Finite Group Databasebeta

← #11860740

Subgroups — #11860740

Order 1152.

790 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596646C211yesmaximal, characteristic, complemented
2#10596642C211yesmaximal, characteristic
3C2×SD16×C3⋊D3C211yesmaximal, characteristic
4#10593829C211yesmaximal, characteristic, complemented
5#10593814C211yesmaximal, characteristic
6#10593782C214yesmaximal, complemented
7SD16×#157C214yesmaximal, complemented
8#10593768C211yesmaximal, characteristic, complemented
9#10593765C211yesmaximal, characteristic, complemented
10C2×Q8×C3⋊D3C2211yescharacteristic
11C2×D4×C3⋊D3C2211yescharacteristic
12C2×C22⋊#157—22no—
13Q8×#157—22no—
14Q8×#157C2214yescomplemented
15D4×#157—22no—
16D4×#157C2214yes—
17#64286—22no—
18#64286C2211yescharacteristic
19#64286C2211yescharacteristic
20#64286C2211yescharacteristic
21#64283C2211yescharacteristic
22C2×C32×SD16C411yescharacteristic, complemented
23C2×#3755C411yescharacteristic, complemented
24C2×#3754C411yescharacteristic, complemented
25SD16×C3⋊D3C412yescomplemented
26SD16×C3⋊D3C412yescomplemented
27SD16×C3⋊D3C2212yes—
28SD16×C3⋊D3C2212yes—
29C2×#3744C411yescharacteristic, complemented
30C2×C8×C3⋊D3C2211yescharacteristic
31#63784C2214yescomplemented
32#63782C2214yes—
33#63769C2212yescomplemented
34#63768C2212yescomplemented
35#63767C2212yescomplemented
36C8×#157C2212yescomplemented
37C2×D3×SD16—62no—
38C23×C3⋊D3—21no—
39C22×#157—24no—
40C2×C32×Q8C2×C411yescharacteristic, complemented
41C2×C32×D4C2×C411yescharacteristic
42C2×#638—21no—
43Q8×C3⋊D3—21no—
44Q8×C3⋊D3—21no—
45Q8×C3⋊D3C2×C412yescomplemented
46Q8×C3⋊D3C2312yes—
47D4×C3⋊D3—21no—
48D4×C3⋊D3—21no—
49D4×C3⋊D3C2×C412yes—
50D4×C3⋊D3C2312yes—
51C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×#634—21no—
55C2×#634C2×C411yescharacteristic, complemented
56C22⋊#157—21no—
57C22⋊#157—21no—
58C22⋊#157—24no—
59C22⋊#157D412yes—
60#3792—21no—
61C4⋊#157—24no—
62C4⋊#157D412yes—
63C4⋊#157C2312yes—
64C4⋊#157C2312yes—
65C4×#157—24no—
66C4×#157—21no—
67C4×#157—21no—
68C4×#157C2312yes—
69#3788—21no—
70#3787C2312yes—
71C32×SD16C2×C412yescomplemented
72C32×SD16C2×C412yescomplemented
73C2×C32×C8C2×C411yescharacteristic, complemented
74#3755C2×C412yescomplemented
75#3755C2×C412yescomplemented
76#3754C2×C412yescomplemented
77#3754C2×C412yescomplemented
78C2×C3⋊(C3⋊C8)C2×C411yescharacteristic, complemented
79#3744C2×C412yescomplemented
80#3744C2×C412yescomplemented
81C8×C3⋊D3C2×C411yescharacteristic, complemented
82C8×C3⋊D3C2×C411yescharacteristic, complemented
83C8×C3⋊D3C2311yescharacteristic
84C8×C3⋊D3C2311yescharacteristic
85#2949—91nomaximal, Sylow
86C2×D3×Q8—62no—
87C2×D3×D4—62no—
88C2×C3×SD16—22no—
89C2×#215—62no—
90C2×#214—62no—
91D3×SD16—64no—
92D3×SD16—64no—
93D3×SD16—64no—
94D3×SD16—64no—
95C2×#204—62no—
96C2×D3×C8—62no—
97C23×C32—21no—
98C22×C3⋊D3—21no—
99C22×C3⋊D3—22no—
100C22×C3⋊D3—22no—
101C22×C3⋊D3—82no—
102C22×C3⋊D3C2×D411yescharacteristic
103C2×#157—22no—
104C2×#157—22no—
105C2×#157—84no—
106C2×#157C2×D414yes—
107C32×Q8—21no—
108C32×Q8C22×C412yes—
109C32×D4—21no—
110C32×D4C22×C412yes—
111C2×C32×C4—21no—
112C2×C32×C4C22×C411yescharacteristic
113#638—22no—
