Finite Group Databasebeta

← #11868976

Subgroups — #11868976

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5500C211yesmaximal, characteristic, complemented
2#10594996C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic
4C3×#4964C211yesmaximal, characteristic, complemented
5#10591138C211yesmaximal, characteristic, complemented
6#10591117C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic
8#10590470C212yesmaximal, complemented
9#10590468C212yesmaximal, complemented
10#10590466C212yesmaximal, complemented
11#10590464C212yesmaximal, complemented
12#83474—31nomaximal
13#79242—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C3×#924—22no—
21C2×C3×#208C2211yescharacteristic
22C3×#890—21no—
23C3×#890C2212yescomplemented
24C3×#888—21no—
25C3×#888C2212yescomplemented
26#63974—22no—
27#63894—21no—
28#63894—21no—
29#63894C2212yes—
30#63894C2212yes—
31#63636C2212yes—
32#63636C2212yes—
33C3×#808C2212yescomplemented
34C3×#807C2212yescomplemented
35#63576C2211yescharacteristic, complemented
36#63576C2211yescharacteristic, complemented
37#63574C2211yescharacteristic, complemented
38#63574C2211yescharacteristic, complemented
39Dic3⋊(C3⋊C8)C2212yescomplemented
40Dic3⋊(C3⋊C8)C2212yescomplemented
41#63564C2212yes—
42#63564C2212yes—
43C3×#544—31no—
44#5521—31no—
45#5521—31no—
46#5500D311yescharacteristic, complemented
47C3×#428—31no—
48#5131—31no—
49#5119—31no—
50#5087—32no—
51#5084—32no—
52#5066—32no—
53#5066—32no—
54#5001—31no—
55#4999—31no—
56#4998—31no—
57#4998—31no—
58C2×#809—31no—
59C2×#809—31no—
60C2×#809—61no—
61#4964D311yescharacteristic, complemented
62#4891—32no—
63#4890—32no—
64#4871—32no—
65#4870—32no—
66C23×C3⋊D3—21no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)Q814yescomplemented
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C3×Dic6—22no—
74C2×#624—22no—
75C2×#624—22no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78C2×C3⋊(C3⋊C8)—22no—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C3×#217—21no—
82C3×#217—21no—
83C3×#217D412yes—
84C3×C4⋊Dic3—22no—
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—21no—
94C3×C4×Dic3—21no—
95C3×C4×Dic3C2312yes—
96C3×#208—22no—
97C2×C3×C3⋊C8C2312yes—
98#3722—22no—
99#3722—22no—
100#3081—91noSylow
101C22×D12—31no—
102C22×D12—31no—
103C22×D12—61no—
104C2×C3×M16—31no—
105C3×C4⋊Q8—32no—
106C3×C4⋊Q8—61no—
107C3×#125—32no—
108C3×#125—61no—
109C3×C22⋊Q8—62no—
110C3×#117—31no—
111C3×#117—31no—
112C3×#117—31no—
113C2×C3×C4⋊C4—21no—
114C2×C3×C4⋊C4C2×D311yescharacteristic
115C2×C3×C4⋊C4C2×D311yescharacteristic
116#926C2×D311yescharacteristic
117#926C2×D311yescharacteristic
118#926C2×D311yescharacteristic
119#924—22no—
120C2×#208C2×D311yescharacteristic
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124#893—32no—
125#893—32no—
126#893—61no—
127#893—61no—
128#890—21no—
129#890C2×D312yescomplemented
130#888—21no—
131#888C2×D312yescomplemented
132D3×C22⋊C4—62no—
133D3×C22⋊C4—62no—
134C4×D12—32no—
135C4×D12—32no—
136C4×D12—61no—
137C4×D12—61no—
138C3×#107—32no—
139C3×#106—32no—
140#821—32no—
141#821—32no—
142Dic3⋊C8—32no—
143Dic3⋊C8—32no—
144#809—32no—
145#809—32no—
146#809—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—62no—
151#809—62no—
152#808—31no—
153#808—31no—
154#808—31no—
155#808—31no—
156#808C2×D312yescomplemented
157#807—31no—
158#807—31no—
159#807—31no—
160#807—31no—
161#807C2×D312yescomplemented
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)—32no—
164C23×C32C2×D411yescharacteristic
165C22×C3⋊D3—22no—
166C22×C3⋊D3—24no—
167C22×C3⋊D3—81no—
168C22×C3⋊D3—81no—
169C2×C32×C4—22no—
170C2×C32×C4—81no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×Q812yes—
173C2×C32×C4#4112yes—
174C2×C32×C4C2411yescharacteristic
