Finite Group Databasebeta

← #11869693

Subgroups — #11869693

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#10595995C211yesmaximal, characteristic
2#10594969C211yesmaximal, characteristic, complemented
3C3×#4998C212yesmaximal, complemented
4#10591105C212yesmaximal, complemented
5C2×#63557C211yesmaximal, characteristic, complemented
6#10590451C212yesmaximal, complemented
7#10590450C212yesmaximal, complemented
8#10590445C211yesmaximal, characteristic, complemented
9#10590444C211yesmaximal, characteristic, complemented
10#10590443C211yesmaximal, characteristic, complemented
11#10590442C211yesmaximal, characteristic, complemented
12#79185—32nomaximal
13C2×#3828C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C32×#117C2211yescharacteristic
16#64106C2211yescharacteristic
17#64106C2211yescharacteristic
18#64104C2211yescharacteristic
19#64104C2211yescharacteristic
20#64095—21no—
21#64091—21no—
22C4×C4⋊(C3⋊D3)—21no—
23C4×C4⋊(C3⋊D3)—21no—
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×#808C2212yescomplemented
34C3×#808C2212yescomplemented
35C3×#807C2212yescomplemented
36C3×#807C2212yescomplemented
37#63567C2212yescomplemented
38#63567C2212yescomplemented
39#63564C2212yescomplemented
40#63564C2212yescomplemented
41#63557C2211yescharacteristic
42#63557C2211yescharacteristic
43#63557C2212yes—
44#5524—32no—
45#5524—61no—
46D3×#117—32no—
47C3×#427—32no—
48#5113—32no—
49C2×(C2×D3)⋊C8—32no—
50#5002—32no—
51#4998D312yescomplemented
52#4888—32no—
53#4885—32no—
54#4884—32no—
55#4882—32no—
56#4868—32no—
57#4866—32no—
58#4863—32no—
59#4862—32no—
60C23×C3⋊D3D411yescharacteristic
61C22×C32×C4C2311yescharacteristic
62C2×#638—21no—
63C22×C3⋊Dic3D411yescharacteristic
64#3828—24no—
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—24no—
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3D411yescharacteristic
71C2×C4×C3⋊D3D411yescharacteristic
72C2×C4×C3⋊D3C2311yescharacteristic
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×#634C2311yescharacteristic
75C2×#624—21no—
76C2×#624—21no—
77C32×C4⋊C4C2311yescharacteristic
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80C32×C42—21no—
81#3752—21no—
82#3752—21no—
83#3752—21no—
84#3752—21no—
85C4⋊(C3⋊Dic3)—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×#235—32no—
100C2×#235—61no—
101C22×C4×D3—32no—
102C22×C4×D3—61no—
103C22×C3×C8—32no—
104C3×#117—21no—
105C3×#117—32no—
106C3×#117C2×D312yes—
107#926C2×D312yes—
108C22×C3⋊C8C2×D312yes—
109#897—32no—
110#897—32no—
111#897—61no—
112#897—61no—
113#895—32no—
114#895—32no—
115#895—61no—
116#895—61no—
117#892—32no—
118#892—32no—
119D3×C4⋊C4—32no—
120D3×C4⋊C4—32no—
121#886—62no—
122#886—62no—
123#882—62no—
124#882—62no—
125D3×C22⋊C4—62no—
126#877—62no—
127C4×D12—62no—
128C4×D12—62no—
129C4×D12—62no—
130C4×D12—62no—
131#872—62no—
132C42×D3—62no—
133C3×#107—32no—
134C3×#107—32no—
135C3×#106—32no—
136C3×#106—32no—
137#821—32no—
138#821—32no—
139(C2×D3)⋊C8—32no—
140(C2×D3)⋊C8—32no—
141(C2×D3)⋊C8—32no—
142(C2×D3)⋊C8—32no—
143#816—32no—
144#816—32no—
145#810—32no—
146#810—32no—
147#809—32no—
148#809—32no—
149#808C2×D312yescomplemented
150#808C2×D312yescomplemented
151#807C2×D312yescomplemented
152#807C2×D312yescomplemented
153C23×C32C2×D411yescharacteristic
154C22×C3⋊D3—21no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—41no—
158C22×C3⋊D3C2×D411yescharacteristic
159C22×C3⋊D3C2×D411yescharacteristic
160C2×C32×C4—21no—
161C2×C32×C4—21no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4#4114yes—
