Finite Group Databasebeta

← #11793866

Subgroups — #11793866

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594795C211yesmaximal, characteristic
2#10592831C211yesmaximal, characteristic, complemented
3C2×C3×#825C211yesmaximal, characteristic, complemented
4#10591115C211yesmaximal, characteristic, complemented
5C2×#63570C211yesmaximal, characteristic, complemented
6#10591076C211yesmaximal, characteristic, complemented
7C3×C3⋊#338C211yesmaximal, characteristic, complemented
8#70379—31nomaximal
9#68719—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63833—21no—
18#63831—21no—
19#63830—21no—
20#63829—22no—
21#63825—21no—
22#63651—21no—
23#63650—21no—
24C3×#825—21no—
25C3×#825—21no—
26Dic3⋊(C3⋊C8)—22no—
27#63570—21no—
28#63570—21no—
29#63560—21no—
30#63558—21no—
31#5822—31no—
32#5748—31no—
33C2×C3×#104—31no—
34#5237—31no—
35C2×#825—31no—
36C2×#825D311yescharacteristic, complemented
37#5132—31no—
38#5132—31no—
39#5132—31no—
40#5132—61no—
41#5118—31no—
42C2×#805—31no—
43#4924—31no—
44C3×#338—31no—
45C3⋊#338D311yescharacteristic, complemented
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48#3828—21no—
49#3828—21no—
50#3828—21no—
51#3828—21no—
52C2×C4⋊(C3⋊D3)D411yescharacteristic
53C2×C4×C3⋊D3—21no—
54C2×#634D411yescharacteristic
55C2×C3×#67—21no—
56C22×C3×Dic3—21no—
57C3×#235—21no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—21no—
61C2×C3×D12D411yescharacteristic
62C2×C3×C4×D3—21no—
63C2×C3×Dic6D411yescharacteristic
64C32×M16—21no—
65C32×M16—21no—
66C2×C32×C8—21no—
67#3748—21no—
68#3748—21no—
69C2×C3⋊(C3⋊C8)—21no—
70C3×C4×Dic3—21no—
71C3×C4×Dic3D411yescharacteristic
72C3×C4×Dic3D411yescharacteristic
73C3×#208—21no—
74C3×#208—21no—
75C3×#208—21no—
76C3×#208—21no—
77C2×C3×C3⋊C8—21no—
78C2×C3×C3⋊C8D412yes—
79#3719—22no—
80#3717—22no—
81#3716—22no—
82#3714—22no—
83#2050—91noSylow
84C2×C3×#41—31no—
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C2×#235C2×D311yescharacteristic
89C2×C3×M16—21no—
90C2×C3×M16—31no—
91C2×C3×M16—31no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×C42—31no—
95#951—61no—
96#950—62no—
97#949—61no—
98#942—61no—
99#932—61no—
100C2×C4×Dic3C2×D311yescharacteristic
101C2×#208—31no—
102C2×#208—31no—
103C2×#208—61no—
104C2×#208C2×D311yescharacteristic
105C2×#208C2×D311yescharacteristic
106#909—61no—
107#909—61no—
108#908—61no—
109#908—61no—
110#904—62no—
111C3×#104—61no—
112C3×#104—61no—
113#836—61no—
114#833—61no—
115#825—21no—
116#825—21no—
117#825—61no—
118#825—61no—
119#824—61no—
120#824—61no—
121#824—62no—
122#824—61no—
123#823—61no—
124#823—61no—
125#823—62no—
126#823—61no—
127Dic3⋊C8—62no—
128#805—61no—
129#805—61no—
130C4⋊(C3⋊C8)—62no—
131C23×C32#4111yescharacteristic
132C22×C3⋊D3—21no—
133C22×C3×D3—21no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4#4111yescharacteristic
139C2×C32×C4#4111yescharacteristic
140#638—41no—
141#638—41no—
142C2×C3⋊Dic3—21no—
143C4⋊(C3⋊D3)—21no—
144C4⋊(C3⋊D3)—21no—
145C4×C3⋊D3—41no—
146C4×C3⋊D3—41no—
147#634—21no—
148#634—21no—
149C3×#67—41no—
150C3×#67—41no—
151C2×C3×Dic3—21no—
152C2×C3×Dic3—21no—
153C2×C3×Dic3—21no—
154C2×C3×Dic3—42no—
155C3×D12—21no—
156C3×D12—21no—
157C3×C4×D3—41no—
158C3×C4×D3—41no—
159C3×Dic6—21no—
160C3×Dic6—21no—
161C32×C8—41no—
162C3⋊(C3⋊C8)—41no—
163C3×C3⋊C8—22no—
164C3×C3⋊C8—41no—
165#575—91no—
166#423—91no—
167C2×#104—31no—
168C2×#104—91no—
169#413—91no—
170#413—91no—
171#338—31no—
172C3×#41—61no—
173C3×#41—61no—
174C3×#41—61no—
175C3×#41—61no—
176C2×C3×Q8—31no—
177C2×C3×D4—31no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—61no—
181C22×C3×C4—61no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C2×#67—21no—
