—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—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235C2×C412yes—
57C3×#235D412yes—
58C2×C3×D12D411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×Dic6D411yescharacteristic
61#3757—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4×C3⋊Dic3—21no—
64#3748—21no—
65#3748D412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#216—22no—
68C3×#215—22no—
69C3×#214—22no—
70C3×#213—22no—
71C3×#208—21no—
72C3×#208—21no—
73C3×#208—21no—
74C3×#208C2×C412yes—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8—21no—
79C2×C3×C3⋊C8D412yes—
80#3711—24no—
81D3×C3⋊C8—24no—
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—
94C2×C3×M16—31no—
95C22×C3×C8—31no—
96#951—21no—
97#950—22no—
98#949—21no—
99#948—62no—
100#948—62no—
101#942Dic312yescomplemented
102#932Dic312yescomplemented
103#926—31no—
104#926—31no—
105#926—61no—
106C2×#208—31no—
107C2×#208—31no—
108C2×#208—61no—
109C2×#208—62no—
110C2×#208C2×D311yescharacteristic
111C2×#208C2×D311yescharacteristic
112C22×C3⋊C8C2×D311yescharacteristic
113#907—62no—
114D3×M16—62no—
115#901—62no—
116C3×C22⋊C8—62no—
117#837—62no—
118#837—62no—
119#837—64no—
120#835—61no—
121#832—61no—
122#830—22no—
123#821—61no—
124#816—61no—
125C23×C32—21no—
126C23×C32#4111yescharacteristic
127C22×C3×D3—21no—
128C32×Q8—21no—
129C32×Q8—21no—
130C32×D4—21no—
131C32×D4—21no—
132C32×D4—41no—
133C32×D4—41no—
134C2×C32×C4—21no—
135C2×C32×C4—41no—
136C2×C32×C4—41no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C2×C3⋊Dic3—41no—
144C3×#67—22no—
145C3×#67—22no—
146C2×C3×Dic3—21no—
147C3×D12—21no—
148C3×D12C22⋊C412yes—
149C3×C4×D3—22no—
150C3×C4×D3—22no—
151C3×Dic6—21no—
152C3×Dic6C22⋊C412yes—
153C3⋊(C3⋊C8)—22no—
154C3×C3⋊C8—22no—
155C3×C3⋊C8—22no—
156C3×C3⋊C8—41no—
157#575—31no—
158#568—91no—
159#421—91no—
160#416—91no—
161#408—31no—
162#344—91no—
163#341—91no—
164C3×#41—22no—
165C3×#41—22no—
166C3×#41—21no—
167C3×#41—21no—
168C3×#41—21no—
169C3×#41—21no—
170C3×#41—21no—
171C3×#41—21no—
172C3×#41—21no—
173C3×#41—21no—
174C3×#41—32no—
175C3×#41—32no—
176C3×#41—41no—
177C3×#41—41no—
178C3×#41—61no—
179C3×#41—61no—
180C2×C3×Q8—21no—
181C2×C3×Q8—31no—
182C2×C3×Q8C4×D311yescharacteristic
183C2×C3×Q8C2×Dic311yescharacteristic
184C2×C3×D4—21no—
185C2×C3×D4—21no—
186C2×C3×D4—21no—
187C2×C3×D4—31no—
188C2×C3×D4—41no—
189C2×C3×D4—61no—
190C2×C3×D4C4×D311yescharacteristic
191C2×C3×D4C2×Dic311yescharacteristic
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—41no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—21no—
200#235—21no—
201#235—21no—
202#235C2×Dic312yes—
203#235#6712yes—
204C2×D12#6711yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6#6711yescharacteristic
207C3×Q16—62no—
208C3×SD16—62no—
209C3×SD16—62no—
210C3×D8—62no—
211C3×M16—32no—
212C3×M16—61no—
213C3×M16—61no—
214C3×M16—61no—
215C2×C3×C8—32no—
216C2×C3×C8—61no—
217C2×C3×C8—61no—
218C2×C3×C8—61no—
219C2×C3×C8—61no—
220#217—61no—
221#217—61no—
222#217—121no—
223#216—22no—
224#215—22no—
225#214—22no—
