Finite Group Databasebeta

← #11860695

Subgroups — #11860695

Order 1152.

1225 conjugacy classes of subgroups.

The subgroup lattice has 487 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic
4C3×#5001C211yesmaximal, characteristic, complemented
5C3×#4998C211yesmaximal, characteristic, complemented
6#10591096C211yesmaximal, characteristic, complemented
7#10591059C211yesmaximal, characteristic, complemented
8#10590462C214yesmaximal, complemented
9#10590459C214yesmaximal, complemented
10#79167—31nomaximal
11#78915—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C32×#117C2211yescharacteristic
15#64135C2211yescharacteristic
16#64102C2214yescomplemented
17C22⋊C4×C3⋊D3—22no—
18C4×C4⋊(C3⋊D3)—22no—
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22D3×#217—22no—
23#63898C2214yescomplemented
24Dic3×D12—22no—
25C2×#3714C418yescomplemented
26C2×#3714C2212yes—
27C2×#3714C2212yes—
28C3×#809C2214yescomplemented
29C3×#808C2212yescomplemented
30C3×#807C2212yescomplemented
31#63564C2214yescomplemented
32#63555C2212yescomplemented
33#63553C2212yescomplemented
34#5798—31no—
35C22×#213—31no—
36C22×D24—31no—
37#5521—31no—
38#5521—31no—
39#5521—31no—
40#5521—61no—
41C3×#427—31no—
42C3×#418—31no—
43#5131—31no—
44#5122—31no—
45#5101—31no—
46#5001—31no—
47#5001D311yescharacteristic, complemented
48#4998D311yescharacteristic, complemented
49#4872—34no—
50#4869—34no—
51#4785—34no—
52#4756—34no—
53C23×C3⋊D3—21no—
54C23×C3×D3—21no—
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)C2×C414yescomplemented
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×C4×C3⋊D3—24no—
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12C2×C414yescomplemented
64C2×C3×D12C2312yes—
65C2×D3×Dic3—24no—
66C32×C4⋊C4C2312yes—
67C32×C22⋊C4—21no—
68C32×C42—21no—
69#3757D412yes—
70#3752—24no—
71C4⋊(C3⋊Dic3)D412yes—
72C4×C3⋊Dic3C2312yes—
73C3×#217—21no—
74C3×C4⋊Dic3C2312yes—
75C3×C4×Dic3—21no—
76C3×#208—22no—
77C2×C3×C3⋊C8C2×C414yescomplemented
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2311yescharacteristic
80C2×C3×C3⋊C8C2311yescharacteristic
81(C2×D3)⋊Dic3—24no—
82#3714C2×C418yescomplemented
83#3714C2×C418yescomplemented
84#2948—91noSylow
85C22×C3×D4—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×D12C2×D311yescharacteristic
90C2×C3×M16—31no—
91C22×C3×C8—31no—
92C3×#117—21no—
93C3×#117—31no—
94C3×#117C2×D311yescharacteristic
95C3×#117C2×D311yescharacteristic
96C2×#217—62no—
97D4×Dic3—34no—
98D4×Dic3—62no—
99C2×#213—38no—
100C2×#213—32no—
101C2×#213—32no—
102#926—31no—
103#926—31no—
104#926—61no—
105#926C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×D24—38no—
109C2×D24—32no—
110C2×D24—32no—
111#893—34no—
112#893—34no—
113#893—34no—
114#893—64no—
115D3×C22⋊C4—62no—
116D3×C22⋊C4—62no—
117D3×C22⋊C4—62no—
118D3×C22⋊C4—64no—
119C4×D12—62no—
120C4×D12—62no—
121C4×D12—62no—
122C4×D12—64no—
123C3×#107—32no—
124C3×#106—32no—
125C3×#102—34no—
126#821—34no—
127#815—32no—
128#815—32no—
129C8×Dic3—32no—
130C8×Dic3—32no—
131#809—34no—
132#809C2×D314yescomplemented
133#808C2×D312yescomplemented
134#807C2×D312yescomplemented
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3—82no—
139C22×C3×D3—22no—
140C22×C3×D3—24no—
141C22×C3×D3—82no—
142C2×C32×C4—22no—
143C2×C32×C4C22×C412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3C2×D414yes—
148C4⋊(C3⋊D3)—24no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)C22×C414yes—
151C4×C3⋊D3—84no—
152C2×C3×Dic3—22no—
153C3×D12—24no—
154C3×D12—22no—
155C3×D12C22×C414yes—
156D3×Dic3—84no—
157C3×C3⋊C8—22no—
158C3×C3⋊C8C22×C412yes—
159C3×C3⋊C8C22×C412yes—