164C2×C32×C4C2411yescharacteristic
165#638—42no—
166C2×C3⋊Dic3—21no—
167C2×C3⋊Dic3—22no—
168C2×C3⋊Dic3C2×D411yescharacteristic
169C2×C3⋊Dic3C2×D411yescharacteristic
170C4⋊(C3⋊D3)—22no—
171C4⋊(C3⋊D3)—42no—
172C4⋊(C3⋊D3)—42no—
173C4×C3⋊D3—22no—
174C4×C3⋊D3—22no—
175C4×C3⋊D3—22no—
176C4×C3⋊D3—22no—
177C4×C3⋊D3—42no—
178#634—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—32no—
194#416—92no—
195C2×C22⋊C8—91no—
196C23×D3—32no—
197C23×D3—61no—
198C22×C3×C4—21no—
199C22×C3×C4C22×D312yes—
200C2×#67—62no—
201C2×#67—62no—
202C22×Dic3—32no—
203C22×Dic3—61no—
204#235—64no—
205#235—64no—
206#235—124no—
207C2×D12—32no—
208C2×D12—61no—
209C2×D12—62no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—62no—
213C2×C4×D3—32no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—32no—
217C2×C4×D3—61no—
218C2×C4×D3—61no—
219C2×C4×D3—61no—
220C2×C4×D3—61no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×C4×D3—124no—
228C2×Dic6—32no—
229C2×Dic6—61no—
230C2×C3×C8—32no—
231C2×C3×C8—32no—
232C2×C3×C8—64no—
233C3×C4⋊C4—21no—
234C3×C4⋊C4—21no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4C22×D312yes—
238C3×C4⋊C4C22×D312yes—
239C3×C22⋊C4—22no—
240C3×C22⋊C4—22no—
241C3×C22⋊C4—62no—
242C3×C42—22no—
243C3×C42—22no—
244C3×C42—62no—
245#217—22no—
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—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—62no—
253(C2×D3)⋊C4—62no—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256C4⋊Dic3—62no—
257C4⋊Dic3—62no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3C22×D312yes—
261C4⋊Dic3C22×D312yes—
262Dic3⋊C4—62no—
263Dic3⋊C4—62no—
264C4×Dic3—22no—
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#12312yes—
273C22×C32C22×D411yescharacteristic
274C2×C3⋊D3—21no—
275C2×C3⋊D3—21no—
276C2×C3⋊D3—21no—
277C2×C3⋊D3—21no—
278C2×C3⋊D3—21no—
279C2×C3⋊D3—44no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3#13512yes—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4#12312yes—
287C32×C4C2×#4112yes—
288C3⋊Dic3—21no—
289C3⋊Dic3—21no—
290C3⋊Dic3—41no—
291C3×Dic3—42no—
292C3×Dic3—42no—
293C2×#41—91no—
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—181no—
307#117—181no—
308#117D3211yescharacteristic
309C2×C4⋊C4—91no—
310C2×C4⋊C4—91no—
311C2×C22⋊C4—181no—
312C2×C42—181no—
313#107—32no—
314#107—32no—
315#106—32no—
316#106—32no—
317#103—92no—
318#103—92no—
319#102—92no—
320#102—92no—
321C22⋊C8—91no—
322C22⋊C8—91no—
323C22⋊C8—92no—
324C23×C3—21no—
325C23×C3D3×D412yes—
326C22×D3—32no—
327C22×D3—32no—
328C22×D3—61no—
329C22×D3—61no—
330C22×D3—64no—
331C22×D3—64no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—122no—
337C22×D3—122no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—24no—
344C2×C3×C4—21no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4#23514yes—
348C2×C3×C4D3×D412yes—
349C2×C3×C4#23914yes—
350C2×C3×C4C23×D312yes—
351#67—124no—
352#67—124no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—64no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—122no—
363D12—62no—
364D12—62no—
365D12—122no—
366D12—124no—
367D12—124no—
368D12—124no—
369D12—124no—
370C4×D3—64no—
371C4×D3—64no—
372C4×D3—62no—
373C4×D3—62no—
374C4×D3—62no—
375C4×D3—62no—
376C4×D3—122no—
377C4×D3—122no—
378C4×D3—122no—
379C4×D3—122no—
380C4×D3—124no—
381C4×D3—124no—
382C4×D3—124no—
383C4×D3—124no—
384Dic6—62no—
385Dic6—62no—
386Dic6—122no—
387C3×C8—62no—
388C3×C8—62no—
389C3⋊C8—22no—
390C3⋊C8—22no—
391C2×C32—22no—
392C2×C32C2×#12311yescharacteristic
393C2×C32C2×#13511yescharacteristic
394C2×C32#57511yescharacteristic
