Finite Group Databasebeta

← #11793989

Subgroups — #11793989

Order 1152.

607 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594795C211yesmaximal, characteristic
2#10592812C211yesmaximal, characteristic, complemented
3C3×#5113C211yesmaximal, characteristic, complemented
4C3×#5102C211yesmaximal, characteristic, complemented
5#10591232C211yesmaximal, characteristic, complemented
6#10591231C211yesmaximal, characteristic, complemented
7#10589158C211yesmaximal, characteristic, complemented
8#70547—31nomaximal
9#70296—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13#64135C2211yescharacteristic
14C3×#926C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63833—21no—
18#63831—21no—
19#63830—21no—
20#63829—22no—
21#63825—21no—
22#63648—21no—
23#63643—21no—
24C3×#821—21no—
25C3×#816—21no—
26C3×Dic3⋊C8—22no—
27#63581—22no—
28#63580—22no—
29#5822—31no—
30#5748—31no—
31C3×#424—31no—
32C3×#416—31no—
33#5240—31no—
34#5113—31no—
35#5113—31no—
36#5113—61no—
37#5113D311yescharacteristic, complemented
38#5102D311yescharacteristic, complemented
39#5006—31no—
40#5006—31no—
41#5006—31no—
42#4557—31no—
43#4531—31no—
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828—21no—
49#3828—21no—
50C2×C4⋊(C3⋊D3)D411yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634D411yescharacteristic
53C2×C3×#67—21no—
54C3×#235—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235—21no—
58C2×C3×D12D411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×Dic6D411yescharacteristic
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64#3757—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4×C3⋊Dic3—21no—
67C3×#217—21no—
68C3×#217D412yes—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—21no—
71C3×C4×Dic3—21no—
72C3×C4×Dic3—21no—
73C3×#208—21no—
74C3×#208—21no—
75C2×C3×C3⋊C8D412yes—
76#3719—22no—
77#3717—22no—
78#3716—22no—
79#3714—22no—
80#2053—91noSylow
81C2×C3×#41—31no—
82C2×#235—31no—
83C2×#235—31no—
84C2×#235—61no—
85C2×#235C2×D311yescharacteristic
86C2×C3×M16—31no—
87C22×C3×C8—21no—
88C22×C3×C8C2×D311yescharacteristic
89C22×C3×C8C2×D311yescharacteristic
90C3×#117—31no—
91C3×#117—31no—
92#951—61no—
93#950—62no—
94#949—61no—
95#942—61no—
96#932—61no—
97#926—31no—
98#926—31no—
99#926—61no—
100#926C2×D311yescharacteristic
101#926C2×D311yescharacteristic
102C2×#208C2×D311yescharacteristic
103#909—61no—
104#909—61no—
105#908—61no—
106#908—61no—
107#904—62no—
108C3×C4⋊C8—62no—
109C3×#103—61no—
110C3×#102—61no—
111#834—62no—
112#821—21no—
113#821—61no—
114#821—61no—
115#821—62no—
116#816—21no—
117#816—61no—
118#816—61no—
119#816—62no—
120Dic3⋊C8—22no—
121#806—62no—
122#806—62no—
123#806—62no—
124C23×C32C2×D411yescharacteristic
125C22×C3⋊D3—21no—
126C22×C3×D3—21no—
127C2×C32×C4C2×D411yescharacteristic
128C2×C32×C4C2×D411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4#4111yescharacteristic
131C2×C32×C4#4111yescharacteristic
132C2×C32×C4#4111yescharacteristic
133#638—41no—
134#638—41no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—41no—
137C4⋊(C3⋊D3)—21no—
138C4⋊(C3⋊D3)—21no—
139C4×C3⋊D3—41no—
140C4×C3⋊D3—41no—
141#634—21no—
142#634—21no—
143C3×#67—41no—
144C3×#67—41no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—21no—
147C2×C3×Dic3—41no—
148C3×D12—21no—
149C3×D12—21no—
150C3×C4×D3—41no—
151C3×C4×D3—41no—
152C3×Dic6—21no—
153C3×Dic6—21no—
154C32×C8—41no—
155C3×C3⋊C8—22no—
156#575—91no—
157#424—31no—
158#416—31no—
159#416—91no—
160#410—91no—
161#410—91no—
162H(3,ℤ/4)—91no—
163C3×#41—61no—
164C3×#41—61no—
165C3×#41—61no—
166C3×#41—61no—
167C2×C3×Q8—31no—
168C2×C3×D4—31no—
169C2×C3×D4—61no—
170C22×C3×C4—21no—
171C22×C3×C4—61no—
