Finite Group Databasebeta

← #11860901

Subgroups — #11860901

Order 1152.

1023 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63807C211yesmaximal, characteristic
2#10594359C212yesmaximal, complemented
3#10592572C211yesmaximal, characteristic, complemented
4C3×D3×#107C211yesmaximal, characteristic, complemented
5C3×#4872C211yesmaximal, characteristic, complemented
6#10590807C211yesmaximal, characteristic, complemented
7#10590777C211yesmaximal, characteristic, complemented
8#10590692C211yesmaximal, characteristic, complemented
9#10590607C212yesmaximal, complemented
10#10590590C212yesmaximal, complemented
11#10590461C212yesmaximal, complemented
12#79589—31nomaximal
13#79136—31nomaximal
14C2×#3795C2212yes—
15C2×#3746C2211yescharacteristic
16#64096C2212yes—
17C2×C3×D24C2211yescharacteristic
18C2×C3×D3×C8C2211yescharacteristic
19C3×#893C2212yes—
20C3×D3×C4⋊C4C2212yes—
21C4×#625—22no—
22#63898C2212yes—
23#63879—22no—
24#63878—22no—
25D3×Dic3⋊C4—22no—
26#63855C2211yescharacteristic
27#63844C2212yes—
28C2×#3716C2212yes—
29C2×#3711C2211yescharacteristic
30#63807C418yescomplemented
31C32×#107C2211yescharacteristic
32C8×C3⋊Dic3C2211yescharacteristic
33#63637C2212yes—
34C3×#818C2211yescharacteristic
35C3×C8×Dic3C2211yescharacteristic
36C3×#809C2212yes—
37C3×#807C2212yes—
38#63567C2212yes—
39#63562C2212yes—
40#63555C2211yescharacteristic
41#63554C2211yescharacteristic
42C2×#912—31no—
43C2×#904—31no—
44#5546—32no—
45#5504—32no—
46C3×C4×D8—31no—
47C2×C3×#107—31no—
48Dic3×D8—31no—
49#5101—31no—
50#5018—32no—
51#4966—32no—
52#4889—32no—
53#4889—32no—
54D3×#107D311yescharacteristic, complemented
55#4873—31no—
56#4873—31no—
57#4873—31no—
58#4873—61no—
59#4872—31no—
60#4872D311yescharacteristic, complemented
61#4771—32no—
62#4757—32no—
63C4×Dic12—31no—
64#4689—31no—
65C2×#634C2312yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3C2311yescharacteristic
70C2×#625—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3795—24no—
74#3795C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C32×C4⋊C4C2312yes—
77#3750—22no—
78C4×C3⋊Dic3—22no—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81#3746C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×C4⋊Dic3C2312yes—
84C3×Dic3⋊C4—22no—
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2311yescharacteristic
87C2×C3×C3⋊C8C2311yescharacteristic
88C3×D24C2×C414yescomplemented
89C3×D3×C8C2×C414yescomplemented
90#3724—22no—
91Dic3⋊Dic3D411yescharacteristic
92Dic3⋊Dic3D411yescharacteristic
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3D411yescharacteristic
95(C2×D3)⋊Dic3D411yescharacteristic
96Dic32—22no—
97#3716C2×C418yescomplemented
98#3711—22no—
99#2951—91noSylow
100C2×#237—32no—
101C2×#235—32no—
102C2×C3×D8—31no—
103C22×C3×C8—31no—
104C3×C4×D4—32no—
105C2×C3×C4⋊C4—32no—
106D4×Dic3—32no—
107C2×#214—32no—
108C4×#67—62no—
109C4×#67—62no—
110C4×#67—62no—
111#926—31no—
112C2×Dic3⋊C4—62no—
113C2×#208—31no—
114#912—38no—
