Finite Group Databasebeta

← #11868988

Subgroups — #11868988

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
1#10595052C211yesmaximal, characteristic, complemented
2#10594996C211yesmaximal, characteristic
3C2×#63648C211yesmaximal, characteristic
4C3×#5106C211yesmaximal, characteristic, complemented
5C3×#5102C211yesmaximal, characteristic, complemented
6#10591131C211yesmaximal, characteristic, complemented
7#10591096C211yesmaximal, characteristic
8#10590774C212yesmaximal, complemented
9#10590769C212yesmaximal, complemented
10#10590764C212yesmaximal, complemented
11#10590759C212yesmaximal, complemented
12#79197—31nomaximal
13#79090—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21#63982—22no—
22#63974—22no—
23#63918—21no—
24#63918C2212yescomplemented
25#63894—21no—
26#63894—21no—
27#63894C2212yes—
28#63894C2212yes—
29#63869—21no—
30#63869C2212yescomplemented
31#63648C2212yes—
32#63648C2212yes—
33C3×#818C2211yescharacteristic, complemented
34C3×#818C2211yescharacteristic, complemented
35C3×#817C2211yescharacteristic, complemented
36C3×#817C2211yescharacteristic, complemented
37C3×Dic3⋊C8C2212yescomplemented
38C3×Dic3⋊C8C2212yescomplemented
39#63575C2212yescomplemented
40#63573C2212yescomplemented
41#63564C2212yes—
42#63564C2212yes—
43#5521—31no—
44#5521—31no—
45#5519—31no—
46#5519—31no—
47C3×#427—31no—
48C3×#424—31no—
49#5131—31no—
50#5121—31no—
51C2×#821—31no—
52C2×#821—31no—
53C2×#821—61no—
54#5106D311yescharacteristic, complemented
55#5102D311yescharacteristic, complemented
56#5001—31no—
57#4995—31no—
58#4891—32no—
59#4890—32no—
60#4871—32no—
61#4870—32no—
62#4847—32no—
63#4847—32no—
64#4846—32no—
65#4842—32no—
66C23×C3⋊D3—21no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)Q814yescomplemented
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×#627—22no—
74C2×#624—22no—
75C2×#624—22no—
76C2×C32×C8—22no—
77C2×C32×C8C2311yescharacteristic
78C2×C32×C8C2311yescharacteristic
79C4⋊(C3⋊Dic3)—21no—
80C4⋊(C3⋊Dic3)C2312yes—
81C3×#217—21no—
82C3×#217—21no—
83C3×#217D412yes—
84C3×C4⋊Dic3D411yescharacteristic
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2311yescharacteristic
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4×Dic3—21no—
91C3×C4×Dic3—21no—
92C3×C4×Dic3C2312yes—
93C3×#208—22no—
94C2×C3×C3⋊C8C2312yes—
95#3724—22no—
96Dic3⋊Dic3—22no—
97Dic3⋊Dic3—22no—
98#3722—22no—
99#3722—22no—
100#3081—91noSylow
101C22×D12—31no—
102C22×D12—31no—
103C22×D12—61no—
104C2×C3×M16—31no—
105C22×C3×C8—21no—
106C22×C3×C8C2×D311yescharacteristic
107C22×C3×C8C2×D311yescharacteristic
108C3×#117—31no—
109C3×#117—31no—
110C3×#117—31no—
111#926C2×D311yescharacteristic
112#926C2×D311yescharacteristic
113#926C2×D311yescharacteristic
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—61no—
117C2×#208C2×D311yescharacteristic
118#893—32no—
119#893—32no—
120#893—61no—
121#893—61no—
122#890—32no—
123#890—61no—
124#888—32no—
125#888—61no—
126D3×C22⋊C4—62no—
127D3×C22⋊C4—62no—
128#878—62no—
129#878—62no—
130C4×D12—32no—
131C4×D12—32no—
132C4×D12—61no—
133C4×D12—61no—
134#870—32no—
135#870—61no—
136#869—32no—
137#869—61no—
138C3×#107—31no—
139C3×#107—31no—
140C3×#106—31no—
141C3×#106—31no—
142C3×C4⋊C8—32no—
143C3×C4⋊C8—32no—
144#821—32no—
145#821—32no—
146#821—32no—
147#821—32no—
148#821—32no—
149#821—32no—
150#821—62no—
151#821—62no—
152#818—32no—
153#818C2×D311yescharacteristic, complemented
154#818C2×D311yescharacteristic, complemented
155#817—32no—
156#817C2×D311yescharacteristic, complemented
157#817C2×D311yescharacteristic, complemented
158Dic3⋊C8C2×D312yescomplemented
159Dic3⋊C8C2×D312yescomplemented
160#809—32no—