226#213—22no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—121no—
230C4×Dic3—62no—
231C4×Dic3—61no—
232C4×Dic3—61no—
233#208—21no—
234#208—21no—
235#208—21no—
236#208—32no—
237#208—32no—
238#208—62no—
239#208—64no—
240#208—61no—
241#208—61no—
242#208—121no—
243#208C2×Dic312yes—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—21no—
248C2×C3⋊C8—64no—
249C2×C3⋊C8—61no—
250C2×C3⋊C8—61no—
251C2×C3⋊C8—121no—
252C2×C3⋊C8#6712yes—
253ΓL(1,𝔽25)—64no—
254D3×C8—64no—
255C22×C32—41no—
256C22×C32—41no—
257C22×C32—42no—
258C22×C32C4×D411yescharacteristic
259C22×C32#12111yescharacteristic
260C22×C32#12311yescharacteristic
261C2×C3×D3—22no—
262C2×C3×D3—81no—
263C32×C4—41no—
264C32×C4C2×C22⋊C411yescharacteristic
265C32×C4C4×D411yescharacteristic
266C32×C4#12011yescharacteristic
267C32×C4#12111yescharacteristic
268C3⋊Dic3—81no—
269C3×Dic3—22no—
270C2×#41—31no—
271C2×#41D3211yescharacteristic
272#137—32no—
273#137—61no—
274AGL(1,ℤ/8)—32no—
275AGL(1,ℤ/8)—61no—
276#135—62no—
277#131—182no—
278#131—182no—
279C2×M16—31no—
280C2×M16—31no—
281C2×M16—91no—
282C2×M16—182no—
283C22×C8—31no—
284#117—91no—
285#104—182no—
286#103—181no—
287#102—181no—
288C22⋊C8—62no—
289C23×C3—21no—
290C23×C3—21no—
291C23×C3—21no—
292C23×C3—41no—
293C23×C3—61no—
294C23×C3#23511yescharacteristic
295C23×C3#23711yescharacteristic
296C22×D3—21no—
297C3×Q8—22no—
298C3×Q8—21no—
299C3×Q8—21no—
300C3×Q8—21no—
301C3×Q8—21no—
302C3×Q8—32no—
303C3×Q8—41no—
304C3×Q8—61no—
305C3×D4—22no—
306C3×D4—21no—
307C3×D4—21no—
308C3×D4—21no—
309C3×D4—21no—
310C3×D4—32no—
311C3×D4—41no—
312C3×D4—42no—
313C3×D4—42no—
314C3×D4—41no—
315C3×D4—41no—
316C3×D4—41no—
317C3×D4—41no—
318C3×D4—62no—
319C3×D4—62no—
320C3×D4—61no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—41no—
330C2×C3×C4—42no—
331C2×C3×C4—42no—
332C2×C3×C4—41no—
333C2×C3×C4—41no—
334C2×C3×C4—41no—
335C2×C3×C4—41no—
336C2×C3×C4—61no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4C2×C4×D311yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4#23711yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4C22×Dic311yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351#67—22no—
352#67—22no—
353C2×Dic3—21no—
354C2×Dic3—122no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357D12—21no—
358D12#21712yes—
359C4×D3—22no—
360C4×D3—22no—
361Dic6—21no—
362Dic6#21712yes—
363C3×C8—62no—
364C3×C8—62no—
365C3×C8—121no—
366C3⋊C8—22no—
367C3⋊C8—22no—
368C3⋊C8—41no—
369C3⋊C8—62no—
370C3⋊C8—62no—
371C3⋊C8—122no—
372C2×C32—21no—
373C2×C32—21no—
374C2×C32—21no—
375C2×C32—81no—
376C2×C32#38611yescharacteristic
377C3×D3—42no—
378#41—21no—
379#41—21no—
380#41—21no—
381#41—21no—
382#41—32no—
383#41—32no—
384#41—61no—
385#41—61no—
386C2×Q8—31no—
387C2×Q8D3×Dic311yescharacteristic
388C2×D4—21no—
389C2×D4—31no—
390C2×D4—61no—
391C2×D4D3×Dic311yescharacteristic
392C22×C4—21no—
393C22×C4—61no—
394C22×C4C2×D3211yescharacteristic
395Q16—62no—
396SD16—62no—
397SD16—62no—
398D8—62no—
399M16—32no—
400M16—61no—
401M16—61no—
402M16—61no—
403M16—92no—
404M16—184no—
405M16—181no—
