Finite Group Databasebeta

← #11860699

Subgroups — #11860699

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3753C211yesmaximal, characteristic
2C3×#5798C211yesmaximal, characteristic, complemented
3#10594996C211yesmaximal, characteristic, complemented
4C3×#5215C211yesmaximal, characteristic, complemented
5#10591404C214yesmaximal, complemented
6#10591400C214yesmaximal, complemented
7#10591138C211yesmaximal, characteristic, complemented
8#10591096C211yesmaximal, characteristic, complemented
9#10591057C211yesmaximal, characteristic, complemented
10#82538—31nomaximal
11#78915—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×#3753C418yescomplemented
15C2×#3753C2212yes—
16C2×#3753C2212yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—22no—
19C3×D4×Dic3—22no—
20C3×D4×Dic3C2214yescomplemented
21C3×#926C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25#63974—22no—
26#63894—22no—
27#63894C2214yescomplemented
28C3×#832C2214yescomplemented
29#63576C2212yescomplemented
30#63574C2212yescomplemented
31#63564C2214yescomplemented
32#63554C2212yescomplemented
33Dic3×C3⋊C8C2212yescomplemented
34C3×#518—31no—
35#5798D311yescharacteristic, complemented
36C22×#213—31no—
37C22×#213—31no—
38C22×#213—61no—
39#5521—31no—
40#5521—31no—
41C3×#418—31no—
42#5215D311yescharacteristic, complemented
43#5131—31no—
44#5122—31no—
45#5014—34no—
46C4×#213—34no—
47#5001—31no—
48#4998—31no—
49#4998—31no—
50#4997—31no—
51#4785—34no—
52#4756—34no—
53C24×C32—21no—
54C23×C3⋊D3—21no—
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4C2×C414yescomplemented
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)C2×C414yescomplemented
63C2×C4⋊(C3⋊D3)C2312yes—
64C22×C3×Dic3—24no—
65C2×#624—24no—
66#3753C2×C418yescomplemented
67#3753C2×C418yescomplemented
68C2×C3⋊(C3⋊C8)C2×C414yescomplemented
69C2×C3⋊(C3⋊C8)C2311yescharacteristic
70C2×C3⋊(C3⋊C8)C2311yescharacteristic
71C3×#217—21no—
72C3×#217—21no—
73C3×#217—24no—
74C3×#217D412yes—
75C3×C4⋊Dic3D412yes—
76C3×C4⋊Dic3C2312yes—
77C3×C4⋊Dic3C2312yes—
78C3×C4×Dic3—21no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3C2312yes—
81C3×#208—22no—
82C2×C3×C3⋊C8C2312yes—
83#3722—24no—
84#2948—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4C2×D311yescharacteristic
87C22×C3×D4C2×D311yescharacteristic
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C2×C3×M16—31no—
92C3×C4×D4—34no—
93C3×C4×D4—62no—
94C3×#117—31no—
95C3×#117—31no—
96C3×#117—31no—
97C2×C3×C22⋊C4—62no—
98C2×#217—22no—
99D4×Dic3—22no—
100D4×Dic3C2×D314yescomplemented
101C2×#213—38no—
102C2×#213—38no—
103C2×#213—32no—
104C2×#213—32no—
105C2×#213—32no—
106C2×#213—32no—
107C2×#213—68no—
108C2×#213—62no—
109C2×#213—62no—
110#926C2×D311yescharacteristic
111#926C2×D311yescharacteristic
112#926C2×D311yescharacteristic