161#809—32no—
162#808—32no—
163#807—32no—
164C23×C32C2×D411yescharacteristic
165C22×C3⋊D3—22no—
166C22×C3⋊D3—24no—
167C22×C3⋊D3—81no—
168C22×C3⋊D3—81no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×Q812yes—
171C2×C32×C4#4112yes—
172C2×C32×C4C2411yescharacteristic
173C2×C3⋊Dic3—22no—
174C2×C3⋊Dic3—81no—
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—
184#627—82no—
185#624—82no—
186#624—82no—
187C32×C8—21no—
188C32×C8—21no—
189C3×C3⋊C8—22no—
190#544—91no—
191#518—91no—
192#478—92no—
193#478—92no—
194#476—92no—
195#474—92no—
196#428—91no—
197#427—31no—
198#424—31no—
199#418—91no—
200C2×#102—91no—
201C23×D3—61no—
202C23×D3—61no—
203C23×D3—121no—
204C22×C3×C4—21no—
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—121no—
210C2×D12—34no—
211C2×D12—34no—
212C2×D12—32no—
213C2×D12—32no—
214C2×D12—62no—
215C2×D12—64no—
216C2×D12—61no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—62no—
220C2×D12—121no—
221C2×D12—122no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C3×M16—62no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—32no—
234C2×C3×C8—42no—
235C2×C3×C8C22×D311yescharacteristic
236C2×C3×C8C22×D311yescharacteristic
237C2×C3×C8C22×D311yescharacteristic
238C2×C3×C8C22×D311yescharacteristic
239C3×C4⋊C4—31no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—31no—
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#217D1212yes—
254(C2×D3)⋊C4—62no—
255(C2×D3)⋊C4—62no—
256(C2×D3)⋊C4—62no—
257(C2×D3)⋊C4—62no—
258C4⋊Dic3—32no—
259C4⋊Dic3—32no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4⋊Dic3—62no—
265C4⋊Dic3—121no—
266C4⋊Dic3D1211yescharacteristic
267C4⋊Dic3D1211yescharacteristic
268C4⋊Dic3C22×D311yescharacteristic
269C4⋊Dic3C22×D311yescharacteristic
270C4⋊Dic3C22×D311yescharacteristic
271C4⋊Dic3C22×D311yescharacteristic
272Dic3⋊C4—62no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275Dic3⋊C4—62no—
276C4×Dic3—21no—
277C4×Dic3—21no—
278C4×Dic3C22×D312yes—
279#208—22no—
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×C4C22⋊Q812yes—
290C32×C4C22×Q811yescharacteristic
291C32×C4C2×#4111yescharacteristic
292C3⋊Dic3—42no—
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×C8D3211yescharacteristic
302C4⋊Q8—92no—
303C4⋊Q8—181no—
304#125—92no—
305#125—181no—
306C22⋊Q8—182no—
307C4×D4—92no—
308C4×D4—92no—
309C4×D4—181no—
310C4×D4—181no—
311#117—31no—
312#117—31no—
313#117—31no—
314C2×C4⋊C4—91no—
315C2×C22⋊C4—182no—
316#107—31no—
317#107—31no—
318#107—92no—
319#106—31no—
320#106—31no—
321#106—92no—
322C4⋊C8—32no—
323C4⋊C8—32no—
324#102—92no—
325#102—92no—
326#102—92no—
327#102—92no—
328C23×C3—21no—
329C23×C3C2×D1211yescharacteristic
330C23×C3D3×D411yescharacteristic
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—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—21no—
346C2×C3×C4—22no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—61no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4C2×D1211yescharacteristic
354C2×C3×C4#23512yes—
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4#23712yes—
357C2×C3×C4D3×Q812yes—
358C2×C3×C4D3×Q812yes—
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—122no—
368C2×Dic3—241no—
369C2×Dic3—241no—
370C2×Dic3—242no—
371C2×Dic3C2×D1212yes—
372C2×Dic3C2×D1212yes—
373D12—34no—
374D12—34no—
375D12—64no—
376D12—64no—
377D12—64no—
378D12—62no—
379D12—62no—
380D12—122no—
381D12—124no—
382C4×D3—242no—
383C4×D3—242no—
384C4×D3—242no—
385C4×D3—242no—
386Dic6—242no—
387Dic6—242no—
388C3×C8—21no—
389C3×C8—21no—
390C3×C8—21no—
391C3×C8—21no—
392C3×C8—41no—
393C3×C8—41no—
394C3×C8—62no—
395C3⋊C8—22no—
396C2×C32—22no—
397C2×C32C2×C22⋊Q811yescharacteristic
