Finite Group Databasebeta

← #11897570

Subgroups — #11897570

Order 1152.

815 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593958C211yesmaximal, characteristic, complemented
2#10593903C211yesmaximal, characteristic, complemented
3C4×#3745C211yesmaximal, characteristic
4C3×#4680C211yesmaximal, characteristic, complemented
5C3×#4679C211yesmaximal, characteristic, complemented
6#10590892C212yesmaximal, complemented
7#10590769C212yesmaximal, complemented
8#10590768C212yesmaximal
9#10590759C212yesmaximal, complemented
10#10590313C211yesmaximal, characteristic, complemented
11#10590300C211yesmaximal, characteristic, complemented
12#81905—31nomaximal
13#79975—31nomaximal
14C2×#3797—21no—
15C2×#3745C2211yescharacteristic
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C4×C4⋊(C3⋊D3)C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918C2212yes—
22#63900—21no—
23#63895—22no—
24#63894C2212yes—
25#63894C2212yes—
26#63888—22no—
27#63871—21no—
28#63871—21no—
29#63869C2212yes—
30C32×C4×C8C2211yescharacteristic
31#63648C2211yescharacteristic
32#63648C2211yescharacteristic
33#63645C2211yescharacteristic
34C3×#817C2212yes—
35C3×#817C2212yes—
36C3×#815C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C4⋊(C3⋊C8)C2211yescharacteristic
39#63575C2212yes—
40#63573C2212yes—
41#63564C2212yes—
42#63564C2212yes—
43#5730—31no—
44#5727—31no—
45#5579—31no—
46Q8×D12—31no—
47C3×#498—31no—
48C3×#446—31no—
49#5087—31no—
50#5084—31no—
51#4871—32no—
52#4870—32no—
53#4869—32no—
54#4856—32no—
55#4847—32no—
56#4846—31no—
57#4842—31no—
58#4842—32no—
59#4711—32no—
60#4702—32no—
61C4×D24—31no—
62C4×D24—31no—
63C4×D24—61no—
64#4680D311yescharacteristic, complemented
65#4679D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—21no—
70C2×C3×Dic6—21no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D411yescharacteristic
73C2×#627—22no—
74C2×#624—22no—
75C2×#624—22no—
76#3797—44no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C32×C42C2311yescharacteristic
80#3752—21no—
81#3752—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3745Q814yescomplemented
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4D412yes—
91C3×C4×Dic3C2312yes—
92C2×C3×C3⋊C8C2312yes—
93#3724—22no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96#3722—22no—
97#3722—22no—
98#3384—91noSylow
99C2×D3×Q8—61no—
100C2×D3×Q8—61no—
101C3×C4⋊Q8—31no—
102C3×C4⋊Q8—31no—
103C3×C4×Q8—31no—
104#946—61no—
105#946—61no—
106#946—62no—
107C2×D24—31no—
108C2×D24—31no—
109C2×D24—61no—
110#897—62no—
111#897—61no—
112#897—61no—
113#896—62no—
114#896—62no—
115#893—32no—
116#893—32no—
117D3×C4⋊C4—61no—
118D3×C4⋊C4—61no—
119#890—32no—
120#888—32no—
121C4×D12—31no—
122C4×D12—31no—
123C4×D12—31no—
124C4×D12—31no—
125C4×D12—32no—
126C4×D12—32no—
127C4×D12—61no—
128C4×D12—61no—
129#870—32no—
130#869—32no—
131#869C2×D311yescharacteristic
132#869C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134C3×#106—32no—
135C3×#106—32no—
136C3×C4⋊C8—32no—
137C3×C4⋊C8—31no—
138C3×#97—32no—
139C3×C4×C8—21no—
140C3×C4×C8C2×D311yescharacteristic
141C3×C4×C8C2×D311yescharacteristic
142#821—31no—
143#821—31no—
144#821—31no—
145#821—31no—
146#821—32no—
147#821—32no—
148#821—61no—
149#821—61no—
150#818—31no—
151#818—31no—
152#818—32no—
153#818—61no—
154#817—32no—
155#817C2×D312yes—
156#817C2×D312yes—
157#815C2×D312yes—
158Dic3⋊C8C2×D312yes—
159#809—32no—
160#809—32no—
161#808—32no—
162#807—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C4⋊(C3⋊D3)—21no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)C2×Q812yes—
174C4⋊(C3⋊D3)C2×Q812yescomplemented
