Finite Group Databasebeta

← #11895362

Subgroups — #11895362

Order 1152.

785 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#10593951C211yesmaximal, characteristic, complemented
3C4×#3744C211yesmaximal, characteristic, complemented
4C3×#4694C211yesmaximal, characteristic, complemented
5C3×C8×Dic6C211yesmaximal, characteristic, complemented
6#10590863C212yesmaximal, complemented
7#10590860C212yesmaximal, complemented
8#10590772C212yesmaximal, complemented
9#10590745C212yesmaximal, complemented
10#10590355C211yesmaximal, characteristic
11#10590284C211yesmaximal, characteristic, complemented
12#81585—31nomaximal
13#79927—31nomaximal
14C2×#3744C2211yescharacteristic
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16C4×#634C2211yescharacteristic
17C3×#874C2211yescharacteristic
18C3×#869C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20#63900—21no—
21#63898—21no—
22#63894C2212yes—
23Dic3×D12C2212yes—
24#63888—22no—
25#63884—22no—
26#63871—21no—
27#63869C2212yes—
28#63863—21no—
29#63860C2212yes—
30C2×#3714C2212yes—
31C32×C4×C8C2211yescharacteristic
32#63648C2211yescharacteristic
33#63644C2211yescharacteristic
34#63643C2211yescharacteristic
35C3×#821C2212yes—
36C3×#821C2212yes—
37C3×Dic3⋊C8C2212yes—
38C3×C8×Dic3C2212yes—
39C3×C4⋊(C3⋊C8)C2211yescharacteristic
40#63575C2212yes—
41#63567C2212yes—
42#63563C2212yes—
43#5730—31no—
44#5713—31no—
45#5585—31no—
46#5579—31no—
47C3×#486—31no—
48C3×C8×Q8—31no—
49#5091—31no—
50#5072—31no—
51#4850—31no—
52#4847—32no—
53#4844—32no—
54#4843—31no—
55#4787—32no—
56#4768—32no—
57#4763—32no—
58#4756—32no—
59#4697—32no—
60#4694D311yescharacteristic, complemented
61C4×D24—32no—
62C4×#204—31no—
63C4×#204—31no—
64C4×#204—61no—
65C8×Dic6D311yescharacteristic, complemented
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634C2311yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6—21no—
73C2×C3×Dic6D411yescharacteristic
74C2×#624—22no—
75C2×D3×Dic3—22no—
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78C32×C42C2311yescharacteristic
79#3752—21no—
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—21no—
83C4×C3⋊Dic3—21no—
84#3744—22no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3C2312yes—
90C2×C3×C3⋊C8C2312yes—
91#3724—22no—
92Dic3⋊Dic3—22no—
93#3722—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3714—24no—
98#3361—91noSylow
99C3×C4⋊Q8—31no—
100C3×#127—31no—
101C3×C4×Q8—31no—
102#947—61no—
103#946—61no—
104#946—62no—
105#936—32no—
106#936—61no—
107#935—62no—
108D4×Dic3—32no—
109D4×Dic3—61no—
110C2×#213—32no—
111C2×D24—32no—
112C2×#204—31no—
113C2×#204—31no—
114C2×#204—61no—
115#897—61no—
116#896—62no—
117#894—62no—
118#893—32no—
119#893—61no—
120D3×C4⋊C4—61no—
121D3×C4⋊C4—61no—
122#890—32no—
123#875—32no—
124#874C2×D311yescharacteristic
125C4×D12—32no—
126C4×D12—31no—
127C4×D12—31no—
128C4×D12—32no—
129C4×D12—61no—
130#870—32no—
131#869C2×D311yescharacteristic
132C4×Dic6—31no—
133C4×Dic6—31no—
134C4×Dic6—61no—
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—32no—
137C3×C4⋊C8—31no—
138C3×#102—32no—
139C3×#102—32no—
140C3×C4×C8—21no—
141C3×C4×C8—32no—
142C3×C4×C8C2×D311yescharacteristic
143C3×C4×C8C2×D311yescharacteristic
144#832—32no—
145#821—32no—
146#821—31no—
147#821—31no—
148#821—61no—
149#821C2×D312yes—
150#821C2×D312yes—
151#818—32no—
152#817—31no—
153#817—31no—
154#817—61no—
155#816—31no—
156#816—31no—
157#816—32no—
158#816—61no—
159Dic3⋊C8C2×D312yes—
160C8×Dic3C2×D312yes—
161#810—32no—
162#807—32no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C22×C3⋊D3—21no—
165C22×C3×D3—22no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—21no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C4⋊(C3⋊D3)—21no—
