Finite Group Databasebeta

← #11860880

Subgroups — #11860880

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#10593887C212yesmaximal, complemented
3C4×#3746C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic, complemented
5C3×#4689C211yesmaximal, characteristic, complemented
6#10590807C211yesmaximal, characteristic, complemented
7Dic3×D24C211yesmaximal, characteristic, complemented
8#10590747C212yesmaximal, complemented
9D3×#818C211yesmaximal, characteristic, complemented
10#10590670C212yesmaximal, complemented
11#10590360C212yesmaximal, complemented
12#79589—31nomaximal
13#78562—31nomaximal
14C2×#3795C2212yes—
15C2×#3746C2211yescharacteristic
16C4×#634C2212yes—
17C2×C3×D24C2211yescharacteristic
18C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
19C2×C3×D3×C8C2211yescharacteristic
20C3×C4×D12C2212yes—
21C3×#872C2211yescharacteristic
22#63902—22no—
23Dic3×D12C2212yes—
24D3×C4⋊Dic3C2212yes—
25#63879—22no—
26#63878—22no—
27D3×Dic3⋊C4—22no—
28#63844C2212yes—
29C2×#3716C2212yes—
30#63807C418yescomplemented
31C32×C4×C8C2211yescharacteristic
32#63645C2211yescharacteristic
33#63643C2212yes—
34C3×#821C2212yes—
35C3×#818C2211yescharacteristic
36C3×#815C2211yescharacteristic
37C3×C8×Dic3C2211yescharacteristic
38C3×#803C2211yescharacteristic
39#63575C2212yes—
40#63567C2212yes—
41#63563C2212yes—
42C2×#912—31no—
43C2×#904—31no—
44#5546—32no—
45#5523—32no—
46C3×C4×D8—31no—
47C3×#405—31no—
48Dic3×D8—31no—
49#5133—32no—
50C2×#818—31no—
51#5018—32no—
52D3×#107—31no—
53#4873—31no—
54#4771—32no—
55#4757—32no—
56#4710—32no—
57#4710—32no—
58C4×Dic12—31no—
59C4×Dic12—31no—
60C4×Dic12—31no—
61C4×Dic12—61no—
62C4×D24—31no—
63C4×D24D311yescharacteristic, complemented
64#4689D311yescharacteristic, complemented
65C2×#634C2312yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3C2311yescharacteristic
69C2×#625—22no—
70C2×D3×Dic3—22no—
71C2×D3×Dic3—22no—
72C2×D3×Dic3—22no—
73#3795—24no—
74#3795C2×C418yescomplemented
75C2×C32×C8C2311yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C32×C42C2311yescharacteristic
78C4⋊(C3⋊Dic3)C2312yes—
79#3750—22no—
80C4×C3⋊Dic3—22no—
81#3746C2×C414yescomplemented
82C3×(C2×D3)⋊C4—22no—
83C3×(C2×D3)⋊C4D411yescharacteristic
84C3×(C2×D3)⋊C4D411yescharacteristic
85C3×C4⋊Dic3C2312yes—
86C3×Dic3⋊C4D411yescharacteristic
87C3×Dic3⋊C4D411yescharacteristic
88C3×C4×Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2311yescharacteristic
91C3×D24C2×C414yescomplemented
92C3×ΓL(1,𝔽25)—22no—
93C3×D3×C8C2×C414yescomplemented
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3716C2×C418yescomplemented
99#2951—91noSylow
100C2×#237—32no—
101C2×#235—32no—
102C2×C3×D8—31no—
103C2×C3×M16—31no—
104C22×C3×C8—31no—
105C3×C4×D4—32no—
106C3×#117—31no—
107D4×Dic3—32no—
108C2×#214—32no—
109C4×#67—62no—
110C2×C4⋊Dic3—32no—
111C2×Dic3⋊C4—62no—
112#912—38no—
113C2×Dic12—31no—
114C2×Dic12—31no—
115C2×Dic12—61no—
116#904—38no—
117C2×D24C2×D311yescharacteristic
118C2×#204—32no—
119C2×ΓL(1,𝔽25)C2×D311yescharacteristic
120C2×D3×C8C2×D311yescharacteristic
121#892—62no—
122D3×C4⋊C4—32no—
123D3×C4⋊C4—62no—
124#887—32no—
125#67⋊C4—62no—
126#67⋊C4—62no—
127#67⋊C4—62no—
128#877—62no—
129C4×D12—32no—
130C4×D12C2×D312yes—
131#872C2×D311yescharacteristic
132C4×Dic6—32no—
133C4×Dic6—32no—
134C4×Dic6—32no—
135C4×Dic6—62no—
136C3×#107—31no—
137C3×#102—32no—
138C3×#97—31no—
139C3×#97—31no—
140C3×C4×C8—21no—
141C3×C4×C8—31no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#832—32no—
