Finite Group Databasebeta

← #11860878

Subgroups — #11860878

Order 1152.

1035 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63808C211yesmaximal, characteristic
2#10593890C212yesmaximal, complemented
3C4×#3745C211yesmaximal, characteristic, complemented
4C3×C4×Dic12C211yesmaximal, characteristic, complemented
5C3×#4689C211yesmaximal, characteristic, complemented
6Dic3×Dic12C211yesmaximal, characteristic, complemented
7#10590795C212yesmaximal, complemented
8#10590763C211yesmaximal, characteristic, complemented
9D3×#818C211yesmaximal, characteristic, complemented
10#10590671C212yesmaximal, complemented
11#10590362C212yesmaximal, complemented
12#79721—31nomaximal
13#78562—31nomaximal
14C2×#3799C2212yes—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2212yes—
17C2×C3×Dic12C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×#872C2211yescharacteristic
21C3×C4×Dic6C2212yes—
22#63894C2212yes—
23D3×C4⋊Dic3C2212yes—
24#63883—22no—
25#63881—22no—
26#63880—22no—
27Dic3×Dic6C2212yes—
28#63836—22no—
29C2×#3717C2212yes—
30#63808C418yescomplemented
31C32×C4×C8C2211yescharacteristic
32#63648C2212yes—
33#63645C2211yescharacteristic
34C3×#818C2211yescharacteristic
35C3×#816C2212yes—
36C3×#815C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×#803C2211yescharacteristic
39#63575C2212yes—
40#63566C2212yes—
41#63564C2212yes—
42C2×#919—31no—
43C2×#904—31no—
44#5574—32no—
45#5523—32no—
46C3×C4×Q16—31no—
47C3×#405—31no—
48Dic3×Q16—31no—
49#5133—32no—
50C2×#818—31no—
51#5026—32no—
52D3×#107—31no—
53#4872—31no—
54#4817—32no—
55#4803—32no—
56#4710—32no—
57#4710—32no—
58C4×Dic12—31no—
59C4×Dic12D311yescharacteristic, complemented
60C4×D24—31no—
61C4×D24—31no—
62C4×D24—31no—
63C4×D24—61no—
64#4689D311yescharacteristic, complemented
65C2×C4⋊(C3⋊D3)C2312yes—
66C2×C4×C3⋊D3—22no—
67C2×C3×C4×D3C2311yescharacteristic
68C2×C3×Dic6C2312yes—
69C2×#626—22no—
70C2×#624—22no—
71C2×#624—22no—
72C2×D3×Dic3—22no—
73#3799—24no—
74#3799C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78#3752—22no—
79C4⋊(C3⋊Dic3)C2312yes—
80#3745C2×C414yescomplemented
81C3×(C2×D3)⋊C4D411yescharacteristic
82C3×(C2×D3)⋊C4D411yescharacteristic
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×Dic3⋊C4D411yescharacteristic
86C3×Dic3⋊C4D411yescharacteristic
87C3×C4×Dic3—22no—
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×Dic12C2×C414yescomplemented
92C3×ΓL(1,𝔽25)—22no—
93C3×D3×C8C2×C414yescomplemented
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97Dic32—22no—
98#3717C2×C418yescomplemented
99#2951—91noSylow
100C2×#239—32no—
101C2×#235—32no—
102C2×C3×Q16—31no—
103C2×C3×M16—31no—
104C22×C3×C8—31no—
105C3×C4×Q8—32no—
106C3×#117—31no—
107Q8×Dic3—32no—
108C2×#215—32no—
109C2×C4⋊Dic3—32no—
110#919—38no—
111C2×Dic12C2×D311yescharacteristic
112#904—38no—
113C2×D24—31no—