172C22×C3×C4C22×D311yescharacteristic
173C22×C3×C4C22×D311yescharacteristic
174C2×#67—21no—
175C2×#67—61no—
176C2×#67—61no—
177C2×#67—121no—
178#235—21no—
179#235—21no—
180#235—21no—
181#235—21no—
182#235—62no—
183#235—62no—
184#235—61no—
185#235—61no—
186#235—61no—
187#235—61no—
188#235—61no—
189#235—61no—
190#235—61no—
191#235—61no—
192#235—121no—
193#235—121no—
194C2×D12—31no—
195C2×D12—31no—
196C2×D12—61no—
197C2×D12#6711yescharacteristic
198C2×C4×D3—21no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×C4×D3—121no—
202C2×Dic6—31no—
203C2×Dic6—31no—
204C2×Dic6—61no—
205C2×Dic6#6711yescharacteristic
206C3×M16—61no—
207C3×M16—61no—
208C2×C3×C8—22no—
209C2×C3×C8—21no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—21no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—32no—
216C2×C3×C8—41no—
217C2×C3×C8—41no—
218C3×C4⋊C4—61no—
219C3×C4⋊C4—61no—
220C3×C22⋊C4—32no—
221C3×C22⋊C4—61no—
222C3×C42—61no—
223C3×C42—61no—
224#217—21no—
225#217—61no—
226#217—61no—
227#217—121no—
228#217D1212yes—
229#216—62no—
230#215—62no—
231#214—62no—
232#213—62no—
233C4⋊Dic3—21no—
234C4⋊Dic3—21no—
235C4⋊Dic3—62no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4×Dic3—21no—
239C4×Dic3—21no—
240C4×Dic3—61no—
241C4×Dic3—61no—
242C4×Dic3—121no—
243#208—21no—
244#208—21no—
245C2×C3⋊C8#6712yes—
246Dic12—62no—
247D24—62no—
248#204—62no—
249#204—62no—
250C22×C32—41no—
251C22×C32#12111yescharacteristic
252C22×C32#12111yescharacteristic
253C22×C32#12111yescharacteristic
254C2×C3⋊D3—41no—
255C2×C3⋊D3—81no—
256C2×C3×D3—41no—
257C2×C3×D3—81no—
258C32×C4#12011yescharacteristic
259C32×C4#12311yescharacteristic
260C32×C4#12311yescharacteristic
261C32×C4#12411yescharacteristic
262C3⋊Dic3—41no—
263C3⋊Dic3—81no—
264C3×Dic3—42no—
265C3×Dic3—41no—
266C3×Dic3—81no—
267C2×#41—31no—
268C2×#41—91no—
269#137—181no—
270#137—181no—
271AGL(1,ℤ/8)—181no—
272AGL(1,ℤ/8)—181no—
273#135—182no—
274C2×M16—31no—
275C22×C8D3211yescharacteristic
276#117—31no—
277#117—31no—
278#117—91no—
279C4⋊C8—62no—
280#103—61no—
281#103—181no—
282#102—61no—
283#102—181no—
284#99—182no—
285#99—182no—
286C23×C3—21no—
287C23×C3—61no—
288C23×C3C2×D1211yescharacteristic
289C23×C3D3×D411yescharacteristic
290C22×D3—21no—
291C22×D3—61no—
292C22×D3—61no—
293C22×D3—121no—
294C3×Q8—61no—
295C3×Q8—61no—
296C3×D4—61no—
297C3×D4—61no—
298C3×D4—121no—
299C3×D4—121no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—21no—
303C2×C3×C4—21no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—62no—
307C2×C3×C4—61no—
308C2×C3×C4—121no—
309C2×C3×C4—121no—
310C2×C3×C4—121no—
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4#23511yescharacteristic
313C2×C3×C4#23511yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4D3×D411yescharacteristic
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4#23711yescharacteristic
319C2×C3×C4#23911yescharacteristic
320C2×C3×C4#23911yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322C2×C3×C4C2×#6711yescharacteristic
323#67—41no—
324#67—41no—
325#67—122no—
326#67—122no—
327#67—121no—
328#67—121no—
329#67—121no—
330#67—121no—
331C2×Dic3—22no—
332C2×Dic3—21no—
333C2×Dic3—41no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—121no—
337C2×Dic3—122no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340D12—21no—
341D12—21no—
342D12—62no—
343D12—61no—
344D12—61no—
345D12—61no—
346D12—61no—
347D12—121no—
348C4×D3—41no—
349C4×D3—41no—
350C4×D3—122no—
351C4×D3—122no—
352C4×D3—121no—
353C4×D3—121no—
354C4×D3—121no—
355C4×D3—121no—
356Dic6—21no—
357Dic6—21no—
358Dic6—62no—
359Dic6—61no—
360Dic6—61no—
361Dic6—61no—
362Dic6—61no—
363Dic6—121no—
364C3×C8—42no—
365C3×C8—41no—
366C3×C8—41no—
367C3×C8—62no—
