Finite Group Databasebeta

← #11860759

Subgroups — #11860759

Order 1152.

1153 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595992C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic
4C3×#5004C211yesmaximal, characteristic, complemented
5C3×#4998C211yesmaximal, characteristic, complemented
6#10591096C211yesmaximal, characteristic
7#10591059C211yesmaximal, characteristic, complemented
8#10590484C214yesmaximal, complemented
9#10590483C214yesmaximal, complemented
10#79168—31nomaximal
11#78947—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C32×#117C2211yescharacteristic
15#64135C2211yescharacteristic
16#64102C2214yes—
17C22⋊C4×C3⋊D3—22no—
18C4×C4⋊(C3⋊D3)—22no—
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22#63955—22no—
23#63843C2214yescomplemented
24Dic3×Dic6—22no—
25C2×#3717C418yescomplemented
26C2×#3717C2212yes—
27C2×#3717C2212yes—
28C3×#810C2214yescomplemented
29C3×#808C2212yescomplemented
30C3×#807C2212yescomplemented
31#63564C2214yes—
32#63555C2212yescomplemented
33#63553C2212yescomplemented
34#5812—31no—
35C22×#215—31no—
36C22×#204—31no—
37#5521—31no—
38#5521—31no—
39#5521—61no—
40#5516—31no—
41C3×#427—31no—
42C3×#419—31no—
43#5131—31no—
44#5122—31no—
45#5101—31no—
46#5004D311yescharacteristic, complemented
47#5001—31no—
48#4998D311yescharacteristic, complemented
49#4889—34no—
50#4852—34no—
51#4817—34no—
52#4788—34no—
53C23×C3⋊D3—21no—
54C22×C32×C4C2311yescharacteristic
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)C2×C414yes—
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—24no—
60C22×C3×Dic3—21no—
61C2×C3×Dic6—21no—
62C2×C3×Dic6—22no—
63C2×C3×Dic6C2×C414yescomplemented
64C2×C3×Dic6C2312yes—
65C32×C4⋊C4C2312yes—
66C32×C22⋊C4—21no—
67C32×C42—21no—
68#3757D412yes—
69#3752—24no—
70C4⋊(C3⋊Dic3)D412yes—
71C4×C3⋊Dic3C2312yes—
72C3×#217—21no—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3—21no—
75C3×#208—22no—
76C2×C3×C3⋊C8C2×C414yescomplemented
77C2×C3×C3⋊C8C2312yes—
78C2×C3×C3⋊C8C2311yescharacteristic
79C2×C3×C3⋊C8C2311yescharacteristic
80Dic3⋊Dic3—24no—
81Dic32—24no—
82#3717C2×C418yescomplemented
83#3717C2×C418yescomplemented
84#2949—91noSylow
85C22×C3×Q8—31no—
86C22×D12—31no—
87C22×D12—31no—
88C22×D12—61no—
89C22×Dic6C2×D311yescharacteristic
90C2×C3×M16—31no—
91C22×C3×C8—31no—
92C3×#117—21no—
93C3×#117—31no—
94C3×#117C2×D311yescharacteristic
95C3×#117C2×D311yescharacteristic
96Q8×Dic3—34no—
97Q8×Dic3—62no—
98C2×#215—38no—
99C2×#215—32no—
100C2×#215—32no—
101#926—31no—
102#926—31no—
103#926—61no—
104#926—62no—
105#926C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107C22×C3⋊C8C2×D311yescharacteristic
108C2×#204—38no—
109C2×#204—32no—
110C2×#204—32no—
111#893—34no—
112#893—34no—
113#893—64no—
114#887—34no—
115D3×C22⋊C4—62no—
116D3×C22⋊C4—62no—
117D3×C22⋊C4—64no—
118#877—62no—
119C4×D12—62no—
120C4×D12—62no—
121C4×D12—64no—
122C4×Dic6—62no—
123C3×#107—32no—
124C3×#106—32no—
125C3×#103—34no—
126#821—34no—
127#815—32no—
128#815—32no—
129C8×Dic3—32no—
130C8×Dic3—32no—
131#810C2×D314yescomplemented
132#809—34no—
133#808C2×D312yescomplemented
134#807C2×D312yescomplemented
135C23×C32C2×D411yescharacteristic
136C22×C3⋊D3—22no—
137C22×C3⋊D3—24no—
138C22×C3⋊D3—82no—
139C2×C32×C4—22no—
140C2×C32×C4C22×C412yes—
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4112yes—
143C2×C32×C4C2411yescharacteristic
144C2×C3⋊Dic3C2×D414yes—
145C4⋊(C3⋊D3)—24no—
146C4⋊(C3⋊D3)—22no—
147C4⋊(C3⋊D3)C22×C414yes—
