Finite Group Databasebeta

← #11869685

Subgroups — #11869685

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 563 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596299C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic, complemented
3C3×#5233C212yesmaximal, complemented
4#10591561C212yesmaximal, complemented
5#10591555C211yesmaximal, characteristic, complemented
6#10591553C211yesmaximal, characteristic, complemented
7#10591425C212yesmaximal, complemented
8#10591419C211yesmaximal, characteristic, complemented
9#10591417C211yesmaximal, characteristic, complemented
10#10591122C212yesmaximal, complemented
11C2×#63557C211yesmaximal, characteristic, complemented
12#78842—32nomaximal
13C2×C32×#41C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15#64155C2211yescharacteristic
16#64155C2211yescharacteristic
17#64147C2211yescharacteristic
18#64147C2211yescharacteristic
19#64146—21no—
20#64144—21no—
21C4×#638—21no—
22C4×#638—21no—
23#64135C2211yescharacteristic
24C3×#926C2212yes—
25C22×C3×C3⋊C8C2212yes—
26#63974—21no—
27#63957—21no—
28#63900C2211yescharacteristic
29#63900C2211yescharacteristic
30C4×#624—21no—
31#63874—21no—
32#63849C2212yes—
33C3×#835C2212yescomplemented
34C3×#835C2212yescomplemented
35C3×#832C2212yescomplemented
36C3×#832C2212yescomplemented
37#63575C2212yescomplemented
38#63575C2212yescomplemented
39#63573C2212yescomplemented
40#63573C2212yescomplemented
41#63557C2211yescharacteristic
42#63557C2211yescharacteristic
43#63557C2212yes—
44#5828—32no—
45#5828—61no—
46D3×#117—32no—
47C3×#416—32no—
48#5233D312yescomplemented
49C2×(C2×D3)⋊C8—32no—
50#5106—32no—
51#4998—32no—
52#4815—32no—
53#4814—32no—
54#4811—32no—
55#4805—32no—
56#4784—32no—
57#4779—32no—
58#4777—32no—
59#4774—32no—
60C23×C3⋊D3D411yescharacteristic
61C32×#41—24no—
62C2×C32×Q8C2311yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4C2311yescharacteristic
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C2×#638—21no—
68C2×#638—21no—
69C22×C3⋊Dic3D411yescharacteristic
70C2×C4×C3⋊D3—24no—
71C2×C4×C3⋊D3D411yescharacteristic
72C2×C4×C3⋊D3D411yescharacteristic
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×C4×C3⋊D3C2311yescharacteristic
75C2×#624—21no—
76C2×#624—21no—
77#3757—21no—
78#3757—21no—
79#3757—21no—
80#3752—21no—
81#3752—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84#3750—21no—
85#3750—21no—
86C4×C3⋊Dic3—21no—
87C3×#217—22no—
88C3×C4⋊Dic3C2312yes—
89C3×C4⋊Dic3C2312yes—
90C3×C4×Dic3—22no—
91C2×C3×C3⋊C8—24no—
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2312yes—
94#3724—21no—
95#3724—21no—
96#3722—22no—
97Dic32—22no—
98#3091—91noSylow
99C2×C3×#41—21no—
100C2×C3×#41C2×D312yes—
101C22×C4×D3—32no—
102C22×C4×D3—61no—
103C22×C3×C8—32no—
104C3×#117—32no—
105#946—32no—
106#946—32no—
107#946—61no—
108#946—61no—
109#938—32no—
110#938—32no—
111#938—61no—
112#938—61no—
113#937—62no—
114#937—62no—
115#935—62no—
116#935—62no—
117C4×#67—62no—
118C4×#67—62no—
119C4×#67—62no—
120C4×#67—62no—
121#926—32no—
122#926—61no—
123#926C2×D312yes—
124C22×C3⋊C8C2×D312yes—
125#892—32no—
126#892—32no—
127D3×C4⋊C4—32no—
128D3×C4⋊C4—32no—
129D3×C22⋊C4—62no—
130#877—62no—
131#872—62no—
132C42×D3—62no—
133C3×#103—32no—
134C3×#103—32no—
135C3×#102—32no—
136C3×#102—32no—
137#835C2×D312yescomplemented
138#835C2×D312yescomplemented
139#832C2×D312yescomplemented
140#832C2×D312yescomplemented
141(C2×D3)⋊C8—32no—
142(C2×D3)⋊C8—32no—
143(C2×D3)⋊C8—32no—
144(C2×D3)⋊C8—32no—
145#818—32no—
146#818—32no—
147#817—32no—
148#817—32no—
149#808—32no—
150#808—32no—
151#807—32no—
152#807—32no—
153C23×C32—21no—
154C23×C32C2×D411yescharacteristic
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—41no—
158C22×C3⋊D3C2×D411yescharacteristic
159C22×C3⋊D3C2×D411yescharacteristic
160C32×Q8—22no—
161C32×D4—22no—
162C32×D4—42no—
163C2×C32×C4—21no—
164C2×C32×C4—42no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4#4114yes—
167C2×C32×C4C2411yescharacteristic