114C2×D24—31no—
115C2×D24—61no—
116C2×#204—32no—
117C2×ΓL(1,𝔽25)C2×D311yescharacteristic
118C2×D3×C8C2×D311yescharacteristic
119#893—32no—
120#893—62no—
121#892—62no—
122D3×C4⋊C4—32no—
123D3×C4⋊C4—62no—
124D3×C4⋊C4—62no—
125#67⋊C4—62no—
126#67⋊C4—62no—
127C4×D12—32no—
128C4×D12—32no—
129C4×D12—32no—
130C4×D12—62no—
131C4×D12—62no—
132#872—62no—
133#872C2×D311yescharacteristic
134C4×Dic6—32no—
135C4×Dic6C2×D312yes—
136C3×#107—31no—
137C3×#103—32no—
138C3×#97—31no—
139C3×#97—31no—
140C3×C4×C8—21no—
141C3×C4×C8—31no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#835—32no—
145#821—32no—
146#821—32no—
147#821—32no—
148#821—62no—
149#818—31no—
150#818—31no—
151#818—32no—
152#818—61no—
153#818C2×D311yescharacteristic
154#816—32no—
155#816C2×D312yes—
156#815C2×D311yescharacteristic
157C8×Dic3C2×D311yescharacteristic
158#809—32no—
159#807—32no—
160#803C2×D311yescharacteristic
161C22×C3⋊D3—22no—
162C22×C3×D3C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)C22×C414yes—
169C4×C3⋊D3—82no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C2×C3×Dic3C2×D411yescharacteristic
175C3×C4×D3C22×C412yes—
176C3×C4×D3#4112yes—
177C3×Dic6—22no—
178C3×Dic6C22×C414yes—
179#626—28no—
180#624—28no—
181#624—82no—
182D3×Dic3—82no—
183C32×C8—21no—
184C32×C8C22×C412yes—
185C3×C3⋊C8—21no—
186C3×C3⋊C8C22×C412yes—
187C2×#135—91no—
188#520—92no—
189#440—92no—
190#440—92no—
191C4×Q16—31no—
192C4×Q16—91no—
193C4×D8—91no—
194C4×D8—91no—
195C2×#107—91no—
196#417—92no—
197#405—31no—
198C2×C3×Q8—32no—
199C22×C3×C4—31no—
200C2×#67—62no—
201C22×Dic3—62no—
202#239—38no—
203#239—64no—
204#235—38no—
205#235—64no—
206C2×D12—32no—
207C2×D12—32no—
208C2×D12—62no—
209C2×D12—62no—
210C2×C4×D3—62no—
211C2×C4×D3—62no—
212C2×C4×D3—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—122no—
218C2×C4×D3C22×D311yescharacteristic
219C2×Dic6C22×D312yes—
220C3×Q16—34no—
221C3×M16—62no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—31no—
225C2×C3×C8—34no—
226C2×C3×C8—31no—
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C3×C4⋊C4—31no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—62no—
235C3×C22⋊C4—31no—
236C3×C22⋊C4—31no—
237C3×C42—21no—
238C3×C42—31no—
239C3×C42—62no—
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D311yescharacteristic
242#215—38no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—122no—
248(C2×D3)⋊C4D1211yescharacteristic
249(C2×D3)⋊C4D1211yescharacteristic
250C4⋊Dic3—32no—
251C4⋊Dic3—32no—
252C4⋊Dic3—62no—
253C4⋊Dic3—62no—
254C4⋊Dic3—62no—
255C4⋊Dic3C22×D312yes—
256Dic3⋊C4—22no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4D1211yescharacteristic
260Dic3⋊C4D1211yescharacteristic
261C4×Dic3—22no—
262C4×Dic3—62no—
263C4×Dic3—62no—
264C4×Dic3C22×D311yescharacteristic
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267Dic12C4×D314yescomplemented