175C4×C3⋊D3—42no—
176C4×C3⋊D3—42no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×Dic6—22no—
182C3×Dic6—42no—
183C3×Dic6—81no—
184#627—44no—
185#624—44no—
186#624—82no—
187C32×C8—21no—
188C32×C8C2×Q812yescomplemented
189C3×C3⋊C8—22no—
190#554—91no—
191D4×Q8—91no—
192#501—92no—
193#498—31no—
194#478—92no—
195#476—92no—
196#476—91no—
197#474—91no—
198#446—31no—
199#442—92no—
200C4×D8—91no—
201C2×C3×Q8—31no—
202C2×C3×Q8—61no—
203C2×C3×Q8—61no—
204D3×Q8—124no—
205D3×Q8—124no—
206C2×D12—31no—
207C2×D12—31no—
208C2×D12—31no—
209C2×D12—31no—
210C2×D12—61no—
211C2×D12—61no—
212C2×C4×D3—62no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—61no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3—121no—
221C2×C4×D3—121no—
222C2×Dic6—21no—
223C2×Dic6—21no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6D1211yescharacteristic
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—32no—
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C22×D311yescharacteristic
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—61no—
239C3×C4⋊C4—61no—
240C3×C42—21no—
241C3×C42—32no—
242C3×C42C22×D311yescharacteristic
243C3×C42C22×D311yescharacteristic
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—61no—
247(C2×D3)⋊C4—61no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—121no—
253(C2×D3)⋊C4—121no—
254C4⋊Dic3—21no—
255C4⋊Dic3—21no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3—62no—
264C4⋊Dic3D1211yescharacteristic
265C4⋊Dic3C22×D312yes—
266C4⋊Dic3C22×D312yes—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4D1212yes—
272C4×Dic3C22×D312yes—
273C2×C3⋊C8C22×D312yes—
274D24—34no—
275D24—34no—
276D24—64no—
277C22×C32C22×D411yescharacteristic
278C2×C3⋊D3—22no—
279C2×C3⋊D3—22no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—41no—
284C32×C4—21no—
285C32×C4AGL(1,ℤ/8)12yes—
286C32×C4C22×Q811yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—41no—
289C3⋊Dic3—41no—
290C3×Dic3—22no—
291C3×Dic3—22no—
292C3×Dic3—42no—
293C3×Dic3—42no—
294C22×Q8—181no—
295C2×D8—91no—
296C4⋊Q8—31no—
297C4⋊Q8—31no—
298C4⋊Q8—92no—
299#125—92no—
300C22⋊Q8—182no—
301C22⋊Q8—181no—
302C22⋊Q8—182no—
303C22⋊Q8—181no—
304C4×Q8—31no—
305C4×D4—92no—
306C4×D4—92no—
307C4×D4—91no—
308C4×D4—91no—
309C2×C4⋊C4—181no—
310#107—92no—
311#107—91no—
312#106—32no—
313#106—32no—
314#106—92no—
315C4⋊C8—32no—
316C4⋊C8—31no—
317#102—92no—
318#102—92no—
319#102—91no—
320#102—91no—
321#97—32no—
322C4×C8D3211yescharacteristic
323C22×D3—61no—
324C22×D3—61no—
325C22×D3—61no—
326C22×D3—61no—
327C22×D3—121no—
328C22×D3—121no—
329C3×Q8—62no—
330C3×Q8—122no—
331C3×Q8—241no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—32no—
336C2×C3×C4—32no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4C2×D1211yescharacteristic
340C2×C3×C4C2×D1211yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—121no—
352C2×Dic3—121no—
353C2×Dic3C2×D1212yes—
354C2×Dic3C2×D1212yes—
355D12—32no—
356D12—32no—
357D12—32no—
358D12—32no—
359D12—62no—
360D12—62no—
361D12—61no—
362D12—61no—
363D12—61no—
364D12—61no—
365D12—121no—
366D12—121no—
367C4×D3—124no—
368C4×D3—124no—
369C4×D3—122no—
370C4×D3—122no—
371C4×D3—122no—
372C4×D3—122no—
373C4×D3—242no—
374C4×D3—242no—
375C4×D3—242no—
376C4×D3—242no—
377Dic6—22no—
378Dic6—42no—
379Dic6—81no—
380Dic6—124no—
381Dic6—124no—
382C3×C8—21no—
383C3×C8—21no—
384C3×C8—22no—
385C3×C8—41no—
386C3×C8—62no—
387C3×C8D3×Q812yescomplemented
388C3×C8D3×Q812yescomplemented
389C3⋊C8—22no—
390C2×C32D4×Q811yescharacteristic
391C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