168#638—42no—
169#638—42no—
170C2×C3⋊Dic3—21no—
171C2×C3⋊Dic3—21no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3C2×D411yescharacteristic
174C2×C3⋊Dic3C2×D411yescharacteristic
175C4×C3⋊D3—22no—
176C4×C3⋊D3—22no—
177C4×C3⋊D3—22no—
178C4×C3⋊D3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181#624—42no—
182#624—42no—
183C3×C3⋊C8—22no—
184C3×C3⋊C8—22no—
185#525—91no—
186C2×#117—91no—
187#485—92no—
188#484—91no—
189#483—91no—
190#482—92no—
191#481—91no—
192#480—91no—
193#427—92no—
194#416—32no—
195C2×C22⋊C8—91no—
196C23×D3—32no—
197C23×D3—61no—
198C3×#41—24no—
199C3×#41—24no—
200C3×#41—44no—
201C2×C3×Q8—21no—
202C2×C3×Q8C22×D312yes—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—21no—
206C2×C3×D4C22×D312yes—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4C22×D312yes—
211C2×#67—62no—
212C2×#67—62no—
213C2×#67—62no—
214C2×#67—62no—
215C22×Dic3—32no—
216C22×Dic3—61no—
217C2×C4×D3—32no—
218C2×C4×D3—32no—
219C2×C4×D3—32no—
220C2×C4×D3—32no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—61no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—62no—
228C2×C4×D3—62no—
229C2×C4×D3—124no—
230C2×C3×C8—32no—
231C2×C3×C8—32no—
232C2×C3×C8—64no—
233C3×C4⋊C4—32no—
234C3×C4⋊C4—32no—
235C3×C22⋊C4—62no—
236C3×C42—62no—
237#217—22no—
238#217—62no—
239#217—62no—
240#217—62no—
241#217—62no—
242#217—62no—
243#217—62no—
244(C2×D3)⋊C4—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—
250C4⋊Dic3—32no—
251C4⋊Dic3—32no—
252C4⋊Dic3—61no—
253C4⋊Dic3—61no—
254C4⋊Dic3C22×D312yes—
255C4⋊Dic3C22×D312yes—
256Dic3⋊C4—62no—
257Dic3⋊C4—62no—
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260Dic3⋊C4—62no—
261Dic3⋊C4—62no—
262C4×Dic3—22no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265C4×Dic3—62no—
266C4×Dic3—62no—
267C2×C3⋊C8—24no—
268C2×C3⋊C8C22×D312yes—
269C2×C3⋊C8C22×D312yes—
270C22×C32—21no—
271C22×C32—21no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32#12312yes—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—21no—
280C2×C3⋊D3—21no—
281C2×C3⋊D3—21no—
282C2×C3⋊D3—44no—
283C2×C3⋊D3#13512yes—
284C32×C4—41no—
285C32×C4#12312yes—
286C32×C4C2×#4112yes—
287C3⋊Dic3—21no—
288C3⋊Dic3—21no—
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C2×#41D3211yescharacteristic
294C23×C4—91no—
295C22×C8—32no—
296#123—181no—
297C22⋊Q8—91no—
298C22⋊Q8—91no—
299#121—91no—
300#121—91no—
301#120—181no—
302C4×D4—181no—
303C4×D4—181no—
304#117—32no—
305#117—92no—
306#117—91no—
307#117—181no—
308#117—181no—
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C22⋊C4—181no—
312C2×C42—181no—
313#107—92no—
314#107—92no—
315#106—92no—
316#106—92no—
317#103—32no—
318#103—32no—
319#102—32no—
320#102—32no—
321C22⋊C8—91no—
322C22⋊C8—91no—
323C22⋊C8—92no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—21no—
327C23×C3D3×D412yes—
328C22×D3—32no—
329C22×D3—32no—
330C22×D3—61no—
331C22×D3—61no—
332C22×D3—64no—
333C22×D3—64no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—122no—
337C22×D3—122no—
338C3×Q8—22no—
339C3×Q8—22no—
340C3×Q8—42no—
341C3×D4—22no—
342C3×D4—22no—
343C3×D4—42no—
344C3×D4—44no—
345C3×D4—44no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—24no—
350C2×C3×C4—21no—
351C2×C3×C4—44no—
352C2×C3×C4—44no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4#23514yes—
356C2×C3×C4D3×D412yes—
357C2×C3×C4#23714yes—
358C2×C3×C4C23×D312yes—
359#67—124no—
360#67—124no—
361#67—124no—
362#67—124no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—32no—
366C2×Dic3—32no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—64no—
370C2×Dic3—62no—
371C2×Dic3—62no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—122no—
375C4×D3—64no—
376C4×D3—64no—
377C4×D3—62no—
378C4×D3—62no—
379C4×D3—62no—
380C4×D3—62no—
381C4×D3—122no—
382C4×D3—122no—
383C4×D3—122no—
384C4×D3—122no—
385C4×D3—124no—
386C4×D3—124no—
387C3×C8—62no—
388C3×C8—62no—
389C3⋊C8—22no—
390C3⋊C8—22no—
391C2×C32—22no—
392C2×C32—81no—