185C2×#67—62no—
186C2×#67—61no—
187C2×#67—61no—
188C22×Dic3—21no—
189#235—21no—
190#235—21no—
191#235—21no—
192#235—21no—
193#235—61no—
194#235—61no—
195#235—61no—
196#235—61no—
197#235—61no—
198#235—61no—
199#235—61no—
200#235—61no—
201#235—121no—
202#235—121no—
203#235—121no—
204#235—121no—
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—61no—
208C2×D12D1211yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—62no—
211C2×C4×D3—61no—
212C2×C4×D3—61no—
213C2×Dic6—31no—
214C2×Dic6—31no—
215C2×Dic6—61no—
216C2×Dic6D1211yescharacteristic
217C3×M16—22no—
218C3×M16—21no—
219C3×M16—21no—
220C3×M16—21no—
221C3×M16—21no—
222C3×M16—41no—
223C3×M16—61no—
224C3×M16—61no—
225C3×M16—61no—
226C3×M16—61no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—32no—
230C2×C3×C8—41no—
231C2×C3×C8—61no—
232C3×C42—31no—
233C3×C42—31no—
234C3×C42—61no—
235#216—62no—
236#215—62no—
237#214—62no—
238#213—62no—
239C4×Dic3—21no—
240C4×Dic3#6711yescharacteristic
241C4×Dic3#6711yescharacteristic
242#208—21no—
243#208—21no—
244#208—21no—
245#208—21no—
246#208—62no—
247#208—61no—
248#208—61no—
249#208—61no—
250#208—61no—
251#208—121no—
252C2×C3⋊C8—21no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—121no—
256C2×C3⋊C8D1212yes—
257Dic12—62no—
258D24—62no—
259#204—62no—
260#204—62no—
261C22×C32—41no—
262C22×C32#12111yescharacteristic
263C22×C32#12311yescharacteristic
264C22×C32#12311yescharacteristic
265C2×C3⋊D3—41no—
266C2×C3⋊D3—81no—
267C2×C3×D3—41no—
268C2×C3×D3—81no—
269C32×C4#12011yescharacteristic
270C32×C4#12111yescharacteristic
271C32×C4#12111yescharacteristic
272C32×C4#12411yescharacteristic
273C3⋊Dic3—41no—
274C3×Dic3—22no—
275C3×Dic3—41no—
276C3×Dic3—41no—
277C2×#41—31no—
278C2×#41—91no—
279#137—181no—
280#137—181no—
281AGL(1,ℤ/8)—181no—
282AGL(1,ℤ/8)—181no—
283#135—182no—
284C2×M16—31no—
285C2×M16—31no—
286C2×M16—91no—
287C2×M16D3211yescharacteristic
288C2×C42—31no—
289C4⋊C8—182no—
290#104—61no—
291#104—61no—
292#104—181no—
293#104—181no—
294#101—181no—
295#101—181no—
296#100—181no—
297#100—181no—
298C23×C3—21no—
299C23×C3—61no—
300C23×C3#23711yescharacteristic
301C23×C3#23911yescharacteristic
302C22×D3—21no—
303C22×D3—62no—
304C22×D3—61no—
305C22×D3—61no—
306C3×Q8—61no—
307C3×Q8—61no—
308C3×D4—61no—
309C3×D4—61no—
310C3×D4—121no—
311C3×D4—121no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—61no—
319C2×C3×C4—61no—
320C2×C3×C4—61no—
321C2×C3×C4—122no—
322C2×C3×C4—121no—
323C2×C3×C4—121no—
324C2×C3×C4C2×D1211yescharacteristic
325C2×C3×C4C2×D1211yescharacteristic
326C2×C3×C4#23511yescharacteristic
327C2×C3×C4#23511yescharacteristic
328C2×C3×C4#23511yescharacteristic
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D411yescharacteristic
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4#23711yescharacteristic
335C2×C3×C4C2×#6711yescharacteristic
336#67—41no—
337#67—41no—
338#67—122no—
339#67—122no—
340#67—121no—
341#67—121no—
342#67—121no—
343#67—121no—
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—21no—
347C2×Dic3—42no—
348C2×Dic3—62no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351D12—21no—
352D12—21no—
353D12—61no—
354D12—61no—
355D12—61no—
356D12—61no—
357D12—121no—
358D12—121no—
359C4×D3—41no—
360C4×D3—41no—
361C4×D3—122no—
362C4×D3—122no—
363C4×D3—121no—
364C4×D3—121no—
365C4×D3—121no—
366C4×D3—121no—
367Dic6—21no—
368Dic6—21no—
369Dic6—61no—
370Dic6—61no—
371Dic6—61no—
372Dic6—61no—
373Dic6—121no—
374Dic6—121no—
375C3×C8—42no—
376C3×C8—41no—
377C3×C8—41no—
378C3×C8—62no—
379C3×C8—121no—
380C3⋊C8—22no—
381C3⋊C8—41no—
382C3⋊C8—122no—
383C3⋊C8—121no—
384C3⋊C8—121no—
385C2×C32—21no—
386C2×C32—21no—
