Finite Group Databasebeta

← #11868989

Subgroups — #11868989

Order 1152.

853 conjugacy classes of subgroups.

The subgroup lattice has 547 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595051C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic
3#10592805C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic
5C3×#5102C211yesmaximal, characteristic, complemented
6#10591130C211yesmaximal, characteristic, complemented
7#10591086C211yesmaximal, characteristic
8#10590772C212yesmaximal, complemented
9#10590767C212yesmaximal, complemented
10#10590762C212yesmaximal, complemented
11#10590757C212yesmaximal, complemented
12#79090—31nomaximal
13#78731—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16#64135C2211yescharacteristic
17#64135C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21D3×#217—22no—
22#63964—22no—
23#63919—21no—
24#63918C2212yescomplemented
25#63898—21no—
26#63898—21no—
27Dic3×D12C2212yes—
28Dic3×D12C2212yes—
29#63872—21no—
30#63869C2212yescomplemented
31#63645C2211yescharacteristic, complemented
32#63645C2211yescharacteristic, complemented
33#63644C2211yescharacteristic, complemented
34#63644C2211yescharacteristic, complemented
35C3×#821C2212yes—
36C3×#821C2212yes—
37C3×Dic3⋊C8C2212yescomplemented
38C3×Dic3⋊C8C2212yescomplemented
39#63575C2212yescomplemented
40#63573C2212yescomplemented
41#63563C2212yes—
42#63563C2212yes—
43#5798—31no—
44#5521—31no—
45#5519—31no—
46#5500—31no—
47C3×#424—31no—
48C2×C3×#102—31no—
49#5215—31no—
50#5131—31no—
51#5121—31no—
52C2×#821D311yescharacteristic
53#5106—31no—
54#5106—31no—
55#5106—61no—
56#5102D311yescharacteristic, complemented
57#4964—31no—
58#4847—32no—
59#4847—32no—
60#4846—32no—
61#4842—32no—
62#4766—32no—
63#4763—32no—
64#4761—32no—
65#4759—32no—
66C23×C3×D3—21no—
67C22×C32×C4C2311yescharacteristic
68C22×C3×Dic3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12Q814yescomplemented
72C2×C3×D12C2312yes—
73C2×#627—22no—
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76C2×C32×C8—22no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79#3757—21no—
80#3757—21no—
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83C4⋊(C3⋊Dic3)C2311yescharacteristic
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C4×C3⋊Dic3—21no—
86C4×C3⋊Dic3—21no—
87C3×#217D412yes—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×C4×Dic3C2312yes—
93C3×#208—22no—
94C2×C3×C3⋊C8C2312yes—
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3081—91noSylow
101C22×C3×D4—31no—
102C22×D12C2×D311yescharacteristic
103C2×C3×M16—31no—
104C22×C3×C8—21no—
105C22×C3×C8C2×D311yescharacteristic
106C22×C3×C8C2×D311yescharacteristic
107C3×#117—31no—
108C2×C3×C4⋊C4—31no—
109C2×#217—62no—
110D4×Dic3—32no—
111D4×Dic3—32no—
112D4×Dic3—61no—
113D4×Dic3—61no—
114#926—31no—
115#926—31no—
116#926—31no—
117#926—31no—
118#926—61no—
119#926—61no—
120#926C2×D311yescharacteristic
121C2×C4⋊Dic3C2×D311yescharacteristic
122#924—62no—
123C2×#208C2×D311yescharacteristic
124#893—61no—
125#893—61no—
126#890—32no—
127#890—61no—
128#890—61no—
129#888—32no—
130#888—61no—
131#888—61no—
132D3×C22⋊C4—62no—
133#878—62no—
134C4×D12—32no—
135C4×D12—32no—
136#870—32no—
137#869—32no—
138C3×C4⋊C8—32no—
139C3×C4⋊C8—32no—
140C3×#102—32no—
141C3×#102—32no—
142#832—32no—
143#832—32no—
144#821—32no—
145#821—32no—
146#821C2×D312yes—
147#821C2×D312yes—
148#818—31no—
149#818—31no—
150#818—31no—
151#818—31no—
152#818—32no—
153#818—61no—
154#818—61no—
155#817—31no—
156#817—31no—
157#817—31no—
158#817—31no—
159#817—32no—
160#817—61no—
161#817—61no—
162Dic3⋊C8C2×D312yescomplemented
163Dic3⋊C8C2×D312yescomplemented
164#808—32no—
165#807—32no—
166C23×C32C2×D411yescharacteristic
167C22×C3×D3—22no—
168C22×C3×D3—24no—
169C22×C3×D3—81no—
170C22×C3×D3—81no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×Q812yes—
173C2×C32×C4#4112yes—
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