115C2×Dic12—31no—
116C2×Dic12—31no—
117C2×Dic12—61no—
118#904—38no—
119C2×D24C2×D311yescharacteristic
120C2×#204—32no—
121C2×ΓL(1,𝔽25)—31no—
122C2×D3×C8C2×D311yescharacteristic
123#893—32no—
124#893C2×D312yes—
125#892—62no—
126D3×C4⋊C4—62no—
127D3×C4⋊C4C2×D312yes—
128#887—32no—
129#887—32no—
130#887—32no—
131#887—62no—
132#67⋊C4—62no—
133#877—62no—
134#872—31no—
135C4×Dic6—32no—
136C3×#107—21no—
137C3×#107—31no—
138C3×#107—32no—
139C3×#107C2×D311yescharacteristic
140C3×#107C2×D311yescharacteristic
141C3×#102—32no—
142C3×C4×C8—31no—
143#832—32no—
144#818C2×D311yescharacteristic
145#816—32no—
146#815—31no—
147#815—31no—
148#815—31no—
149C8×Dic3—31no—
150C8×Dic3—31no—
151C8×Dic3—61no—
152C8×Dic3C2×D311yescharacteristic
153#810—32no—
154#810—32no—
155#810—32no—
156#810—62no—
157#809—32no—
158#809C2×D312yes—
159#807C2×D312yes—
160#803—31no—
161C22×C3×D3—22no—
162C22×C3×D3C2×D411yescharacteristic
163C2×C32×C4—22no—
164C2×C32×C4C2411yescharacteristic
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3C2×D411yescharacteristic
167C2×C3⋊Dic3C2×D411yescharacteristic
168#634—22no—
169#634C22×C414yes—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D411yescharacteristic
172C2×C3×Dic3C2×D411yescharacteristic
173C2×C3×Dic3C2×D411yescharacteristic
174C3×D12—22no—
175C3×D12C22×C414yes—
176C3×C4×D3—82no—
177C3×C4×D3—82no—
178C3×C4×D3C22×C412yes—
179C3×C4×D3#4112yes—
180#625—28no—
181D3×Dic3—28no—
182D3×Dic3—82no—
183C32×C8C22×C412yes—
184C3⋊(C3⋊C8)—21no—
185C3×C3⋊C8—21no—
186C3×C3⋊C8C22×C412yes—
187C2×#135—91no—
188#520—92no—
189#440—92no—
190#440—92no—
191C4×Q16—91no—
192C4×Q16—91no—
193C4×D8—31no—
194C4×D8—91no—
195C2×#107—31no—
196#417—92no—
197#405—91no—
198C2×C3×D4—32no—
199C22×C3×C4—31no—
200C22×C3×C4—62no—
201C22×C3×C4—62no—
202C2×#67—62no—
203C2×#67—62no—
204C22×Dic3—62no—
205C22×Dic3—62no—
206#237—38no—
207#237—64no—
208#235—38no—
209#235—64no—
210C2×D12C22×D312yes—
211C2×C4×D3—22no—
212C2×C4×D3—22no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3C22×D311yescharacteristic
216C2×Dic6—32no—
217C2×Dic6—32no—
218C2×Dic6—62no—
219C3×D8—34no—
220C2×C3×C8—21no—
221C2×C3×C8—31no—
222C2×C3×C8—34no—
223C2×C3×C8—31no—
224C2×C3×C8C22×D311yescharacteristic
225C2×C3×C8C22×D311yescharacteristic
226C3×C4⋊C4—22no—
227C3×C4⋊C4—32no—
228C3×C4⋊C4—62no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C22×D312yes—
231C3×C22⋊C4—62no—
232C3×C42—31no—
233#217—31no—
234#217—31no—
235#217—62no—
236#214—38no—
237(C2×D3)⋊C4—22no—
238(C2×D3)⋊C4—31no—
239(C2×D3)⋊C4—31no—
240(C2×D3)⋊C4—62no—
241C4⋊Dic3—31no—
242C4⋊Dic3—31no—
243C4⋊Dic3C22×D312yes—
244Dic3⋊C4—22no—
245Dic3⋊C4—31no—
246Dic3⋊C4—31no—
247Dic3⋊C4—62no—
248Dic3⋊C4—62no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—122no—
252C4×Dic3—31no—
253C4×Dic3—31no—
254C4×Dic3—61no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C4×Dic3—62no—
258C4×Dic3—62no—
259C4×Dic3—122no—
260C4×Dic3C22×D311yescharacteristic