173C4⋊(C3⋊D3)#4112yes—
174C4×C3⋊D3—42no—
175#634—21no—
176#634—21no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3C2×D412yes—
179C2×C3×Dic3C2×D412yes—
180C3×D12—22no—
181C3×D12—22no—
182C3×D12—42no—
183C3×D12—81no—
184C3×Dic6—22no—
185C3×Dic6—81no—
186#624—82no—
187D3×Dic3—82no—
188C32×C8—21no—
189C32×C8—21no—
190C3×C3⋊C8—22no—
191#559—91no—
192#554—91no—
193#488—92no—
194#486—31no—
195#478—92no—
196#477—91no—
197#463—92no—
198#459—91no—
199C8×Q8—31no—
200C4×SD16—91no—
201C4×D8—92no—
202C2×C3×Q8—31no—
203C2×C3×Q8—61no—
204C2×C3×D4—32no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C22×Dic3—62no—
208C2×D12—21no—
209C2×D12—21no—
210C2×D12—31no—
211C2×D12—31no—
212C2×D12—61no—
213C2×D12C22×D312yes—
214C2×C4×D3—61no—
215C2×C4×D3—61no—
216C2×C4×D3—62no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—121no—
220C2×Dic6—21no—
221C2×Dic6—31no—
222C2×Dic6—31no—
223C2×Dic6—61no—
224C2×Dic6D1211yescharacteristic
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—32no—
228C2×C3×C8C22×D311yescharacteristic
229C2×C3×C8C22×D311yescharacteristic
230C2×C3×C8C22×D311yescharacteristic
231C2×C3×C8C22×D311yescharacteristic
232C3×C4⋊C4—31no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—61no—
236C3×C42—21no—
237C3×C42—32no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—62no—
241#217—62no—
242#217—62no—
243#213—64no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—61no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—121no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3D1211yescharacteristic
261C4⋊Dic3C22×D312yes—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264Dic3⋊C4—61no—
265Dic3⋊C4—61no—
266Dic3⋊C4—62no—
267Dic3⋊C4—121no—
268Dic3⋊C4D1212yes—
269C4×Dic3—61no—
270C4×Dic3—61no—
271C4×Dic3—121no—
272C4×Dic3C22×D312yes—
273C2×C3⋊C8C22×D312yes—
274D24—64no—
275#204—62no—
276#204—62no—
277#204—64no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—22no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—21no—
286C32×C4#13512yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3⋊Dic3—41no—
292C3×Dic3—22no—
293C3×Dic3—22no—
294C3×Dic3—42no—
295C2×SD16—91no—
296C2×D8—92no—
297C4⋊Q8—31no—
298#127—31no—
299#125—92no—
300#124—92no—
301#124—181no—
302#123—182no—
303C22⋊Q8—182no—
304C22⋊Q8—181no—
305C4×Q8—31no—
306C4×Q8—91no—
307C4×D4—92no—
308C4×D4—92no—
309C4×D4—91no—
310C4×D4—181no—
311C2×C4⋊C4—181no—
312#107—92no—
313#106—91no—
314C4⋊C8—32no—
315C4⋊C8—31no—
316#103—92no—
317#103—91no—
318#102—32no—
319#102—32no—
320#102—92no—
321#102—91no—
322C4×C8—32no—
323C4×C8D3211yescharacteristic
324C23×C3—62no—
325C22×D3—22no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—121no—
329C3×Q8—62no—
330C3×Q8—241no—
331C3×D4—62no—
332C3×D4—62no—
333C3×D4—122no—
334C3×D4—241no—
335C2×C3×C4—21no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—32no—
339C2×C3×C4—32no—
340C2×C3×C4—62no—
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4C2×D1211yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4C23×D311yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×Dic3—22no—
348C2×Dic3—61no—
349C2×Dic3—61no—
350C2×Dic3—61no—
351C2×Dic3—61no—
352C2×Dic3—61no—
353C2×Dic3—61no—
354C2×Dic3—121no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—242no—
358C2×Dic3C2×D1212yes—
359C2×Dic3C2×D1212yes—
360D12—22no—
361D12—22no—
362D12—32no—
363D12—32no—
364D12—42no—
365D12—62no—
366D12—61no—
367D12—61no—
368D12—81no—
369D12—121no—
370C4×D3—122no—
371C4×D3—122no—
372C4×D3—242no—
373C4×D3—242no—
374C4×D3—242no—
375C4×D3—242no—
376Dic6—22no—
377Dic6—62no—
378Dic6—61no—
379Dic6—61no—
380Dic6—61no—
381Dic6—61no—
