Finite Group Databasebeta

← #11858322

Subgroups — #11858322

Order 1152.

1117 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M16×C3⋊D3C211yesmaximal, characteristic
2C2×#63874C211yesmaximal, characteristic
3C2×#63818C211yesmaximal, characteristic
4C3×#5118C212yesmaximal, complemented
5#10591115C212yesmaximal, complemented
6#10590702C214yesmaximal, complemented
7#10590701C214yesmaximal, complemented
8#79048—32nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C2×#3748C2211yescharacteristic
12M16×C3⋊D3—24no—
13C2×#3743C2212yes—
14C2×C8×C3⋊D3C2212yes—
15C2×C3×C4×Dic3C2212yes—
16C2×C3×#208C2212yes—
17C2×#3724C412yes—
18C2×#3722C412yes—
19#63874C412yes—
20#63874C412yes—
21#63874C2212yes—
22#63874C2212yes—
23C2×#3712C2212yes—
24#63818—24no—
25C2×#3710C2212yes—
26C3×Dic3⋊C8C2218yescomplemented
27Dic3⋊(C3⋊C8)C2218yescomplemented
28C2×D3×M16—32no—
29C2×D3×M16—32no—
30C2×D3×M16—61no—
31C2×#872—32no—
32C3×#423—32no—
33#5118—32no—
34#5118D312yescomplemented
35#4924—32no—
36#4839—38no—
37#4839—38no—
38C23×C3⋊D3C2×C411yescharacteristic
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3C2×C411yescharacteristic
41C2×C4×C3⋊D3C2×C411yescharacteristic
42C2×C4×C3⋊D3C2×C411yescharacteristic
43C2×C4×C3⋊D3D414yes—
44C2×C4×C3⋊D3Q814yes—
45C2×C4×C3⋊D3C2311yescharacteristic
46C2×C4×C3⋊D3C2311yescharacteristic
47C22×C3×Dic3C2×C414yes—
48C32×M16—22no—
49C2×C32×C8C2312yes—
50#3748—22no—
51C2×C3⋊(C3⋊C8)C2312yes—
52#3743—24no—
53C8×C3⋊D3—24no—
54C3×C4×Dic3C2×C414yes—
55C3×C4×Dic3C2314yes—
56C3×#208—24no—
57C2×C3×C3⋊C8C2314yes—
58#3724C2×C414yes—
59#3724C2×C414yes—
60#3722C2×C414yes—
61#3722C2×C414yes—
62#3712—24no—
63#3710—24no—
64#2905—91noSylow
65C22×C4×D3—32no—
66C22×C4×D3—61no—
67C2×C3×M16—21no—
68C2×C3×M16—32no—
69C2×C3×M16C2×D312yes—
70C2×C3×C42—32no—
71C2×(C2×D3)⋊C4—34no—
72C2×Dic3⋊C4—34no—
73C2×C4×Dic3C2×D312yes—
74C2×#208—32no—
75C2×#208—61no—
76C2×#208C2×D312yes—
77D3×M16—68no—
78D3×M16—68no—
79D3×M16—68no—
80C2×ΓL(1,𝔽25)—34no—
81C2×ΓL(1,𝔽25)—34no—
82C2×ΓL(1,𝔽25)—62no—
83C2×D3×C8—34no—
84C2×D3×C8—34no—
85C2×D3×C8—62no—
86#872—34no—
87#872—34no—
88#872—34no—
89#872—34no—
90C3×C4⋊C8—38no—
91Dic3⋊C8—38no—
92Dic3⋊C8C2×D318yescomplemented
93C4⋊(C3⋊C8)—38no—
94C23×C32C22×C411yescharacteristic
95C22×C3⋊D3—42no—
96C22×C3⋊D3C4⋊C414yes—
97C22×C3⋊D3C22×C411yescharacteristic
98C22×C3⋊D3C22×C411yescharacteristic
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C2×D412yes—
101C2×C32×C4C2×Q812yes—
102C2×C32×C4C2411yescharacteristic
103C2×C3⋊Dic3C4⋊C414yes—
104C2×C3⋊Dic3C22×C411yescharacteristic
105C2×C3⋊Dic3C22×C411yescharacteristic
106C4×C3⋊D3C4⋊C414yes—
