Finite Group Databasebeta

← #11895365

Subgroups — #11895365

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#10596201C211yesmaximal, characteristic, complemented
2#10593951C211yesmaximal, characteristic, complemented
3C3×#5091C211yesmaximal, characteristic, complemented
4C3×#5088C211yesmaximal, characteristic, complemented
5#10590540C212yesmaximal, complemented
6#10590539C212yesmaximal, complemented
7#10590473C212yesmaximal, complemented
8#10590459C212yesmaximal, complemented
9C4×#3717C211yesmaximal, characteristic, complemented
10#10590355C211yesmaximal, characteristic
11#10590254C211yesmaximal, characteristic, complemented
12#81585—31nomaximal
13#81134—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64155—22no—
16#64106—21no—
17#64102C2212yes—
18C4⋊C4×C3⋊D3—21no—
19#64099C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×#874C2211yescharacteristic
23C3×C4×Dic6C2211yescharacteristic
24#63898C2212yes—
25Dic3×D12—21no—
26#63884—22no—
27#63863C2212yes—
28#63860—21no—
29C2×#3717C2211yescharacteristic
30C2×#3714C2212yes—
31C3×#810C2212yes—
32C3×#809C2212yes—
33C3×#809C2212yes—
34C3×#807C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2211yescharacteristic
38#63572C2212yes—
39#63566C2211yescharacteristic
40#63564C2211yescharacteristic
41#63563C2212yes—
42#63553C2212yes—
43#5730—31no—
44#5730—31no—
45#5730—61no—
46#5713—31no—
47#5585—31no—
48C3×#486—31no—
49C3×#477—31no—
50#5091D311yescharacteristic, complemented
51#5088D311yescharacteristic, complemented
52#5072—31no—
53C4×#215—31no—
54#4891—32no—
55#4872—32no—
56#4843—31no—
57#4830—31no—
58#4819—32no—
59#4800—32no—
60#4787—32no—
61#4768—32no—
62#4763—32no—
63#4756—32no—
64C4×#204—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
70C2×#634D411yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12C2312yes—
74C2×C3×Dic6C2311yescharacteristic
75C2×D3×Dic3—22no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C32×C42C2311yescharacteristic
79#3752—21no—
80#3752—22no—
81C4⋊(C3⋊Dic3)—22no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—22no—
85#3750D412yes—
86C4×C3⋊Dic3C2312yes—
87C3×C4⋊Dic3C2311yescharacteristic
88C3×Dic3⋊C4—21no—
89C3×C4×Dic3—21no—
90C2×C3×C3⋊C8C2311yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96#3717—22no—
97#3714—24no—
98#3361—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8C2×D311yescharacteristic
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×#127—31no—
103C3×C4×Q8—31no—
104#947—32no—
105#946—62no—
106#946—62no—
107#946—64no—
108C2×#215—31no—
109#936—32no—
110#936—61no—
111#935—62no—
112D4×Dic3—32no—
113D4×Dic3—61no—
114C2×#213—32no—
115C2×D24—32no—
116C2×#204—31no—
117#897—61no—
118#897—61no—
119#897—62no—
120#894—62no—
121#893—32no—
122#893—32no—
123#893—32no—
124#893—62no—
125D3×C4⋊C4—61no—
126D3×C4⋊C4—61no—
127D3×C4⋊C4—62no—
128#890—32no—
129#890—32no—
130#890—62no—
131#875—61no—
132#874C2×D311yescharacteristic
133C4×D12—31no—
134C4×D12—31no—
135C4×D12—61no—
136C4×D12—61no—
137C4×Dic6—31no—
138C4×Dic6—31no—
139C4×Dic6—61no—
140C4×Dic6C2×D311yescharacteristic
141C3×#107—32no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144C3×#102—32no—
145C3×#102—32no—
146C3×C4×C8—31no—
147#835—31no—
148#832—32no—
149#821—32no—
150#821—31no—
151#817—31no—
152#816—31no—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155C8×Dic3—32no—
156C8×Dic3—32no—
