Finite Group Databasebeta

← #11860879

Subgroups — #11860879

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63810C211yesmaximal, characteristic
2#10593889C212yesmaximal, complemented
3#10592388C211yesmaximal, characteristic, complemented
4C3×C4×Dic12C211yesmaximal, characteristic, complemented
5C3×C4×D24C211yesmaximal, characteristic, complemented
6#10590957C212yesmaximal, complemented
7#10590818C211yesmaximal, characteristic, complemented
8#10590777C211yesmaximal, characteristic, complemented
9#10590743C212yesmaximal, complemented
10#10590687C211yesmaximal, characteristic, complemented
11#10590358C212yesmaximal, complemented
12#79721—31nomaximal
13#79589—31nomaximal
14C2×#3796C2212yes—
15C2×#3743C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17#64081C2211yescharacteristic
18C2×C3×Dic12C2211yescharacteristic
19C2×C3×D24C2211yescharacteristic
20C3×C4×D12C2212yes—
21C3×C4×Dic6C2212yes—
22#63904—22no—
23#63900C2212yes—
24#63898C2212yes—
25#63880—22no—
26#63877—22no—
27D3×Dic3⋊C4—22no—
28#63843C2212yes—
29C2×#3715C2212yes—
30#63810C418yescomplemented
31C32×C4×C8C2211yescharacteristic
32#63642C2211yescharacteristic
33C8×C3⋊Dic3C2211yescharacteristic
34#63630C2211yescharacteristic
35C3×#821C2212yes—
36C3×#818C2211yescharacteristic
37C3×#818C2211yescharacteristic
38C3×#816C2212yes—
39#63576C2212yes—
40#63565C2212yes—
41#63562C2212yes—
42C2×#919—31no—
43C2×#912—31no—
44#5574—32no—
45#5546—32no—
46C3×C4×Q16—31no—
47C3×C4×D8—31no—
48Dic3×Q16—31no—
49Dic3×D8—31no—
50#5026—32no—
51#5018—32no—
52D3×#107—31no—
53D3×#107—31no—
54#4873—31no—
55#4872—31no—
56#4817—32no—
57#4803—32no—
58#4771—32no—
59#4757—32no—
60C4×Dic12D311yescharacteristic, complemented
61C4×D24D311yescharacteristic, complemented
62#4689—31no—
63#4689—31no—
64#4689—61no—
65C2×C4×C3⋊D3C2311yescharacteristic
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×Dic6C2312yes—
69C2×#626—22no—
70C2×#624—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3796—24no—
74#3796C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78#3752D411yescharacteristic
79#3752D411yescharacteristic
80#3750D411yescharacteristic
81#3750D411yescharacteristic
82C4×C3⋊Dic3C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85#3743—22no—
86C8×C3⋊D3C2×C414yescomplemented
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—22no—
91C3×C4×Dic3—22no—
92C3×Dic12C2×C414yescomplemented
93C3×D24C2×C414yescomplemented
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3715C2×C418yescomplemented
99#2951—91noSylow
100C2×#239—32no—
101C2×#237—32no—
102C2×C3×Q16—31no—
103C2×C3×D8—31no—
104C3×C4×Q8—32no—
105C3×C4×D4—32no—
106Q8×Dic3—32no—
107C2×#215—32no—
108D4×Dic3—32no—
109C2×#214—32no—
110C4×#67—62no—
111C2×Dic3⋊C4—62no—
112#919—38no—
113#912—38no—
114C2×Dic12C2×D311yescharacteristic
115C2×D24C2×D311yescharacteristic
116C2×ΓL(1,𝔽25)—31no—
117C2×ΓL(1,𝔽25)—31no—
118C2×ΓL(1,𝔽25)—61no—
119C2×D3×C8—31no—
120C2×D3×C8—31no—
121C2×D3×C8—61no—
122#893—32no—
123#893—62no—
124D3×C4⋊C4—32no—
125D3×C4⋊C4—32no—
126D3×C4⋊C4—62no—
127#887—32no—
128#67⋊C4—62no—
129#877—62no—
130C4×D12—62no—
131C4×D12C2×D312yes—
132#872—31no—
133#872—31no—
134#872—61no—
135#872—62no—
136C4×Dic6C2×D312yes—
137C3×#107—31no—
138C3×#107—31no—
139C3×#103—32no—
140C3×#102—32no—
141C3×C4×C8—21no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#835—32no—
145#832—32no—
146#821C2×D312yes—
147#818C2×D311yescharacteristic
148#818C2×D311yescharacteristic
149#816C2×D312yes—
150#815—31no—
151#815—31no—
152#815—61no—
153C8×Dic3—31no—
154C8×Dic3—31no—
155C8×Dic3—61no—
156#810—32no—
157#809—32no—
158#807—32no—
159#807—32no—
160#803—31no—
161#803—31no—
162#803—61no—
163C22×C3⋊D3C2×D411yescharacteristic
164C22×C3×D3—22no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3C2×D411yescharacteristic