113C2×#208C2×D311yescharacteristic
114C22×C3⋊C8—31no—
115C22×C3⋊C8—31no—
116C22×C3⋊C8—61no—
117#893—34no—
118#893—62no—
119D3×C22⋊C4—62no—
120D3×C22⋊C4—62no—
121C4×D12—34no—
122C4×D12—62no—
123C3×#102—34no—
124#832C2×D314yescomplemented
125#821—34no—
126#815—32no—
127C8×Dic3—32no—
128#809—34no—
129#808—32no—
130#808—32no—
131#807—32no—
132#807—32no—
133#803—32no—
134C4×C3⋊C8—32no—
135C23×C32—22no—
136C23×C32—24no—
137C23×C32—82no—
138C23×C32C2×D411yescharacteristic
139C22×C3⋊D3—22no—
140C22×C3⋊D3—24no—
141C22×C3⋊D3—82no—
142C32×D4—24no—
143C32×D4—22no—
144C32×D4C22×C414yes—
145C2×C32×C4C22×C412yes—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C4⋊(C3⋊D3)—24no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)C22×C414yes—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—84no—
155C2×C3×Dic3C2×D414yes—
156#624—84no—
157C3⋊(C3⋊C8)C22×C412yes—
158C3⋊(C3⋊C8)C22×C412yes—
159C3×C3⋊C8—22no—
160C22×D8—91no—
161#518—31no—
162#518—91no—
163#442—94no—
164C4×D8—94no—
165#427—91no—
166#418—31no—
167#418—91no—
168#405—91no—
169C24×C3—21no—
170C24×C3—21no—
171C24×C3—41no—
172C23×D3—61no—
173C23×D3—61no—
174C23×D3—121no—
175C2×C3×D4—22no—
176C2×C3×D4—21no—
177C2×C3×D4—22no—
178C2×C3×D4—21no—
179C2×C3×D4—24no—
180C2×C3×D4—22no—
181C2×C3×D4—42no—
182C2×C3×D4—41no—
183C2×C3×D4C4×D314yescomplemented
184C2×C3×D4C4×D314yescomplemented
185C2×C3×D4C22×D312yes—
186C2×C3×D4C22×D312yes—
187C22×C3×C4—21no—
188C22×C3×C4—64no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—24no—
192C2×D12—34no—
193C2×D12—34no—
194C2×D12—32no—
195C2×D12—32no—
196C2×D12—64no—
197C2×D12—62no—
198C2×D12—62no—
199C2×D12—61no—
200C2×D12—62no—
201C2×D12—61no—
202C2×D12—122no—
203C2×D12—121no—
204C2×C4×D3—64no—
205C2×C4×D3—64no—
206C3×M16—62no—
207C2×C3×C8—32no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—32no—
210C3×C4⋊C4—32no—
211C3×C22⋊C4—32no—
212C3×C22⋊C4—64no—
213C3×C22⋊C4—61no—
214C3×C22⋊C4—61no—
215C3×C42—32no—
216C3×C42—61no—
217C3×C42—61no—
218#217—21no—
219#217—21no—
220#217—24no—
221#217#6712yes—
222#213—38no—
223#213—38no—
224#213—38no—
225#213—38no—
226#213—68no—
227#213—68no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—64no—
230C4⋊Dic3#6712yes—
231C4⋊Dic3C22×D312yes—
232C4⋊Dic3C22×D312yes—
233C4×Dic3—21no—
234C4×Dic3—21no—
235C4×Dic3C22×D312yes—
236#208—22no—
237C2×C3⋊C8—34no—
238C2×C3⋊C8—34no—
239C2×C3⋊C8—31no—
240C2×C3⋊C8—31no—
241C2×C3⋊C8—31no—
242C2×C3⋊C8—31no—
243C2×C3⋊C8—64no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8C22×D312yes—
247C22×C32—22no—
248C22×C32—24no—
249C22×C32—44no—
250C22×C32—84no—
251C22×C32C4×D412yes—
252C22×C32C22×D411yescharacteristic
253C2×C3⋊D3—24no—
254C2×C3⋊D3—44no—
255C2×C3⋊D3—84no—
256C32×C4C4×D412yes—
257C32×C4C23×C411yescharacteristic
