Finite Group Databasebeta

← #11868680

Subgroups — #11868680

Order 1152.

991 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C3×#4924C211yesmaximal, characteristic, complemented
4#10591130C212yesmaximal, complemented
5#10591086C212yesmaximal
6#10590272C212yesmaximal, complemented
7#10590271C214yesmaximal, complemented
8#10590268C212yesmaximal, complemented
9#82296—31nomaximal
10#79059—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3—21no—
13C2×C32×C42C2211yescharacteristic
14#64135C2212yes—
15#64133—21no—
16#64133—21no—
17#64079C2212yescomplemented
18#64078C2211yescharacteristic, complemented
19#64078C2211yescharacteristic, complemented
20C4×#634—21no—
21C4×#634—21no—
22C2×C3×(C2×D3)⋊C4—21no—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2212yes—
25C3×C4×D12—21no—
26C3×C4×D12—21no—
27C3×C4×D12C2212yes—
28C3×C4×D12C2212yes—
29C3×C4⋊(C3⋊C8)C2212yescomplemented
30C3×C4⋊(C3⋊C8)C2212yescomplemented
31#63575C2214yescomplemented
32#63573C2214yescomplemented
33#63563C2214yes—
34#63563C2214yes—
35C2×C3×C4×D4—31no—
36C2×C4×D12D311yescharacteristic
37#5470—31no—
38#5470—31no—
39#5470—61no—
40C3×#423—31no—
41#5215—32no—
42#5131—32no—
43#5121—32no—
44#5009—34no—
45#5008—32no—
46#5007—32no—
47#4964—32no—
48#4924D311yescharacteristic, complemented
49#4847—34no—
50#4846—32no—
51#4842—32no—
52C23×C3×D3—21no—
53C22×C32×C4D411yescharacteristic
54C22×C32×C4D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×#634—21no—
57C2×#634—21no—
58C22×C3×Dic3—21no—
59C2×C3×D12—21no—
60C2×C3×D12—22no—
61C2×C3×D12Q814yescomplemented
62C2×C3×D12C2312yes—
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3—44no—
66C32×C42D411yescharacteristic
67C32×C42D411yescharacteristic
68C32×C42C2311yescharacteristic
69C32×C42C2311yescharacteristic
70#3757—22no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C4⋊(C3⋊Dic3)C2312yes—
75#3750—22no—
76#3750—22no—
77C4×C3⋊Dic3—22no—
78C3×(C2×D3)⋊C4—22no—
79C3×(C2×D3)⋊C4—22no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3C2312yes—
82C3×#208—24no—
83C2×C3×C3⋊C8C2314yes—
84#3077—91noSylow
85C22×C3×D4—31no—
86C23×C3×C4—61no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3—21no—
89C2×C3×M16—32no—
90C3×C4×D4—32no—
91C3×C4×D4—32no—
92C3×C4×D4—61no—
93C3×C4×D4—61no—
94C2×C3×C4⋊C4—31no—
95C2×C3×C22⋊C4—61no—
96C2×C3×C42—21no—
97C2×C3×C42C2×D311yescharacteristic
98C2×C3×C42C2×D311yescharacteristic
99C2×(C2×D3)⋊C4—21no—
100#926—32no—
101#926—32no—
102#926—62no—
103C2×C4⋊Dic3C2×D311yescharacteristic
104#924—62no—
105#924—62no—
106#924—61no—
107#924—61no—
108#924—61no—
109#924—61no—
110C2×#208C2×D312yes—
111C4×D12—21no—
112C4×D12—21no—
113C4×D12C2×D312yes—
114C4×D12C2×D312yes—
115#870—32no—
116#870—32no—
117#870—62no—
118#869—31no—
119#869—31no—
120#869—31no—
121#869—31no—
122#869—61no—
123#869—61no—
124C4×Dic6—62no—
125C4×Dic6—62no—
126C4×Dic6—61no—
127C4×Dic6—61no—
128C4×Dic6—61no—
