Finite Group Databasebeta

← #11895420

Subgroups — #11895420

Order 1152.

835 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593906C211yesmaximal, characteristic
2#10593856C211yesmaximal, characteristic, complemented
3#10592529C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×#4842C211yesmaximal, characteristic, complemented
6#10590885C212yesmaximal, complemented
7#10590876C212yesmaximal, complemented
8#10590776C212yesmaximal, complemented
9#10590775C212yesmaximal, complemented
10C4×#3715C211yesmaximal, characteristic, complemented
11#10590277C211yesmaximal, characteristic, complemented
12#81090—31nomaximal
13#80369—31nomaximal
14C2×#3795—21no—
15C4×#634C2211yescharacteristic
16C2×C3×#204C2212yes—
17C3×#874C2211yescharacteristic
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63919C2212yes—
22#63918—21no—
23#63914C2212yes—
24#63908—21no—
25#63898C2212yes—
26#63885—22no—
27#63844—21no—
28#63843C2212yes—
29#63839—22no—
30C2×#3715C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63641C2212yes—
33C8×C3⋊Dic3C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#821C2212yes—
36C3×#821C2212yes—
37C3×#817C2212yes—
38#63574C2211yescharacteristic
39#63565C2211yescharacteristic
40#63562C2212yes—
41#63562C2212yes—
42#63562C2211yescharacteristic
43#5722—31no—
44#5718—31no—
45Q8×Dic6—31no—
46#5553—31no—
47C3×#476—31no—
48C3×#460—31no—
49#5163—32no—
50Dic3×SD16—32no—
51#5088—31no—
52#5070—31no—
53C4×#215—31no—
54C4×#214—31no—
55#4870—32no—
56#4852—32no—
57#4848D311yescharacteristic, complemented
58#4842D311yescharacteristic, complemented
59#4830—31no—
60#4830—31no—
61#4830—61no—
62#4762—32no—
63#4761—32no—
64#4760—32no—
65#4760—32no—
66C2×#634D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—21no—
69C2×C3×D12C2312yes—
70C2×C3×D12C2311yescharacteristic
71C2×C3×C4×D3—21no—
72C2×C3×Dic6—21no—
73C2×C3×Dic6C2311yescharacteristic
74C2×#627—22no—
75C2×#625—22no—
76C2×#625—22no—
77C2×D3×Dic3—22no—
78#3795—44no—
79C2×C32×C8C2312yes—
80C32×C42C2311yescharacteristic
81C4⋊(C3⋊Dic3)D411yescharacteristic
82#3750D412yes—
83C4×C3⋊Dic3C2312yes—
84C2×C3⋊(C3⋊C8)C2311yescharacteristic
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3—21no—
93C3×#204—24no—
94#3724—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3715—22no—
99#3362—91noSylow
100C2×#237—61no—
101C2×#235—61no—
102C2×C3×SD16—32no—
103C3×C4⋊Q8—31no—
104C3×#127—31no—
105C3×C4×Q8—31no—
106C3×C4×D4—31no—
107Q8×Dic3—32no—
108#944—62no—
109C2×#215—31no—
110#940—32no—
111#940—32no—
112#939—62no—
113#938—61no—
114D4×Dic3—32no—
115C2×#214—31no—
116#930—61no—
117C2×#204C2×D312yes—
118#893—32no—
119#888—32no—
120#888—32no—
121#888—61no—
122#888—62no—
123#887—32no—
124#887—61no—
125#884—62no—
126#874C2×D311yescharacteristic
127C4×D12C2×D311yescharacteristic
128#869—61no—
129#869C2×D311yescharacteristic
130C4×Dic6—31no—
131C4×Dic6—31no—
132C4×Dic6—61no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C3×#106—32no—
136C3×C4⋊C8—21no—
137C3×C4⋊C8C2×D311yescharacteristic
138C3×C4⋊C8C2×D311yescharacteristic
139C3×#102—32no—
140C3×#102—32no—
141#835—31no—
142#832—32no—
143#832—32no—
144#832—31no—
145#821C2×D312yes—
146#821C2×D312yes—
147#817C2×D312yes—
148Dic3⋊C8—32no—
149Dic3⋊C8—32no—
150Dic3⋊C8—62no—
151C8×Dic3—32no—
152C8×Dic3—32no—
153C8×Dic3—62no—
154#810—31no—
155#809—32no—
156#809—31no—
157#809—32no—
158#808—31no—
159#808—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3×D3—22no—
164C22×C3×D3—21no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3C2×D412yes—
169C2×C3⋊Dic3C2×D412yes—
170#634SD1614yescomplemented