114#638—22no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3#4111yescharacteristic
117C4⋊(C3⋊D3)—21no—
118C4⋊(C3⋊D3)C22×C412yes—
119C4×C3⋊D3—22no—
120C4×C3⋊D3—22no—
121C4×C3⋊D3C22×C411yescharacteristic
122C4×C3⋊D3C2×D411yescharacteristic
123C4×C3⋊D3#4111yescharacteristic
124C4×C3⋊D3C2411yescharacteristic
125#634—21no—
126#634—22no—
127#634—22no—
128#634C22×C412yes—
129#622—22no—
130C32×C8C22×C411yescharacteristic
131C32×C8C22×C411yescharacteristic
132C3⋊(C3⋊C8)C22×C411yescharacteristic
133C3⋊(C3⋊C8)C22×C411yescharacteristic
134C22×SD16—91no—
135#519—91no—
136#518—91no—
137#440—94no—
138C4×SD16—94no—
139#427—91no—
140#419—91no—
141#418—91no—
142#405—91no—
143C23×D3—122no—
144C2×C3×Q8—22no—
145C2×C3×D4—22no—
146C2×#67—122no—
147D3×Q8—64no—
148D3×Q8—64no—
149D3×Q8—122no—
150D3×Q8—122no—
151D3×D4—64no—
152D3×D4—64no—
153D3×D4—122no—
154D3×D4—122no—
155C2×D12—62no—
156C2×C4×D3—62no—
157C2×C4×D3—122no—
158C2×Dic6—62no—
159C2×Dic6—122no—
160C3×SD16—24no—
161C3×SD16—24no—
162C2×C3×C8—22no—
163#215—64no—
164#215—64no—
165#214—64no—
166#214—64no—
167C2×C3⋊C8—62no—
168#204—64no—
169#204—64no—
170D3×C8—62no—
171D3×C8—62no—
172D3×C8—62no—
173D3×C8—62no—
174C22×C32—22no—
175C22×C32—81no—
176C22×C32C4×D411yescharacteristic
177C2×C3⋊D3—22no—
178C2×C3⋊D3—22no—
179C2×C3⋊D3—44no—
180C2×C3⋊D3—82no—
181C2×C3⋊D3—81no—
182C2×C3⋊D3C4×D411yescharacteristic
183C2×C3⋊D3C22×D411yescharacteristic
184#157—24no—
185#157—42no—
186#157—42no—
187C32×C4—22no—
188C32×C4C4×D411yescharacteristic
189C32×C4C23×C411yescharacteristic
190C3⋊Dic3—22no—
191C3⋊Dic3C4×D411yescharacteristic
192C3⋊Dic3C2×#4111yescharacteristic
193C22×Q8—91no—
194C22×D4—91no—
195C2×SD16—91no—
196C2×SD16—91no—
197C2×SD16—92no—
198C2×SD16—92no—
199C2×SD16—92no—
200C2×SD16—92no—
201C2×SD16—91no—
202C2×SD16#15711yescharacteristic, complemented
203C2×M16—91no—
204C22×C8—91no—
205C4×Q8—94no—
206C4×Q8—182no—
207C4×D4—94no—
208C4×D4—182no—
209#117—91no—
210#117—91no—
211#117—91no—
212#117—182no—
213C2×C22⋊C4—182no—
214#107—92no—
215#106—92no—
216#103—94no—
217#102—94no—
218#97—92no—
219C4×C8—92no—
220C23×C3—42no—
221C22×D3—62no—
222C22×D3—124no—
223C22×D3—124no—
224C22×D3—122no—
225C22×D3—248no—
226C3×Q8—24no—
227C3×Q8—42no—
228C3×D4—24no—
229C3×D4—42no—
230C2×C3×C4—22no—
231C2×C3×C4—42no—
232#67—124no—
233#67—124no—
234C2×Dic3—62no—
235C2×Dic3—122no—
236D12—64no—
237D12—122no—
238C4×D3—62no—
239C4×D3—62no—
240C4×D3—62no—
241C4×D3—62no—
242C4×D3—124no—
243C4×D3—124no—
244Dic6—64no—
245Dic6—124no—
246Dic6—124no—
247Dic6—122no—
248C3×C8—22no—
249C3×C8—22no—
250C3⋊C8—62no—
251C3⋊C8—62no—
252C2×C32—21no—
253C2×C32—42no—
254C2×C32C2×C4×D411yescharacteristic
255C3⋊D3—21no—
256C3⋊D3—42no—
257C3⋊D3#57712yes—
258C24—181no—
259C2×Q8—92no—
260C2×Q8—92no—
261C2×Q8—91no—
262C2×Q8—181no—
263C2×Q8—181no—
264C2×Q8—181no—
265C2×Q8C2×#15711yescharacteristic, complemented
266C2×D4—92no—
267C2×D4—92no—
268C2×D4—91no—
269C2×D4—181no—
270C2×D4—181no—
271C2×D4—181no—
272C2×D4C2×#15711yescharacteristic
273C22×C4—91no—
274C22×C4—181no—
275C22×C4—184no—
276SD16—92no—
277SD16—92no—
278SD16—92no—
279SD16—92no—
280SD16—92no—
281SD16—92no—
282SD16C2×#15712yescomplemented
283SD16C2×#15712yescomplemented
284M16—181no—
285M16—181no—
286C2×C8—91no—