175C4⋊(C3⋊D3)—24no—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)C2×Q814yes—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C3×Dic6—82no—
185#624—82no—
186#624—82no—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)—21no—
189C3×C3⋊C8—22no—
190#544—31no—
191#518—91no—
192#478—92no—
193#478—92no—
194#476—92no—
195#474—92no—
196#428—31no—
197#427—91no—
198#424—91no—
199#418—91no—
200C2×#102—91no—
201C23×D3—61no—
202C23×D3—61no—
203C23×D3—121no—
204C2×C3×Q8—62no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—41no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×D12—34no—
212C2×D12—34no—
213C2×D12—32no—
214C2×D12—32no—
215C2×D12—62no—
216C2×D12—64no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—62no—
220C2×D12—61no—
221C2×D12—122no—
222C2×D12—121no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×C4×D3—62no—
227C2×Dic6—22no—
228C3×M16—62no—
229C2×C3×C8—32no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—31no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—31no—
238C3×C4⋊C4—31no—
239C3×C4⋊C4—41no—
240C3×C4⋊C4—62no—
241C3×C4⋊C4—62no—
242C3×C4⋊C4—62no—
243C3×C4⋊C4C22×D312yes—
244C3×C4⋊C4C22×D312yes—
245C3×C22⋊C4—32no—
246C3×C22⋊C4—61no—
247C3×C22⋊C4—61no—
248C3×C42—32no—
249C3×C42—61no—
250C3×C42—61no—
251#217—21no—
252#217—21no—
253#217#6712yes—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—22no—
259C4⋊Dic3#6711yescharacteristic
260C4⋊Dic3#6711yescharacteristic
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D311yescharacteristic
264C4⋊Dic3C22×D311yescharacteristic
265Dic3⋊C4—22no—
266Dic3⋊C4—22no—
267C4×Dic3—21no—
268C4×Dic3—21no—
269C4×Dic3C22×D312yes—
270#208—22no—
271C2×C3⋊C8—31no—
272C2×C3⋊C8—31no—
273C2×C3⋊C8—31no—
274C2×C3⋊C8—31no—
275C2×C3⋊C8—61no—
276C2×C3⋊C8—61no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—122no—
280C2×C3⋊C8C22×D312yes—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32C22⋊Q812yes—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—24no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C2×C3⋊D3—84no—
289C32×C4—42no—
290C32×C4C22⋊Q812yes—
291C32×C4C22×Q811yescharacteristic
292C32×C4C2×#4111yescharacteristic
293C3×Dic3—22no—
294C3×Dic3—22no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C3×Dic3—41no—
298C3×Dic3—41no—
299C22×D4—91no—
300C2×M16—31no—
301C22×C8—91no—
302C4⋊Q8—32no—
303C4⋊Q8—61no—
304#125—32no—
305#125—61no—
306C22⋊Q8—62no—
307C4×D4—92no—
308C4×D4—92no—
309C4×D4—181no—
310C4×D4—181no—
311#117—31no—
312#117—31no—
313#117—31no—
314C2×C4⋊C4D3211yescharacteristic
315C2×C22⋊C4—182no—
316#107—32no—
317#107—91no—
318#107—91no—
319#106—32no—
320#106—91no—
321#106—91no—
322C4⋊C8—92no—
323C4⋊C8—92no—
324#102—92no—
325#102—92no—
326#102—92no—
327#102—92no—
328C23×C3—21no—
329C23×C3D3×D411yescharacteristic
330C23×C3C2×#6711yescharacteristic
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—64no—
334C22×D3—64no—
335C22×D3—122no—
336C22×D3—124no—
337C22×D3—241no—
338C22×D3—241no—
339C22×D3—241no—
340C22×D3—241no—
341C22×D3—242no—
342C22×D3—242no—
343C3×Q8—242no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—22no—
349C2×C3×C4—21no—
350C2×C3×C4—32no—
351C2×C3×C4—32no—
352C2×C3×C4—42no—
353C2×C3×C4—61no—
354C2×C3×C4—61no—
355C2×C3×C4—61no—
356C2×C3×C4—61no—
357C2×C3×C4—81no—
358C2×C3×C4—81no—
359C2×C3×C4—82no—
360C2×C3×C4#23512yes—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×Q812yes—
363C2×C3×C4D3×Q812yes—
364C2×C3×C4#23912yes—
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—21no—
372C2×Dic3C2×#6712yes—
373C2×Dic3C2×#6712yes—
374D12—34no—
375D12—34no—
376D12—64no—
377D12—64no—
378D12—64no—
379D12—62no—
380D12—62no—
381D12—122no—
382D12—124no—
383C4×D3—242no—
384C4×D3—242no—
385C4×D3—242no—
386C4×D3—242no—
387Dic6—82no—
388C3×C8—62no—
389C3⋊C8—22no—
390C3⋊C8—61no—
391C3⋊C8—61no—
392C3⋊C8—61no—
