Finite Group Databasebeta

← #11787646

Subgroups — #11787646

Order 1152.

699 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#10594780C211yesmaximal, characteristic, complemented
3#10592812C211yesmaximal, characteristic, complemented
4C3×#5110C211yesmaximal, characteristic, complemented
5#10591110C211yesmaximal, characteristic, complemented
6C3×#4552C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#70012—31nomaximal
9#68947—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C32×C8C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63833C412yescomplemented
18#63831—21no—
19#63830C412yescomplemented
20#63829—22no—
21#63825—21no—
22#63818—22no—
23#63817—22no—
24#63817—22no—
25#63648—21no—
26#63643—21no—
27C3×(C2×D3)⋊C8—22no—
28#63568—22no—
29#5822—31no—
30#5748—31no—
31#5745—31no—
32#5745—31no—
33C3×#408—31no—
34#5236—31no—
35#5139—31no—
36#5113—31no—
37#5113—31no—
38#5113—61no—
39#5110D311yescharacteristic, complemented
40C3×#341—31no—
41#4559—31no—
42#4556—31no—
43#4552D311yescharacteristic, complemented
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828C2×C412yes—
49#3828D412yes—
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×D12C2×C411yescharacteristic
59C2×C3×C4×D3—21no—
60C2×C3×Dic6C2×C411yescharacteristic
61C2×C32×C8—21no—
62C2×C32×C8—21no—
63C2×C32×C8—21no—
64#3757—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4×C3⋊Dic3—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208C2×C412yes—
72C3×#208D412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D412yes—
76#3719—22no—
77#3717—22no—
78#3716—22no—
79#3714—22no—
80#3712—24no—
81#3710—24no—
82#1881—91noSylow
83C2×C3×#41—31no—
84C2×#235—31no—
85C2×#235—31no—
86C2×#235—61no—
87C2×#235C2×D311yescharacteristic
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C2×C3×M16—31no—
91C22×C3×C8—21no—
92C22×C3×C8C2×D311yescharacteristic
93C22×C3×C8C2×D311yescharacteristic
94#951—61no—
95#950—62no—
96#949—61no—
97#942—32no—
98#932—32no—
99#926—31no—
100#926—31no—
101#926—61no—
102C2×#208C2×D311yescharacteristic
103C2×#208C2×D311yescharacteristic
104C2×#208C2×D311yescharacteristic
105#909—32no—
106#909—61no—
107#908—32no—
108#908—61no—
109#907—62no—
110#907—62no—
111D3×M16—62no—
112D3×M16—62no—
113#904—62no—
114#901—62no—
115#901—62no—
116C3×C22⋊C8—62no—
117#837—62no—
118#825—62no—
119#821—61no—
120#821—61no—
121#821—62no—
122(C2×D3)⋊C8—22no—
123#816—61no—
124#816—61no—
125#816—62no—
126C23×C32#4111yescharacteristic
127C22×C3⋊D3—21no—
128C22×C3×D3—21no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4C2×D411yescharacteristic
134C2×C32×C4#4111yescharacteristic
135#638—22no—
136#638—22no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—41no—
139C4⋊(C3⋊D3)—21no—
140C4⋊(C3⋊D3)C22⋊C412yes—
141C4×C3⋊D3—22no—
142C4×C3⋊D3—22no—
143#634—21no—
144#634C22⋊C412yes—
145C3×#67—41no—
146C3×#67—41no—
147C2×C3×Dic3—21no—
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—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—22no—
158#575—91no—
159#568—91no—
160#421—91no—
161#416—91no—
162#408—31no—
163#344—91no—
164#341—31no—
165C3×#41—61no—
166C3×#41—61no—
167C3×#41—61no—
168C3×#41—61no—
169C2×C3×Q8—31no—
170C2×C3×D4—31no—
171C2×C3×D4—61no—
172C22×C3×C4—21no—
173C22×C3×C4—61no—
174C22×C3×C4C22×D311yescharacteristic
175C22×C3×C4C22×D311yescharacteristic
176C2×#67—21no—
177C2×#67—61no—
178C2×#67—61no—
179C2×#67—121no—
180#235—21no—
181#235—21no—
182#235—21no—
183#235—21no—
184#235—32no—
185#235—32no—
186#235—32no—
187#235—32no—
188#235—62no—