160C22×D8—91no—
161#518—91no—
162#518—91no—
163#442—94no—
164C4×D8—94no—
165#427—31no—
166#418—31no—
167#418—91no—
168#405—91no—
169C24×C3—61no—
170C23×D3—21no—
171C23×D3—62no—
172C23×D3—61no—
173C23×D3—61no—
174C2×C3×D4—34no—
175C2×C3×D4—32no—
176C2×C3×D4—61no—
177C2×C3×D4—62no—
178C22×C3×C4—21no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C22×Dic3—64no—
182C2×D12—21no—
183C2×D12—22no—
184C2×D12—34no—
185C2×D12—34no—
186C2×D12—32no—
187C2×D12—32no—
188C2×D12—62no—
189C2×D12—64no—
190C2×D12—62no—
191C2×D12—64no—
192C2×D12—61no—
193C2×D12—61no—
194C2×D12—62no—
195C2×D12—62no—
196C2×D12C4×D314yescomplemented
197C2×D12C22×D312yes—
198C2×C4×D3—64no—
199C2×C4×D3—64no—
200C2×C4×D3—64no—
201C2×C4×D3—68no—
202C3×M16—62no—
203C2×C3×C8—34no—
204C2×C3×C8—31no—
205C2×C3×C8—31no—
206C2×C3×C8—32no—
207C3×C4⋊C4—22no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4C22×D312yes—
210C3×C4⋊C4C22×D312yes—
211C3×C22⋊C4—22no—
212C3×C22⋊C4—21no—
213C3×C22⋊C4—21no—
214C3×C22⋊C4—61no—
215C3×C42—22no—
216C3×C42—21no—
217C3×C42—21no—
218C3×C42—61no—
219#217—21no—
220#217—32no—
221#217—32no—
222#217—62no—
223#217—64no—
224#213—38no—
225#213—38no—
226(C2×D3)⋊C4—64no—
227(C2×D3)⋊C4—64no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—68no—
230C4⋊Dic3—32no—
231C4⋊Dic3—32no—
232C4⋊Dic3—62no—
233C4⋊Dic3C22×D312yes—
234C4×Dic3—21no—
235C4×Dic3—32no—
236C4×Dic3—32no—
237C4×Dic3—62no—
238#208—22no—
239C2×C3⋊C8C4×D314yescomplemented
240C2×C3⋊C8C22×D312yes—
241C2×C3⋊C8C22×D311yescharacteristic
242C2×C3⋊C8C22×D311yescharacteristic
243D24—38no—
244D24—38no—
245C22×C32—22no—
246C22×C32C4×D412yes—
247C22×C32C22×D411yescharacteristic
248C2×C3⋊D3—24no—
249C2×C3⋊D3—44no—
250C2×C3⋊D3—84no—
251C2×C3×D3—24no—
252C2×C3×D3—44no—
253C2×C3×D3—84no—
254C32×C4—42no—
255C32×C4C4×D412yes—
256C32×C4C23×C411yescharacteristic
257C32×C4C2×#4111yescharacteristic
258C3⋊Dic3—24no—
259C3×Dic3—42no—
260C22×D4—31no—
261C22×D4—91no—
262C2×D8—98no—
263C2×D8—92no—
264C2×D8—92no—
265C2×M16—31no—
266C22×C8—31no—
267C4×D4—94no—
268C4×D4—94no—
269C4×D4—182no—
270C4×D4—182no—
271#117—31no—
272#117—91no—
273#117D3211yescharacteristic
274C2×C22⋊C4—182no—
275C2×C22⋊C4—182no—
276#107—32no—
277#106—32no—
278#102—34no—
279#102—94no—
280#97—92no—
281C4×C8—92no—
282C23×C3—21no—
283C23×C3—62no—
284C23×C3—64no—
285C23×C3—242no—
286C23×C3D3×D411yescharacteristic
287C23×C3D3×D411yescharacteristic
288C22×D3—22no—
289C22×D3—24no—
290C22×D3—64no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—68no—
294C22×D3—64no—
295C22×D3—64no—
296C22×D3—82no—
297C22×D3—242no—
298C22×D3—242no—
299C22×D3—244no—
300C3×D4—34no—
301C3×D4—64no—
302C3×D4—62no—
303C2×C3×C4—24no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—21no—
307C2×C3×C4—22no—
308C2×C3×C4—22no—
309C2×C3×C4—21no—
310C2×C3×C4—62no—
311C2×C3×C4C2×C4×D312yes—
312C2×C3×C4C2×C4×D312yes—
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4#23712yes—
316C2×C3×C4#23912yes—
317C2×C3×C4C23×D311yescharacteristic
318C2×C3×C4C23×D311yescharacteristic
319C2×Dic3—22no—
320C2×Dic3—34no—
321C2×Dic3—34no—
322C2×Dic3—64no—
323C2×Dic3—244no—
324D12—24no—
325D12—22no—
326D12—34no—
327D12—34no—
328D12—64no—
329D12—64no—
330D12—68no—
331D12—64no—
332D12—64no—
333D12—62no—
334D12—62no—
335D12C2×C4×D314yes—
336C4×D3—244no—
337C4×D3—244no—
338C4×D3—244no—
339C4×D3—248no—
340C3×C8—32no—
341C3×C8—32no—
342C3×C8—62no—
343C3⋊C8—22no—
344C3⋊C8C2×C4×D312yes—
345C3⋊C8C2×C4×D312yes—
346C2×C32—22no—
347C2×C32C2×C4×D411yescharacteristic
348C2×C32#57612yes—
349C3⋊D3—44no—
350C3×D3—44no—
351C24—61no—
352C24—181no—
353C2×D4—32no—