393C2×C32C2×#12311yescharacteristic
394C2×C32C2×#13511yescharacteristic
395C2×C32#57511yescharacteristic
396C3⋊D3—22no—
397C3⋊D3—41no—
398C24—91no—
399#41—24no—
400C2×Q8C2×D3211yescharacteristic
401C2×D4—21no—
402C2×D4—181no—
403C2×D4—181no—
404C2×D4C2×D3211yescharacteristic
405C22×C4—21no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—181no—
412C22×C4—181no—
413C22×C4—184no—
414C22×C4C2×D3211yescharacteristic
415C2×C8—32no—
416C2×C8—32no—
417C2×C8—64no—
418C4⋊C4—32no—
419C4⋊C4—32no—
420C4⋊C4—91no—
421C4⋊C4—91no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4—181no—
425C4⋊C4—181no—
426C22⋊C4—62no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—182no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—181no—
433C42—62no—
434C42—182no—
435C42—181no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—22no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—42no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—42no—
446C22×C3—42no—
447C22×C3—42no—
448C22×C3#88314yes—
449C22×C3C2×D3×D412yes—
450C2×D3—34no—
451C2×D3—62no—
452C2×D3—62no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—62no—
457C2×D3—62no—
458C2×D3—121no—
459C2×D3—121no—
460C2×D3—121no—
461C2×D3—121no—
462C2×D3—128no—
463C2×D3—128no—
464C3×C4—22no—
465C3×C4—22no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—122no—
469C3×C4—122no—
470C3×C4#88314yes—
471C3×C4C2×#23512yes—
472C3×C4C2×#23712yes—
473Dic3—42no—
474Dic3—42no—
475Dic3—62no—
476Dic3—62no—
477Dic3—121no—
478Dic3—121no—
479Dic3—122no—
480Dic3—122no—
481Dic3—122no—
482Dic3—122no—
483C32#309111yescharacteristic, complemented, Sylow
484C23—21no—
485C23—91no—
486C23—91no—
487C23—182no—
488C23—182no—
489C23—361no—
490C23#381111yescharacteristic
491Q8—22no—
492D4—22no—
493D4—42no—
494D4—362no—
495D4—362no—
496C2×C4—21no—
497C2×C4—42no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—91no—
501C2×C4—91no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—182no—
506C2×C4—182no—
507C2×C4—181no—
508C2×C4—181no—
509C2×C4—362no—
510C2×C4—362no—
511C2×C4#380414yes—
512C2×C4#381111yescharacteristic
513C2×C4C22×D3211yescharacteristic
514C8—62no—
515C8—62no—
516C2×C3—24no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—42no—
521C2×C3—82no—
522C2×C3—82no—
523C2×C3C2×#88312yes—
524C2×C3D3×#13512yes—
525C2×C3#576812yes—
526D3—64no—
527D3—122no—
528D3—122no—
529D3—122no—
530C22—21no—
531C22—21no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—92no—
536C22—181no—
537C22—181no—
538C22—181no—
539C22—181no—
540C22—181no—
541C22—364no—
542C22#6397512yes—
543C22C2×#381111yescharacteristic
544C4—41no—
545C4—122no—
546C4—122no—
547C4—181no—
548C4—181no—
549C4—361no—
550C4—361no—
551C4#6397512yes—
552C4C2×#380412yes—
553C3—21no—
554C3#7884212yescomplemented
555C2—22no—
556C2—81no—
557C2—182no—
558C2—361no—
559C2#1059545911yescharacteristic
560C2#1059546011yescharacteristic
561C2C2×#6397511yescharacteristic
subgroupG/H
centerC2×C4#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radical#10596299C2
hypercenterC2×#41D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594969C2semidirect
3. C3×#5233C2semidirect
4. #10591561C2semidirect
5. #10591555C2semidirect
6. #10591553C2semidirect
7. #10591425C2semidirect
8. #10591419C2semidirect
9. #10591417C2semidirect
10. #10591122C2semidirect
11. C2×#63557C2semidirect
33. C3×#835C22semidirect
34. C3×#835C22semidirect
35. C3×#832C22semidirect
36. C3×#832C22semidirect
37. #63575C22semidirect
38. #63575C22semidirect
39. #63573C22semidirect
40. #63573C22semidirect
48. #5233D3semidirect
137. #835C2×D3semidirect
138. #835C2×D3semidirect
139. #832C2×D3semidirect
140. #832C2×D3semidirect
483. C32#3091semidirect
554. C3#78842semidirect

Maximal subgroups

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

subgroupindex
#105962992
#105949692
C3×#52332
#105915612
#105915552
#105915532
#105914252
#105914192
#105914172
#105911222
C2×#635572
#788423