Finite Group Databasebeta

← #11898387

Subgroups — #11898387

Order 1152.

780 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593879C211yesmaximal, characteristic, complemented
2#10593865C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic, complemented
4C3×#4841C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590862C212yesmaximal
7#10590859C212yesmaximal, complemented
8#10590813C212yesmaximal, complemented
9#10590793C212yesmaximal, complemented
10#10590386C211yesmaximal, characteristic, complemented
11C4×#3714C211yesmaximal, characteristic
12#80421—31nomaximal
13#79912—31nomaximal
14C2×#3744C2212yes—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×#204C2212yes—
18C3×C4×D12C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63871—21no—
22#63864C2212yes—
23#63861—22no—
24#63860C2212yes—
25#63856—21no—
26#63849—21no—
27#63848—22no—
28#63844C2212yes—
29Dic3×Dic6C2212yes—
30#63841—21no—
31C2×#3719C2212yes—
32C2×#3719C2212yes—
33C2×#3714C2211yescharacteristic
34C32×C4⋊C8C2211yescharacteristic
35#63643C2212yes—
36C3×#816C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4×C3⋊C8C2211yescharacteristic
40#63575C2211yescharacteristic
41#63564C2211yescharacteristic
42#63563C2211yescharacteristic
43#5732—31no—
44#5584—31no—
45#5584—31no—
46#5542—31no—
47C3×#461—31no—
48C3×C8×Q8—31no—
49#5168—32no—
50#5166—32no—
51#5092—31no—
52C4×#213—31no—
53#4845—32no—
54#4845—32no—
55#4841—31no—
56#4841—31no—
57#4841—61no—
58#4841D311yescharacteristic, complemented
59#4830D311yescharacteristic, complemented
60#4798—32no—
61#4790—32no—
62#4699—31no—
63C4×Dic12—32no—
64#4696—32no—
65C4×D24—31no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2312yes—
69C2×C3×D12C2311yescharacteristic
70C2×C3×C4×D3—21no—
71C2×C3×Dic6D411yescharacteristic
72C2×C3×Dic6C2312yes—
73C2×C32×C8C2312yes—
74C32×C42C2311yescharacteristic
75#3752—21no—
76C4⋊(C3⋊Dic3)—21no—
77C4⋊(C3⋊Dic3)—21no—
78C4⋊(C3⋊Dic3)C2311yescharacteristic
79#3744—42no—
80C3×(C2×D3)⋊C4—21no—
81C3×C4⋊Dic3—21no—
82C3×C4⋊Dic3—21no—
83C3×C4⋊Dic3D411yescharacteristic
84C3×C4⋊Dic3C2311yescharacteristic
85C3×Dic3⋊C4D412yes—
86C3×C4×Dic3C2312yes—
87C2×C3×C3⋊C8C2311yescharacteristic
88C2×C3×C3⋊C8C2311yescharacteristic
89C3×#204—42no—
90#3724—22no—
91Dic3⋊Dic3—22no—
92#3722—22no—
93#3722—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96Dic32—22no—
97Dic32—22no—
98#3719—24no—
99#3719—42no—
100#3714—22no—
101#3393—91noSylow
102C2×C3×SD16—32no—
103C3×C4⋊Q8—31no—
104C3×C4×Q8—31no—
105C3×C4×D4—31no—
106#947—32no—
107#946—61no—
108#946—61no—
109Q8×Dic3—32no—
110C2×#216—32no—
111C2×#216—32no—
112#936—32no—
113C2×#213—31no—
114#926—61no—
115#924—61no—
116C2×Dic12—32no—
117C2×Dic12—32no—
118C2×D24—31no—
119C2×#204—32no—
120C2×#204—32no—
121C2×#204—62no—
122C2×#204C2×D312yes—
123#898—62no—
124#898—62no—
125#898—62no—
126#897—61no—
127#892—61no—
128#892—61no—
129#892—61no—
130#887—32no—
131#879—62no—
132#875—32no—
133#875—32no—
134C4×D12—31no—
135C4×D12—31no—
136C4×D12—61no—
137C4×D12C2×D311yescharacteristic
138#869—31no—
139#869—31no—
140#869—61no—
141#869C2×D311yescharacteristic
142C4×Dic6—32no—
143C4×Dic6—32no—
144C4×Dic6C2×D311yescharacteristic
145C3×C4⋊C8—21no—
146C3×C4⋊C8—32no—
147C3×C4⋊C8C2×D311yescharacteristic
148C3×C4⋊C8C2×D311yescharacteristic
149C3×#103—32no—
150C3×C4×C8—32no—
151C3×C4×C8—31no—
152#832—31no—
153#821—31no—
154#821—31no—
155#818—31no—
156#816—32no—
157#816—32no—
158#816—62no—
159#816C2×D312yes—
160Dic3⋊C8C2×D312yes—
161C8×Dic3C2×D312yes—
162#809—31no—
163#807—31no—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2411yescharacteristic