145#821—32no—
146#821C2×D312yes—
147#818—31no—
148#818—31no—
149#818—32no—
150#818—61no—
151#818C2×D311yescharacteristic
152#816—32no—
153#816—32no—
154#816—32no—
155#816—62no—
156#815C2×D311yescharacteristic
157C8×Dic3C2×D311yescharacteristic
158#810—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—
167C2×C3⋊Dic3—22no—
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×D3C22×C412yes—
178C3×C4×D3#4112yes—
179#625—28no—
180D3×Dic3—28no—
181D3×Dic3—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—91no—
192C4×Q16—91no—
193C4×D8—31no—
194C4×D8—91no—
195C2×#107—91no—
196#417—92no—
197#405—31no—
198C2×C3×D4—32no—
199C22×C3×C4—31no—
200C22×C3×C4—62no—
201C2×#67—62no—
202C2×#67—62no—
203C22×Dic3—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—62no—
213C2×C4×D3—62no—
214C2×C4×D3—62no—
215C2×C4×D3C22×D311yescharacteristic
216C2×Dic6—32no—
217C2×Dic6—32no—
218C2×Dic6—62no—
219C3×D8—34no—
220C3×M16—62no—
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—31no—
224C2×C3×C8—34no—
225C2×C3×C8—31no—
226C2×C3×C8C22×D311yescharacteristic
227C2×C3×C8C22×D311yescharacteristic
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—32no—
233C3×C22⋊C4—31no—
234C3×C22⋊C4—31no—
235C3×C22⋊C4—62no—
236C3×C42—21no—
237C3×C42—31no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—62no—
241#214—38no—
242(C2×D3)⋊C4—22no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4D1211yescharacteristic
245(C2×D3)⋊C4D1211yescharacteristic
246C4⋊Dic3—32no—
247C4⋊Dic3—32no—
248C4⋊Dic3—62no—
249C4⋊Dic3—62no—
250C4⋊Dic3C22×D312yes—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253Dic3⋊C4—62no—
254Dic3⋊C4—62no—
255Dic3⋊C4—62no—
256Dic3⋊C4—122no—
257Dic3⋊C4D1211yescharacteristic
258Dic3⋊C4D1211yescharacteristic
259C4×Dic3—62no—
260C4×Dic3—62no—
261C4×Dic3—62no—
262C4×Dic3—62no—
263C4×Dic3—122no—
264C4×Dic3C22×D311yescharacteristic
265C2×C3⋊C8C22×D311yescharacteristic
266C2×C3⋊C8C22×D311yescharacteristic
267Dic12—34no—
268Dic12—34no—
269Dic12—64no—
270D24C4×D314yescomplemented
271#204—38no—
272ΓL(1,𝔽25)—22no—
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—21no—
282C32×C4—21no—
283C32×C4C23×C411yescharacteristic
284C32×C4C2×#4111yescharacteristic
285C3⋊Dic3—24no—
286C3⋊Dic3—42no—
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—31no—
297C22×C8—31no—
298C4×Q8—92no—
299C4×Q8—92no—
300C4×D4—32no—
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—92no—
312#103—92no—
313#102—32no—
314#102—92no—
315#97—31no—
316#97—31no—
317C4×C8—31no—
318C4×C8D3211yescharacteristic
319C23×C3—31no—
320C23×C3—62no—
321C22×D3—22no—
322C22×D3C2×D1211yescharacteristic
323C3×D4—34no—
324C3×D4—62no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
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—62no—
334C2×C3×C4—242no—
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341#67—68no—
342#67—68no—
343C2×Dic3—22no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—68no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—242no—
352C2×Dic3—242no—
353C2×Dic3C2×D1211yescharacteristic
354C2×Dic3C2×D1211yescharacteristic
355C2×Dic3C2×D1211yescharacteristic
356D12—22no—
357D12C2×C4×D314yes—
358C4×D3—68no—
359C4×D3—82no—
360C4×D3—242no—
361C4×D3—242no—
362C4×D3C2×C4×D312yes—
363C4×D3#23512yes—
364Dic6—34no—
365Dic6—34no—
366Dic6—64no—
367Dic6—62no—
368Dic6—62no—
369Dic6—122no—
370C3×C8—21no—
371C3×C8—21no—
372C3×C8—22no—
373C3×C8—32no—
374C3×C8—41no—
375C3×C8—61no—
376C3×C8C2×C4×D312yes—