171C2×C3×Dic3—21no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—21no—
174C2×C3×Dic3—21no—
175C3×D12—21no—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—22no—
179C3×D12—42no—
180C3×D12—81no—
181C3×C4×D3—42no—
182C3×Dic6—21no—
183C3×Dic6—81no—
184C3×Dic6#4112yescomplemented
185#627—82no—
186#625—44no—
187#625—82no—
188D3×Dic3—44no—
189C32×C8—22no—
190C3⋊(C3⋊C8)—21no—
191C3⋊(C3⋊C8)—21no—
192Q82—91no—
193#550—91no—
194#486—92no—
195#486—91no—
196#476—31no—
197#476—92no—
198#460—31no—
199#460—92no—
200C8×Q8—91no—
201C4×SD16—92no—
202C4×SD16—91no—
203C2×C3×Q8—31no—
204C2×C3×Q8—61no—
205C2×C3×D4—32no—
206C2×C3×D4—31no—
207C2×C3×D4—61no—
208C2×C3×D4—61no—
209C22×C3×C4—61no—
210C2×#67—62no—
211C2×#67—62no—
212C2×#67—62no—
213C2×#67—62no—
214C22×Dic3—62no—
215#237—124no—
216#235—124no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12C22×D312yes—
220C2×D12C22×D311yescharacteristic
221C2×C4×D3—21no—
222C2×C4×D3—62no—
223C2×Dic6—21no—
224C2×Dic6—31no—
225C2×Dic6—31no—
226C2×Dic6—61no—
227C2×Dic6—62no—
228C2×Dic6—62no—
229C2×Dic6C22×D311yescharacteristic
230C3×SD16—64no—
231C2×C3×C8—22no—
232C2×C3×C8C22×D312yes—
233C2×C3×C8C22×D312yes—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—61no—
238C3×C4⋊C4—61no—
239C3×C22⋊C4—61no—
240C3×C42—21no—
241C3×C42—61no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244#217—62no—
245#215—62no—
246#214—62no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—62no—
249C4⋊Dic3—21no—
250C4⋊Dic3—31no—
251C4⋊Dic3—31no—
252C4⋊Dic3—61no—
253C4⋊Dic3—62no—
254C4⋊Dic3C22×D311yescharacteristic
255C4⋊Dic3C22×D311yescharacteristic
256C4⋊Dic3C22×D312yes—
257Dic3⋊C4—21no—
258Dic3⋊C4—32no—
259Dic3⋊C4—32no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264C4×Dic3—21no—
265C4×Dic3—32no—
266C4×Dic3—32no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—61no—
276#204—24no—
277C22×C32C22×D411yescharacteristic
278C2×C3×D3—41no—
279C2×C3×D3—42no—
280C2×C3×D3—42no—
281C2×C3×D3—41no—
282C2×C3×D3—41no—
283C2×C3×D3—42no—
284C32×C4—21no—
285C32×C4C2×SD1612yes—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—22no—
289C3⋊Dic3C2×SD1614yes—
290C3×Dic3—22no—
291C3×Dic3—41no—
292C3×Dic3—41no—
293C3×Dic3—42no—
294C2×#41—181no—
295C2×SD16—32no—
296C2×SD16—91no—
297C4⋊Q8—31no—
298C4⋊Q8—92no—
299C4⋊Q8—181no—
300C4⋊Q8—182no—
301#127—31no—
302#127—92no—
303#121—182no—
304#121—181no—
305C4×Q8—31no—
306C4×Q8—91no—
307C4×Q8—92no—
308C4×Q8—181no—
309C4×D4—31no—
310C4×D4—92no—
311#106—32no—
312#106—91no—
313C4⋊C8—92no—
314C4⋊C8D3211yescharacteristic
315#103—91no—
316#102—32no—
317#102—32no—
318#102—91no—
319#102—92no—
320#102—92no—
321C4×C8—92no—
322C4×C8—91no—
323C23×C3—62no—
324C23×C3—61no—
325C22×D3—21no—
326C22×D3—22no—
327C3×Q8—32no—
328C3×Q8—61no—
329C3×Q8—241no—
330C3×D4—61no—
331C3×D4—62no—
332C3×D4—62no—
333C3×D4—61no—
334C3×D4—122no—
335C3×D4—241no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—61no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—122no—
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350#67—124no—
351#67—124no—
352#67—242no—
353#67—242no—
354C2×Dic3—21no—
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—21no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—124no—
365D12—22no—
366D12—21no—
367D12—21no—
368D12—22no—
369D12—42no—
370D12—81no—
371C4×D3—42no—
372C4×D3—124no—
373Dic6—21no—
374Dic6—34no—
375Dic6—34no—
376Dic6—64no—
377Dic6—81no—
378Dic6—242no—
379Dic6—242no—
380Dic6#23712yescomplemented
381C3×C8—22no—
382C3×C8—22no—
383C3×C8—42no—
384C3⋊C8—62no—
385C3⋊C8—61no—
386C3⋊C8—61no—
387C3⋊C8—61no—
388C3⋊C8—61no—
389C3⋊C8—121no—