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—22no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)—21no—
174C4×C3⋊D3—42no—
175#634—22no—
176#634—22no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—21no—
182C3×D12—21no—
183C3×C4×D3—42no—
184C3×Dic6—22no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C32×C8—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8#4112yes—
190#556—91no—
191#556—91no—
192#495—92no—
193#494—91no—
194#464—92no—
195#464—92no—
196#461—31no—
197#461—91no—
198C8×Q8—31no—
199C4×Q16—92no—
200C4×D8—91no—
201C2×C3×Q8—31no—
202C2×C3×Q8—32no—
203C2×C3×D4—31no—
204C22×C3×C4—61no—
205C2×D12—31no—
206C2×D12—31no—
207C2×D12—61no—
208C2×D12C22×D311yescharacteristic
209C2×C4×D3—21no—
210C2×C4×D3—61no—
211C2×C4×D3—61no—
212C2×C4×D3—121no—
213C2×Dic6—32no—
214C2×Dic6—32no—
215C2×Dic6—62no—
216C2×Dic6D1211yescharacteristic
217C2×Dic6C22×D312yes—
218C3×SD16—122no—
219C2×C3×C8—22no—
220C2×C3×C8—31no—
221C2×C3×C8—31no—
222C2×C3×C8C22×D312yes—
223C2×C3×C8C22×D312yes—
224C3×C4⋊C4—31no—
225C3×C4⋊C4—32no—
226C3×C4⋊C4—31no—
227C3×C4⋊C4—61no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—61no—
230C3×C42—21no—
231C3×C42—32no—
232C3×C42C22×D311yescharacteristic
233C3×C42C22×D311yescharacteristic
234#217—62no—
235#217—62no—
236#216—64no—
237#216—122no—
238#213—62no—
239(C2×D3)⋊C4—21no—
240(C2×D3)⋊C4—62no—
241(C2×D3)⋊C4—62no—
242(C2×D3)⋊C4—62no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—61no—
245(C2×D3)⋊C4—61no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—121no—
249C4⋊Dic3—21no—
250C4⋊Dic3—21no—
251C4⋊Dic3—31no—
252C4⋊Dic3—31no—
253C4⋊Dic3—61no—
254C4⋊Dic3—61no—
255C4⋊Dic3—61no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—121no—
260C4⋊Dic3—121no—
261C4⋊Dic3D1211yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—62no—
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4D1212yes—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C4×Dic3C22×D312yes—
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D311yescharacteristic
274Dic12—64no—
275Dic12—122no—
276D24—62no—
277#204—42no—
278#204—122no—
279#204—122no—
280#204—124no—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—21no—
289C32×C4#13512yes—
290C32×C4C2×#4111yescharacteristic
291C32×C4H(5,𝔽2)11yescharacteristic
292C3⋊Dic3—42no—
293C3⋊Dic3—41no—
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C2×Q16—92no—
299C2×Q16—92no—
300C2×SD16—32no—
301C2×SD16—92no—
302C2×D8—91no—
303C4⋊Q8—31no—
304C4⋊Q8—91no—
305#126—182no—
306#126—182no—
307#124—92no—
308#124—92no—
309C22⋊Q8—181no—
310C22⋊Q8—181no—
311C4×Q8—31no—
312C4×Q8—92no—
313C4×Q8—92no—
314C4×D4—31no—
315C4×D4—91no—
316#117—181no—
317#117—181no—
318#107—91no—
319C4⋊C8—32no—
320C4⋊C8D3211yescharacteristic
321#103—32no—
322#103—92no—
323#102—91no—
324#102—91no—
325C4×C8—32no—
326C4×C8—31no—
327C23×C3—61no—
328C22×D3—21no—
329C22×D3—61no—
330C22×D3—61no—
331C22×D3—121no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×Q8—62no—
335C3×D4—61no—
336C3×D4—61no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—32no—
341C2×C3×C4—32no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4—122no—
345C2×C3×C4C2×D1211yescharacteristic
346C2×C3×C4C2×D1211yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—61no—
354C2×Dic3—62no—
355C2×Dic3—61no—
356C2×Dic3—62no—
357C2×Dic3—121no—
358C2×Dic3—122no—
359C2×Dic3C2×D1212yes—
360C2×Dic3C2×D1212yes—
361D12—21no—
362D12—21no—
363D12—62no—
364D12—61no—
365D12—61no—
366D12—61no—
367D12—61no—
368D12—121no—
369C4×D3—42no—
370C4×D3—122no—
371C4×D3—122no—
372C4×D3—242no—
373Dic6—22no—