157#810C2×D312yes—
158#809—31no—
159#809C2×D312yes—
160#809C2×D312yes—
161#808—31no—
162#807C2×D312yes—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—22no—
167C32×Q8—81no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)#4112yes—
177C4×C3⋊D3—42no—
178C4×C3⋊D3—82no—
179#634—22no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C3×D12—22no—
183C3×D12—22no—
184C3×D12—42no—
185C3×D12—81no—
186C3×Dic6—21no—
187C3×Dic6—21no—
188D3×Dic3—82no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192#559—91no—
193#554—91no—
194#488—92no—
195#486—31no—
196#478—92no—
197#477—31no—
198#463—92no—
199#459—91no—
200C8×Q8—91no—
201C4×SD16—91no—
202C4×D8—92no—
203C2×C3×Q8—22no—
204C2×C3×Q8—21no—
205C2×C3×Q8—21no—
206C2×C3×Q8—31no—
207C2×C3×D4—32no—
208C2×C3×D4—61no—
209C2×C3×D4—61no—
210C22×Dic3—62no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—31no—
214C2×D12—31no—
215C2×D12—61no—
216C2×D12C22×D312yes—
217C2×C4×D3—62no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—64no—
224C2×Dic6—31no—
225C2×Dic6—31no—
226C2×Dic6—61no—
227C2×Dic6C22×D311yescharacteristic
228C2×C3×C8—31no—
229C2×C3×C8—32no—
230C2×C3×C8—31no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—21no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4C22×D312yes—
238C3×C4⋊C4C22×D312yes—
239C3×C42—21no—
240C3×C42—61no—
241C3×C42C22×D311yescharacteristic
242C3×C42C22×D311yescharacteristic
243#217—62no—
244#217—62no—
245#217—62no—
246#215—62no—
247#213—64no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—64no—
255(C2×D3)⋊C4—61no—
256(C2×D3)⋊C4—61no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3—62no—
264C4⋊Dic3—62no—
265C4⋊Dic3—64no—
266C4⋊Dic3C22×D311yescharacteristic
267Dic3⋊C4—21no—
268Dic3⋊C4—32no—
269Dic3⋊C4—32no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—64no—
274C4×Dic3—21no—
275C4×Dic3—32no—
276C4×Dic3—32no—
277C4×Dic3—62no—
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D312yes—
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—21no—
291C32×C4—42no—
292C32×C4#13512yes—
293C32×C4C2×#4111yescharacteristic
294C32×C42−1+411yescharacteristic
295C3⋊Dic3—22no—
296C3⋊Dic3—22no—
297C3⋊Dic3—41no—
298C3×Dic3—41no—
299C3×Dic3—41no—
300C2×SD16—91no—
301C2×D8—92no—
302C4⋊Q8D3211yescharacteristic
303#127—31no—
304#125—92no—
305#124—92no—
306#124—181no—
307#123—182no—
308C22⋊Q8—181no—
309C22⋊Q8—182no—
310C4×Q8—31no—
311C4×Q8—91no—
312C4×D4—92no—
313C4×D4—92no—
314C4×D4—91no—
315C4×D4—181no—
316C2×C4⋊C4—181no—
317#107—32no—
318#106—91no—
319C4⋊C8—31no—
320C4⋊C8—92no—
321#103—32no—
322#103—91no—
323#102—32no—
324#102—32no—
325#102—91no—
326#102—92no—
327C4×C8—31no—
328C4×C8—92no—
329C23×C3—62no—
330C22×D3—22no—
331C22×D3—62no—
332C22×D3—61no—
333C22×D3—61no—
334C3×Q8—61no—
335C3×Q8—61no—
336C3×Q8—81no—
337C3×Q8—81no—
338C3×Q8—82no—
339C3×D4—62no—
340C3×D4—62no—
341C3×D4—122no—
342C3×D4—241no—
343C2×C3×C4—24no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—32no—
362C2×Dic3—32no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—242no—
369D12—22no—
370D12—22no—
371D12—32no—
372D12—32no—
373D12—42no—
374D12—62no—
375D12—62no—
376D12—61no—
377D12—61no—
378D12—81no—
379C4×D3—124no—
380C4×D3—122no—
381C4×D3—122no—
382C4×D3—242no—
383C4×D3—242no—
384C4×D3—242no—
385C4×D3—244no—
386Dic6—21no—
387Dic6—21no—
388Dic6—62no—
389Dic6—62no—
390Dic6—122no—
391C3×C8—61no—