177C2×C3⋊Dic3—21no—
178C2×C3⋊Dic3—21no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—81no—
181C2×C3×Dic3C2×D412yes—
182C2×C3×Dic3C2×D412yes—
183C3×D12—24no—
184C3×D12—22no—
185C3×D12C2×Q814yes—
186#627—82no—
187D3×Dic3—82no—
188D3×Dic3—82no—
189C32×C8—21no—
190C32×C8—21no—
191C3×C3⋊C8—22no—
192#544—91no—
193#518—91no—
194#478—92no—
195#478—92no—
196#476—92no—
197#474—92no—
198#428—91no—
199#427—91no—
200#424—31no—
201#418—91no—
202C2×#102—31no—
203C24×C3—61no—
204C23×D3—21no—
205C2×C3×D4—34no—
206C2×C3×D4—32no—
207C2×C3×D4—61no—
208C2×C3×D4—62no—
209C22×C3×C4—21no—
210C22×C3×C4—61no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C22×Dic3—21no—
214C22×Dic3—62no—
215C22×Dic3—62no—
216C2×D12—21no—
217C2×D12—22no—
218C2×D12Dic614yescomplemented
219C2×D12C22×D312yes—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C3×M16—62no—
225C2×C3×C8—24no—
226C2×C3×C8—22no—
227C2×C3×C8—22no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—32no—
231C2×C3×C8C22×D311yescharacteristic
232C2×C3×C8C22×D311yescharacteristic
233C2×C3×C8C22×D311yescharacteristic
234C2×C3×C8C22×D311yescharacteristic
235C3×C4⋊C4—31no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—32no—
238C3×C4⋊C4—61no—
239C3×C22⋊C4—32no—
240C3×C42—32no—
241#217—61no—
242#217—61no—
243#217—61no—
244#217—61no—
245#217—62no—
246#217—62no—
247#217—121no—
248#217—121no—
249#217D1212yes—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—31no—
258C4⋊Dic3—31no—
259C4⋊Dic3—31no—
260C4⋊Dic3—31no—
261C4⋊Dic3—61no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3—62no—
266C4⋊Dic3—62no—
267C4⋊Dic3D1211yescharacteristic
268C4⋊Dic3D1211yescharacteristic
269C4⋊Dic3C22×D312yes—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274C4×Dic3—61no—
275C4×Dic3—61no—
276C4×Dic3—61no—
277C4×Dic3—61no—
278C4×Dic3—121no—
279C4×Dic3—121no—
280C4×Dic3C22×D312yes—
281#208—22no—
282C2×C3⋊C8C22×D312yes—
283C22×C32—21no—
284C22×C32—21no—
285C22×C32C22⋊Q812yes—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—24no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—84no—
291C32×C4C22⋊Q812yes—
292C32×C4C22×Q811yescharacteristic
293C32×C4C2×#4111yescharacteristic
294C3⋊Dic3—41no—
295C3⋊Dic3—41no—
296C3⋊Dic3—41no—
297C3⋊Dic3—41no—
298C3×Dic3—22no—
299C3×Dic3—22no—
300C3×Dic3—42no—
301C22×D4—31no—
302C2×M16—31no—
303C22×C8D3211yescharacteristic
304C4⋊Q8—92no—
305C4⋊Q8—181no—
306#125—92no—
307#125—181no—
308C22⋊Q8—182no—
309C4×D4—92no—
310C4×D4—92no—
311C4×D4—181no—
312C4×D4—181no—
313#117—31no—
314#117—91no—
315#117—91no—
316C2×C4⋊C4—31no—
317C2×C22⋊C4—182no—
318#107—92no—
319#107—91no—
320#107—91no—
321#106—92no—
322#106—91no—
323#106—91no—
324C4⋊C8—32no—
325C4⋊C8—32no—
326#102—32no—
327#102—32no—
328#102—92no—
329#102—92no—
330C23×C3—21no—
331C23×C3—62no—
332C23×C3—64no—
333C23×C3—241no—
334C23×C3—241no—
335C23×C3C2×D1211yescharacteristic
336C23×C3D3×D411yescharacteristic
337C22×D3—22no—
338C22×D3—24no—
339C22×D3—81no—
340C22×D3—81no—
341C3×D4—34no—
342C3×D4—64no—
343C3×D4—62no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—62no—
351C2×C3×C4—241no—
352C2×C3×C4C2×Dic612yes—
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4#23712yes—
356C2×C3×C4#23712yes—
357C2×C3×C4D3×Q812yes—
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×Dic3—22no—
361C2×Dic3—61no—
362C2×Dic3—61no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—81no—
370C2×Dic3—121no—
371C2×Dic3—121no—
372C2×Dic3—121no—
373C2×Dic3—121no—
374C2×Dic3—242no—
375C2×Dic3—242no—
376C2×Dic3C2×D1212yes—
377C2×Dic3C2×D1212yes—
378D12—24no—
379D12—22no—
380D12C2×Dic614yes—
381C4×D3—242no—
382C4×D3—242no—
383Dic6—242no—
384Dic6—242no—
385C3×C8—22no—
386C3×C8—22no—
387C3×C8—21no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—21no—
391C3×C8—62no—
392C3⋊C8—22no—
393C2×C32—22no—
394C2×C32C2×C22⋊Q811yescharacteristic
395C2×C32#57611yescharacteristic