368C3⋊C8—22no—
369C2×C32—21no—
370C2×C32—21no—
371C2×C32—21no—
372C2×C32#39411yescharacteristic
373C3⋊D3—81no—
374C3×D3—81no—
375#41—61no—
376#41—61no—
377#41—61no—
378#41—61no—
379#41—181no—
380#41—181no—
381#41—181no—
382#41—181no—
383C2×Q8—31no—
384C2×Q8—91no—
385C2×D4—31no—
386C2×D4—61no—
387C2×D4—91no—
388C2×D4—181no—
389C22×C4—61no—
390C22×C4—181no—
391C22×C4C2×D3211yescharacteristic
392Q16—182no—
393SD16—182no—
394SD16—182no—
395D8—182no—
396M16—61no—
397M16—61no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—32no—
402C4⋊C4—61no—
403C4⋊C4—61no—
404C4⋊C4—181no—
405C22⋊C4—32no—
406C22⋊C4—61no—
407C22⋊C4—181no—
408C42—61no—
409C42—61no—
410C42—181no—
411C22×C3—21no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—42no—
417C22×C3—121no—
418C22×C3—241no—
419C22×C3#88411yescharacteristic
420C22×C3#88411yescharacteristic
421C22×C3#89511yescharacteristic
422C22×C3#89511yescharacteristic
423C22×C3#93011yescharacteristic
424C22×C3#93911yescharacteristic
425C2×D3—41no—
426C2×D3—81no—
427C2×D3—122no—
428C2×D3—121no—
429C2×D3—121no—
430C2×D3—242no—
431C2×D3—241no—
432C2×D3—241no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—122no—
438C3×C4—121no—
439C3×C4—241no—
440C3×C4#88311yescharacteristic
441C3×C4#88511yescharacteristic
442C3×C4#89411yescharacteristic
443C3×C4#89411yescharacteristic
444C3×C4#92911yescharacteristic
445C3×C4#93711yescharacteristic
446C3×C4#93711yescharacteristic
447C3×C4#94711yescharacteristic
448Dic3—42no—
449Dic3—41no—
450Dic3—81no—
451Dic3—122no—
452Dic3—121no—
453Dic3—121no—
454Dic3—242no—
455Dic3—241no—
456Dic3—241no—
457C32#205311yescharacteristic, complemented, Sylow
458C23—61no—
459C23—181no—
460C23D3×D1211yescharacteristic
461Q8—61no—
462Q8—61no—
463Q8—181no—
464Q8—181no—
465D4—61no—
466D4—61no—
467D4—121no—
468D4—121no—
469D4—181no—
470D4—181no—
471D4—361no—
472D4—361no—
473C2×C4—61no—
474C2×C4—62no—
475C2×C4—121no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—181no—
479C2×C4—361no—
480C2×C4—361no—
481C2×C4—361no—
482C2×C4#379611yescharacteristic
483C2×C4#379811yescharacteristic
484C2×C4#379911yescharacteristic
485C2×C4D3×#6711yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C2×C4#381111yescharacteristic
488C8—41no—
489C8—62no—
490C2×C3—22no—
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—241no—
501C2×C3#495911yescharacteristic
502C2×C3#499111yescharacteristic
503D3—81no—
504D3—242no—
505D3—241no—
506D3—241no—
507C22—41no—
508C22—121no—
509C22—241no—
510C22—361no—
511C22—721no—
512C22#6388611yescharacteristic
513C22#6390611yescharacteristic
514C22#6391011yescharacteristic
515C4—122no—
516C4—121no—
517C4—241no—
518C4—361no—
519C4—721no—
520C4#6385011yescharacteristic
521C4#6385311yescharacteristic
522C4#6390711yescharacteristic
523C4#6398311yescharacteristic
524C3—21no—
525C3#7029611yescharacteristic, complemented
526C3#7054711yescharacteristic, complemented
527C2—21no—
528C2—21no—
529C2—21no—
530C2—241no—
531C2—721no—
532C2#1059129111yescharacteristic
subgroupG/H
centerC4#63907
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC2×C32#394
prime radical#10594795C2
hypercenterC22×C8D32
hypocenterC32#2053
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10592812C2semidirect
3. C3×#5113C2semidirect
4. C3×#5102C2semidirect
5. #10591232C2semidirect
6. #10591231C2semidirect
7. #10589158C2semidirect
37. #5113D3semidirect
38. #5102D3semidirect
457. C32#2053semidirect
525. C3#70296semidirect
526. C3#70547semidirect

Maximal subgroups

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

subgroupindex
#105947952
#105928122
C3×#51132
C3×#51022
#105912322
#105912312
#105891582
#705473
#702963