374Dic6—22no—
375Dic6—22no—
376Dic6—62no—
377Dic6—62no—
378Dic6—62no—
379Dic6—62no—
380Dic6—122no—
381Dic6—122no—
382C3×C8—22no—
383C3×C8—22no—
384C3×C8—32no—
385C3×C8—42no—
386C3×C8—61no—
387C3⋊C8—21no—
388C3⋊C8#23912yes—
389C2×C32#55011yescharacteristic
390C2×C32C2×#13511yescharacteristic
391C2×C32#57811yescharacteristic
392C3⋊D3—81no—
393C3×D3—81no—
394C2×Q8—31no—
395C2×Q8—32no—
396C2×Q8—92no—
397C2×D4—31no—
398C2×D4—91no—
399C22×C4—61no—
400C22×C4—181no—
401Q16—184no—
402Q16—362no—
403SD16—122no—
404SD16—362no—
405D8—182no—
406C2×C8—31no—
407C2×C8—31no—
408C2×C8C2×D3212yes—
409C4⋊C4—31no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—61no—
413C4⋊C4—61no—
414C4⋊C4—91no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C22⋊C4—61no—
420C22⋊C4—182no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—181no—
425C42—32no—
426C42—182no—
427C42—182no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3—121no—
433C22×C3C22×D1211yescharacteristic
434C22×C3C2×D3×D411yescharacteristic
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—41no—
438C2×D3—122no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—241no—
446C2×D3—241no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—21no—
452C3×C4—41no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—121no—
456C3×C4—122no—
457C3×C4#90412yes—
458C3×C4#91612yes—
459C3×C4#100411yescharacteristic
460C3×C4C2×#23911yescharacteristic
461C3×C4D3×#4111yescharacteristic
462C3×C4#100911yescharacteristic
463Dic3—22no—
464Dic3—22no—
465Dic3—41no—
466Dic3—42no—
467Dic3—121no—
468Dic3—121no—
469Dic3—122no—
470Dic3—122no—
471Dic3—242no—
472Dic3—241no—
473C32#339311yescharacteristic, complemented, Sylow
474C23—61no—
475C23—181no—
476Q8—62no—
477Q8—62no—
478Q8—62no—
479Q8—182no—
480Q8—182no—
481D4—61no—
482D4—61no—
483D4—181no—
484D4—181no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—122no—
490C2×C4—181no—
491C2×C4—182no—
492C2×C4—362no—
493C2×C4D3×D1211yescharacteristic
494C2×C4D3×D1211yescharacteristic
495C2×C4C22×D3211yescharacteristic
496C8—22no—
497C8—32no—
498C8—61no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—241no—
503C2×C3#557711yescharacteristic
504C2×C3#559911yescharacteristic
505C2×C3C2×#90411yescharacteristic
506C2×C3#575311yescharacteristic
507C2×C3C2×#91611yescharacteristic
508C2×C3#577911yescharacteristic
509D3—81no—
510D3—242no—
511D3—241no—
512D3—241no—
513C22—121no—
514C22—121no—
515C22—121no—
516C22—361no—
517C22—361no—
518C22—361no—
519C22C2×D3×D1211yescharacteristic
520C4—21no—
521C4—62no—
522C4—62no—
523C4—121no—
524C4—122no—
525C4—361no—
526C4—362no—
527C4#6380612yes—
528C4#6431411yescharacteristic
529C4D3×#23911yescharacteristic
530C3—21no—
531C3#7991211yescharacteristic, complemented
532C3#8042111yescharacteristic, complemented
533C2—241no—
534C2—721no—
535C2#1059452411yescharacteristic
536C2C2×#6380611yescharacteristic
537C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊C8D32
hypocenterC32#3393
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
1. #10593879C2semidirect
2. #10593865C2semidirect
3. #10592540C2semidirect
4. C3×#4841C2semidirect
5. C3×#4830C2semidirect
7. #10590859C2semidirect
8. #10590813C2semidirect
9. #10590793C2semidirect
10. #10590386C2semidirect
58. #4841D3semidirect
59. #4830D3semidirect
473. C32#3393semidirect
531. C3#79912semidirect
532. C3#80421semidirect

Maximal subgroups

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

subgroupindex
#105938792
#105938652
#105925402
C3×#48412
C3×#48302
#105908622
#105908592
#105908132
#105907932
#105903862
C4×#37142
#804213
#799123