Finite Group Databasebeta

← #11897566

Subgroups — #11897566

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596198C211yesmaximal, characteristic, complemented
2#10593956C211yesmaximal, characteristic, complemented
3C3×#5087C211yesmaximal, characteristic, complemented
4C3×#5080C211yesmaximal, characteristic, complemented
5#10590546C212yesmaximal, complemented
6#10590472C212yesmaximal, complemented
7#10590462C212yesmaximal
8#10590435C212yesmaximal, complemented
9C4×#3714C211yesmaximal, characteristic
10#10590300C211yesmaximal, characteristic, complemented
11#10590296C211yesmaximal, characteristic, complemented
12#81905—31nomaximal
13#80959—31nomaximal
14C2×Q8×C3⋊D3—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64155—21no—
17#64105—22no—
18#64102C2212yes—
19#64097C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24#63898C2212yes—
25D3×C4⋊Dic3—21no—
26#63887—22no—
27#63872C2212yes—
28#63857—21no—
29C2×#3714C2211yescharacteristic
30C3×#809C2212yes—
31C3×#808C2212yes—
32C3×#808C2212yes—
33C3×#807C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36#63575C2211yescharacteristic
37#63573C2212yes—
38#63572C2212yes—
39#63564C2212yes—
40#63564C2211yescharacteristic
41#63563C2211yescharacteristic
42#63555C2212yes—
43#5730—31no—
44#5727—31no—
45#5727—31no—
46#5727—61no—
47#5543—31no—
48C3×#498—31no—
49C3×#474—31no—
50#5087D311yescharacteristic, complemented
51#5084—31no—
52#5080D311yescharacteristic, complemented
53C4×#213—31no—
54#4891—32no—
55#4876—32no—
56#4871—32no—
57#4870—32no—
58#4869—32no—
59#4856—32no—
60#4842—31no—
61#4831—31no—
62#4785—32no—
63#4761—32no—
64C4×D24—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67Q8×C3⋊D3—44no—
68C2×C4⋊(C3⋊D3)C2311yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—22no—
71C2×#634—22no—
72C2×#634D411yescharacteristic
73C2×C3×D12C2311yescharacteristic
74C2×C3×C4×D3—21no—
75C2×C3×Dic6—21no—
76C2×D3×Dic3—22no—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79C32×C42C2311yescharacteristic
80#3752—21no—
81#3752—22no—
82C4⋊(C3⋊Dic3)D411yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—22no—
85#3750D412yes—
86C4×C3⋊Dic3C2312yes—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97#3714Q814yescomplemented
98#3384—91noSylow
99C2×D3×Q8—61no—
100C2×D3×Q8—61no—
101C2×D3×Q8—62no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×C4⋊Q8C2×D311yescharacteristic
106C3×C4×D4—31no—
107#946—62no—
108#946—61no—
109#946—61no—
110#946—62no—
111D4×Dic3—32no—
112C2×#213—31no—
113C2×C4⋊Dic3—61no—
114#924—61no—
115C2×D24—31no—
116#897—61no—
117#896—62no—
118#896—62no—
119#896—64no—
120#893—32no—
121#893—32no—
122#893—32no—
123#893—62no—
124D3×C4⋊C4—61no—
125#890—32no—
126#890—32no—
127#888—32no—
128#888—32no—
129#888—62no—
130#878—62no—
131C4×D12—31no—
132C4×D12—31no—
133C4×D12—61no—
134C4×D12C2×D311yescharacteristic
135#869C2×D311yescharacteristic
136C4×Dic6—31no—
137C4×Dic6—31no—
138C4×Dic6—61no—
139C3×#107—32no—
140C3×#106—32no—
141C3×#106—32no—
142C3×C4⋊C8—31no—
143C3×#102—32no—
144C3×C4×C8—31no—
145#832—31no—
146#821—31no—
147#821—31no—
148#821—32no—
149#818—31no—
150#817—32no—
151#815—32no—
152#815—32no—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155#809—32no—
156#809—31no—
157#809C2×D312yes—
158#808—32no—
159#808C2×D312yes—
160#808C2×D312yes—
161#807—31no—
162#807C2×D312yes—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C32×Q8—42no—
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)C2×Q812yes—
177C4×C3⋊D3—44no—
178C4×C3⋊D3—42no—
179#634—22no—
180#634—44no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—21no—