268D24—34no—
269D24—34no—
270D24—64no—
271#204—38no—
272ΓL(1,𝔽25)—22no—
273D3×C8C4×D314yescomplemented
274C22×C32C22×D411yescharacteristic
275C2×C3⋊D3—24no—
276C2×C3⋊D3—42no—
277C2×C3⋊D3—42no—
278C2×C3×D3—21no—
279C2×C3×D3—21no—
280C2×C3×D3C4×D412yes—
281C32×C4—21no—
282C32×C4—21no—
283C32×C4C23×C411yescharacteristic
284C32×C4C2×#4111yescharacteristic
285C3⋊Dic3—42no—
286C3×Dic3—24no—
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C2×#41—92no—
292#135—98no—
293C2×Q16—31no—
294C2×SD16—92no—
295C2×D8—91no—
296C2×M16—31no—
297C22×C8—31no—
298C4×Q8—32no—
299C4×Q8—92no—
300C4×D4—92no—
301C4×D4—92no—
302C4×D4—182no—
303C4×D4—182no—
304#117—31no—
305#117—182no—
306C2×C4⋊C4—92no—
307C2×C4⋊C4—182no—
308#107—31no—
309#107—92no—
310#107—91no—
311#103—32no—
312#103—92no—
313#102—92no—
314#102—92no—
315#97—31no—
316#97—31no—
317C4×C8—31no—
318C4×C8D3211yescharacteristic
319C23×C3—31no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—122no—
323C22×D3C2×D1211yescharacteristic
324C3×Q8—34no—
325C3×Q8—62no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—31no—
330C2×C3×C4—32no—
331C2×C3×C4—32no—
332C2×C3×C4—31no—
333C2×C3×C4—31no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D411yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342#67—68no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C2×Dic3—242no—
349C2×Dic3C2×D1211yescharacteristic
350C2×Dic3C2×D1211yescharacteristic
351C2×Dic3C2×D1211yescharacteristic
352D12—34no—
353D12—34no—
354D12—64no—
355D12—68no—
356D12—62no—
357D12—62no—
358D12—122no—
359C4×D3—68no—
360C4×D3—68no—
361C4×D3—242no—
362C4×D3—242no—
363C4×D3—242no—
364C4×D3—242no—
365C4×D3—242no—
366C4×D3—244no—
367C4×D3C2×C4×D312yes—
368C4×D3#23512yes—
369Dic6—22no—
370Dic6C2×C4×D314yes—
371C3×C8—21no—
372C3×C8—21no—
373C3×C8—22no—
374C3×C8—32no—
375C3×C8—41no—
376C3×C8—61no—
377C3×C8C2×C4×D312yes—
378C3×C8C2×C4×D312yes—
379C3⋊C8—21no—
380C3⋊C8C2×C4×D312yes—
381C2×C32C2×C4×D411yescharacteristic
382C2×C32#57611yescharacteristic
383C2×C32#57811yescharacteristic
384C3⋊D3—44no—
385C3×D3—22no—
386#41—98no—
387#41—184no—
388C2×Q8—32no—
389C2×D4—92no—
390C2×D4—182no—
391C22×C4—31no—
392C22×C4—182no—
393C22×C4—182no—
394C22×C4—182no—
395C22×C4—182no—
396Q16—34no—
397SD16—98no—
398D8—94no—
399M16—62no—
400C2×C8—31no—
401C2×C8—34no—
402C2×C8—31no—
403C2×C8C2×D3211yescharacteristic
404C2×C8C2×D3211yescharacteristic
405C4⋊C4—31no—
406C4⋊C4—31no—
407C4⋊C4—32no—
408C4⋊C4—62no—
409C4⋊C4—92no—
410C4⋊C4—182no—
411C4⋊C4—182no—
412C22⋊C4—31no—
413C22⋊C4—31no—
414C22⋊C4—182no—
415C22⋊C4—182no—
416C42—31no—
417C42—62no—
418C42—182no—
419C42C2×D3211yescharacteristic
420C22×C3—21no—
421C22×C3—32no—
422C22×C3—61no—
423C22×C3—61no—
424C22×C3C22×D1211yescharacteristic
425C22×C3C2×D3×D411yescharacteristic
426C2×D3—21no—
427C2×D3—21no—
428C2×D3—64no—