392C3×C8—61no—
393C3×C8—62no—
394C3⋊C8—22no—
395C3⋊C8—21no—
396C3⋊C8—21no—
397C2×C32#54811yescharacteristic
398C2×C32C2×#13511yescharacteristic
399C2×C32#57611yescharacteristic
400C3⋊D3—42no—
401C3×D3—82no—
402C2×Q8—21no—
403C2×Q8—31no—
404C2×Q8—91no—
405C2×D4—32no—
406C2×D4—61no—
407C2×D4—61no—
408C2×D4—91no—
409C22×C4—182no—
410C22×C4—182no—
411C22×C4—181no—
412SD16—182no—
413D8—184no—
414C2×C8—31no—
415C2×C8—31no—
416C2×C8—32no—
417C4⋊C4—21no—
418C4⋊C4—31no—
419C4⋊C4—61no—
420C4⋊C4—91no—
421C4⋊C4—92no—
422C4⋊C4—91no—
423C4⋊C4—182no—
424C4⋊C4—182no—
425C4⋊C4C2×D3212yes—
426C22⋊C4—182no—
427C22⋊C4—182no—
428C22⋊C4—182no—
429C22⋊C4—182no—
430C22⋊C4—181no—
431C42—61no—
432C42—92no—
433C42C2×D3211yescharacteristic
434C22×C3—21no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3C2×D3×D411yescharacteristic
439C22×C3C2×D3×D411yescharacteristic
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—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—41no—
458C3×C4—44no—
459C3×C4—42no—
460C3×C4—42no—
461C3×C4—121no—
462C3×C4—121no—
463C3×C4#91612yes—
464C3×C4#91912yes—
465C3×C4#100711yescharacteristic
466C3×C4D3×#4111yescharacteristic
467C3×C4D3×#4111yescharacteristic
468C3×C4#101011yescharacteristic
469Dic3—41no—
470Dic3—41no—
471Dic3—62no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—122no—
476Dic3—122no—
477Dic3—122no—
478Dic3—121no—
479Dic3—121no—
480C32#336111yescharacteristic, complemented, Sylow
481C23—62no—
482C23—181no—
483Q8—61no—
484Q8—61no—
485Q8—81no—
486Q8—182no—
487D4—62no—
488D4—62no—
489D4—92no—
490D4—122no—
491D4—181no—
492D4—241no—
493C2×C4—22no—
494C2×C4—61no—
495C2×C4—61no—
496C2×C4—92no—
497C2×C4—92no—
498C2×C4—181no—
499C2×C4—362no—
500C2×C4—722no—
501C2×C4—722no—
502C2×C4#381111yescharacteristic
503C2×C4#381111yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—61no—
506C8—62no—
507C8—61no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—242no—
512C2×C3#563311yescharacteristic
513C2×C3#567711yescharacteristic
514C2×C3#575711yescharacteristic
515C2×C3C2×#91611yescharacteristic
516C2×C3C2×#91911yescharacteristic
517C2×C3#577411yescharacteristic
518D3—82no—
519D3—124no—
520D3—122no—
521D3—122no—
522C22—122no—
523C22—122no—
524C22—122no—
525C22—182no—
526C22—361no—
527C22—361no—
528C22C2×#381111yescharacteristic
529C4—21no—
530C4—42no—
531C4—121no—
532C4—121no—
533C4—182no—
534C4—182no—
535C4—361no—
536C4#6395012yes—
537C4#6431511yescharacteristic
538C4#6431911yescharacteristic
539C3—21no—
540C3#8113411yescharacteristic, complemented
541C3#8158511yescharacteristic, complemented
542C2—242no—
543C2—362no—
544C2#1059510211yescharacteristic
545C2C2×#6395011yescharacteristic
546C2#1059536211yescharacteristic
subgroupG/H
centerC22C2×#3811
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 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. #10593951C2semidirect
3. C3×#5091C2semidirect
4. C3×#5088C2semidirect
5. #10590540C2semidirect
6. #10590539C2semidirect
7. #10590473C2semidirect
8. #10590459C2semidirect
9. C4×#3717C2semidirect
11. #10590254C2semidirect
50. #5091D3semidirect
51. #5088D3semidirect
480. C32#3361semidirect
540. C3#81134semidirect
541. C3#81585semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105939512
C3×#50912
C3×#50882
#105905402
#105905392
#105904732
#105904592
C4×#37172
#105903552
#105902542
#815853
#811343