148C4×C3⋊D3—84no—
149C2×C3×Dic3—24no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C3×Dic6—24no—
153C3×Dic6—22no—
154C3×Dic6C22×C414yes—
155C3×C3⋊C8—22no—
156C3×C3⋊C8C22×C412yes—
157C3×C3⋊C8C22×C412yes—
158C22×SD16—91no—
159#519—91no—
160#518—91no—
161#440—94no—
162C4×SD16—94no—
163#427—31no—
164#419—31no—
165#418—91no—
166#405—91no—
167C23×D3—62no—
168C23×D3—61no—
169C23×D3—61no—
170C2×C3×Q8—34no—
171C2×C3×Q8—32no—
172C2×C3×Q8—61no—
173C2×C3×Q8—62no—
174C22×C3×C4—21no—
175C22×C3×C4—61no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×Dic3—21no—
179C2×D12—34no—
180C2×D12—34no—
181C2×D12—32no—
182C2×D12—32no—
183C2×D12—62no—
184C2×D12—64no—
185C2×D12—62no—
186C2×D12—64no—
187C2×D12—61no—
188C2×D12—61no—
189C2×D12—62no—
190C2×D12—62no—
191C2×C4×D3—64no—
192C2×C4×D3—64no—
193C2×C4×D3—68no—
194C2×Dic6—21no—
195C2×Dic6—22no—
196C2×Dic6C4×D314yescomplemented
197C2×Dic6C22×D312yes—
198C3×M16—62no—
199C2×C3×C8—34no—
200C2×C3×C8—31no—
201C2×C3×C8—31no—
202C2×C3×C8—32no—
203C3×C4⋊C4—22no—
204C3×C4⋊C4—32no—
205C3×C4⋊C4C22×D312yes—
206C3×C4⋊C4C22×D312yes—
207C3×C22⋊C4—22no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C22⋊C4—61no—
211C3×C42—22no—
212C3×C42—21no—
213C3×C42—21no—
214C3×C42—61no—
215#217—21no—
216#217—32no—
217#217—32no—
218#217—62no—
219#215—38no—
220#215—38no—
221(C2×D3)⋊C4—64no—
222(C2×D3)⋊C4—64no—
223(C2×D3)⋊C4—68no—
224C4⋊Dic3—32no—
225C4⋊Dic3—32no—
226C4⋊Dic3—62no—
227C4⋊Dic3—64no—
228C4⋊Dic3C22×D312yes—
229Dic3⋊C4—64no—
230C4×Dic3—21no—
231C4×Dic3—32no—
232C4×Dic3—32no—
233C4×Dic3—62no—
234C4×Dic3—64no—
235C4×Dic3—64no—
236#208—22no—
237C2×C3⋊C8C4×D314yescomplemented
238C2×C3⋊C8C22×D312yes—
239C2×C3⋊C8C22×D311yescharacteristic
240C2×C3⋊C8C22×D311yescharacteristic
241#204—38no—
242#204—38no—
243C22×C32—22no—
244C22×C32C4×D412yes—
245C22×C32C22×D411yescharacteristic
246C2×C3⋊D3—24no—
247C2×C3⋊D3—44no—
248C2×C3⋊D3—84no—
249C32×C4—42no—
250C32×C4C4×D412yes—
251C32×C4C23×C411yescharacteristic
252C32×C4C2×#4111yescharacteristic
253C3⋊Dic3—24no—
254C3×Dic3—24no—
255C3×Dic3—42no—
256C22×Q8—31no—
257C22×D4—91no—
258C2×SD16—98no—
259C2×SD16—92no—
260C2×SD16—92no—
261C2×M16—31no—
262C22×C8—31no—
263C4×Q8—94no—
264C4×Q8—182no—
265C4×D4—94no—
266C4×D4—182no—
267#117—31no—
268#117—91no—
269#117—182no—
270#117D3211yescharacteristic
271C2×C22⋊C4—182no—
272#107—32no—
273#106—32no—
274#103—34no—
275#102—94no—
276#97—92no—
277C4×C8—92no—
278C23×C3—21no—
279C23×C3D3×D411yescharacteristic
280C23×C3D3×D411yescharacteristic
281C22×D3—64no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—68no—
285C22×D3—64no—
286C22×D3—64no—
287C22×D3—242no—
288C22×D3—242no—
289C22×D3—244no—
290C3×Q8—34no—
291C3×Q8—64no—
292C3×Q8—62no—
293C2×C3×C4—24no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—64no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4C2×C4×D312yes—
304C2×C3×C4C2×C4×D312yes—
305C2×C3×C4D3×D411yescharacteristic
306C2×C3×C4D3×D411yescharacteristic
307C2×C3×C4#23712yes—
308C2×C3×C4#23912yes—
309C2×C3×C4C23×D311yescharacteristic
310C2×C3×C4C23×D311yescharacteristic
311C2×Dic3—24no—
312C2×Dic3—22no—
313C2×Dic3—22no—
314C2×Dic3—34no—
315C2×Dic3—34no—
316C2×Dic3—64no—
317D12—34no—
318D12—34no—
319D12—64no—
320D12—64no—
321D12—68no—
322D12—64no—
323D12—64no—
324D12—62no—
325D12—62no—
326C4×D3—244no—
327C4×D3—244no—
328C4×D3—248no—
329Dic6—24no—
330Dic6—22no—
331Dic6C2×C4×D314yes—
332C3×C8—32no—
333C3×C8—32no—
334C3×C8—62no—