261#208—62no—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—61no—
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267Dic12—34no—
268Dic12—34no—
269Dic12—64no—
270D24C4×D314yescomplemented
271#204—38no—
272ΓL(1,𝔽25)—62no—
273D3×C8C4×D314yescomplemented
274C22×C32C22×D411yescharacteristic
275C2×C3×D3—21no—
276C2×C3×D3—21no—
277C2×C3×D3—24no—
278C2×C3×D3—42no—
279C2×C3×D3—42no—
280C2×C3×D3C4×D412yes—
281C32×C4—42no—
282C32×C4C23×C411yescharacteristic
283C32×C4C2×#4111yescharacteristic
284C3⋊Dic3—21no—
285C3⋊Dic3—24no—
286C3⋊Dic3—21no—
287C3×Dic3—21no—
288C3×Dic3—21no—
289C3×Dic3—42no—
290C3×Dic3C4×D412yes—
291C2×#41—92no—
292#135—98no—
293C2×Q16—91no—
294C2×SD16—92no—
295C2×D8—31no—
296C2×M16—91no—
297C22×C8—31no—
298C4×Q8—92no—
299C4×Q8—92no—
300C4×D4—32no—
301C4×D4—92no—
302C4×D4—182no—
303C4×D4—182no—
304#117—91no—
305#117—182no—
306C2×C4⋊C4—32no—
307C2×C4⋊C4—182no—
308#107—31no—
309#107—32no—
310#107D3211yescharacteristic
311#103—92no—
312#103—92no—
313#102—32no—
314#102—92no—
315#97—91no—
316#97—91no—
317C4×C8—31no—
318C4×C8—91no—
319C23×C3—31no—
320C23×C3—62no—
321C22×D3—22no—
322C22×D3D3×D411yescharacteristic
323C3×D4—34no—
324C3×D4—62no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—31no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—31no—
332C2×C3×C4—31no—
333C2×C3×C4—42no—
334C2×C3×C4—62no—
335C2×C3×C4—242no—
336C2×C3×C4—242no—
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339#67—68no—
340#67—68no—
341C2×Dic3—22no—
342C2×Dic3—31no—
343C2×Dic3—31no—
344C2×Dic3—31no—
345C2×Dic3—31no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—68no—
351C2×Dic3—122no—
352C2×Dic3—242no—
353C2×Dic3D3×D411yescharacteristic
354C2×Dic3D3×D411yescharacteristic
355C2×Dic3D3×D411yescharacteristic
356D12—22no—
357D12C2×C4×D314yes—
358C4×D3—68no—
359C4×D3—82no—
360C4×D3—82no—
361C4×D3—242no—
362C4×D3C2×C4×D312yes—
363C4×D3#23912yes—
364Dic6—34no—
365Dic6—34no—
366Dic6—64no—
367Dic6—62no—
368Dic6—62no—
369Dic6—122no—
370C3×C8—22no—
371C3×C8—32no—
372C3×C8—61no—
373C3×C8C2×C4×D312yes—
374C3×C8C2×C4×D312yes—
375C3⋊C8—21no—
376C3⋊C8—61no—
377C3⋊C8—61no—
378C3⋊C8—121no—
379C3⋊C8C2×C4×D312yes—
380C2×C32C2×C4×D411yescharacteristic
381C2×C32#57611yescharacteristic
382C2×C32#57811yescharacteristic
383C3×D3—22no—
384C3×D3—44no—
385#41—98no—
386#41—184no—
387C2×Q8—92no—
388C2×D4—32no—
389C2×D4—182no—
390C22×C4—31no—
391C22×C4—62no—
392C22×C4—62no—
393C22×C4—182no—
394C22×C4—182no—
395Q16—94no—
396SD16—98no—
397D8—34no—
398M16—182no—
399C2×C8—31no—
400C2×C8—34no—
401C2×C8—31no—
402C2×C8—91no—
403C2×C8C2×D3211yescharacteristic
404C4⋊C4—32no—
405C4⋊C4—62no—
406C4⋊C4—91no—
407C4⋊C4—91no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4C2×D3212yes—
411C22⋊C4—62no—
412C22⋊C4—91no—
413C22⋊C4—91no—
414C22⋊C4—182no—
415C42—31no—
416C42—91no—
417C42—182no—
418C42—182no—
419C22×C3—21no—
420C22×C3—32no—
421C22×C3—61no—
422C22×C3—61no—