258C32×C4C2×#4111yescharacteristic
259C3×Dic3—24no—
260C3×Dic3—42no—
261C3×Dic3—42no—
262C22×D4—91no—
263C22×D4D3211yescharacteristic
264C2×D8—98no—
265C2×D8—92no—
266C2×D8—92no—
267C2×M16—31no—
268C22×C8—91no—
269C4×D4—34no—
270C4×D4—62no—
271C4×D4—94no—
272C4×D4—182no—
273#117—31no—
274#117—31no—
275#117—31no—
276C2×C22⋊C4—62no—
277C2×C22⋊C4—182no—
278#107—92no—
279#106—92no—
280#102—34no—
281#102—94no—
282#97—92no—
283C4×C8—92no—
284C23×C3—22no—
285C23×C3—22no—
286C23×C3—24no—
287C23×C3—24no—
288C23×C3—21no—
289C23×C3—42no—
290C23×C3—44no—
291C23×C3—82no—
292C23×C3—82no—
293C23×C3—84no—
294C23×C3D3×D411yescharacteristic
295C23×C3C2×#6711yescharacteristic
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—64no—
299C22×D3—64no—
300C22×D3—122no—
301C22×D3—124no—
302C22×D3—242no—
303C22×D3—242no—
304C22×D3—244no—
305C3×D4—24no—
306C3×D4—24no—
307C3×D4—22no—
308C3×D4—22no—
309C3×D4—24no—
310C3×D4—42no—
311C3×D4—44no—
312C3×D4C2×C4×D314yes—
313C3×D4C2×C4×D314yes—
314C2×C3×C4—21no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—21no—
318C2×C3×C4—34no—
319C2×C3×C4—62no—
320C2×C3×C4—62no—
321C2×C3×C4—244no—
322C2×C3×C4C2×C4×D312yes—
323C2×C3×C4C2×C4×D312yes—
324C2×C3×C4#23512yes—
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4#23712yes—
327C2×C3×C4C2×#6711yescharacteristic
328C2×C3×C4C23×D311yescharacteristic
329C2×C3×C4C23×D311yescharacteristic
330C2×Dic3—22no—
331C2×Dic3—22no—
332C2×Dic3—84no—
333C2×Dic3C2×#6714yes—
334D12—34no—
335D12—34no—
336D12—64no—
337D12—64no—
338D12—64no—
339D12—62no—
340D12—62no—
341D12—122no—
342D12—124no—
343C4×D3—244no—
344C4×D3—244no—
345C3×C8—62no—
346C3⋊C8—22no—
347C3⋊C8—32no—
348C3⋊C8—32no—
349C3⋊C8—32no—
350C3⋊C8—32no—
351C3⋊C8—62no—
352C3⋊C8—62no—
353C2×C32—22no—
354C2×C32—44no—
355C2×C32C2×C4×D411yescharacteristic
356C2×C32#57612yes—
357C3⋊D3—44no—
358C24—21no—
359C24—181no—
360C2×D4—22no—
361C2×D4—21no—
362C2×D4—92no—
363C2×D4—94no—
364C2×D4—182no—
365C2×D4—181no—
366C2×D4#62414yescomplemented
367C2×D4C2×D3212yes—
368C22×C4—64no—
369C22×C4—184no—
370C22×C4C2×D3211yescharacteristic
371D8—98no—
372D8—98no—
373M16—62no—
374C2×C8—32no—
375C2×C8—91no—
376C2×C8—91no—
377C2×C8—94no—
378C4⋊C4—32no—
379C4⋊C4—32no—
380C4⋊C4—32no—
381C22⋊C4—32no—
382C22⋊C4—64no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—184no—
386C42—32no—
387C42—61no—
388C42—61no—
389C22×C3—24no—
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—24no—
393C22×C3—24no—
394C22×C3—21no—
395C22×C3—22no—
396C22×C3—44no—
397C22×C3—44no—
398C22×C3—44no—
399C22×C3—84no—
400C22×C3—84no—
401C22×C3—84no—
402C22×C3—88no—
403C22×C3#67⋊C412yes—
404C22×C3C4×#6712yes—
405C22×C3C2×D3×D411yescharacteristic
406C22×C3C22×#6711yescharacteristic
407C2×D3—64no—
408C2×D3—64no—
409C2×D3—124no—
410C2×D3—124no—