377C3×C8C2×C4×D312yes—
378C3⋊C8—21no—
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—182no—
393C22×C4—182no—
394C22×C4—182no—
395Q16—94no—
396SD16—98no—
397D8—34no—
398M16—62no—
399C2×C8—31no—
400C2×C8—34no—
401C2×C8—31no—
402C2×C8C2×D3211yescharacteristic
403C2×C8C2×D3211yescharacteristic
404C4⋊C4—31no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4—92no—
408C4⋊C4—182no—
409C4⋊C4—182no—
410C4⋊C4—182no—
411C22⋊C4—31no—
412C22⋊C4—31no—
413C22⋊C4—62no—
414C22⋊C4—182no—
415C42—31no—
416C42—182no—
417C42—182no—
418C42C2×D3211yescharacteristic
419C22×C3—21no—
420C22×C3—32no—
421C22×C3—61no—
422C22×C3—61no—
423C22×C3—64no—
424C22×C3—122no—
425C22×C3—122no—
426C22×C3C22×D1211yescharacteristic
427C22×C3C2×D3×D411yescharacteristic
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—24no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3C4×D1212yes—
434C3×C4—22no—
435C3×C4—21no—
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—32no—
442C3×C4—41no—
443C3×C4—61no—
444C3×C4—61no—
445C3×C4—122no—
446C3×C4C22×C4×D311yescharacteristic
447C3×C4C22×C4×D311yescharacteristic
448C3×C4C2×#23511yescharacteristic
449C3×C4D3×#4111yescharacteristic
450Dic3—21no—
451Dic3—21no—
452Dic3—42no—
453Dic3—64no—
454Dic3—64no—
455Dic3—124no—
456Dic3—122no—
457Dic3—122no—
458Dic3—242no—
459Dic3C4×D1212yes—
460C32#295111yescharacteristic, complemented, Sylow
461C23—31no—
462C23—62no—
463Q8—94no—
464Q8—182no—
465D4—34no—
466D4—62no—
467D4—188no—
468C2×C4—31no—
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—31no—
472C2×C4—31no—
473C2×C4—62no—
474C2×C4—188no—
475C2×C4—182no—
476C2×C4—182no—
477C2×C4—242no—
478C2×C4—722no—
479C2×C4—722no—
480C2×C4D3×D1211yescharacteristic
481C2×C4D3×D1211yescharacteristic
482C2×C4C22×D3211yescharacteristic
483C8—21no—
484C8—32no—
485C8—61no—
486C8C4×D3212yes—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—62no—
491C2×C3—124no—
492C2×C3C2×C4×D1211yescharacteristic
493C2×C3C4×D3×D411yescharacteristic
494C2×C3#575211yescharacteristic
495C2×C3#575311yescharacteristic
496C2×C3#575711yescharacteristic
497C2×C3#577111yescharacteristic
498D3—22no—
499D3—44no—
500C22—32no—
501C22—61no—
502C22—61no—
503C22—64no—
504C22—122no—
505C22—122no—
506C22C2×D3×D1211yescharacteristic
507C4—21no—
508C4—21no—
509C4—32no—
510C4—61no—
511C4—61no—
512C4—122no—
513C4—184no—
514C4—362no—
515C4C2×C4×D3211yescharacteristic
516C4D3×#23511yescharacteristic
517C3—21no—
518C3#7856211yescharacteristic, complemented
519C3#7958911yescharacteristic, complemented
520C2—62no—
521C2—124no—
522C2C4×D3×D1211yescharacteristic
523C2#1059467811yescharacteristic
524C2#1059469211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#63807C2
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. #10593887C2semidirect
3. C4×#3746C2semidirect
4. C3×C4×D24C2semidirect
5. C3×#4689C2semidirect
6. #10590807C2semidirect
7. Dic3×D24C2semidirect
8. #10590747C2semidirect
9. D3×#818C2semidirect
10. #10590670C2semidirect
11. #10590360C2semidirect
30. #63807C4semidirect
63. C4×D24D3semidirect
64. #4689D3semidirect
74. #3795C2×C4semidirect
81. #3746C2×C4semidirect
91. C3×D24C2×C4semidirect
93. C3×D3×C8C2×C4semidirect
98. #3716C2×C4semidirect
270. D24C4×D3semidirect
273. D3×C8C4×D3semidirect
460. C32#2951semidirect
518. C3#78562semidirect
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
#105938872
C4×#37462
C3×C4×D242
C3×#46892
#105908072
Dic3×D242
#105907472
D3×#8182
#105906702
#105903602
#795893
#785623