Finite Group Databasebeta

← #11868676

Subgroups — #11868676

Order 1152.

1093 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2#10593854C211yesmaximal, characteristic, complemented
3C3×#5009C212yesmaximal, complemented
4#10591495C211yesmaximal, characteristic, complemented
5#10591494C211yesmaximal, characteristic, complemented
6#10591426C212yesmaximal
7#10590583C212yesmaximal, complemented
8#10590433C211yesmaximal, characteristic, complemented
9#10590430C211yesmaximal, characteristic, complemented
10#10590340C211yesmaximal, characteristic, complemented
11#10590308C212yesmaximal, complemented
12#81166—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3—21no—
15C32×C4×D4C2211yescharacteristic
16D4×C3⋊Dic3C2211yescharacteristic
17C4×#638—21no—
18#64102C2211yescharacteristic
19C4⋊C4×C3⋊D3C2211yescharacteristic
20#64090—21no—
21C22⋊C4×C3⋊D3—21no—
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C42×C3⋊D3C2211yescharacteristic
24C3×#870C2212yescomplemented
25#63919C2211yescharacteristic, complemented
26#63919C2211yescharacteristic, complemented
27#63865—21no—
28#63865—21no—
29#63849C2212yes—
30#63838—21no—
31#63838—21no—
32C2×#3712C2212yes—
33C3×#832C2212yes—
34C3×#832C2212yes—
35C3×#808C2212yescomplemented
36C3×#807C2212yescomplemented
37C3×C4⋊(C3⋊C8)C2212yescomplemented
38#63575C2212yescomplemented
39#63573C2212yescomplemented
40#63572C2211yescharacteristic, complemented
41#63572C2211yescharacteristic, complemented
42#63564C2212yes—
43#63564C2212yes—
44#5688—32no—
45C4×D3×D4—32no—
46C4×D3×D4—61no—
47C3×#478—32no—
48#5066—32no—
49#5009D312yescomplemented
50#4890—32no—
51#4881—32no—
52#4870—32no—
53#4861—32no—
54#4847—32no—
55#4837—32no—
56#4770—32no—
57#4770—32no—
58#4761—32no—
59#4759—32no—
60C23×C3⋊D3—21no—
61C2×C32×D4C2311yescharacteristic
62C22×C32×C4—21no—
63C2×#638—21no—
64C22×C3⋊Dic3—21no—
65D4×C3⋊D3—22no—
66D4×C3⋊D3Q814yescomplemented
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3—44no—
72C2×C4×C3⋊D3D411yescharacteristic
73C2×C4×C3⋊D3D411yescharacteristic
74C2×C4×C3⋊D3C2311yescharacteristic
75C2×#627—21no—
76C2×#627—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42C2311yescharacteristic
80#3757—21no—
81#3752—21no—
82#3752—21no—
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85C4×C3⋊Dic3D411yescharacteristic
86C4×C3⋊Dic3D411yescharacteristic
87C4×C3⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2312yes—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—21no—
95#3724—21no—
96#3722—22no—
97Dic32—22no—
98#3712—24no—
99#3077—91noSylow
100C2×D3×D4—32no—
101C2×D3×D4—61no—
102C22×C4×D3—62no—
103C22×C4×D3—62no—
104C3×#125—32no—
105C3×C4×D4—21no—
106C3×C4×D4C2×D312yes—
107D4×Dic3—32no—
108D4×Dic3—61no—
109C4×#67—62no—
110C4×#67—62no—
111C2×ΓL(1,𝔽25)—32no—
112C2×ΓL(1,𝔽25)—32no—
113#896—62no—
114#896—62no—
115#893—32no—
116#893—61no—
117#892—32no—
118#892—32no—
119D3×C4⋊C4—32no—
120D3×C4⋊C4—61no—
121#888—32no—
122#888—32no—
123#887—62no—
124#887—62no—
125#67⋊C4—62no—
126#67⋊C4—62no—
127D3×C22⋊C4—62no—
128D3×C22⋊C4—62no—
129C4×D12—32no—
130C4×D12—61no—
131C42×D3—32no—
132C42×D3—61no—
133#870C2×D312yescomplemented
134C3×#107—32no—
135C3×#106—32no—
136C3×C4⋊C8—32no—
137C3×#102—32no—
138C3×#102—32no—
139#832C2×D312yes—
140#832C2×D312yes—
141#821—32no—
142#821—32no—
143#818—32no—
144#817—32no—
145Dic3⋊C8—32no—
146Dic3⋊C8—32no—
147#809—32no—
148#809—32no—
149#808—32no—
150#808C2×D312yescomplemented
151#807—32no—
152#807C2×D312yescomplemented
153C4⋊(C3⋊C8)C2×D312yescomplemented
154C23×C32—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—24no—
157C22×C3⋊D3—42no—
158C22×C3⋊D3—42no—
159C22×C3⋊D3C2×D411yescharacteristic
160C32×D4—21no—
161C32×D4C2×Q812yes—
162C2×C32×C4—21no—
163C2×C32×C4—42no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2411yescharacteristic