189#235—62no—
190#235—61no—
191#235—61no—
192#235—61no—
193#235—61no—
194#235—121no—
195#235—121no—
196C2×D12—31no—
197C2×D12—31no—
198C2×D12—61no—
199C2×D12C4×D311yescharacteristic
200C2×C4×D3—21no—
201C2×C4×D3—61no—
202C2×C4×D3—61no—
203C2×C4×D3—121no—
204C2×Dic6—31no—
205C2×Dic6—31no—
206C2×Dic6—61no—
207C2×Dic6C4×D311yescharacteristic
208C3×M16—32no—
209C3×M16—32no—
210C3×M16—61no—
211C3×M16—61no—
212C3×M16—61no—
213C3×M16—61no—
214C2×C3×C8—22no—
215C2×C3×C8—21no—
216C2×C3×C8—21no—
217C2×C3×C8—21no—
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—32no—
222C2×C3×C8—41no—
223C2×C3×C8—41no—
224C2×C3×C8—61no—
225C2×C3×C8—61no—
226#217—61no—
227#217—61no—
228#217—121no—
229#216—62no—
230#215—62no—
231#214—62no—
232#213—62no—
233C4⋊Dic3—62no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4×Dic3—61no—
237C4×Dic3—61no—
238C4×Dic3—121no—
239#208—21no—
240#208—21no—
241#208—21no—
242#208—21no—
243#208C4×D312yes—
244#208D1212yes—
245C2×C3⋊C8—21no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8#6712yes—
248Dic12—62no—
249D24—62no—
250#204—62no—
251#204—62no—
252ΓL(1,𝔽25)—64no—
253ΓL(1,𝔽25)—64no—
254D3×C8—64no—
255D3×C8—64no—
256C22×C32—41no—
257C22×C32C4×D411yescharacteristic
258C22×C32#12111yescharacteristic
259C22×C32#12311yescharacteristic
260C2×C3⋊D3—22no—
261C2×C3⋊D3—81no—
262C2×C3×D3—42no—
263C2×C3×D3—41no—
264C32×C4C2×C22⋊C411yescharacteristic
265C32×C4C4×D411yescharacteristic
266C32×C4#12011yescharacteristic
267C32×C4#12111yescharacteristic
268C3⋊Dic3—22no—
269C3⋊Dic3—81no—
270C3×Dic3—41no—
271C2×#41—31no—
272C2×#41—91no—
273#137—92no—
274#137—181no—
275AGL(1,ℤ/8)—92no—
276AGL(1,ℤ/8)—181no—
277#135—182no—
278#131—182no—
279#131—182no—
280C2×M16—31no—
281C2×M16—31no—
282C2×M16—31no—
283C2×M16—182no—
284C22×C8D3211yescharacteristic
285#117—91no—
286#104—182no—
287#103—181no—
288#102—181no—
289C22⋊C8—62no—
290C23×C3—21no—
291C23×C3—61no—
292C23×C3#23511yescharacteristic
293C23×C3#23911yescharacteristic
294C22×D3—21no—
295C22×D3—61no—
296C22×D3—61no—
297C22×D3—121no—
298C3×Q8—61no—
299C3×Q8—61no—
300C3×D4—61no—
301C3×D4—61no—
302C3×D4—121no—
303C3×D4—121no—
304C2×C3×C4—21no—
305C2×C3×C4—21no—
306C2×C3×C4—21no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—61no—
311C2×C3×C4—121no—
312C2×C3×C4—121no—
313C2×C3×C4C2×C4×D311yescharacteristic
314C2×C3×C4C2×C4×D311yescharacteristic
315C2×C3×C4C2×D1211yescharacteristic
316C2×C3×C4#23511yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4D3×D411yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4D3×D411yescharacteristic
323C2×C3×C4#23711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325#67—41no—
326#67—41no—
327#67—62no—
328#67—62no—
329#67—62no—
330#67—62no—
331#67—122no—
332#67—122no—
333C2×Dic3—21no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—121no—
337C2×Dic3—122no—
338C2×Dic3—121no—
339C2×Dic3—121no—
340D12—21no—
341D12—21no—
342D12—32no—
343D12—32no—
344D12—62no—
345D12—61no—
346D12—61no—
347D12—121no—
348C4×D3—41no—
349C4×D3—41no—
350C4×D3—62no—
351C4×D3—62no—
352C4×D3—62no—
353C4×D3—62no—
354C4×D3—122no—
355C4×D3—122no—
356Dic6—21no—
357Dic6—21no—
358Dic6—32no—
359Dic6—32no—
360Dic6—62no—
361Dic6—61no—
362Dic6—61no—
363Dic6—121no—
364C3×C8—42no—
365C3×C8—41no—
366C3×C8—41no—
367C3×C8—62no—
368C3×C8—62no—
369C3×C8—62no—
370C3⋊C8—22no—
371C3⋊C8—22no—
372C3⋊C8—22no—
373C2×C32—21no—
374C2×C32—21no—
375C2×C32—21no—
376C2×C32#38611yescharacteristic
377C3⋊D3—42no—
378C3×D3—81no—
379#41—61no—
380#41—61no—
381#41—61no—
382#41—61no—
383#41—92no—