395C3⋊D3—22no—
396C3⋊D3—41no—
397C3⋊D3—81no—
398C24—91no—
399#41—184no—
400C2×Q8—91no—
401C2×D4—91no—
402C2×D4—181no—
403C2×D4—181no—
404C2×D4—181no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—181no—
411C22×C4—181no—
412C22×C4—184no—
413C22×C4—181no—
414C22×C4C2×D3211yescharacteristic
415C2×C8—32no—
416C2×C8—32no—
417C2×C8—64no—
418C4⋊C4—32no—
419C4⋊C4—32no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C4⋊C4—181no—
424C4⋊C4C2×D3211yescharacteristic
425C4⋊C4C2×D3211yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—62no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4—181no—
432C22⋊C4—182no—
433C42—21no—
434C42—62no—
435C42—182no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—22no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3#89414yes—
443C22×C3C2×D3×D412yes—
444C2×D3—34no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—62no—
448C2×D3—62no—
449C2×D3—62no—
450C2×D3—62no—
451C2×D3—62no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—128no—
457C2×D3—128no—
458C2×D3—122no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C3×C4—22no—
465C3×C4—22no—
466C3×C4—42no—
467C3×C4—42no—
468C3×C4—42no—
469C3×C4—42no—
470C3×C4—122no—
471C3×C4—122no—
472C3×C4#89414yes—
473C3×C4C2×#23512yes—
474C3×C4C2×#23912yes—
475Dic3—42no—
476Dic3—42no—
477Dic3—62no—
478Dic3—62no—
479Dic3—121no—
480Dic3—121no—
481Dic3—122no—
482Dic3—122no—
483C32#309111yescharacteristic, complemented, Sylow
484C23—91no—
485C23—91no—
486C23—182no—
487C23—182no—
488C23—181no—
489C23—361no—
490C23#381111yescharacteristic
491Q8—182no—
492D4—182no—
493D4—362no—
494D4—362no—
495D4—362no—
496C2×C4—21no—
497C2×C4—21no—
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—362no—
509C2×C4—362no—
510C2×C4—362no—
511C2×C4#379914yes—
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×C3C2×#89412yes—
522C2×C3D3×#13512yes—
523C2×C3#576812yes—
524D3—64no—
525D3—122no—
526D3—122no—
527D3—122no—
528D3—242no—
529D3—242no—
530C22—21no—
531C22—21no—
532C22—92no—
533C22—181no—
534C22—181no—
535C22—181no—
536C22—181no—
537C22—181no—
538C22—364no—
539C22—361no—
540C22—361no—
541C22—361no—
542C22#6389712yes—
543C22C2×#381111yescharacteristic
544C4—41no—
545C4—41no—
546C4—122no—
547C4—122no—
548C4—181no—
549C4—181no—
550C4—361no—
551C4#6389712yes—
552C4C2×#379912yes—
553C3—21no—
554C3#7918512yescomplemented
555C2—22no—
556C2—182no—
557C2—361no—
558C2—721no—
559C2C2×#6389711yescharacteristic
560C2#1059545911yescharacteristic
561C2#1059546011yescharacteristic
subgroupG/H
centerC2×C4#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595995C2
hypercenter#117D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594969C2semidirect
3. C3×#4998C2semidirect
4. #10591105C2semidirect
5. C2×#63557C2semidirect
6. #10590451C2semidirect
7. #10590450C2semidirect
8. #10590445C2semidirect
9. #10590444C2semidirect
10. #10590443C2semidirect
11. #10590442C2semidirect
33. C3×#808C22semidirect
34. C3×#808C22semidirect
35. C3×#807C22semidirect
36. C3×#807C22semidirect
37. #63567C22semidirect
38. #63567C22semidirect
39. #63564C22semidirect
40. #63564C22semidirect
51. #4998D3semidirect
149. #808C2×D3semidirect
150. #808C2×D3semidirect
151. #807C2×D3semidirect
152. #807C2×D3semidirect
483. C32#3091semidirect
554. C3#79185semidirect

Maximal subgroups

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

subgroupindex
#105959952
#105949692
C3×#49982
#105911052
C2×#635572
#105904512
#105904502
#105904452
#105904442
#105904432
#105904422
#791853