167#638—24no—
168C2×C3⋊Dic3—21no—
169C2×C3⋊Dic3—42no—
170C2×C3⋊Dic3C2×D411yescharacteristic
171C2×C3⋊Dic3C2×D411yescharacteristic
172C2×C3⋊Dic3C2×D411yescharacteristic
173C4⋊(C3⋊D3)—21no—
174C4⋊(C3⋊D3)C2×Q812yes—
175C4×C3⋊D3—22no—
176C4×C3⋊D3—41no—
177C4×C3⋊D3—42no—
178C4×C3⋊D3—42no—
179C4×C3⋊D3—42no—
180C4×C3⋊D3C2×Q812yes—
181C4×C3⋊D3#4112yes—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184#627—42no—
185#627—42no—
186C3×C3⋊C8—22no—
187C3×C3⋊C8—22no—
188#533—91no—
189C2×C4×D4—91no—
190#478—32no—
191#478—92no—
192#476—91no—
193#476—91no—
194#474—91no—
195#474—91no—
196#428—92no—
197#423—91no—
198#418—92no—
199C23×D3—62no—
200C23×D3—62no—
201C2×C3×D4—21no—
202C2×C3×D4C22×D312yes—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C2×#67—62no—
206C2×#67—62no—
207C22×Dic3—62no—
208C22×Dic3—62no—
209D3×D4—38no—
210D3×D4—64no—
211D3×D4—64no—
212D3×D4—64no—
213C2×D12—32no—
214C2×D12—61no—
215C2×C4×D3—32no—
216C2×C4×D3—32no—
217C2×C4×D3—32no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—62no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—128no—
228C2×C4×D3—128no—
229C2×Dic6—62no—
230C2×Dic6—62no—
231C2×C3×C8—32no—
232C2×C3×C8—32no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—32no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4C22×D312yes—
239C3×C22⋊C4—22no—
240C3×C22⋊C4—22no—
241C3×C42—21no—
242C3×C42C22×D312yes—
243#217—62no—
244#217—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—62no—
251C4⋊Dic3—32no—
252C4⋊Dic3—61no—
253C4⋊Dic3C22×D312yes—
254C4⋊Dic3C22×D312yes—
255Dic3⋊C4—22no—
256Dic3⋊C4—22no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261C4×Dic3—32no—
262C4×Dic3—32no—
263C4×Dic3—32no—
264C4×Dic3—61no—
265C4×Dic3—61no—
266C4×Dic3—61no—
267C4×Dic3—62no—
268C4×Dic3—62no—
269C2×C3⋊C8C22×D312yes—
270C2×C3⋊C8C22×D312yes—
271ΓL(1,𝔽25)—64no—
272ΓL(1,𝔽25)—64no—
273C22×C32—22no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—22no—
280C2×C3⋊D3—48no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3C22⋊Q812yes—
284C32×C4—21no—
285C32×C4—21no—
286C32×C4—41no—
287C32×C4C22×Q811yescharacteristic
288C32×C4C2×#4111yescharacteristic
289C3⋊Dic3—21no—
290C3⋊Dic3—41no—
291C3⋊Dic3C22⋊Q812yes—
292C3⋊Dic3AGL(1,ℤ/8)12yes—
293C3×Dic3—42no—
294C3×Dic3—42no—
295C22×D4—91no—
296C23×C4—181no—
297C2×M16—92no—
298C4⋊Q8—91no—
299C4⋊Q8—91no—
300#125—32no—
301C22⋊Q8—181no—
302C22⋊Q8—181no—
303C4×Q8—181no—
304C4×Q8—181no—
305C4×D4—91no—
306C4×D4—91no—
307C4×D4—91no—
308C4×D4—181no—
309C4×D4—181no—
310C4×D4D3211yescharacteristic
311#117—92no—
312C2×C4⋊C4—91no—
313C2×C22⋊C4—181no—
314C2×C42—91no—
315#107—32no—
316#107—92no—
317#106—32no—
318#106—92no—
319C4⋊C8—32no—
320C4⋊C8—91no—
321C4⋊C8—91no—
322#102—32no—
323#102—32no—
324#102—92no—
325#102—92no—
326C23×C3—22no—
327C23×C3—22no—
328C22×D3—32no—
329C22×D3—61no—
330C22×D3—68no—
331C22×D3—62no—
332C22×D3—68no—
333C22×D3—62no—
334C22×D3—124no—
335C22×D3—124no—
336C22×D3—124no—
337C22×D3—124no—
338C3×D4—22no—
339C3×D4—22no—
340C3×D4—22no—
341C3×D4D3×Q814yes—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—44no—
348C2×C3×C4—44no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4D3×D412yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4C23×D312yes—
354#67—68no—
355#67—68no—
356C2×Dic3—22no—
357C2×Dic3—22no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—32no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—124no—
367C2×Dic3—124no—
368D12—34no—
369D12—62no—
370D12—62no—
371D12—62no—
372C4×D3—34no—
373C4×D3—34no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—64no—
377C4×D3—64no—
378C4×D3—124no—
379C4×D3—122no—
380C4×D3—124no—
381C4×D3—124no—
382C4×D3—124no—
383C4×D3—122no—
384C4×D3—124no—
385C4×D3—124no—
386Dic6—124no—
387Dic6—124no—
388C3×C8—62no—
389C3×C8—62no—