129C4×Dic6—61no—
130C3×C4⋊C8—32no—
131C3×C4⋊C8—32no—
132#832—34no—
133#832—34no—
134#821—34no—
135#821—34no—
136#818—34no—
137#817—34no—
138#808—34no—
139#807—34no—
140C4⋊(C3⋊C8)C2×D312yescomplemented
141C4⋊(C3⋊C8)C2×D312yescomplemented
142C23×C32C2×D411yescharacteristic
143C22×C3×D3—24no—
144C22×C3×D3—22no—
145C22×C3×D3—42no—
146C22×C3×D3—42no—
147C2×C32×C4—22no—
148C2×C32×C4—41no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×Q812yes—
155C2×C32×C4#4112yes—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—22no—
159#634—42no—
160#634—42no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C3×D12—24no—
164C3×D12—22no—
165C3×D12C2×Q814yes—
166C3×C4×D3—44no—
167C3×C4×D3—44no—
168C3×C3⋊C8—24no—
169#533—91no—
170C2×C4×D4—31no—
171#478—94no—
172#476—92no—
173#474—92no—
174#428—92no—
175#423—31no—
176#418—92no—
177C24×C3—61no—
178C23×D3—21no—
179C2×C3×D4—34no—
180C2×C3×D4—32no—
181C2×C3×D4—61no—
182C2×C3×D4—62no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—61no—
187C22×C3×C4—62no—
188C22×C3×C4—62no—
189C22×C3×C4—124no—
190C22×C3×C4D1211yescharacteristic
191C22×C3×C4D1211yescharacteristic
192C22×C3×C4#6711yescharacteristic
193C22×C3×C4#6711yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×Dic3—21no—
197C2×D12—22no—
198C2×D12—21no—
199C2×D12Dic614yescomplemented
200C2×D12C22×D312yes—
201C2×C4×D3—22no—
202C2×C4×D3—22no—
203C2×C4×D3—44no—
204C2×Dic6—62no—
205C2×Dic6—62no—
206C2×Dic6—61no—
207C2×Dic6—61no—
208C2×Dic6—61no—
209C2×Dic6—61no—
210C3×M16—64no—
211C2×C3×C8—34no—
212C3×C4⋊C4—32no—
213C3×C4⋊C4—61no—
214C3×C22⋊C4—62no—
215C3×C22⋊C4—62no—
216C3×C42—21no—
217C3×C42—21no—
218C3×C42—21no—
219C3×C42—21no—
220C3×C42D1211yescharacteristic
221C3×C42D1211yescharacteristic
222C3×C42#6711yescharacteristic
223C3×C42#6711yescharacteristic
224C3×C42C22×D311yescharacteristic
225C3×C42C22×D311yescharacteristic
226C3×C42C22×D311yescharacteristic
227C3×C42C22×D311yescharacteristic
228#217—64no—
229#217—62no—
230#217—62no—
231(C2×D3)⋊C4—22no—
232(C2×D3)⋊C4—22no—
233C4⋊Dic3—21no—
234C4⋊Dic3—32no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—32no—
238C4⋊Dic3—62no—
239C4⋊Dic3—62no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3C22×D312yes—
247Dic3⋊C4—64no—
248Dic3⋊C4—64no—
249Dic3⋊C4—62no—
250Dic3⋊C4—62no—
251Dic3⋊C4—62no—
252Dic3⋊C4—62no—
253C4×Dic3—64no—
254C4×Dic3—62no—
255C4×Dic3—62no—
256#208—24no—
257C2×C3⋊C8C22×D314yes—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32C22⋊Q812yes—
261C22×C32C22×D411yescharacteristic
262C2×C3×D3—24no—
263C2×C3×D3—48no—
264C2×C3×D3—42no—
265C2×C3×D3—42no—
266C32×C4—21no—
267C32×C4—21no—
268C32×C4—21no—
269C32×C4C22⋊Q812yes—
270C32×C4AGL(1,ℤ/8)12yes—
271C32×C4C22×Q811yescharacteristic
272C32×C4C2×#4111yescharacteristic
273C3⋊Dic3—42no—
274C3⋊Dic3—42no—
275C3×Dic3—42no—
276C22×D4—31no—
277C23×C4—61no—
278C2×M16—32no—
279C4⋊Q8—91no—