183C3×D12—21no—
184C3×D12C2×Q812yescomplemented
185C3×C4×D3—42no—
186C3×Dic6—81no—
187D3×Dic3—82no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—22no—
190C3×C3⋊C8C2×Q812yescomplemented
191#554—91no—
192D4×Q8—91no—
193#501—92no—
194#498—31no—
195#478—92no—
196#476—92no—
197#476—91no—
198#474—31no—
199#446—91no—
200#442—92no—
201C4×D8—91no—
202C2×C3×Q8—22no—
203C2×C3×Q8—21no—
204C2×C3×Q8—21no—
205C2×C3×Q8—61no—
206C2×C3×D4—31no—
207C22×C3×C4—61no—
208C22×Dic3—62no—
209D3×Q8—128no—
210D3×Q8—124no—
211D3×Q8—124no—
212C2×D12—31no—
213C2×D12—31no—
214C2×D12—61no—
215C2×D12C22×D311yescharacteristic
216C2×C4×D3—21no—
217C2×C4×D3—62no—
218C2×C4×D3—62no—
219C2×C4×D3—62no—
220C2×C4×D3—64no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—62no—
224C2×Dic6—21no—
225C2×Dic6—31no—
226C2×Dic6—31no—
227C2×Dic6—61no—
228C2×Dic6—62no—
229C2×Dic6—62no—
230C2×Dic6—64no—
231C2×C3×C8—31no—
232C2×C3×C8—31no—
233C2×C3×C8—32no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—32no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4C22×D312yes—
242C3×C4⋊C4C22×D312yes—
243C3×C22⋊C4—61no—
244C3×C42—21no—
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247#217—62no—
248#213—34no—
249(C2×D3)⋊C4—21no—
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—21no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—31no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—62no—
265C4⋊Dic3—62no—
266C4⋊Dic3C22×D311yescharacteristic
267C4⋊Dic3C22×D312yes—
268Dic3⋊C4—32no—
269Dic3⋊C4—32no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—64no—
276C4×Dic3—32no—
277C4×Dic3—32no—
278C4×Dic3—62no—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D312yes—
281C2×C3⋊C8C22×D311yescharacteristic
282D24—34no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—22no—
285C2×C3⋊D3—41no—
286C2×C3⋊D3—41no—
287C2×C3×D3—22no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C32×C4—21no—
291C32×C4—42no—
292C32×C4AGL(1,ℤ/8)12yes—
293C32×C4C22×Q811yescharacteristic
294C32×C42−1+411yescharacteristic
295C3⋊Dic3—22no—
296C3⋊Dic3—22no—
297C3⋊Dic3—41no—
298C3×Dic3—41no—
299C3×Dic3—42no—
300C22×Q8—181no—
301C2×D8—91no—
302C4⋊Q8—31no—
303C4⋊Q8—92no—
304C4⋊Q8D3211yescharacteristic
305#125—92no—
306C22⋊Q8—182no—
307C22⋊Q8—182no—
308C22⋊Q8—181no—
309C22⋊Q8—181no—
310C4×Q8—91no—
311C4×D4—31no—
312C4×D4—92no—
313C4×D4—92no—
314C4×D4—91no—
315C2×C4⋊C4—181no—
316#107—32no—
317#107—91no—
318#106—32no—
319#106—32no—
320#106—92no—
321C4⋊C8—31no—
322C4⋊C8—92no—
323#102—32no—
324#102—91no—
325#102—92no—
326#102—91no—
327#97—92no—
328C4×C8—31no—
329C23×C3—61no—
330C22×D3—21no—
331C22×D3—62no—
332C22×D3—61no—
333C22×D3—61no—
334C3×Q8—44no—
335C3×Q8—42no—
336C3×Q8—42no—
337C3×Q8—241no—
338C3×D4—32no—
339C3×D4—61no—
340C2×C3×C4—24no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—122no—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×Dic3—21no—
356C2×Dic3—22no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—242no—
367D12—21no—
368D12—32no—
369D12—32no—
370D12—62no—
371D12—62no—
372D12—61no—
373D12—61no—
374D12D3×Q812yescomplemented
375C4×D3—42no—
376C4×D3—128no—
377C4×D3—124no—
378C4×D3—124no—
379C4×D3—124no—
380C4×D3—122no—
381C4×D3—122no—
382C4×D3—242no—
383Dic6—64no—
384Dic6—62no—
385Dic6—62no—
386Dic6—81no—
387Dic6—128no—
388Dic6—124no—
389Dic6—124no—
390C3×C8—32no—
391C3×C8—62no—
392C3×C8—61no—
393C3⋊C8—21no—
394C3⋊C8—22no—
395C3⋊C8D3×Q812yescomplemented
396C2×C32D4×Q811yescharacteristic
397C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
398C2×C32#57711yescharacteristic