396C2×C32#57711yescharacteristic
397C3×D3—44no—
398C24—61no—
399C2×Q8—182no—
400C2×D4—32no—
401C2×D4—34no—
402C2×D4—61no—
403C2×D4—62no—
404C22×C4—61no—
405C22×C4—182no—
406C22×C4—182no—
407C22×C4C2×D3211yescharacteristic
408M16—62no—
409C2×C8—22no—
410C2×C8—32no—
411C2×C8C2×D3211yescharacteristic
412C2×C8C2×D3211yescharacteristic
413C4⋊C4—31no—
414C4⋊C4—31no—
415C4⋊C4—32no—
416C4⋊C4—61no—
417C4⋊C4—91no—
418C4⋊C4—91no—
419C4⋊C4—91no—
420C4⋊C4—91no—
421C4⋊C4—182no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C22⋊C4—32no—
425C22⋊C4—182no—
426C22⋊C4—182no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C42—32no—
430C42—181no—
431C42—181no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—22no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—64no—
441C22×C3—122no—
442C22×C3—122no—
443C22×C3—244no—
444C22×C3#87812yes—
445C22×C3#89712yes—
446C22×C3C22×D1211yescharacteristic
447C22×C3C2×D3×D411yescharacteristic
448C2×D3—24no—
449C2×D3—42no—
450C2×D3—42no—
451C2×D3—84no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—22no—
455C3×C4—62no—
456C3×C4—62no—
457C3×C4—122no—
458C3×C4#87812yes—
459C3×C4#89712yes—
460C3×C4C22×Dic611yescharacteristic
461C3×C4C2×#23711yescharacteristic
462C3×C4C2×#23711yescharacteristic
463C3×C4C2×D3×Q811yescharacteristic
464Dic3—22no—
465Dic3—22no—
466Dic3—42no—
467Dic3—121no—
468Dic3—121no—
469Dic3—121no—
470Dic3—121no—
471Dic3—121no—
472Dic3—121no—
473Dic3—121no—
474Dic3—121no—
475Dic3—241no—
476Dic3—241no—
477Dic3—241no—
478Dic3—241no—
479C32#308111yescharacteristic, complemented, Sylow
480C23—62no—
481C23—64no—
482C23—241no—
483C23—241no—
484C23D3×D1211yescharacteristic
485Q8—722no—
486D4—34no—
487D4—62no—
488D4—64no—
489C2×C4—32no—
490C2×C4—32no—
491C2×C4—62no—
492C2×C4—181no—
493C2×C4—181no—
494C2×C4—181no—
495C2×C4—181no—
496C2×C4—241no—
497C2×C4—722no—
498C2×C4—722no—
499C2×C4D3×Dic612yes—
500C2×C4D3×D1211yescharacteristic
501C2×C4#380512yes—
502C2×C4C22×D3211yescharacteristic
503C8—21no—
504C8—21no—
505C8—62no—
506C2×C3—22no—
507C2×C3—22no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—42no—
512C2×C3—124no—
513C2×C3C2×#87811yescharacteristic
514C2×C3C2×#89711yescharacteristic
515C2×C3#575111yescharacteristic
516C2×C3#575211yescharacteristic
517C2×C3#575711yescharacteristic
518C2×C3#576211yescharacteristic
519D3—44no—
520C22—21no—
521C22—21no—
522C22—64no—
523C22—122no—
524C22—122no—
525C22—244no—
526C22#6389312yes—
527C22C2×D3×D1211yescharacteristic
528C4—62no—
529C4—62no—
530C4—122no—
531C4—361no—
532C4—361no—
533C4—361no—
534C4—361no—
535C4#6389312yes—
536C4C2×D3×Dic611yescharacteristic
537C4C2×#380511yescharacteristic
538C3—21no—
539C3#7873111yescharacteristic, complemented
540C3#7909011yescharacteristic, complemented
541C2—22no—
542C2—124no—
543C2#1059467711yescharacteristic
544C2#1059467811yescharacteristic
545C2C2×#6389311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC22×C8D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10595051C2semidirect
3. #10592805C2semidirect
5. C3×#5102C2semidirect
6. #10591130C2semidirect
8. #10590772C2semidirect
9. #10590767C2semidirect
10. #10590762C2semidirect
11. #10590757C2semidirect
24. #63918C22semidirect
30. #63869C22semidirect
31. #63645C22semidirect
32. #63645C22semidirect
33. #63644C22semidirect
34. #63644C22semidirect
37. C3×Dic3⋊C8C22semidirect
38. C3×Dic3⋊C8C22semidirect
39. #63575C22semidirect
40. #63573C22semidirect
56. #5102D3semidirect
71. C2×C3×D12Q8semidirect
162. Dic3⋊C8C2×D3semidirect
163. Dic3⋊C8C2×D3semidirect
218. C2×D12Dic6semidirect
479. C32#3081semidirect
539. C3#78731semidirect
540. C3#79090semidirect

Maximal subgroups

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

subgroupindex
#105950512
#105949822
#105928052
C2×C3×#8212
C3×#51022
#105911302
#105910862
#105907722
#105907672
#105907622
#105907572
#790903
#787313