Finite Group Databasebeta

← #11895353

Subgroups — #11895353

Order 1152.

838 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596050C211yesmaximal, characteristic, complemented
2C3×#5585C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4C4×#3717C211yesmaximal, characteristic, complemented
5#10590356C212yesmaximal, complemented
6#10590355C211yesmaximal, characteristic
7C4×#3714C212yesmaximal, complemented
8#10590283C211yesmaximal, characteristic, complemented
9#10590274C212yesmaximal, complemented
10#10590273C211yesmaximal, characteristic, complemented
11#10590271C212yesmaximal, complemented
12#83713—31nomaximal
13#79927—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15#64155—21no—
16#64105—22no—
17C4⋊C4×C3⋊D3—21no—
18C4×C4⋊(C3⋊D3)C2212yes—
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20#64079C2212yes—
21#64078C2211yescharacteristic
22C3×#947—21no—
23C3×#894—22no—
24C3×#893—21no—
25C3×#875C2212yes—
26C3×#874C2211yescharacteristic
27C3×C4×D12C2212yes—
28C3×C4×Dic6C2211yescharacteristic
29C2×#3717C2211yescharacteristic
30C2×#3714C2212yes—
31C3×C4⋊(C3⋊C8)C2212yes—
32C3×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×C4×C3⋊C8C2211yescharacteristic
34C3×C4×C3⋊C8C2212yes—
35#63575C2212yes—
36#63573C2211yescharacteristic
37#63566C2211yescharacteristic
38#63566C2212yes—
39#63564C2211yescharacteristic
40#63563C2212yes—
41#63563C2212yes—
42#63563C2212yes—
43C3×#559—31no—
44#5585D311yescharacteristic, complemented
45#5579—31no—
46#5579—31no—
47#5579—61no—
48C3×C8×Q8—31no—
49#5072—31no—
50#5070—31no—
51#5057—32no—
52#5056—32no—
53C4×#215—31no—
54Q8×C3⋊C8D311yescharacteristic, complemented
55#5021—31no—
56C4×#213—32no—
57#5009—32no—
58#4850—31no—
59#4847—32no—
60#4844—32no—
61#4843—31no—
62#4697—32no—
63#4694—31no—
64C4×D24—32no—
65C4×#204—31no—
66C2×C32×Q8D411yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
70C2×#634—21no—
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×Dic6C2311yescharacteristic
76C32×C4⋊C4D411yescharacteristic
77C32×C4⋊C4D412yes—
78C32×C42C2311yescharacteristic
79C32×C42C2312yes—
80#3752—21no—
81#3752—22no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—22no—
86#3750—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×(C2×D3)⋊C4—22no—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3—21no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96#3717—22no—
97#3714—24no—
98#3361—91noSylow
99C3×#127—31no—
100C3×#124—32no—
101C3×#124—61no—
102C3×#123—62no—
103C3×C4×Q8—21no—
104C3×C4×Q8—31no—
105C3×C4×Q8C2×D311yescharacteristic
106C3×C4×Q8C2×D311yescharacteristic
107C3×C4×D4—32no—
108C3×C4×D4—61no—
109#947—21no—
110#946—62no—
111#946—61no—
112#946—61no—
113C2×#215—31no—
114C2×#213—32no—
115C2×D24—32no—
116C2×#204—31no—
117#896—64no—
118#896—62no—
119#896—62no—
120#894—22no—
121#893—21no—
122D3×C4⋊C4—62no—
123D3×C4⋊C4—61no—
124D3×C4⋊C4—61no—
125#875C2×D312yes—
126#874C2×D311yescharacteristic
127C4×D12—31no—
128C4×D12—32no—
129C4×D12—32no—
130C4×D12—31no—
131C4×D12—62no—
132C4×D12—61no—
133C4×D12C2×D312yes—
134#870—32no—
135#870—32no—
136#870—62no—
137#869—31no—
138#869—31no—
139#869—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×C4⋊C8—31no—
142C3×C4⋊C8—32no—
143C3×C4×C8—31no—
144C3×C4×C8—32no—
145#835—32no—
146#835—31no—
147#832—32no—
148#832—32no—
149#832—32no—
150#821—32no—
151#821—32no—
152#821—32no—
153#821—31no—
154#818—32no—
155#817—31no—
156#816—31no—
157#816—32no—
158#809—31no—
159#808—31no—
160#807—32no—
161C4⋊(C3⋊C8)C2×D312yes—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4×C3⋊C8C2×D312yes—
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—22no—
167C32×Q8—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—21no—
174C2×C3⋊Dic3—22no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)#4112yes—