411C2×D3—124no—
412C2×D3—244no—
413C2×D3—244no—
414C2×D3—244no—
415C2×D3—248no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—22no—
419C3×C4—64no—
420C3×C4—122no—
421C3×C4—122no—
422C3×C4#67⋊C412yes—
423C3×C4C4×#6712yes—
424C3×C4C22×C4×D311yescharacteristic
425C3×C4C22×C4×D311yescharacteristic
426C3×C4C2×#23511yescharacteristic
427C3×C4C2×#23711yescharacteristic
428Dic3—24no—
429Dic3—42no—
430Dic3—42no—
431C32#294811yescharacteristic, complemented, Sylow
432C23—22no—
433C23—24no—
434C23—82no—
435C23—182no—
436C23—184no—
437C23—722no—
438C23D3×#6711yescharacteristic
439D4—22no—
440D4—24no—
441D4—94no—
442D4—182no—
443D4—184no—
444D4C2×#62414yes—
445C2×C4—34no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—244no—
449C2×C4—724no—
450C2×C4#380412yes—
451C2×C4C2×#62412yes—
452C2×C4D3×#6711yescharacteristic
453C2×C4C22×D3211yescharacteristic
454C8—62no—
455C8—92no—
456C8—92no—
457C2×C3—24no—
458C2×C3—22no—
459C2×C3—22no—
460C2×C3—22no—
461C2×C3—21no—
462C2×C3—44no—
463C2×C3—44no—
464C2×C3—84no—
465C2×C3C2×#67⋊C411yescharacteristic
466C2×C3#577412yes—
467C2×C3C2×C4×#6711yescharacteristic
468C2×C3#583512yes—
469D3—124no—
470D3—124no—
471D3—244no—
472C22—22no—
473C22—24no—
474C22—44no—
475C22—84no—
476C22—184no—
477C22—364no—
478C22—724no—
479C22#6395212yes—
480C22C2×D3×#6711yescharacteristic
481C4—64no—
482C4—122no—
483C4—122no—
484C4#6395212yes—
485C4C2×#380411yescharacteristic
486C4C22×#62411yescharacteristic
487C3—21no—
488C3#7891511yescharacteristic, complemented
489C3#8253811yescharacteristic, complemented
490C2—22no—
491C2—44no—
492C2—364no—
493C2#1059509712yes—
494C2C2×#6395211yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC22×#3753C2
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5798C2semidirect
3. #10594996C2semidirect
4. C3×#5215C2semidirect
5. #10591404C2semidirect
6. #10591400C2semidirect
7. #10591138C2semidirect
8. #10591096C2semidirect
9. #10591057C2semidirect
14. C2×#3753C4semidirect
20. C3×D4×Dic3C22semidirect
27. #63894C22semidirect
28. C3×#832C22semidirect
29. #63576C22semidirect
30. #63574C22semidirect
31. #63564C22semidirect
32. #63554C22semidirect
33. Dic3×C3⋊C8C22semidirect
35. #5798D3semidirect
42. #5215D3semidirect
57. C2×C32×D4C2×C4semidirect
62. C2×C4⋊(C3⋊D3)C2×C4semidirect
66. #3753C2×C4semidirect
67. #3753C2×C4semidirect
68. C2×C3⋊(C3⋊C8)C2×C4semidirect
100. D4×Dic3C2×D3semidirect
124. #832C2×D3semidirect
183. C2×C3×D4C4×D3semidirect
184. C2×C3×D4C4×D3semidirect
366. C2×D4#624semidirect
431. C32#2948semidirect
488. C3#78915semidirect
489. C3#82538semidirect

Maximal subgroups

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

subgroupindex
C22×#37532
C3×#57982
#105949962
C3×#52152
#105914042
#105914002
#105911382
#105910962
#105910572
#825383
#789153