387C2×C32—21no—
388C2×C32#39411yescharacteristic
389C3⋊D3—81no—
390C3×D3—81no—
391#41—61no—
392#41—61no—
393#41—61no—
394#41—61no—
395#41—181no—
396#41—181no—
397#41—181no—
398#41—181no—
399C2×Q8—31no—
400C2×Q8—91no—
401C2×D4—31no—
402C2×D4—61no—
403C2×D4—91no—
404C2×D4—181no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—181no—
408C22×C4C2×D3211yescharacteristic
409Q16—182no—
410SD16—182no—
411SD16—182no—
412D8—182no—
413M16—21no—
414M16—21no—
415M16—61no—
416M16—61no—
417M16—61no—
418M16—61no—
419M16—181no—
420M16—181no—
421C2×C8—21no—
422C2×C8—32no—
423C2×C8—61no—
424C2×C8—181no—
425C42—31no—
426C42—31no—
427C42—61no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—41no—
432C22×C3—41no—
433C22×C3—81no—
434C22×C3—121no—
435C22×C3—241no—
436C22×C3#88311yescharacteristic
437C22×C3#88611yescharacteristic
438C22×C3#89411yescharacteristic
439C22×C3#89411yescharacteristic
440C22×C3#89511yescharacteristic
441C22×C3#93911yescharacteristic
442C2×D3—41no—
443C2×D3—81no—
444C2×D3—122no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—241no—
448C2×D3—241no—
449C2×D3—242no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—62no—
455C3×C4—121no—
456C3×C4—121no—
457C3×C4#87511yescharacteristic
458C3×C4#88211yescharacteristic
459C3×C4#88211yescharacteristic
460C3×C4#88411yescharacteristic
461C3×C4#88411yescharacteristic
462C3×C4#88511yescharacteristic
463C3×C4#93011yescharacteristic
464C3×C4#93811yescharacteristic
465Dic3—22no—
466Dic3—41no—
467Dic3—41no—
468Dic3—122no—
469Dic3—121no—
470Dic3—121no—
471C32#205011yescharacteristic, complemented, Sylow
472C23—61no—
473C23—181no—
474C23#379611yescharacteristic
475Q8—61no—
476Q8—61no—
477Q8—181no—
478Q8—181no—
479D4—61no—
480D4—61no—
481D4—121no—
482D4—121no—
483D4—181no—
484D4—181no—
485D4—361no—
486D4—361no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—122no—
491C2×C4—121no—
492C2×C4—121no—
493C2×C4—181no—
494C2×C4—361no—
495C2×C4—361no—
496C2×C4#379811yescharacteristic
497C2×C4D3×D1211yescharacteristic
498C2×C4D3×D1211yescharacteristic
499C2×C4#380411yescharacteristic
500C2×C4D3×#6711yescharacteristic
501C2×C4#381111yescharacteristic
502C8—41no—
503C8—62no—
504C8—121no—
505C8—361no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—41no—
514C2×C3—41no—
515C2×C3—41no—
516C2×C3—241no—
517C2×C3#467211yescharacteristic
518C2×C3#496111yescharacteristic
519D3—81no—
520D3—242no—
521D3—241no—
522D3—241no—
523C22—41no—
524C22—121no—
525C22—241no—
526C22—361no—
527C22—721no—
528C22#6385311yescharacteristic
529C22#6388611yescharacteristic
530C22#6389011yescharacteristic
531C4—62no—
532C4—121no—
533C4—121no—
534C4—361no—
535C4#6385211yescharacteristic
536C4#6390611yescharacteristic
537C4#6392311yescharacteristic
538C4#6395811yescharacteristic
539C3—21no—
540C3#6871911yescharacteristic, complemented
541C3#7037911yescharacteristic, complemented
542C2—21no—
543C2—21no—
544C2—21no—
545C2—241no—
546C2—721no—
547C2#1059131211yescharacteristic
subgroupG/H
centerC4#63852
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#394
prime radical#10594795C2
hypercenterC2×M16D32
hypocenterC32#2050
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592831C2semidirect
3. C2×C3×#825C2semidirect
4. #10591115C2semidirect
5. C2×#63570C2semidirect
6. #10591076C2semidirect
7. C3×C3⋊#338C2semidirect
36. C2×#825D3semidirect
45. C3⋊#338D3semidirect
471. C32#2050semidirect
540. C3#68719semidirect
541. C3#70379semidirect

Maximal subgroups

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

subgroupindex
#105947952
#105928312
C2×C3×#8252
#105911152
C2×#635702
#105910762
C3×C3⋊#3382
#703793
#687193