177C4×C3⋊D3—42no—
178C4×C3⋊D3—82no—
179#634—81no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—42no—
185C3×D12—81no—
186C3×C4×D3—82no—
187C3×Dic6—21no—
188C3×Dic6—21no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#559—31no—
193#554—91no—
194#488—92no—
195#486—91no—
196#478—92no—
197#477—91no—
198#463—92no—
199#459—91no—
200C8×Q8—31no—
201C4×SD16—91no—
202C4×D8—92no—
203C2×C3×Q8—21no—
204C2×C3×Q8—31no—
205C2×C3×Q8D1211yescharacteristic
206C2×C3×Q8#6711yescharacteristic
207C2×C3×D4—32no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C22×C3×C4—62no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—31no—
214C2×D12—31no—
215C2×D12—61no—
216C2×D12C22×D312yes—
217C2×C4×D3—22no—
218C2×C4×D3—62no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—64no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×Dic6—62no—
225C2×Dic6—61no—
226C2×Dic6—61no—
227C2×Dic6C22×D311yescharacteristic
228C2×C3×C8—32no—
229C2×C3×C8—31no—
230C2×C3×C8—31no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—61no—
235C3×C4⋊C4D1211yescharacteristic
236C3×C4⋊C4D1212yes—
237C3×C4⋊C4#6711yescharacteristic
238C3×C4⋊C4#6712yes—
239C3×C22⋊C4—62no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—62no—
242C3×C42—21no—
243C3×C42—22no—
244C3×C42—61no—
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D312yes—
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D312yes—
249#215—62no—
250#213—64no—
251(C2×D3)⋊C4—22no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—22no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—61no—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—61no—
259(C2×D3)⋊C4—62no—
260C4⋊Dic3—32no—
261C4⋊Dic3—31no—
262C4⋊Dic3—31no—
263C4⋊Dic3—32no—
264C4⋊Dic3—62no—
265C4⋊Dic3—61no—
266C4⋊Dic3—62no—
267C4⋊Dic3—61no—
268C4⋊Dic3—61no—
269C4⋊Dic3C22×D311yescharacteristic
270Dic3⋊C4—21no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276Dic3⋊C4—62no—
277C4×Dic3—21no—
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D312yes—
280C2×C3⋊C8C22×D311yescharacteristic
281D24—64no—
282#204—62no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—22no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C32×C4—22no—
291C32×C4—22no—
292C32×C4—21no—
293C32×C4#13512yes—
294C32×C4C2×#4111yescharacteristic
295C32×C42−1+411yescharacteristic
296C3⋊Dic3—41no—
297C3⋊Dic3—42no—
298C3×Dic3—41no—
299C3×Dic3—41no—
300C2×SD16—91no—
301C2×D8—92no—
302C4⋊Q8—91no—
303#127—31no—
304#125—92no—
305#124—32no—
306#124—61no—
307#123—62no—
308C22⋊Q8—181no—
309C22⋊Q8—182no—
310C4×Q8—31no—
311C4×Q8D3211yescharacteristic
312C4×D4—32no—
313C4×D4—61no—
314C4×D4—92no—
315C4×D4—91no—
316C2×C4⋊C4—181no—
317#107—92no—
318#106—91no—
319C4⋊C8—31no—
320C4⋊C8—32no—
321#103—91no—
322#103—92no—
323#102—91no—
324#102—92no—
325#102—92no—
326#102—92no—
327C4×C8—32no—
328C4×C8—31no—
329C23×C3—62no—
330C22×D3—22no—
331C22×D3—62no—
332C22×D3—61no—
333C22×D3—61no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×Q8—42no—
337C3×Q8—61no—
338C3×Q8—61no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—122no—
342C3×D4—241no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—61no—
349C2×C3×C4—61no—
350C2×C3×C4—242no—
351C2×C3×C4C2×D1212yes—
352C2×C3×C4C2×D1212yes—
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4C2×D1211yescharacteristic
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6712yes—
357C2×C3×C4C2×#6712yes—
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—62no—
364C2×Dic3—64no—
365C2×Dic3—61no—
366C2×Dic3—62no—
367C2×Dic3—61no—
368C2×Dic3—62no—
369D12—22no—
370D12—22no—
371D12—32no—
372D12—32no—
373D12—42no—
374D12—62no—
375D12—62no—
376D12—61no—
377D12—61no—
378D12—81no—
379C4×D3—82no—
380C4×D3—124no—
381C4×D3—122no—