390C2×C32#54811yescharacteristic
391C2×C32C22×SD1611yescharacteristic
392C2×C32#57611yescharacteristic
393C3×D3—81no—
394C3×D3—82no—
395#41—364no—
396C2×Q8—31no—
397C2×Q8—61no—
398C2×Q8—91no—
399C2×Q8—182no—
400C2×D4—31no—
401C2×D4—32no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—182no—
405C2×D4—182no—
406C22×C4—61no—
407C22×C4—182no—
408SD16—64no—
409SD16—182no—
410C2×C8—91no—
411C2×C8—91no—
412C2×C8C2×D3212yes—
413C4⋊C4—31no—
414C4⋊C4—32no—
415C4⋊C4—31no—
416C4⋊C4—61no—
417C4⋊C4—61no—
418C4⋊C4—92no—
419C4⋊C4—91no—
420C4⋊C4—182no—
421C4⋊C4—182no—
422C22⋊C4—61no—
423C22⋊C4—182no—
424C42—61no—
425C42—92no—
426C42—182no—
427C42C2×D3211yescharacteristic
428C22×C3—21no—
429C22×C3—122no—
430C22×C3—122no—
431C22×C3—121no—
432C22×C3—121no—
433C22×C3—122no—
434C22×C3—121no—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C2×D3—41no—
438C2×D3—41no—
439C2×D3—42no—
440C2×D3—42no—
441C2×D3—41no—
442C2×D3—42no—
443C3×C4—21no—
444C3×C4—21no—
445C3×C4—22no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—41no—
449C3×C4—62no—
450C3×C4—121no—
451C3×C4—121no—
452C3×C4—122no—
453C3×C4D3×SD1612yes—
454C3×C4D3×SD1612yes—
455C3×C4C2×#23711yescharacteristic
456C3×C4#100711yescharacteristic
457C3×C4D3×#4111yescharacteristic
458C3×C4#101011yescharacteristic
459Dic3—22no—
460Dic3—34no—
461Dic3—34no—
462Dic3—41no—
463Dic3—42no—
464Dic3—41no—
465Dic3—64no—
466Dic3—62no—
467Dic3—62no—
468Dic3—122no—
469C32#336211yescharacteristic, complemented, Sylow
470C23—61no—
471C23—62no—
472Q8—32no—
473Q8—61no—
474Q8—94no—
475Q8—241no—
476Q8—722no—
477D4—62no—
478D4—61no—
479D4—61no—
480D4—62no—
481D4—122no—
482D4—241no—
483D4—364no—
484D4—722no—
485C2×C4—61no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—61no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—122no—
492C2×C4—364no—
493C2×C4#380211yescharacteristic
494C2×C4#380211yescharacteristic
495C2×C4C22×D3211yescharacteristic
496C8—22no—
497C8—181no—
498C8—181no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—242no—
503C2×C3—241no—
504C2×C3#559811yescharacteristic
505C2×C3#563311yescharacteristic
506C2×C3C2×D3×SD1611yescharacteristic
507C2×C3C2×D3×SD1611yescharacteristic
508C2×C3#577411yescharacteristic
509C2×C3#577411yescharacteristic
510D3—81no—
511D3—82no—
512C22—121no—
513C22—122no—
514C22—122no—
515C22—121no—
516C22—122no—
517C22—121no—
518C22C2×#380211yescharacteristic
519C4—21no—
520C4—62no—
521C4—94no—
522C4—121no—
523C4—122no—
524C4—121no—
525C4—182no—
526C4#6379612yes—
527C4D3×#23711yescharacteristic
528C4#6431511yescharacteristic
529C3—21no—
530C3#8036911yescharacteristic, complemented
531C3#8109011yescharacteristic, complemented
532C2—241no—
533C2—242no—
534C2#1059452511yescharacteristic
535C2C2×#6379611yescharacteristic
536C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593906C2
hypercenterC4⋊C8D32
hypocenterC32#3362
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. #10593856C2semidirect
3. #10592529C2semidirect
4. C3×#4848C2semidirect
5. C3×#4842C2semidirect
6. #10590885C2semidirect
7. #10590876C2semidirect
8. #10590776C2semidirect
9. #10590775C2semidirect
10. C4×#3715C2semidirect
11. #10590277C2semidirect
57. #4848D3semidirect
58. #4842D3semidirect
170. #634SD16semidirect
184. C3×Dic6#41semidirect
380. Dic6#237semidirect
469. C32#3362semidirect
530. C3#80369semidirect
531. C3#81090semidirect

Maximal subgroups

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

subgroupindex
#105939062
#105938562
#105925292
C3×#48482
C3×#48422
#105908852
#105908762
#105907762
#105907752
C4×#37152
#105902772
#810903
#803693