287C2×C8—91no—
288C2×C8—91no—
289C2×C8—91no—
290C2×C8—91no—
291C2×C8—92no—
292C2×C8C2×#15711yescharacteristic, complemented
293C4⋊C4—92no—
294C4⋊C4—92no—
295C4⋊C4—92no—
296C4⋊C4—184no—
297C22⋊C4—92no—
298C22⋊C4—184no—
299C22⋊C4—181no—
300C22⋊C4—181no—
301C42—92no—
302C42—181no—
303C42—181no—
304C42—184no—
305C22×C3—22no—
306C22×C3—44no—
307C22×C3—84no—
308C2×D3—62no—
309C2×D3—62no—
310C2×D3—68no—
311C2×D3—124no—
312C2×D3—248no—
313C2×D3—248no—
314C2×D3—244no—
315C3×C4—22no—
316C3×C4—22no—
317C3×C4—44no—
318Dic3—62no—
319Dic3—62no—
320Dic3—124no—
321C32#294911yescharacteristic, complemented, Sylow
322C23—21no—
323C23—91no—
324C23—182no—
325C23—182no—
326C23—181no—
327C23—722no—
328Q8—21no—
329Q8—92no—
330Q8—182no—
331Q8—182no—
332Q8—181no—
333Q8C22×#15712yes—
334D4—21no—
335D4—92no—
336D4—182no—
337D4—182no—
338D4—181no—
339D4C22×#15712yes—
340C2×C4—21no—
341C2×C4—91no—
342C2×C4—91no—
343C2×C4—91no—
344C2×C4—91no—
345C2×C4—91no—
346C2×C4—94no—
347C2×C4—182no—
348C2×C4—182no—
349C2×C4—181no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4—724no—
353C2×C4C22×#15711yescharacteristic
354C8—91no—
355C8—91no—
356C8—182no—
357C8C22×#15711yescharacteristic
358C8C22×#15711yescharacteristic
359C2×C3—24no—
360C2×C3—22no—
361C2×C3—84no—
362D3—64no—
363D3—64no—
364D3—244no—
365C22—22no—
366C22—81no—
367C22—91no—
368C22—91no—
369C22—182no—
370C22—182no—
371C22—364no—
372C22—721no—
373C22—722no—
374C22D4×#15711yescharacteristic
375C4—22no—
376C4—91no—
377C4—91no—
378C4—184no—
379C4—182no—
380C4—362no—
381C4—362no—
382C4D4×#15711yescharacteristic
383C4C23×#15711yescharacteristic
384C3—22no—
385C2—21no—
386C2—42no—
387C2—92no—
388C2—181no—
389C2—362no—
390C2C2×D4×#15711yescharacteristic
subgroupG/H
centerC2C2×D4×#157
commutatorC32×C4C23×C4
FrattiniC4C23×#157
FittingC2×C32×SD16C4
socleC2×C32C2×C4×D4
prime radicalC2×D4×C3⋊D3C22
cosocleC4×C3⋊D3C24
hypercenterC2×SD16#157
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10596646C2semidirect
4. #10593829C2semidirect
6. #10593782C2semidirect
7. SD16×#157C2semidirect
8. #10593768C2semidirect
9. #10593765C2semidirect
14. Q8×#157C22semidirect
22. C2×C32×SD16C4semidirect
23. C2×#3755C4semidirect
24. C2×#3754C4semidirect
25. SD16×C3⋊D3C4semidirect
26. SD16×C3⋊D3C4semidirect
29. C2×#3744C4semidirect
31. #63784C22semidirect
33. #63769C22semidirect
34. #63768C22semidirect
35. #63767C22semidirect
36. C8×#157C22semidirect
40. C2×C32×Q8C2×C4semidirect
45. Q8×C3⋊D3C2×C4semidirect
55. C2×#634C2×C4semidirect
71. C32×SD16C2×C4semidirect
72. C32×SD16C2×C4semidirect
73. C2×C32×C8C2×C4semidirect
74. #3755C2×C4semidirect
75. #3755C2×C4semidirect
76. #3754C2×C4semidirect
77. #3754C2×C4semidirect
78. C2×C3⋊(C3⋊C8)C2×C4semidirect
79. #3744C2×C4semidirect
80. #3744C2×C4semidirect
81. C8×C3⋊D3C2×C4semidirect
82. C8×C3⋊D3C2×C4semidirect
202. C2×SD16#157semidirect
265. C2×Q8C2×#157semidirect
282. SD16C2×#157semidirect
283. SD16C2×#157semidirect
292. C2×C8C2×#157semidirect
321. C32#2949semidirect

Maximal subgroups

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

subgroupindex
#105966462
#105966422
C2×SD16×C3⋊D32
#105938292
#105938142
#105937822
SD16×#1572
#105937682
#105937652
#29499