335C3⋊C8—22no—
336C3⋊C8C2×C4×D312yes—
337C3⋊C8C2×C4×D312yes—
338C2×C32—22no—
339C2×C32C2×C4×D411yescharacteristic
340C2×C32#57712yes—
341C3⋊D3—44no—
342C24—181no—
343C2×Q8—32no—
344C2×Q8—34no—
345C2×Q8—62no—
346C2×Q8—61no—
347C2×D4—92no—
348C2×D4—94no—
349C2×D4—182no—
350C2×D4—181no—
351C22×C4—61no—
352C22×C4—184no—
353C22×C4C2×D3211yescharacteristic
354SD16—98no—
355SD16—98no—
356M16—62no—
357C2×C8—31no—
358C2×C8—31no—
359C2×C8—34no—
360C2×C8—32no—
361C4⋊C4—32no—
362C4⋊C4—92no—
363C4⋊C4—184no—
364C4⋊C4C2×D3212yes—
365C22⋊C4—21no—
366C22⋊C4—61no—
367C22⋊C4—92no—
368C22⋊C4—184no—
369C42—21no—
370C42—61no—
371C42—92no—
372C42—184no—
373C22×C3—22no—
374C22×C3—22no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—42no—
378C22×C3#67⋊C412yes—
379C22×C3#89312yes—
380C22×C3C2×D3×D411yescharacteristic
381C22×C3C2×D3×D411yescharacteristic
382C2×D3—68no—
383C2×D3—64no—
384C2×D3—64no—
385C2×D3—128no—
386C2×D3—124no—
387C2×D3—124no—
388C2×D3—244no—
389C2×D3—244no—
390C2×D3—248no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—22no—
394C3×C4—44no—
395C3×C4—42no—
396C3×C4—42no—
397C3×C4—64no—
398C3×C4—122no—
399C3×C4#67⋊C412yes—
400C3×C4#89312yes—
401C3×C4C22×C4×D311yescharacteristic
402C3×C4C22×C4×D311yescharacteristic
403C3×C4C2×#23711yescharacteristic
404C3×C4C2×#23911yescharacteristic
405Dic3—24no—
406Dic3—42no—
407Dic3—64no—
408Dic3—64no—
409Dic3—124no—
410C32#294911yescharacteristic, complemented, Sylow
411C23—182no—
412C23—184no—
413C23—722no—
414C23#381111yescharacteristic
415Q8—34no—
416Q8—62no—
417Q8—64no—
418D4—94no—
419D4—182no—
420D4—184no—
421C2×C4—22no—
422C2×C4—62no—
423C2×C4—64no—
424C2×C4—62no—
425C2×C4—94no—
426C2×C4—724no—
427C2×C4#379612yes—
428C2×C4C4×D3212yes—
429C2×C4#381111yescharacteristic
430C2×C4C22×D3211yescharacteristic
431C8—32no—
432C8—32no—
433C8—62no—
434C2×C3—22no—
435C2×C3—22no—
436C2×C3—21no—
437C2×C3—22no—
438C2×C3—42no—
439C2×C3C2×#67⋊C411yescharacteristic
440C2×C3C2×#89311yescharacteristic
441C2×C3#577012yes—
442C2×C3#577812yes—
443D3—128no—
444D3—124no—
445D3—124no—
446C22—22no—
447C22—184no—
448C22—364no—
449C22—724no—
450C22#6388112yes—
451C22C2×#381111yescharacteristic
452C4—42no—
453C4—64no—
454C4—122no—
455C4—184no—
456C4#6388112yes—
457C4C2×#379611yescharacteristic
458C4C2×C4×D3211yescharacteristic
459C3—21no—
460C3#7894711yescharacteristic, complemented
461C3#7916811yescharacteristic, complemented
462C2—22no—
463C2—364no—
464C2C2×#6388111yescharacteristic
465C2#1059547312yes—
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2949
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
2. #10594818C2semidirect
4. C3×#5004C2semidirect
5. C3×#4998C2semidirect
7. #10591059C2semidirect
8. #10590484C2semidirect
9. #10590483C2semidirect
23. #63843C22semidirect
25. C2×#3717C4semidirect
28. C3×#810C22semidirect
29. C3×#808C22semidirect
30. C3×#807C22semidirect
32. #63555C22semidirect
33. #63553C22semidirect
46. #5004D3semidirect
48. #4998D3semidirect
63. C2×C3×Dic6C2×C4semidirect
76. C2×C3×C3⋊C8C2×C4semidirect
82. #3717C2×C4semidirect
83. #3717C2×C4semidirect
131. #810C2×D3semidirect
133. #808C2×D3semidirect
134. #807C2×D3semidirect
196. C2×Dic6C4×D3semidirect
237. C2×C3⋊C8C4×D3semidirect
410. C32#2949semidirect
460. C3#78947semidirect
461. C3#79168semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105948182
C22×#37172
C3×#50042
C3×#49982
#105910962
#105910592
#105904842
#105904832
#791683
#789473