398C2×C32#57611yescharacteristic
399C2×C32#57711yescharacteristic
400C3⋊D3—44no—
401C24—181no—
402C2×Q8—182no—
403C2×D4—92no—
404C2×D4—94no—
405C2×D4—181no—
406C2×D4—182no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4—181no—
410C22×C4C2×D3211yescharacteristic
411M16—62no—
412C2×C8—22no—
413C2×C8—32no—
414C2×C8C2×D3211yescharacteristic
415C2×C8C2×D3211yescharacteristic
416C4⋊C4—31no—
417C4⋊C4—31no—
418C4⋊C4—31no—
419C4⋊C4—31no—
420C4⋊C4—31no—
421C4⋊C4—31no—
422C4⋊C4—92no—
423C4⋊C4—182no—
424C4⋊C4—182no—
425C4⋊C4—182no—
426C4⋊C4—181no—
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#89712yes—
445C22×C3C22×D1211yescharacteristic
446C22×C3C2×D3×D411yescharacteristic
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—62no—
463C3×C4—62no—
464C3×C4—121no—
465C3×C4—121no—
466C3×C4—121no—
467C3×C4—121no—
468C3×C4#89612yes—
469C3×C4#89712yes—
470C3×C4C2×#23511yescharacteristic
471C3×C4C2×#23711yescharacteristic
472C3×C4C2×D3×Q811yescharacteristic
473C3×C4C2×D3×Q811yescharacteristic
474Dic3—22no—
475Dic3—22no—
476Dic3—41no—
477Dic3—41no—
478Dic3—41no—
479Dic3—41no—
480Dic3—122no—
481Dic3—122no—
482Dic3—242no—
483C32#308111yescharacteristic, complemented, Sylow
484C23—182no—
485C23—184no—
486C23—721no—
487C23—721no—
488C23D3×D1211yescharacteristic
489Q8—722no—
490D4—94no—
491D4—182no—
492D4—184no—
493C2×C4—32no—
494C2×C4—32no—
495C2×C4—61no—
496C2×C4—61no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—182no—
500C2×C4—722no—
501C2×C4—722no—
502C2×C4—721no—
503C2×C4#379712yes—
504C2×C4D3×D1211yescharacteristic
505C2×C4#380412yes—
506C2×C4C22×D3211yescharacteristic
507C8—21no—
508C8—21no—
509C8—62no—
510C2×C3—24no—
511C2×C3—22no—
512C2×C3—22no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3C2×#89611yescharacteristic
517C2×C3C2×#89711yescharacteristic
518C2×C3#575111yescharacteristic
519C2×C3#575211yescharacteristic
520C2×C3#576911yescharacteristic
521C2×C3#577011yescharacteristic
522D3—124no—
523D3—124no—
524D3—244no—
525C22—21no—
526C22—21no—
527C22—184no—
528C22—362no—
529C22—362no—
530C22—724no—
531C22#6389512yes—
532C22C2×D3×D1211yescharacteristic
533C4—62no—
534C4—62no—
535C4—121no—
536C4—121no—
537C4—121no—
538C4—121no—
539C4—362no—
540C4#6389512yes—
541C4C2×#379711yescharacteristic
542C4C2×#380411yescharacteristic
543C3—21no—
544C3#7909011yescharacteristic, complemented
545C3#7919711yescharacteristic, complemented
546C2—22no—
547C2—364no—
548C2#1059467911yescharacteristic
549C2#1059468011yescharacteristic
550C2C2×#6389511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
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. #10595052C2semidirect
4. C3×#5106C2semidirect
5. C3×#5102C2semidirect
6. #10591131C2semidirect
8. #10590774C2semidirect
9. #10590769C2semidirect
10. #10590764C2semidirect
11. #10590759C2semidirect
24. #63918C22semidirect
30. #63869C22semidirect
33. C3×#818C22semidirect
34. C3×#818C22semidirect
35. C3×#817C22semidirect
36. C3×#817C22semidirect
37. C3×Dic3⋊C8C22semidirect
38. C3×Dic3⋊C8C22semidirect
39. #63575C22semidirect
40. #63573C22semidirect
54. #5106D3semidirect
55. #5102D3semidirect
71. C2×C4⋊(C3⋊D3)Q8semidirect
153. #818C2×D3semidirect
154. #818C2×D3semidirect
156. #817C2×D3semidirect
157. #817C2×D3semidirect
158. Dic3⋊C8C2×D3semidirect
159. Dic3⋊C8C2×D3semidirect
483. C32#3081semidirect
544. C3#79090semidirect
545. C3#79197semidirect

Maximal subgroups

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

subgroupindex
#105950522
#105949962
C2×#636482
C3×#51062
C3×#51022
#105911312
#105910962
#105907742
#105907692
#105907642
#105907592
#791973
#790903