423C22×C3—64no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3C2×D3×D411yescharacteristic
427C22×C3C2×D3×D411yescharacteristic
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—24no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3#89312yes—
434C3×C4—21no—
435C3×C4—21no—
436C3×C4—32no—
437C3×C4—42no—
438C3×C4—42no—
439C3×C4—61no—
440C3×C4—61no—
441C3×C4—82no—
442C3×C4—122no—
443C3×C4C22×C4×D311yescharacteristic
444C3×C4C22×C4×D311yescharacteristic
445C3×C4C2×#23911yescharacteristic
446C3×C4D3×#4111yescharacteristic
447Dic3—21no—
448Dic3—21no—
449Dic3—42no—
450Dic3—62no—
451Dic3—61no—
452Dic3—61no—
453Dic3—64no—
454Dic3—61no—
455Dic3—61no—
456Dic3—64no—
457Dic3—124no—
458Dic3—121no—
459Dic3#89312yes—
460C32#295111yescharacteristic, complemented, Sylow
461C23—31no—
462C23—62no—
463Q8—94no—
464Q8—182no—
465D4—34no—
466D4—62no—
467D4—188no—
468C2×C4—22no—
469C2×C4—31no—
470C2×C4—32no—
471C2×C4—32no—
472C2×C4—31no—
473C2×C4—31no—
474C2×C4—62no—
475C2×C4—91no—
476C2×C4—91no—
477C2×C4—188no—
478C2×C4—182no—
479C2×C4—242no—
480C2×C4—242no—
481C2×C4—722no—
482C2×C4C22×D3211yescharacteristic
483C8—32no—
484C8—61no—
485C8—181no—
486C8C4×D3212yes—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—62no—
491C2×C3—124no—
492C2×C3C2×#89311yescharacteristic
493C2×C3C4×D3×D411yescharacteristic
494C2×C3#575711yescharacteristic
495C2×C3#575711yescharacteristic
496C2×C3#576611yescharacteristic
497C2×C3#577111yescharacteristic
498D3—22no—
499D3—44no—
500C22—32no—
501C22—61no—
502C22—61no—
503C22—64no—
504C22—122no—
505C22—122no—
506C22D32×D411yescharacteristic
507C4—32no—
508C4—42no—
509C4—61no—
510C4—61no—
511C4—122no—
512C4—184no—
513C4—181no—
514C4—181no—
515C4C2×C4×D3211yescharacteristic
516C4D3×#23911yescharacteristic
517C3—21no—
518C3#7913611yescharacteristic, complemented
519C3#7958911yescharacteristic, complemented
520C2—62no—
521C2—124no—
522C2D3×#89311yescharacteristic
523C2#1059473111yescharacteristic
524C2#1059476811yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
prime radicalC2×#63807C2
cosocleC2×C32×C4C24
hypercenter#107D32
hypocenterC32#2951
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10594359C2semidirect
3. #10592572C2semidirect
4. C3×D3×#107C2semidirect
5. C3×#4872C2semidirect
6. #10590807C2semidirect
7. #10590777C2semidirect
8. #10590692C2semidirect
9. #10590607C2semidirect
10. #10590590C2semidirect
11. #10590461C2semidirect
30. #63807C4semidirect
54. D3×#107D3semidirect
60. #4872D3semidirect
74. #3795C2×C4semidirect
81. #3746C2×C4semidirect
88. C3×D24C2×C4semidirect
89. C3×D3×C8C2×C4semidirect
97. #3716C2×C4semidirect
270. D24C4×D3semidirect
273. D3×C8C4×D3semidirect
460. C32#2951semidirect
518. C3#79136semidirect
519. C3#79589semidirect

Maximal subgroups

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

subgroupindex
C2×#638072
#105943592
#105925722
C3×D3×#1072
C3×#48722
#105908072
#105907772
#105906922
#105906072
#105905902
#105904612
#795893
#791363