107C4×C3⋊D3C4⋊C414yes—
108C4×C3⋊D3C2×D412yes—
109C4×C3⋊D3C2×D412yes—
110C4×C3⋊D3C2×Q812yes—
111C4×C3⋊D3C2×Q812yes—
112C2×C3×Dic3—44no—
113C2×C3×Dic3C22×C418yes—
114C32×C8—22no—
115C3⋊(C3⋊C8)—22no—
116C3×C3⋊C8—24no—
117C22×M16—91no—
118C22×M16—91no—
119C2×#117—91no—
120#424—94no—
121#424—94no—
122#423—32no—
123#423—92no—
124C23×D3—32no—
125C23×D3—61no—
126C22×C3×C4—21no—
127C22×C3×C4—34no—
128C22×C3×C4C22×D312yes—
129C22×Dic3—32no—
130C22×Dic3—61no—
131C22×Dic3C4×D314yes—
132C2×C4×D3—32no—
133C2×C4×D3—32no—
134C2×C4×D3—38no—
135C2×C4×D3—38no—
136C2×C4×D3—32no—
137C2×C4×D3—32no—
138C2×C4×D3—61no—
139C2×C4×D3—61no—
140C2×C4×D3—64no—
141C2×C4×D3—61no—
142C2×C4×D3—61no—
143C2×C4×D3—64no—
144C3×M16—24no—
145C3×M16—24no—
146C3×M16—64no—
147C2×C3×C8—22no—
148C2×C3×C8—34no—
149C2×C3×C8C22×D314yes—
150C3×C42—34no—
151C3×C42—34no—
152(C2×D3)⋊C4—38no—
153(C2×D3)⋊C4—38no—
154Dic3⋊C4—38no—
155Dic3⋊C4—38no—
156C4×Dic3C4×D314yes—
157C4×Dic3C22×D314yes—
158#208—24no—
159#208—64no—
160#208—64no—
161C2×C3⋊C8—34no—
162C2×C3⋊C8—62no—
163C2×C3⋊C8C22×D314yes—
164ΓL(1,𝔽25)—68no—
165ΓL(1,𝔽25)—68no—
166ΓL(1,𝔽25)—68no—
167D3×C8—68no—
168D3×C8—68no—
169D3×C8—68no—
170C22×C32—22no—
171C22×C32C2×C4⋊C412yes—
172C22×C32C23×C411yescharacteristic
173C2×C3⋊D3—22no—
174C2×C3⋊D3—22no—
175C2×C3⋊D3—44no—
176C2×C3⋊D3C2×C4⋊C412yes—
177C2×C3⋊D3C2×C4⋊C412yes—
178C32×C4C2×C4⋊C412yes—
179C32×C4C22×D411yescharacteristic
180C32×C4C22×Q811yescharacteristic
181C3⋊Dic3C2×C4⋊C412yes—
182C3⋊Dic3C2×C4⋊C412yes—
183C3×Dic3—28no—
184C23×C4—91no—
185C2×M16—32no—
186C2×M16—92no—
187C2×M16—91no—
188C2×M16—92no—
189C2×M16—184no—
190C2×M16—184no—
191C2×M16D3211yescharacteristic
192C22×C8—92no—
193C22×C8—92no—
194#117—92no—
195#117—92no—
196#117—92no—
197#117—92no—
198C2×C4⋊C4—92no—
199C2×C22⋊C4—92no—
200C2×C42—32no—
201C4⋊C8—38no—
202C4⋊C8—98no—
203C23×C3—21no—
204C23×C3C2×C4×D312yes—
205C22×D3—32no—
206C22×D3—32no—
207C22×D3—38no—
208C22×D3—61no—
209C22×D3—64no—
210C22×D3—61no—
211C22×D3—124no—
212C22×D3—124no—
213C2×C3×C4—21no—
214C2×C3×C4—22no—
215C2×C3×C4—21no—
216C2×C3×C4—22no—
217C2×C3×C4—38no—
218C2×C3×C4—124no—
219C2×C3×C4C2×C4×D312yes—
220C2×C3×C4D3×D414yes—
221C2×C3×C4D3×Q814yes—
222C2×C3×C4C23×D312yes—
223C2×Dic3—38no—
224C2×Dic3—32no—
225C2×Dic3—32no—
226C2×Dic3—44no—
227C2×Dic3—64no—
228C2×Dic3—61no—
229C2×Dic3—61no—
230C2×Dic3C2×C4×D318yes—
231C4×D3—38no—
232C4×D3—38no—
233C4×D3—34no—
234C4×D3—34no—
235C4×D3—34no—
236C4×D3—34no—
237C4×D3—64no—
238C4×D3—64no—
239C4×D3—62no—
240C4×D3—62no—
241C4×D3—62no—
242C4×D3—62no—
243C3×C8—24no—
244C3×C8—24no—
245C3×C8—64no—
246C3⋊C8—24no—