392C2×C32#57711yescharacteristic
393C3⋊D3—42no—
394C3⋊D3—42no—
395C2×Q8—31no—
396C2×Q8—61no—
397C2×Q8—61no—
398C2×Q8—182no—
399C2×Q8—364no—
400C2×D4—91no—
401C2×D4—91no—
402C22×C4—182no—
403C22×C4—182no—
404C22×C4—181no—
405C22×C4—181no—
406D8—94no—
407C2×C8—32no—
408C2×C8C2×D3211yescharacteristic
409C2×C8C2×D3211yescharacteristic
410C4⋊C4—31no—
411C4⋊C4—32no—
412C4⋊C4—32no—
413C4⋊C4—32no—
414C4⋊C4—61no—
415C4⋊C4—61no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4—182no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—181no—
424C22⋊C4—181no—
425C42—32no—
426C42C2×D3211yescharacteristic
427C22×C3—21no—
428C22×C3C22×D1211yescharacteristic
429C22×C3C2×D3×D411yescharacteristic
430C2×D3—62no—
431C2×D3—62no—
432C2×D3—62no—
433C2×D3—62no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—121no—
437C2×D3—121no—
438C2×D3—121no—
439C2×D3—121no—
440C2×D3—121no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—241no—
445C2×D3—241no—
446C2×D3—241no—
447C2×D3—241no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—22no—
453C3×C4—41no—
454C3×C4—62no—
455C3×C4—62no—
456C3×C4—122no—
457C3×C4—122no—
458C3×C4#90812yes—
459C3×C4#91412yes—
460C3×C4C2×D3×Q811yescharacteristic
461C3×C4C2×D3×Q811yescharacteristic
462C3×C4#100711yescharacteristic
463C3×C4#101011yescharacteristic
464Dic3—22no—
465Dic3—22no—
466Dic3—42no—
467Dic3—42no—
468Dic3—121no—
469Dic3—121no—
470Dic3—121no—
471Dic3—121no—
472Dic3—241no—
473Dic3—241no—
474C32#338411yescharacteristic, complemented, Sylow
475C23—181no—
476C23—181no—
477Q8—62no—
478Q8—122no—
479Q8—241no—
480Q8—364no—
481D4—92no—
482D4—92no—
483D4—181no—
484D4—181no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—364no—
492C2×C4—362no—
493C2×C4—362no—
494C2×C4—722no—
495C2×C4D3×D1211yescharacteristic
496C2×C4D3×D1211yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—21no—
499C8—62no—
500C8#379712yescomplemented
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3Q8×D1211yescharacteristic
505C2×C3#572711yescharacteristic
506C2×C3C2×#90811yescharacteristic
507C2×C3#575111yescharacteristic
508C2×C3C2×#91411yescharacteristic
509C2×C3#576211yescharacteristic
510D3—122no—
511D3—122no—
512D3—122no—
513D3—122no—
514D3—242no—
515D3—242no—
516C22—182no—
517C22—182no—
518C22—361no—
519C22—361no—
520C22—361no—
521C22—361no—
522C22C2×D3×D1211yescharacteristic
523C4—21no—
524C4—62no—
525C4—62no—
526C4—122no—
527C4—122no—
528C4—361no—
529C4—361no—
530C4#6379412yes—
531C4#6429711yescharacteristic
532C4C2×#379711yescharacteristic
533C3—21no—
534C3#7997511yescharacteristic, complemented
535C3#8190511yescharacteristic, complemented
536C2—362no—
537C2—362no—
538C2#1059390311yescharacteristic
539C2C2×#6379411yescharacteristic
540C2#1059467711yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC2×#3745C22
hypercenterC4×C8D32
hypocenterC32#3384
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. #10593958C2semidirect
2. #10593903C2semidirect
4. C3×#4680C2semidirect
5. C3×#4679C2semidirect
6. #10590892C2semidirect
7. #10590769C2semidirect
9. #10590759C2semidirect
10. #10590313C2semidirect
11. #10590300C2semidirect
64. #4680D3semidirect
65. #4679D3semidirect
84. #3745Q8semidirect
174. C4⋊(C3⋊D3)C2×Q8semidirect
188. C32×C8C2×Q8semidirect
387. C3×C8D3×Q8semidirect
388. C3×C8D3×Q8semidirect
474. C32#3384semidirect
500. C8#3797semidirect
534. C3#79975semidirect
535. C3#81905semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105939032
C4×#37452
C3×#46802
C3×#46792
#105908922
#105907692
#105907682
#105907592
#105903132
#105903002
#819053
#799753