393C3⋊C8—61no—
394C3⋊C8—121no—
395C3⋊C8—121no—
396C2×C32—22no—
397C2×C32C2×C22⋊Q811yescharacteristic
398C2×C32#57611yescharacteristic
399C2×C32#57711yescharacteristic
400C3⋊D3—44no—
401C24—181no—
402C2×Q8—62no—
403C2×D4—92no—
404C2×D4—94no—
405C2×D4—182no—
406C2×D4—181no—
407C22×C4—21no—
408C22×C4—182no—
409C22×C4—182no—
410C22×C4C2×D3211yescharacteristic
411M16—62no—
412C2×C8—32no—
413C2×C8—91no—
414C2×C8—91no—
415C2×C8—182no—
416C4⋊C4—21no—
417C4⋊C4—31no—
418C4⋊C4—31no—
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—31no—
422C4⋊C4—31no—
423C4⋊C4—62no—
424C4⋊C4—62no—
425C4⋊C4—62no—
426C4⋊C4C2×D3212yes—
427C22⋊C4—32no—
428C22⋊C4—61no—
429C22⋊C4—61no—
430C22⋊C4—182no—
431C22⋊C4—182no—
432C42—32no—
433C42—61no—
434C42—61no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3#89612yes—
444C22×C3#94612yes—
445C22×C3C2×D3×D411yescharacteristic
446C22×C3C22×#6711yescharacteristic
447C2×D3—64no—
448C2×D3—64no—
449C2×D3—124no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—242no—
455C2×D3—242no—
456C2×D3—244no—
457C2×D3—244no—
458C2×D3—248no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4—62no—
465C3×C4—62no—
466C3×C4—82no—
467C3×C4—121no—
468C3×C4—121no—
469C3×C4—121no—
470C3×C4—121no—
471C3×C4#89612yes—
472C3×C4#94612yes—
473C3×C4C2×#23511yescharacteristic
474C3×C4C2×D3×Q811yescharacteristic
475C3×C4C2×D3×Q811yescharacteristic
476C3×C4C2×#23911yescharacteristic
477Dic3—22no—
478Dic3—22no—
479Dic3—41no—
480Dic3—41no—
481Dic3—41no—
482Dic3—41no—
483C32#308111yescharacteristic, complemented, Sylow
484C23—182no—
485C23—184no—
486C23—721no—
487C23—721no—
488C23D3×#6711yescharacteristic
489Q8—242no—
490D4—94no—
491D4—182no—
492D4—184no—
493C2×C4—22no—
494C2×C4—32no—
495C2×C4—32no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—61no—
500C2×C4—81no—
501C2×C4—722no—
502C2×C4—722no—
503C2×C4#379712yes—
504C2×C4#379912yes—
505C2×C4D3×#6711yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—62no—
508C8—181no—
509C8—181no—
510C2×C3—24no—
511C2×C3—22no—
512C2×C3—22no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3C2×#89611yescharacteristic
517C2×C3#577411yescharacteristic
518C2×C3#577811yescharacteristic
519C2×C3C2×#94611yescharacteristic
520C2×C3#583511yescharacteristic
521C2×C3#583711yescharacteristic
522D3—124no—
523D3—124no—
524D3—244no—
525C22—21no—
526C22—21no—
527C22—184no—
528C22—362no—
529C22—362no—
530C22—724no—
531C22#6388812yes—
532C22C2×D3×#6711yescharacteristic
533C4—42no—
534C4—62no—
535C4—62no—
536C4—121no—
537C4—121no—
538C4—121no—
539C4—121no—
540C4#6388812yes—
541C4C2×#379711yescharacteristic
542C4C2×#379911yescharacteristic
543C3—21no—
544C3#7924211yescharacteristic, complemented
545C3#8347411yescharacteristic, complemented
546C2—22no—
547C2—364no—
548C2C2×#6388811yescharacteristic
549C2#1059509711yescharacteristic
550C2#1059531911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5500C2semidirect
4. C3×#4964C2semidirect
5. #10591138C2semidirect
6. #10591117C2semidirect
8. #10590470C2semidirect
9. #10590468C2semidirect
10. #10590466C2semidirect
11. #10590464C2semidirect
23. C3×#890C22semidirect
25. C3×#888C22semidirect
33. C3×#808C22semidirect
34. C3×#807C22semidirect
35. #63576C22semidirect
36. #63576C22semidirect
37. #63574C22semidirect
38. #63574C22semidirect
39. Dic3⋊(C3⋊C8)C22semidirect
40. Dic3⋊(C3⋊C8)C22semidirect
46. #5500D3semidirect
61. #4964D3semidirect
71. C2×C4⋊(C3⋊D3)Q8semidirect
129. #890C2×D3semidirect
131. #888C2×D3semidirect
156. #808C2×D3semidirect
161. #807C2×D3semidirect
483. C32#3081semidirect
544. C3#79242semidirect
545. C3#83474semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
#105949962
C2×#636362
C3×#49642
#105911382
#105911172
#105910962
#105904702
#105904682
#105904662
#105904642
#834743
#792423