Finite Group Databasebeta

← #11898309

Subgroups — #11898309

Order 1152.

859 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593906C211yesmaximal, characteristic
2#10593864C211yesmaximal, characteristic, complemented
3C8×#634C211yesmaximal, characteristic, complemented
4C3×#4693C211yesmaximal, characteristic, complemented
5C3×C4×#204C211yesmaximal, characteristic, complemented
6#10590884C212yesmaximal, complemented
7#10590876C212yesmaximal, complemented
8#10590775C212yesmaximal, complemented
9#10590748C212yesmaximal, complemented
10#10590364C211yesmaximal, characteristic, complemented
11#10590363C211yesmaximal, characteristic, complemented
12#81755—31nomaximal
13#79637—31nomaximal
14C2×#3795—21no—
15C4×#634C2211yescharacteristic
16C2×C3×#204C2211yescharacteristic
17C2×C3×#204C2212yes—
18C2×C3×#204C2212yes—
19C3×#874C2211yescharacteristic
20C3×C4×D12C2211yescharacteristic
21C3×#869C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic
23#63914C2212yes—
24#63908—21no—
25#63898C2212yes—
26#63885—22no—
27#63873C2212yes—
28#63869—21no—
29#63847—22no—
30#63844—21no—
31#63843C2212yes—
32C2×#3715C2212yes—
33C2×#3715C2212yes—
34C32×C4×C8C2211yescharacteristic
35#63641C2212yes—
36C8×C3⋊Dic3C2212yes—
37C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
38C3×#821C2211yescharacteristic
39C3×#817C2211yescharacteristic
40C3×#816C2211yescharacteristic
41#63565C2212yes—
42#63562C2212yes—
43#5721—31no—
44#5718—31no—
45#5567—31no—
46#5553—31no—
47C3×#492—31no—
48C3×C4×SD16—31no—
49#5175—32no—
50#5175—32no—
51#5163—32no—
52#5162—32no—
53Dic3×SD16—32no—
54#5083—31no—
55#5075—31no—
56#5027—31no—
57#5019—31no—
58#4852—32no—
59#4818—32no—
60#4762—32no—
61#4693D311yescharacteristic, complemented
62C4×#204D311yescharacteristic, complemented
63C8×Dic6—31no—
64C8×Dic6—31no—
65C8×Dic6—61no—
66C2×#634D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6C2312yes—
73C2×C3×Dic6C2311yescharacteristic
74C2×#625—22no—
75C2×#625—22no—
76C2×D3×Dic3—22no—
77#3795—44no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)D411yescharacteristic
82#3750D412yes—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×Dic3⋊C4—21no—
91C3×C4×Dic3—21no—
92C3×#204—22no—
93C3×#204—24no—
94C3×#204—42no—
95#3724—22no—
96#3724—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99Dic32—22no—
100#3715—42no—
101#3715—42no—
102#3392—91noSylow
103C2×#237—61no—
104C2×#235—61no—
105C2×C3×SD16—32no—
106C2×C3×SD16—31no—
107C2×C3×SD16—32no—
108C3×C4⋊Q8—31no—
109C3×#127—31no—
110C3×C4×Q8—31no—
111C3×C4×D4—31no—
112Q8×Dic3—32no—
113#944—32no—
114#944—32no—
115C2×#215—32no—
116C2×#215—32no—
117#940—32no—
118#940—32no—
119#939—62no—
120#938—61no—
121D4×Dic3—32no—
122C2×#214—32no—
123C2×#214—32no—
124#930—61no—
125C2×#204C2×D311yescharacteristic
126C2×#204C2×D312yes—
127C2×#204C2×D312yes—
128#893—32no—
129#890—61no—
130#889—62no—
131#889—62no—
132#887—32no—
133#887—61no—
134#884—62no—
135#874C2×D311yescharacteristic
136C4×D12C2×D311yescharacteristic
137#870—61no—
138#869C2×D311yescharacteristic
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C4×Dic6—61no—
143C4×Dic6C2×D311yescharacteristic
144C3×#106—31no—
145C3×#103—31no—
146C3×#102—31no—
147C3×C4×C8—21no—
148C3×C4×C8C2×D311yescharacteristic
149C3×C4×C8C2×D311yescharacteristic
150#835—32no—
151#832—32no—
152#821C2×D311yescharacteristic
153#817C2×D311yescharacteristic
154#816C2×D311yescharacteristic
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—62no—
158C8×Dic3—32no—
159C8×Dic3—32no—
160C8×Dic3—62no—
161#810—32no—
162#809—32no—
163C4⋊(C3⋊C8)—31no—
164C4⋊(C3⋊C8)—31no—
165C4⋊(C3⋊C8)—61no—
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3⋊Dic3C2×D412yes—
172C2×C3⋊Dic3C2×D412yes—
173#634SD1614yescomplemented
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C3×D12—21no—
179C3×D12—22no—