247C3⋊C8—64no—
248C3⋊C8—64no—
249C2×C32—22no—
250C2×C32C22×C4⋊C411yescharacteristic
251C2×C32#56812yes—
252C3⋊D3—22no—
253C3⋊D3—22no—
254C24—91no—
255C22×C4—34no—
256C22×C4—91no—
257C22×C4—91no—
258C22×C4—91no—
259C22×C4—94no—
260C22×C4—91no—
261C22×C4—91no—
262C22×C4—94no—
263C22×C4C2×D3211yescharacteristic
264M16—22no—
265M16—64no—
266M16—184no—
267M16—184no—
268M16—182no—
269C2×C8—34no—
270C2×C8—92no—
271C2×C8—184no—
272C2×C8—184no—
273C2×C8C2×D3212yes—
274C4⋊C4—94no—
275C4⋊C4—94no—
276C22⋊C4—94no—
277C22⋊C4—94no—
278C42—34no—
279C42—34no—
280C22×C3—24no—
281C22×C3—21no—
282C22×C3—22no—
283C22×C3—42no—
284C22×C3D3×C4⋊C414yes—
285C22×C3C22×C4×D312yes—
286C2×D3—34no—
287C2×D3—34no—
288C2×D3—62no—
289C2×D3—62no—
290C2×D3—64no—
291C2×D3—64no—
292C2×D3—64no—
293C2×D3—122no—
294C2×D3—128no—
295C2×D3—128no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—22no—
299C3×C4—68no—
300C3×C4D3×C4⋊C414yes—
301C3×C4C2×D3×D412yes—
302C3×C4C2×D3×Q812yes—
303Dic3—28no—
304Dic3—34no—
305Dic3—34no—
306Dic3—62no—
307Dic3—62no—
308C32#290511yescharacteristic, complemented, Sylow
309C23—91no—
310C23—91no—
311C23—94no—
312C23—362no—
313C23C4×D3211yescharacteristic
314C2×C4—38no—
315C2×C4—91no—
316C2×C4—91no—
317C2×C4—94no—
318C2×C4—92no—
319C2×C4—92no—
320C2×C4—92no—
321C2×C4—92no—
322C2×C4—94no—
323C2×C4—94no—
324C2×C4—124no—
325C2×C4#379712yes—
326C2×C4C4×D3211yescharacteristic
327C2×C4#381112yes—
328C2×C4C22×D3211yescharacteristic
329C8—22no—
330C8—64no—
331C8—182no—
332C2×C3—24no—
333C2×C3—21no—
334C2×C3—22no—
335C2×C3—42no—
336C2×C3C2×D3×C4⋊C412yes—
337C2×C3#574514yes—
338D3—64no—
339D3—64no—
340D3—64no—
341D3—122no—
342C22—22no—
343C22—92no—
344C22—92no—
345C22—182no—
346C22—182no—
347C22—364no—
348C22#6388312yes—
349C22C2×C4×D3211yescharacteristic
350C4—68no—
351C4—92no—
352C4—92no—
353C4#6388312yes—
354C4C2×#379711yescharacteristic
355C4C2×#381111yescharacteristic
356C3—21no—
357C3#7904812yescomplemented
358C2—22no—
359C2—182no—
360C2—182no—
361C2#1059472212yes—
362C2C2×#6388311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC2×C32×M16C22
prime radicalC23×C3⋊D3C2×C4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2905
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. C3×#5118C2semidirect
5. #10591115C2semidirect
6. #10590702C2semidirect
7. #10590701C2semidirect
26. C3×Dic3⋊C8C22semidirect
27. Dic3⋊(C3⋊C8)C22semidirect
34. #5118D3semidirect
92. Dic3⋊C8C2×D3semidirect
308. C32#2905semidirect
357. C3#79048semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
C2×#638742
C2×#638182
C3×#51182
#105911152
#105907022
#105907012
#790483