382Dic6—81no—
383Dic6—121no—
384C3×C8—22no—
385C3×C8—21no—
386C3×C8—21no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—41no—
390C3×C8—62no—
391C3⋊C8—22no—
392C2×C32#54811yescharacteristic
393C2×C32C2×#13511yescharacteristic
394C2×C32#57611yescharacteristic
395C3⋊D3—42no—
396C3×D3—82no—
397C2×Q8—31no—
398C2×Q8—61no—
399C2×Q8—91no—
400C2×D4—32no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—91no—
404C22×C4—182no—
405C22×C4—182no—
406C22×C4—181no—
407SD16—182no—
408D8—184no—
409C2×C8—32no—
410C2×C8C2×D3211yescharacteristic
411C2×C8C2×D3211yescharacteristic
412C4⋊C4—31no—
413C4⋊C4—32no—
414C4⋊C4—32no—
415C4⋊C4—61no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4—182no—
419C4⋊C4—182no—
420C4⋊C4—181no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C22⋊C4—181no—
426C42—32no—
427C42—181no—
428C42C2×D3211yescharacteristic
429C22×C3—21no—
430C22×C3—122no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3C22×D1211yescharacteristic
434C22×C3C2×D3×D411yescharacteristic
435C2×D3—42no—
436C2×D3—42no—
437C2×D3—42no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—122no—
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—21no—
451C3×C4—22no—
452C3×C4—41no—
453C3×C4—62no—
454C3×C4—62no—
455C3×C4—122no—
456C3×C4#90412yes—
457C3×C4#91612yes—
458C3×C4#100711yescharacteristic
459C3×C4D3×#4111yescharacteristic
460C3×C4D3×#4111yescharacteristic
461C3×C4#101011yescharacteristic
462Dic3—22no—
463Dic3—22no—
464Dic3—42no—
465Dic3—122no—
466Dic3—121no—
467Dic3—121no—
468Dic3—121no—
469Dic3—121no—
470Dic3—121no—
471Dic3—121no—
472Dic3—241no—
473Dic3—241no—
474C32#336111yescharacteristic, complemented, Sylow
475C23—62no—
476C23—181no—
477Q8—62no—
478Q8—181no—
479Q8—181no—
480Q8—241no—
481D4—62no—
482D4—62no—
483D4—92no—
484D4—122no—
485D4—181no—
486D4—241no—
487C2×C4—32no—
488C2×C4—32no—
489C2×C4—62no—
490C2×C4—181no—
491C2×C4—181no—
492C2×C4—181no—
493C2×C4—362no—
494C2×C4—722no—
495C2×C4—722no—
496C2×C4D3×D1211yescharacteristic
497C2×C4D3×D1211yescharacteristic
498C2×C4C22×D3211yescharacteristic
499C8—21no—
500C8—21no—
501C8—62no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—242no—
506C2×C3#557611yescharacteristic
507C2×C3#567711yescharacteristic
508C2×C3C2×#90411yescharacteristic
509C2×C3#575211yescharacteristic
510C2×C3#575711yescharacteristic
511C2×C3C2×#91611yescharacteristic
512D3—82no—
513D3—122no—
514D3—122no—
515D3—242no—
516C22—122no—
517C22—122no—
518C22—122no—
519C22—182no—
520C22—361no—
521C22—361no—
522C22C2×D3×D1211yescharacteristic
523C4—21no—
524C4—62no—
525C4—62no—
526C4—122no—
527C4—361no—
528C4—361no—
529C4—361no—
530C4#6380612yes—
531C4#6429711yescharacteristic
532C4#6430611yescharacteristic
533C3—21no—
534C3#7992711yescharacteristic, complemented
535C3#8158511yescharacteristic, complemented
536C2—242no—
537C2—362no—
538C2#1059390111yescharacteristic
539C2#1059467811yescharacteristic
540C2C2×#6380611yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10590355C2
hypercenterC4×C8D32
hypocenterC32#3361
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. #10593951C2semidirect
3. C4×#3744C2semidirect
4. C3×#4694C2semidirect
5. C3×C8×Dic6C2semidirect
6. #10590863C2semidirect
7. #10590860C2semidirect
8. #10590772C2semidirect
9. #10590745C2semidirect
11. #10590284C2semidirect
60. #4694D3semidirect
65. C8×Dic6D3semidirect
474. C32#3361semidirect
534. C3#79927semidirect
535. C3#81585semidirect

Maximal subgroups

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

subgroupindex
#105939582
#105939512
C4×#37442
C3×#46942
C3×C8×Dic62
#105908632
#105908602
#105907722
#105907452
#105903552
#105902842
#815853
#799273