180C3×D12—21no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×C4×D3—42no—
185C3×Dic6—21no—
186C3×Dic6—22no—
187C3×Dic6—21no—
188C3×Dic6—22no—
189#625—44no—
190#625—82no—
191D3×Dic3—44no—
192C32×C8—21no—
193C32×C8#4112yescomplemented
194C3⋊(C3⋊C8)—22no—
195#557—91no—
196#550—91no—
197#492—31no—
198#492—92no—
199#461—92no—
200#461—91no—
201#460—92no—
202#460—91no—
203C8×Q8—91no—
204C4×SD16—31no—
205C4×SD16—92no—
206C2×C3×Q8—32no—
207C2×C3×Q8—31no—
208C2×C3×D4—32no—
209C2×C3×D4—31no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C22×C3×C4—61no—
213C2×#67—62no—
214C2×#67—62no—
215C2×#67—62no—
216C2×#67—62no—
217C22×Dic3—62no—
218#237—124no—
219#235—124no—
220C2×D12—21no—
221C2×D12—21no—
222C2×D12C22×D312yes—
223C2×D12C22×D311yescharacteristic
224C2×C4×D3—21no—
225C2×C4×D3—62no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—61no—
229C2×Dic6C22×D312yes—
230C2×Dic6C22×D311yescharacteristic
231C3×SD16—64no—
232C3×SD16—62no—
233C3×SD16—122no—
234C2×C3×C8—21no—
235C2×C3×C8—21no—
236C2×C3×C8C22×D311yescharacteristic
237C2×C3×C8C22×D311yescharacteristic
238C2×C3×C8C22×D311yescharacteristic
239C2×C3×C8C22×D311yescharacteristic
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—61no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—61no—
245C3×C22⋊C4—61no—
246C3×C42—21no—
247C3×C42—61no—
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D311yescharacteristic
250#217—62no—
251#215—122no—
252#215—122no—
253#214—122no—
254#214—122no—
255(C2×D3)⋊C4—21no—
256(C2×D3)⋊C4—62no—
257C4⋊Dic3—21no—
258C4⋊Dic3—21no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3C22×D311yescharacteristic
264C4⋊Dic3C22×D311yescharacteristic
265Dic3⋊C4—21no—
266Dic3⋊C4—32no—
267Dic3⋊C4—32no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274C4×Dic3—21no—
275C4×Dic3—32no—
276C4×Dic3—32no—
277C4×Dic3—62no—
278C4×Dic3—62no—
279C4×Dic3—62no—
280C2×C3⋊C8—32no—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—62no—
283#204—22no—
284#204—24no—
285#204—42no—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—42no—
288C2×C3×D3—41no—
289C2×C3×D3—42no—
290C2×C3×D3—41no—
291C2×C3×D3—41no—
292C2×C3×D3—42no—
293C32×C4—21no—
294C32×C4C2×SD1612yes—
295C32×C4C2×#4111yescharacteristic
296C32×C4H(5,𝔽2)11yescharacteristic
297C3⋊Dic3—22no—
298C3⋊Dic3C2×SD1614yes—
299C3×Dic3—42no—
300C3×Dic3—41no—
301C3×Dic3—41no—
302C3×Dic3—41no—
303C2×#41—181no—
304C2×SD16—31no—
305C2×SD16—32no—
306C2×SD16—32no—
307C2×SD16—92no—
308C2×SD16—92no—
309C4⋊Q8—31no—
310C4⋊Q8—92no—
311#127—31no—
312#127—92no—
313#125—181no—
314#125—182no—
315#121—182no—
316#121—181no—
317C4×Q8—31no—
318C4×Q8—91no—
319C4×Q8—92no—
320C4×Q8—181no—
321C4×D4—31no—
322C4×D4—92no—
323#106—31no—
324C4⋊C8—92no—
325C4⋊C8—91no—
326#103—31no—
327#103—92no—
328#102—31no—
329#102—92no—
330C4×C8—92no—
331C4×C8D3211yescharacteristic
332C23×C3—62no—
333C23×C3—61no—
334C22×D3—21no—
335C22×D3—22no—
336C3×Q8—62no—
337C3×Q8—61no—
338C3×Q8—61no—
339C3×Q8—62no—
340C3×D4—62no—
341C3×D4—61no—
342C3×D4—61no—
343C3×D4—62no—
344C3×D4—122no—
345C3×D4—241no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—61no—
350C2×C3×C4—62no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—122no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360#67—124no—
361#67—124no—
362#67—242no—
363#67—242no—
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—22no—
367C2×Dic3—21no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—32no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—124no—
375D12—21no—
376D12—22no—
377D12—22no—
378D12—21no—
379D12—42no—
380D12—81no—
381C4×D3—42no—
382C4×D3—124no—
383Dic6—21no—
384Dic6—22no—
385Dic6—22no—
386Dic6—21no—
387Dic6—34no—
388Dic6—34no—
389Dic6—64no—
390C3×C8—21no—
391C3×C8—21no—
392C3×C8—22no—
393C3×C8—41no—
394C3×C8#23512yescomplemented
395C3×C8#23712yescomplemented