382C4×D3—122no—
383C4×D3—242no—
384C4×D3—242no—
385C4×D3—244no—
386Dic6—21no—
387Dic6—21no—
388Dic6—241no—
389Dic6—241no—
390Dic6—242no—
391C3×C8—61no—
392C3×C8—62no—
393C3×C8—61no—
394C3⋊C8—21no—
395C3⋊C8—22no—
396C3⋊C8—21no—
397C2×C32#54811yescharacteristic
398C2×C32C2×#13511yescharacteristic
399C2×C32#57611yescharacteristic
400C3⋊D3—42no—
401C3×D3—82no—
402C2×Q8—31no—
403C2×Q8—181no—
404C2×Q8#62611yescharacteristic
405C2×D4—32no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—91no—
409C22×C4—62no—
410C22×C4—181no—
411C22×C4—182no—
412SD16—182no—
413D8—184no—
414C2×C8—31no—
415C2×C8—31no—
416C2×C8—32no—
417C4⋊C4—31no—
418C4⋊C4—61no—
419C4⋊C4—91no—
420C4⋊C4—92no—
421C4⋊C4—182no—
422C4⋊C4—181no—
423C4⋊C4—182no—
424C4⋊C4#62611yescharacteristic
425C4⋊C4#62612yes—
426C22⋊C4—62no—
427C22⋊C4—62no—
428C22⋊C4—62no—
429C22⋊C4—181no—
430C22⋊C4—182no—
431C42—61no—
432C42C2×D3212yes—
433C42C2×D3211yescharacteristic
434C22×C3—21no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3C22×D1211yescharacteristic
439C22×C3C22×#6711yescharacteristic
440C2×D3—42no—
441C2×D3—42no—
442C2×D3—42no—
443C2×D3—64no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C2×D3—121no—
452C3×C4—22no—
453C3×C4—21no—
454C3×C4—22no—
455C3×C4—22no—
456C3×C4—21no—
457C3×C4—22no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—41no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—121no—
465C3×C4—121no—
466C3×C4#90412yes—
467C3×C4#95012yes—
468C3×C4#100711yescharacteristic
469C3×C4D3×#4111yescharacteristic
470C3×C4D3×#4111yescharacteristic
471C3×C4#101011yescharacteristic
472Dic3—41no—
473Dic3—41no—
474Dic3—124no—
475Dic3—122no—
476Dic3—121no—
477Dic3—122no—
478Dic3—121no—
479Dic3—122no—
480C32#336111yescharacteristic, complemented, Sylow
481C23—62no—
482C23—181no—
483Q8—22no—
484Q8—61no—
485Q8—61no—
486Q8—721no—
487D4—62no—
488D4—62no—
489D4—92no—
490D4—122no—
491D4—181no—
492D4—241no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—181no—
496C2×C4—182no—
497C2×C4—242no—
498C2×C4—362no—
499C2×C4—722no—
500C2×C4C2×#62612yes—
501C2×C4C2×#62612yes—
502C2×C4C2×#62611yescharacteristic
503C2×C4C2×#62611yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—61no—
506C8—62no—
507C8—61no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—242no—
512C2×C3#557611yescharacteristic
513C2×C3C2×#90411yescharacteristic
514C2×C3#575211yescharacteristic
515C2×C3C2×#95011yescharacteristic
516C2×C3#583111yescharacteristic
517C2×C3#583511yescharacteristic
518D3—82no—
519D3—124no—
520D3—122no—
521D3—122no—
522C22—122no—
523C22—122no—
524C22—122no—
525C22—182no—
526C22—361no—
527C22—361no—
528C22C22×#62611yescharacteristic
529C4—22no—
530C4—21no—
531C4—22no—
532C4—121no—
533C4—121no—
534C4—362no—
535C4—361no—
536C4#6382912yes—
537C4#6431511yescharacteristic
538C4#6431911yescharacteristic
539C3—21no—
540C3#7992711yescharacteristic, complemented
541C3#8371311yescharacteristic, complemented
542C2—242no—
543C2—362no—
544C2C2×#6382911yescharacteristic
545C2#1059541411yescharacteristic
546C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10590355C2
hypercenterC4×Q8D32
hypocenterC32#3361
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10596050C2semidirect
2. C3×#5585C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
4. C4×#3717C2semidirect
5. #10590356C2semidirect
7. C4×#3714C2semidirect
8. #10590283C2semidirect
9. #10590274C2semidirect
10. #10590273C2semidirect
11. #10590271C2semidirect
44. #5585D3semidirect
54. Q8×C3⋊C8D3semidirect
480. C32#3361semidirect
540. C3#79927semidirect
541. C3#83713semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#55852
C3×Q8×C3⋊C82
C4×#37172
#105903562
#105903552
C4×#37142
#105902832
#105902742
#105902732
#105902712
#837133
#799273