280C4⋊Q8—91no—
281#125—92no—
282C22⋊Q8—181no—
283C22⋊Q8—181no—
284C4×Q8—181no—
285C4×Q8—181no—
286C4×D4—32no—
287C4×D4—32no—
288C4×D4—61no—
289C4×D4—61no—
290#117—92no—
291C2×C4⋊C4—31no—
292C2×C22⋊C4—61no—
293C2×C42D3211yescharacteristic
294#107—94no—
295#106—94no—
296C4⋊C8—32no—
297C4⋊C8—32no—
298#102—94no—
299#102—94no—
300C23×C3—21no—
301C23×C3—64no—
302C23×C3—62no—
303C23×C3—122no—
304C23×C3—122no—
305C23×C3C2×D1211yescharacteristic
306C23×C3C2×#6711yescharacteristic
307C22×D3—24no—
308C22×D3—22no—
309C22×D3—42no—
310C22×D3—42no—
311C3×D4—34no—
312C3×D4—64no—
313C3×D4—62no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—21no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—21no—
321C2×C3×C4—21no—
322C2×C3×C4—21no—
323C2×C3×C4—21no—
324C2×C3×C4—42no—
325C2×C3×C4—41no—
326C2×C3×C4—41no—
327C2×C3×C4—42no—
328C2×C3×C4—62no—
329C2×C3×C4—124no—
330C2×C3×C4—122no—
331C2×C3×C4—124no—
332C2×C3×C4C2×Dic612yes—
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×D1211yescharacteristic
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4#23512yes—
339C2×C3×C4#23712yes—
340C2×C3×C4D3×Q812yes—
341C2×C3×C4C2×#6711yescharacteristic
342C2×C3×C4C2×#6711yescharacteristic
343C2×C3×C4C2×#6711yescharacteristic
344C2×C3×C4C2×#6711yescharacteristic
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C23×D311yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×Dic3—22no—
349C2×Dic3—42no—
350C2×Dic3—64no—
351C2×Dic3—64no—
352C2×Dic3—62no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356D12—24no—
357D12—22no—
358D12C2×Dic614yes—
359C4×D3—44no—
360C4×D3—44no—
361Dic6—124no—
362Dic6—122no—
363Dic6—122no—
364Dic6—124no—
365Dic6—122no—
366Dic6—122no—
367C3×C8—64no—
368C3⋊C8—24no—
369C2×C32—22no—
370C2×C32C2×C22⋊Q811yescharacteristic
371C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
372C2×C32#57511yescharacteristic
373C3×D3—44no—
374C24—61no—
375C2×Q8—181no—
376C2×Q8—181no—
377C2×D4—32no—
378C2×D4—34no—
379C2×D4—62no—
380C2×D4—61no—
381C22×C4—61no—
382C22×C4—62no—
383C22×C4—62no—
384C22×C4—124no—
385C22×C4#62611yescharacteristic
386C22×C4#62611yescharacteristic
387C22×C4C2×D3211yescharacteristic
388M16—64no—
389C2×C8—34no—
390C4⋊C4—32no—
391C4⋊C4—61no—
392C4⋊C4—92no—
393C4⋊C4—92no—
394C4⋊C4—182no—
395C4⋊C4—182no—
396C4⋊C4—181no—
397C4⋊C4—181no—
398C22⋊C4—62no—
399C22⋊C4—62no—
400C22⋊C4—182no—
401C42—182no—
402C42#62611yescharacteristic
403C42#62611yescharacteristic
404C42C2×D3211yescharacteristic
405C42C2×D3211yescharacteristic
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—21no—
409C22×C3—21no—
410C22×C3—21no—
411C22×C3—22no—
412C22×C3—41no—
413C22×C3—41no—
414C22×C3—64no—
415C22×C3—128no—
416C22×C3—122no—
417C22×C3—122no—
418C22×C3#89712yes—
419C22×C3#92412yes—
420C22×C3C22×D1211yescharacteristic
421C22×C3C22×#6711yescharacteristic
422C2×D3—24no—
423C2×D3—48no—
424C2×D3—42no—
425C2×D3—42no—