169C2×C3⋊Dic3C2×D411yescharacteristic
170C2×C3⋊Dic3C2×D411yescharacteristic
171C4×C3⋊D3C22×C412yes—
172C4×C3⋊D3#4112yes—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C3×D12—22no—
177C3×D12C22×C414yes—
178C3×C4×D3—82no—
179C3×Dic6—22no—
180C3×Dic6C22×C414yes—
181#626—28no—
182#624—82no—
183D3×Dic3—28no—
184D3×Dic3—82no—
185C32×C8—21no—
186C32×C8C22×C412yes—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)C22×C412yes—
189C2×#135—91no—
190#520—92no—
191#440—92no—
192#440—92no—
193C4×Q16—31no—
194C4×Q16—91no—
195C4×D8—31no—
196C4×D8—91no—
197C2×#107—91no—
198#417—92no—
199#405—91no—
200C2×C3×Q8—32no—
201C2×C3×D4—32no—
202C22×C3×C4—62no—
203C2×#67—62no—
204C22×Dic3—62no—
205C22×Dic3—62no—
206#239—38no—
207#239—64no—
208#237—38no—
209#237—64no—
210C2×D12—62no—
211C2×D12C22×D312yes—
212C2×C4×D3—22no—
213C2×C4×D3—31no—
214C2×C4×D3—31no—
215C2×C4×D3—61no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×Dic6C22×D312yes—
221C3×Q16—34no—
222C3×D8—34no—
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8C22×D311yescharacteristic
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C3×C4⋊C4—32no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—62no—
232C3×C22⋊C4—62no—
233C3×C42—21no—
234C3×C42—62no—
235C3×C42C22×D311yescharacteristic
236C3×C42C22×D311yescharacteristic
237#217—62no—
238#215—38no—
239#214—38no—
240(C2×D3)⋊C4—22no—
241(C2×D3)⋊C4—31no—
242(C2×D3)⋊C4—31no—
243(C2×D3)⋊C4—31no—
244(C2×D3)⋊C4—31no—
245(C2×D3)⋊C4—61no—
246(C2×D3)⋊C4—61no—
247(C2×D3)⋊C4—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3C22×D312yes—
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—22no—
252Dic3⋊C4—31no—
253Dic3⋊C4—31no—
254Dic3⋊C4—31no—
255Dic3⋊C4—31no—
256Dic3⋊C4—61no—
257Dic3⋊C4—61no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261C4×Dic3—22no—
262C4×Dic3—31no—
263C4×Dic3—31no—
264C4×Dic3—61no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—61no—
273Dic12C4×D314yescomplemented
274D24C4×D314yescomplemented
275ΓL(1,𝔽25)—62no—
276ΓL(1,𝔽25)—62no—
277ΓL(1,𝔽25)—64no—
278D3×C8—34no—
279D3×C8—34no—
280D3×C8—64no—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—21no—
283C2×C3⋊D3—21no—
284C2×C3⋊D3C4×D412yes—
285C2×C3×D3—24no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4C23×C411yescharacteristic
291C32×C4C2×#4111yescharacteristic
292C3⋊Dic3—21no—
293C3⋊Dic3—21no—
294C3⋊Dic3C4×D412yes—
295C3×Dic3—24no—
296C3×Dic3—42no—
297C3×Dic3—42no—
298C2×#41—92no—
299#135—98no—
300C2×Q16—31no—
301C2×SD16—92no—
302C2×D8—31no—
303C2×M16—91no—
304C22×C8—91no—
305C4×Q8—32no—
306C4×Q8—92no—
307C4×D4—32no—
308C4×D4—92no—
309C4×D4—182no—
310C4×D4—182no—
311#117—91no—
312#117—182no—
313C2×C4⋊C4—92no—
314C2×C4⋊C4—182no—
315#107—31no—
316#107—31no—
317#107—92no—
318#103—32no—
319#103—92no—
320#102—32no—
321#102—92no—
322#97—91no—
323#97—91no—
324C4×C8—91no—
325C4×C8D3211yescharacteristic
326C23×C3—62no—
327C22×D3—22no—
328C22×D3—31no—
329C22×D3—31no—
330C22×D3—61no—
331C3×Q8—34no—
332C3×Q8—62no—
333C3×D4—34no—
334C3×D4—62no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—242no—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348#67—68no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—31no—
353C2×Dic3—31no—
354C2×Dic3—31no—
355C2×Dic3—31no—
356C2×Dic3—31no—
357C2×Dic3—31no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—68no—
362C2×Dic3—242no—
363D12—22no—
364D12—68no—
365D12C2×C4×D314yes—
366C4×D3—32no—
367C4×D3—32no—
368C4×D3—32no—
369C4×D3—32no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—68no—
373C4×D3—82no—
374C4×D3—242no—
375C4×D3—242no—
376C4×D3—242no—
377Dic6—22no—
378Dic6C2×C4×D314yes—
379C3×C8—22no—
380C3×C8—21no—
381C3×C8—21no—
382C3×C8—22no—
383C3×C8C2×C4×D312yes—
384C3×C8C2×C4×D312yes—
385C3⋊C8—32no—
386C3⋊C8—32no—
387C3⋊C8—62no—