384#41—92no—
385#41—181no—
386#41—181no—
387C2×Q8—31no—
388C2×Q8—91no—
389C2×D4—31no—
390C2×D4—61no—
391C2×D4—91no—
392C2×D4—181no—
393C22×C4—61no—
394C22×C4—181no—
395C22×C4C2×D3211yescharacteristic
396Q16—182no—
397SD16—182no—
398SD16—182no—
399D8—182no—
400M16—32no—
401M16—32no—
402M16—61no—
403M16—61no—
404M16—61no—
405M16—61no—
406M16—184no—
407C2×C8—21no—
408C2×C8—21no—
409C2×C8—21no—
410C2×C8—32no—
411C2×C8—61no—
412C2×C8—61no—
413C2×C8—184no—
414C4⋊C4—181no—
415C22⋊C4—181no—
416C42—181no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—41no—
421C22×C3—41no—
422C22×C3—42no—
423C22×C3—122no—
424C22×C3—121no—
425C22×C3#88311yescharacteristic
426C22×C3#88411yescharacteristic
427C22×C3#89311yescharacteristic
428C22×C3#89411yescharacteristic
429C22×C3#89511yescharacteristic
430C22×C3C4×#6711yescharacteristic
431C2×D3—42no—
432C2×D3—41no—
433C2×D3—62no—
434C2×D3—62no—
435C2×D3—122no—
436C2×D3—241no—
437C2×D3—241no—
438C2×D3—242no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—121no—
444C3×C4C4×D1211yescharacteristic
445C3×C4D3×C22⋊C411yescharacteristic
446C3×C4D3×C22⋊C411yescharacteristic
447C3×C4#67⋊C411yescharacteristic
448C3×C4#88211yescharacteristic
449C3×C4#88411yescharacteristic
450C3×C4#93711yescharacteristic
451C3×C4#93811yescharacteristic
452Dic3—41no—
453Dic3—62no—
454Dic3—62no—
455Dic3—122no—
456Dic3—242no—
457Dic3—241no—
458Dic3—241no—
459C32#188111yescharacteristic, complemented, Sylow
460C23—61no—
461C23—181no—
462C23#379911yescharacteristic
463Q8—61no—
464Q8—61no—
465Q8—92no—
466Q8—181no—
467D4—61no—
468D4—61no—
469D4—92no—
470D4—121no—
471D4—121no—
472D4—182no—
473D4—182no—
474D4—181no—
475C2×C4—61no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—181no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—361no—
482C2×C4C4×D3211yescharacteristic
483C2×C4D3×D1211yescharacteristic
484C2×C4#380211yescharacteristic
485C2×C4#380411yescharacteristic
486C2×C4D3×#6711yescharacteristic
487C2×C4#381111yescharacteristic
488C8—41no—
489C8—62no—
490C8—62no—
491C8—62no—
492C2×C3—22no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—41no—
501C2×C3—41no—
502C2×C3—241no—
503C2×C3#466511yescharacteristic
504C2×C3#495611yescharacteristic
505D3—81no—
506D3—122no—
507D3—122no—
508D3—242no—
509C22—41no—
510C22—122no—
511C22—121no—
512C22—182no—
513C22—721no—
514C22#6385411yescharacteristic
515C22#6390411yescharacteristic
516C22#6391011yescharacteristic
517C4—121no—
518C4—182no—
519C4—721no—
520C4#6388011yescharacteristic
521C4#6392111yescharacteristic
522C4#6392211yescharacteristic
523C4#6395811yescharacteristic
524C3—21no—
525C3#6894711yescharacteristic, complemented
526C3#7001211yescharacteristic, complemented
527C2—21no—
528C2—21no—
529C2—21no—
530C2—241no—
531C2—362no—
532C2#1059127511yescharacteristic
subgroupG/H
centerC4#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC2×C32#386
prime radical#10594795C2
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1881
LCSG ▷ C2×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. #10594780C2semidirect
3. #10592812C2semidirect
4. C3×#5110C2semidirect
5. #10591110C2semidirect
6. C3×#4552C2semidirect
7. #10589171C2semidirect
17. #63833C4semidirect
19. #63830C4semidirect
39. #5110D3semidirect
43. #4552D3semidirect
459. C32#1881semidirect
525. C3#68947semidirect
526. C3#70012semidirect

Maximal subgroups

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

subgroupindex
#105947952
#105947802
#105928122
C3×#51102
#105911102
C3×#45522
#105891712
#700123
#689473