396C3⋊C8—62no—
397C3⋊C8—62no—
398C3⋊C8—122no—
399C2×C32#55011yescharacteristic
400C2×C32C22×SD1611yescharacteristic
401C2×C32#57711yescharacteristic
402C3×D3—81no—
403C3×D3—82no—
404#41—364no—
405C2×Q8—31no—
406C2×Q8—32no—
407C2×Q8—91no—
408C2×D4—31no—
409C2×D4—32no—
410C2×D4—61no—
411C2×D4—61no—
412C2×D4—182no—
413C2×D4—182no—
414C22×C4—61no—
415C22×C4—182no—
416SD16—62no—
417SD16—64no—
418SD16—122no—
419SD16—362no—
420SD16—362no—
421C2×C8—92no—
422C2×C8C2×D3211yescharacteristic
423C2×C8C2×D3211yescharacteristic
424C4⋊C4—31no—
425C4⋊C4—31no—
426C4⋊C4—61no—
427C4⋊C4—61no—
428C4⋊C4—61no—
429C4⋊C4—92no—
430C4⋊C4—91no—
431C4⋊C4—182no—
432C4⋊C4—182no—
433C4⋊C4—182no—
434C22⋊C4—61no—
435C22⋊C4—182no—
436C42—61no—
437C42—92no—
438C42—182no—
439C42C2×D3211yescharacteristic
440C22×C3—21no—
441C22×C3—121no—
442C22×C3—122no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3—122no—
446C22×C3—122no—
447C22×C3C2×D3×D411yescharacteristic
448C22×C3C2×D3×D411yescharacteristic
449C2×D3—42no—
450C2×D3—41no—
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—41no—
454C2×D3—41no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—22no—
460C3×C4—41no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4—121no—
464C3×C4—122no—
465C3×C4D3×SD1612yes—
466C3×C4D3×SD1612yes—
467C3×C4C2×#23511yescharacteristic
468C3×C4C2×#23711yescharacteristic
469C3×C4#100411yescharacteristic
470C3×C4#100911yescharacteristic
471Dic3—34no—
472Dic3—34no—
473Dic3—42no—
474Dic3—41no—
475Dic3—41no—
476Dic3—41no—
477Dic3—64no—
478Dic3—62no—
479Dic3—62no—
480Dic3—122no—
481C32#339211yescharacteristic, complemented, Sylow
482C23—61no—
483C23—62no—
484Q8—61no—
485Q8—62no—
486Q8—62no—
487Q8—61no—
488Q8—94no—
489D4—61no—
490D4—62no—
491D4—62no—
492D4—61no—
493D4—122no—
494D4—241no—
495D4—364no—
496D4—722no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—62no—
500C2×C4—61no—
501C2×C4—92no—
502C2×C4—92no—
503C2×C4—122no—
504C2×C4—364no—
505C2×C4#380211yescharacteristic
506C2×C4#380211yescharacteristic
507C2×C4C22×D3211yescharacteristic
508C8—21no—
509C8—182no—
510C8#379512yescomplemented
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—242no—
515C2×C3—241no—
516C2×C3#555311yescharacteristic
517C2×C3#571811yescharacteristic
518C2×C3C2×D3×SD1611yescharacteristic
519C2×C3C2×D3×SD1611yescharacteristic
520C2×C3#576211yescharacteristic
521C2×C3#577011yescharacteristic
522D3—81no—
523D3—82no—
524C22—122no—
525C22—121no—
526C22—121no—
527C22—122no—
528C22—122no—
529C22—121no—
530C22C2×#380211yescharacteristic
531C4—21no—
532C4—94no—
533C4—121no—
534C4—122no—
535C4—121no—
536C4—121no—
537C4—182no—
538C4#6379612yes—
539C4C2×#379511yescharacteristic
540C4#6430711yescharacteristic
541C3—21no—
542C3#7963711yescharacteristic, complemented
543C3#8175511yescharacteristic, complemented
544C2—241no—
545C2—242no—
546C2#1059390611yescharacteristic
547C2C2×#6379611yescharacteristic
548C2#1059468611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10593906C2
hypercenterC4×C8D32
hypocenterC32#3392
LCSG ▷ C2×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. #10593864C2semidirect
3. C8×#634C2semidirect
4. C3×#4693C2semidirect
5. C3×C4×#204C2semidirect
6. #10590884C2semidirect
7. #10590876C2semidirect
8. #10590775C2semidirect
9. #10590748C2semidirect
10. #10590364C2semidirect
11. #10590363C2semidirect
61. #4693D3semidirect
62. C4×#204D3semidirect
173. #634SD16semidirect
193. C32×C8#41semidirect
394. C3×C8#235semidirect
395. C3×C8#237semidirect
481. C32#3392semidirect
510. C8#3795semidirect
542. C3#79637semidirect
543. C3#81755semidirect

Maximal subgroups

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

subgroupindex
#105939062
#105938642
C8×#6342
C3×#46932
C3×C4×#2042
#105908842
#105908762
#105907752
#105907482
#105903642
#105903632
#817553
#796373