429C2×D3—64no—
430C2×D3—124no—
431C2×D3—122no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—242no—
436C2×D3—242no—
437C2×D3C4×D1212yes—
438C3×C4—22no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—32no—
446C3×C4—41no—
447C3×C4—64no—
448C3×C4—61no—
449C3×C4—61no—
450C3×C4—122no—
451C3×C4C22×C4×D311yescharacteristic
452C3×C4C22×C4×D311yescharacteristic
453C3×C4C2×#23511yescharacteristic
454C3×C4D3×#4111yescharacteristic
455Dic3—21no—
456Dic3—21no—
457Dic3—24no—
458Dic3—42no—
459Dic3—122no—
460Dic3—122no—
461Dic3—242no—
462Dic3C4×D1212yes—
463C32#295111yescharacteristic, complemented, Sylow
464C23—31no—
465C23—182no—
466Q8—34no—
467Q8—62no—
468D4—94no—
469D4—188no—
470D4—182no—
471C2×C4—31no—
472C2×C4—32no—
473C2×C4—32no—
474C2×C4—31no—
475C2×C4—31no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—188no—
479C2×C4—182no—
480C2×C4—722no—
481C2×C4—722no—
482C2×C4—722no—
483C2×C4D3×D1211yescharacteristic
484C2×C4D3×D1211yescharacteristic
485C2×C4C22×D3211yescharacteristic
486C8—21no—
487C8—32no—
488C8—61no—
489C8C4×D3212yes—
490C2×C3—21no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—62no—
494C2×C3C2×C4×D1211yescharacteristic
495C2×C3C4×D3×D411yescharacteristic
496C2×C3#575211yescharacteristic
497C2×C3#575311yescharacteristic
498C2×C3#576611yescharacteristic
499C2×C3#576911yescharacteristic
500D3—22no—
501D3—124no—
502D3—124no—
503D3—244no—
504C22—32no—
505C22—61no—
506C22—61no—
507C22—184no—
508C22—362no—
509C22—362no—
510C22C2×D3×D1211yescharacteristic
511C4—21no—
512C4—21no—
513C4—32no—
514C4—61no—
515C4—61no—
516C4—64no—
517C4—122no—
518C4—362no—
519C4C2×C4×D3211yescharacteristic
520C4D3×#23511yescharacteristic
521C3—21no—
522C3#7856211yescharacteristic, complemented
523C3#7972111yescharacteristic, complemented
524C2—62no—
525C2—364no—
526C2C4×D3×D1211yescharacteristic
527C2#1059468011yescharacteristic
528C2#1059469111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63808C2
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. #10593890C2semidirect
3. C4×#3745C2semidirect
4. C3×C4×Dic12C2semidirect
5. C3×#4689C2semidirect
6. Dic3×Dic12C2semidirect
7. #10590795C2semidirect
8. #10590763C2semidirect
9. D3×#818C2semidirect
10. #10590671C2semidirect
11. #10590362C2semidirect
30. #63808C4semidirect
59. C4×Dic12D3semidirect
64. #4689D3semidirect
74. #3799C2×C4semidirect
80. #3745C2×C4semidirect
91. C3×Dic12C2×C4semidirect
93. C3×D3×C8C2×C4semidirect
98. #3717C2×C4semidirect
267. Dic12C4×D3semidirect
273. D3×C8C4×D3semidirect
463. C32#2951semidirect
522. C3#78562semidirect
523. C3#79721semidirect

Maximal subgroups

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

subgroupindex
C2×#638082
#105938902
C4×#37452
C3×C4×Dic122
C3×#46892
Dic3×Dic122
#105907952
#105907632
D3×#8182
#105906712
#105903622
#797213
#785623