354C2×D4—34no—
355C2×D4—62no—
356C2×D4—61no—
357C2×D4—92no—
358C2×D4—94no—
359C2×D4—182no—
360C2×D4—181no—
361C22×C4—184no—
362C22×C4—184no—
363C22×C4C2×D3211yescharacteristic
364D8—98no—
365D8—98no—
366M16—62no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—34no—
370C2×C8—32no—
371C4⋊C4—32no—
372C4⋊C4—92no—
373C4⋊C4C2×D3212yes—
374C22⋊C4—21no—
375C22⋊C4—61no—
376C22⋊C4—92no—
377C22⋊C4—184no—
378C22⋊C4—184no—
379C42—21no—
380C42—61no—
381C42—92no—
382C22×C3—22no—
383C22×C3—22no—
384C22×C3—21no—
385C22×C3—22no—
386C22×C3—42no—
387C22×C3—64no—
388C22×C3—124no—
389C22×C3—244no—
390C22×C3#67⋊C412yes—
391C22×C3#89312yes—
392C22×C3C2×D3×D411yescharacteristic
393C22×C3C2×D3×D411yescharacteristic
394C2×D3—24no—
395C2×D3—44no—
396C2×D3—68no—
397C2×D3—64no—
398C2×D3—64no—
399C2×D3—84no—
400C2×D3—128no—
401C2×D3—124no—
402C2×D3—124no—
403C2×D3—244no—
404C2×D3—244no—
405C2×D3—248no—
406C3×C4—21no—
407C3×C4—21no—
408C3×C4—22no—
409C3×C4—44no—
410C3×C4—42no—
411C3×C4—42no—
412C3×C4—122no—
413C3×C4#67⋊C412yes—
414C3×C4#89312yes—
415C3×C4C22×C4×D311yescharacteristic
416C3×C4C22×C4×D311yescharacteristic
417C3×C4C2×#23711yescharacteristic
418C3×C4C2×#23911yescharacteristic
419Dic3—42no—
420Dic3—64no—
421Dic3—64no—
422Dic3—124no—
423C32#294811yescharacteristic, complemented, Sylow
424C23—62no—
425C23—64no—
426C23—182no—
427C23—184no—
428C23—242no—
429C23—722no—
430C23#381111yescharacteristic
431D4—34no—
432D4—62no—
433D4—64no—
434D4—94no—
435D4—182no—
436D4—184no—
437C2×C4—22no—
438C2×C4—62no—
439C2×C4—94no—
440C2×C4—724no—
441C2×C4—724no—
442C2×C4#379612yes—
443C2×C4C4×D3212yes—
444C2×C4#381111yescharacteristic
445C2×C4C22×D3211yescharacteristic
446C8—32no—
447C8—32no—
448C8—62no—
449C2×C3—22no—
450C2×C3—22no—
451C2×C3—21no—
452C2×C3—22no—
453C2×C3—42no—
454C2×C3—124no—
455C2×C3C2×#67⋊C411yescharacteristic
456C2×C3C2×#89311yescharacteristic
457C2×C3#576912yes—
458C2×C3#577412yes—
459D3—44no—
460D3—128no—
461D3—124no—
462D3—124no—
463C22—22no—
464C22—64no—
465C22—124no—
466C22—184no—
467C22—244no—
468C22—364no—
469C22—724no—
470C22#6388112yes—
471C22C2×#381111yescharacteristic
472C4—42no—
473C4—122no—
474C4—184no—
475C4#6388112yes—
476C4C2×#379611yescharacteristic
477C4C2×C4×D3211yescharacteristic
478C3—21no—
479C3#7891511yescharacteristic, complemented
480C3#7916711yescharacteristic, complemented
481C2—22no—
482C2—124no—
483C2—364no—
484C2C2×#6388111yescharacteristic
485C2#1059546112yes—
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×#3714C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2948
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595992C2semidirect
2. #10594982C2semidirect
4. C3×#5001C2semidirect
5. C3×#4998C2semidirect
6. #10591096C2semidirect
7. #10591059C2semidirect
8. #10590462C2semidirect
9. #10590459C2semidirect
16. #64102C22semidirect
23. #63898C22semidirect
25. C2×#3714C4semidirect
28. C3×#809C22semidirect
29. C3×#808C22semidirect
30. C3×#807C22semidirect
31. #63564C22semidirect
32. #63555C22semidirect
33. #63553C22semidirect
47. #5001D3semidirect
48. #4998D3semidirect
58. C2×C4⋊(C3⋊D3)C2×C4semidirect
63. C2×C3×D12C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
82. #3714C2×C4semidirect
83. #3714C2×C4semidirect
132. #809C2×D3semidirect
133. #808C2×D3semidirect
134. #807C2×D3semidirect
196. C2×D12C4×D3semidirect
239. C2×C3⋊C8C4×D3semidirect
423. C32#2948semidirect
479. C3#78915semidirect
480. C3#79167semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105949822
C22×#37142
C3×#50012
C3×#49982
#105910962
#105910592
#105904622
#105904592
#791673
#789153