426C3×C4—22no—
427C3×C4—21no—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—21no—
431C3×C4—21no—
432C3×C4—21no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—22no—
436C3×C4—22no—
437C3×C4—41no—
438C3×C4—41no—
439C3×C4—122no—
440C3×C4#89712yes—
441C3×C4#90812yes—
442C3×C4#92412yes—
443C3×C4#93212yes—
444C3×C4C22×Dic611yescharacteristic
445C3×C4C2×#23511yescharacteristic
446C3×C4C2×#23711yescharacteristic
447C3×C4C2×D3×Q811yescharacteristic
448Dic3—42no—
449Dic3—124no—
450Dic3—124no—
451Dic3—122no—
452Dic3—122no—
453Dic3—122no—
454Dic3—122no—
455C32#307711yescharacteristic, complemented, Sylow
456C23—62no—
457C23—64no—
458C23—122no—
459C23—122no—
460C23C2×#62611yescharacteristic
461Q8—362no—
462Q8—362no—
463D4—34no—
464D4—62no—
465D4—64no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—62no—
469C2×C4—124no—
470C2×C4—122no—
471C2×C4—124no—
472C2×C4—182no—
473C2×C4—182no—
474C2×C4D3×Dic612yes—
475C2×C4#379512yes—
476C2×C4C2×#62611yescharacteristic
477C2×C4C2×#62611yescharacteristic
478C2×C4C2×#62611yescharacteristic
479C2×C4C2×#62611yescharacteristic
480C2×C4C2×#62611yescharacteristic
481C2×C4C22×D3211yescharacteristic
482C8—64no—
483C2×C3—22no—
484C2×C3—22no—
485C2×C3—21no—
486C2×C3—21no—
487C2×C3—21no—
488C2×C3—42no—
489C2×C3—124no—
490C2×C3C2×#89711yescharacteristic
491C2×C3C2×#90811yescharacteristic
492C2×C3#574811yescharacteristic
493C2×C3C2×#92411yescharacteristic
494C2×C3C2×#93211yescharacteristic
495C2×C3#582211yescharacteristic
496D3—44no—
497C22—21no—
498C22—21no—
499C22—64no—
500C22—128no—
501C22—122no—
502C22—122no—
503C22#6385712yes—
504C22C22×#62611yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—122no—
509C4—362no—
510C4—362no—
511C4#6383012yes—
512C4#6385712yes—
513C4C2×D3×Dic611yescharacteristic
514C4C2×#379511yescharacteristic
515C3—21no—
516C3#7905911yescharacteristic, complemented
517C3#8229611yescharacteristic, complemented
518C2—22no—
519C2—124no—
520C2C2×#6383011yescharacteristic
521C2#1059479511yescharacteristic
522C2C2×#6385711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32#3077
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595941C2semidirect
3. C3×#4924C2semidirect
4. #10591130C2semidirect
6. #10590272C2semidirect
7. #10590271C2semidirect
8. #10590268C2semidirect
17. #64079C22semidirect
18. #64078C22semidirect
19. #64078C22semidirect
29. C3×C4⋊(C3⋊C8)C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. #63575C22semidirect
32. #63573C22semidirect
48. #4924D3semidirect
61. C2×C3×D12Q8semidirect
140. C4⋊(C3⋊C8)C2×D3semidirect
141. C4⋊(C3⋊C8)C2×D3semidirect
199. C2×D12Dic6semidirect
455. C32#3077semidirect
516. C3#79059semidirect
517. C3#82296semidirect

Maximal subgroups

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

subgroupindex
#105959412
C2×C3×C4×D122
C3×#49242
#105911302
#105910862
#105902722
#105902712
#105902682
#822963
#790593