406C2×C8—32no—
407C2×C8—61no—
408C2×C8—61no—
409C2×C8—61no—
410C2×C8—61no—
411C2×C8—184no—
412C2×C8—181no—
413C4⋊C4—181no—
414C22⋊C4—181no—
415C42—181no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—41no—
420C22×C3—41no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—41no—
425C22×C3—41no—
426C22×C3—62no—
427C22×C3—81no—
428C22×C3—82no—
429C22×C3—241no—
430C22×C3#88311yescharacteristic
431C22×C3#88411yescharacteristic
432C22×C3C4×#6711yescharacteristic
433C22×C3D4×Dic311yescharacteristic
434C22×C3#93511yescharacteristic
435C22×C3#93911yescharacteristic
436C2×D3—22no—
437C2×D3—81no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—42no—
443C3×C4—41no—
444C3×C4—41no—
445C3×C4—62no—
446C3×C4D3×C22⋊C411yescharacteristic
447C3×C4#67⋊C411yescharacteristic
448C3×C4D4×Dic311yescharacteristic
449C3×C4#93711yescharacteristic
450C3×C4#93711yescharacteristic
451C3×C4#93811yescharacteristic
452C3×C4#93911yescharacteristic
453C3×C4C2×#21711yescharacteristic
454Dic3—22no—
455Dic3—241no—
456Dic3—241no—
457Dic3—242no—
458C32#188111yescharacteristic, complemented, Sylow
459C23—21no—
460C23—61no—
461C23#380411yescharacteristic
462Q8—21no—
463Q8—21no—
464Q8—32no—
465Q8—61no—
466D4—21no—
467D4—21no—
468D4—32no—
469D4—41no—
470D4—41no—
471D4—62no—
472D4—62no—
473D4—61no—
474C2×C4—21no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—61no—
478C2×C4—62no—
479C2×C4—62no—
480C2×C4—361no—
481C2×C4C2×D3×Dic311yescharacteristic
482C2×C4#380511yescharacteristic
483C2×C4D3×#6711yescharacteristic
484C2×C4D3×#6711yescharacteristic
485C2×C4D3×#6711yescharacteristic
486C2×C4#381111yescharacteristic
487C8—62no—
488C8—62no—
489C8—121no—
490C8—182no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—41no—
499C2×C3—41no—
500C2×C3—41no—
501C2×C3—82no—
502C2×C3—81no—
503C2×C3—81no—
504C2×C3—122no—
505C2×C3#495611yescharacteristic
506C2×C3#522011yescharacteristic
507D3—42no—
508C22—41no—
509C22—42no—
510C22—41no—
511C22—62no—
512C22—241no—
513C22#6396911yescharacteristic
514C22#6397111yescharacteristic
515C22Dic3×#6711yescharacteristic
516C4—41no—
517C4—62no—
518C4—721no—
519C4D3×#21711yescharacteristic
520C4#6397011yescharacteristic
521C4#67⋊Dic311yescharacteristic
522C4#6398311yescharacteristic
523C3—21no—
524C3#7001211yescharacteristic, complemented
525C3#7211611yescharacteristic, complemented
526C2—21no—
527C2—21no—
528C2—21no—
529C2—81no—
530C2—122no—
531C2#1059172111yescharacteristic
subgroupG/H
centerC4#63983
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
2. #10594776C2semidirect
3. #10592935C2semidirect
4. C3×#5234C2semidirect
5. #10591084C2semidirect
6. #10589171C2semidirect
7. #10589166C2semidirect
17. C3×#942C4semidirect
18. C3×#932C4semidirect
37. #5234D3semidirect
101. #942Dic3semidirect
102. #932Dic3semidirect
458. C32#1881semidirect
524. C3#70012semidirect
525. C3#72116semidirect

Maximal subgroups

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

subgroupindex
C3×#58222
#105947762
#105929352
C3×#52342
#105910842
#105891712
#105891662
#721163
#700123