388C3⋊C8—62no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C2×C32C2×C4×D411yescharacteristic
392C2×C32#57611yescharacteristic
393C2×C32#57811yescharacteristic
394C3⋊D3—22no—
395C3×D3—44no—
396#41—98no—
397#41—184no—
398C2×Q8—32no—
399C2×D4—32no—
400C2×D4—182no—
401C22×C4—62no—
402C22×C4—91no—
403C22×C4—182no—
404C22×C4—182no—
405C22×C4—182no—
406Q16—34no—
407SD16—98no—
408D8—34no—
409M16—182no—
410C2×C8—91no—
411C2×C8—94no—
412C2×C8—91no—
413C2×C8C2×D3211yescharacteristic
414C2×C8C2×D3211yescharacteristic
415C4⋊C4—32no—
416C4⋊C4—32no—
417C4⋊C4—62no—
418C4⋊C4—91no—
419C4⋊C4—91no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C22⋊C4—62no—
423C22⋊C4—91no—
424C22⋊C4—91no—
425C22⋊C4—182no—
426C42—62no—
427C42—91no—
428C42—182no—
429C42C2×D3211yescharacteristic
430C22×C3—21no—
431C22×C3—64no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3C2×D3×D411yescharacteristic
435C22×C3C2×D3×D411yescharacteristic
436C2×D3—24no—
437C2×D3—32no—
438C2×D3—32no—
439C2×D3—42no—
440C2×D3—42no—
441C2×D3—62no—
442C2×D3—61no—
443C2×D3—61no—
444C2×D3—61no—
445C2×D3—61no—
446C2×D3—121no—
447C2×D3—121no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—41no—
455C3×C4—41no—
456C3×C4—64no—
457C3×C4—122no—
458C3×C4—122no—
459C3×C4C22×C4×D311yescharacteristic
460C3×C4C22×C4×D311yescharacteristic
461C3×C4D3×#4111yescharacteristic
462C3×C4D3×#4111yescharacteristic
463Dic3—24no—
464Dic3—32no—
465Dic3—32no—
466Dic3—42no—
467Dic3—42no—
468Dic3—62no—
469Dic3—61no—
470Dic3—61no—
471Dic3—61no—
472Dic3—61no—
473Dic3—121no—
474Dic3—121no—
475C32#295111yescharacteristic, complemented, Sylow
476C23—62no—
477C23—91no—
478Q8—34no—
479Q8—62no—
480D4—34no—
481D4—62no—
482D4—188no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—91no—
487C2×C4—92no—
488C2×C4—92no—
489C2×C4—91no—
490C2×C4—91no—
491C2×C4—188no—
492C2×C4—242no—
493C2×C4—722no—
494C2×C4—722no—
495C2×C4#380211yescharacteristic
496C2×C4#380211yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—21no—
499C8—92no—
500C8—181no—
501C8C4×D3212yes—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—124no—
506C2×C3C4×D3×D411yescharacteristic
507C2×C3C4×D3×D411yescharacteristic
508C2×C3#575711yescharacteristic
509C2×C3#576611yescharacteristic
510C2×C3#576911yescharacteristic
511C2×C3#577111yescharacteristic
512D3—44no—
513D3—62no—
514D3—62no—
515D3—122no—
516C22—64no—
517C22—92no—
518C22—122no—
519C22—122no—
520C22—181no—
521C22—181no—
522C22C2×#380211yescharacteristic
523C4—21no—
524C4—21no—
525C4—64no—
526C4—92no—
527C4—122no—
528C4—122no—
529C4—181no—
530C4—181no—
531C4C2×C4×D3211yescharacteristic
532C4#6430611yescharacteristic
533C3—21no—
534C3#7958911yescharacteristic, complemented
535C3#7972111yescharacteristic, complemented
536C2—124no—
537C2—182no—
538C2C4×#380211yescharacteristic
539C2#1059468711yescharacteristic
540C2#1059470311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63810C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10593889C2semidirect
3. #10592388C2semidirect
4. C3×C4×Dic12C2semidirect
5. C3×C4×D24C2semidirect
6. #10590957C2semidirect
7. #10590818C2semidirect
8. #10590777C2semidirect
9. #10590743C2semidirect
10. #10590687C2semidirect
11. #10590358C2semidirect
30. #63810C4semidirect
60. C4×Dic12D3semidirect
61. C4×D24D3semidirect
74. #3796C2×C4semidirect
86. C8×C3⋊D3C2×C4semidirect
92. C3×Dic12C2×C4semidirect
93. C3×D24C2×C4semidirect
98. #3715C2×C4semidirect
273. Dic12C4×D3semidirect
274. D24C4×D3semidirect
475. C32#2951semidirect
534. C3#79589semidirect
535. C3#79721semidirect

Maximal subgroups

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

subgroupindex
C2×#638102
#105938892
#105923882
C3×C4×Dic122
C3×C4×D242
#105909572
#105908182
#105907772
#105907432
#105906872
#105903582
#797213
#795893