399C3⋊D3—42no—
400C3×D3—42no—
401C2×Q8—21no—
402C2×Q8—61no—
403C2×Q8—91no—
404C2×Q8—182no—
405C2×Q8—364no—
406C2×D4—31no—
407C2×D4—91no—
408C22×C4—61no—
409C22×C4—182no—
410C22×C4—182no—
411C22×C4—181no—
412D8—94no—
413C2×C8—31no—
414C2×C8—31no—
415C2×C8—32no—
416C4⋊C4—21no—
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—61no—
420C4⋊C4—91no—
421C4⋊C4—92no—
422C4⋊C4—91no—
423C4⋊C4—182no—
424C4⋊C4—182no—
425C4⋊C4—182no—
426C4⋊C4C2×D3212yes—
427C22⋊C4—61no—
428C22⋊C4—182no—
429C22⋊C4—182no—
430C22⋊C4—181no—
431C42—92no—
432C42C2×D3211yescharacteristic
433C22×C3—21no—
434C22×C3—62no—
435C22×C3—121no—
436C22×C3—121no—
437C22×C3C2×D3×D411yescharacteristic
438C22×C3C2×D3×D411yescharacteristic
439C2×D3—22no—
440C2×D3—41no—
441C2×D3—41no—
442C2×D3—64no—
443C2×D3—62no—
444C2×D3—62no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—121no—
448C2×D3—121no—
449C2×D3—121no—
450C2×D3—121no—
451C3×C4—21no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—22no—
456C3×C4—41no—
457C3×C4—44no—
458C3×C4—42no—
459C3×C4—42no—
460C3×C4—121no—
461C3×C4—122no—
462C3×C4#91112yes—
463C3×C4#91412yes—
464C3×C4C2×D3×Q811yescharacteristic
465C3×C4C2×D3×Q811yescharacteristic
466C3×C4#100711yescharacteristic
467C3×C4#101011yescharacteristic
468Dic3—41no—
469Dic3—42no—
470Dic3—64no—
471Dic3—62no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—122no—
476Dic3—122no—
477Dic3—121no—
478Dic3—121no—
479C32#338411yescharacteristic, complemented, Sylow
480C23—61no—
481C23—181no—
482Q8—42no—
483Q8—182no—
484Q8—241no—
485Q8—364no—
486D4—32no—
487D4—61no—
488D4—92no—
489D4—181no—
490C2×C4—22no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—92no—
494C2×C4—92no—
495C2×C4—122no—
496C2×C4—181no—
497C2×C4—364no—
498C2×C4—362no—
499C2×C4—722no—
500C2×C4#381111yescharacteristic
501C2×C4#381111yescharacteristic
502C2×C4C22×D3211yescharacteristic
503C8—32no—
504C8—61no—
505C8—62no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—122no—
510C2×C3#563211yescharacteristic
511C2×C3#572711yescharacteristic
512C2×C3C2×#91111yescharacteristic
513C2×C3C2×#91411yescharacteristic
514C2×C3#576211yescharacteristic
515C2×C3#577811yescharacteristic
516D3—42no—
517D3—124no—
518D3—122no—
519D3—122no—
520C22—62no—
521C22—121no—
522C22—121no—
523C22—182no—
524C22—361no—
525C22—361no—
526C22C2×#381111yescharacteristic
527C4—21no—
528C4—42no—
529C4—121no—
530C4—122no—
531C4—182no—
532C4—182no—
533C4—361no—
534C4#6393712yes—
535C4#6431511yescharacteristic
536C4D32×Q811yescharacteristic
537C3—21no—
538C3#8095911yescharacteristic, complemented
539C3#8190511yescharacteristic, complemented
540C2—122no—
541C2—362no—
542C2C2×#6393711yescharacteristic
543C2#1059532411yescharacteristic
544C2#1059536111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊Q8D32
hypocenterC32#3384
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. #10596198C2semidirect
2. #10593956C2semidirect
3. C3×#5087C2semidirect
4. C3×#5080C2semidirect
5. #10590546C2semidirect
6. #10590472C2semidirect
8. #10590435C2semidirect
10. #10590300C2semidirect
11. #10590296C2semidirect
50. #5087D3semidirect
52. #5080D3semidirect
97. #3714Q8semidirect
184. C3×D12C2×Q8semidirect
190. C3×C3⋊C8C2×Q8semidirect
374. D12D3×Q8semidirect
395. C3⋊C8D3×Q8semidirect
479. C32#3384semidirect
538. C3#80959semidirect
539. C3#81905semidirect

Maximal subgroups

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

subgroupindex
#105961982
#105939562
C3×#50872
C3×#50802
#105905462
#105904722
#105904622
#105904352
C4×#37142
#105903002
#105902962
#819053
#809593