390C3⋊C8—22no—
391C3⋊C8—22no—
392C2×C32—42no—
393C2×C32C2×C22⋊Q811yescharacteristic
394C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
395C2×C32#57511yescharacteristic
396C3⋊D3—22no—
397C3⋊D3—42no—
398C24—181no—
399C2×Q8—181no—
400C2×Q8—181no—
401C2×D4—94no—
402C2×D4—91no—
403C2×D4—182no—
404C2×D4—181no—
405C2×D4C2×D3211yescharacteristic
406C22×C4—21no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—181no—
414C22×C4—364no—
415M16—184no—
416C2×C8—32no—
417C2×C8—32no—
418C4⋊C4—32no—
419C4⋊C4—32no—
420C4⋊C4—62no—
421C4⋊C4—62no—
422C4⋊C4—91no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C4⋊C4C2×D3211yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—181no—
429C22⋊C4—182no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C42—91no—
433C42—91no—
434C42—91no—
435C42—182no—
436C42C2×D3211yescharacteristic
437C22×C3—24no—
438C22×C3—24no—
439C22×C3—21no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3C2×D3×D412yes—
445C2×D3—34no—
446C2×D3—62no—
447C2×D3—62no—
448C2×D3—62no—
449C2×D3—62no—
450C2×D3—62no—
451C2×D3—64no—
452C2×D3—64no—
453C2×D3—1216no—
454C2×D3—1216no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C3×C4—22no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—41no—
465C3×C4—42no—
466C3×C4—42no—
467C3×C4—122no—
468C3×C4—122no—
469C3×C4C2×D3×Q812yes—
470C3×C4D3×#4112yes—
471Dic3—34no—
472Dic3—34no—
473Dic3—42no—
474Dic3—42no—
475Dic3—62no—
476Dic3—62no—
477Dic3—62no—
478Dic3—121no—
479Dic3—122no—
480Dic3—122no—
481C32#307711yescharacteristic, complemented, Sylow
482C23—21no—
483C23—91no—
484C23—184no—
485C23—181no—
486C23—362no—
487C23—362no—
488Q8—362no—
489Q8—362no—
490D4—21no—
491D4—92no—
492D4—184no—
493D4—181no—
494D4#379712yes—
495C2×C4—21no—
496C2×C4—42no—
497C2×C4—62no—
498C2×C4—62no—
499C2×C4—91no—
500C2×C4—91no—
501C2×C4—92no—
502C2×C4—92no—
503C2×C4—91no—
504C2×C4—182no—
505C2×C4—181no—
506C2×C4—361no—
507C2×C4—362no—
508C2×C4—362no—
509C2×C4—362no—
510C2×C4—362no—
511C2×C4#381111yescharacteristic
512C2×C4#381111yescharacteristic
513C2×C4C22×D3211yescharacteristic
514C8—62no—
515C8—62no—
516C2×C3—21no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—44no—
520C2×C3—44no—
521C2×C3D3×C22⋊Q812yes—
522C2×C3#576812yes—
523C2×C3D3×AGL(1,ℤ/8)12yes—
524D3—64no—
525D3—64no—
526D3—124no—
527D3—124no—
528C22—22no—
529C22—41no—
530C22—41no—
531C22—92no—
532C22—181no—
533C22—181no—
534C22—182no—
535C22—368no—
536C22—361no—
537C22—361no—
538C22C2×#381111yescharacteristic
539C4—21no—
540C4—21no—
541C4—41no—
542C4—92no—
543C4—92no—
544C4—122no—
545C4—122no—
546C4—181no—
547C4—361no—
548C4C2×#379711yescharacteristic
549C4#6430611yescharacteristic
550C3—21no—
551C3#8116612yescomplemented
552C2—42no—
553C2—182no—
554C2—362no—
555C2#1059492511yescharacteristic
556C2#1059510011yescharacteristic
557C2#1059546011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
hypercenterC4×D4D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593854C2semidirect
3. C3×#5009C2semidirect
4. #10591495C2semidirect
5. #10591494C2semidirect
7. #10590583C2semidirect
8. #10590433C2semidirect
9. #10590430C2semidirect
10. #10590340C2semidirect
11. #10590308C2semidirect
24. C3×#870C22semidirect
25. #63919C22semidirect
26. #63919C22semidirect
35. C3×#808C22semidirect
36. C3×#807C22semidirect
37. C3×C4⋊(C3⋊C8)C22semidirect
38. #63575C22semidirect
39. #63573C22semidirect
40. #63572C22semidirect
41. #63572C22semidirect
49. #5009D3semidirect
66. D4×C3⋊D3Q8semidirect
133. #870C2×D3semidirect
150. #808C2×D3semidirect
152. #807C2×D3semidirect
153. C4⋊(C3⋊C8)C2×D3semidirect
481. C32#3077semidirect
551. C3#81166semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105938542
C3×#50092
#105914952
#105914942
#105914262
#105905832
#105904332
#105904302
#105903402
#105903082
#811663