Finite Group Databasebeta

← #16846161

Subgroups — #16846161

Order 3968.

598 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11758514C211yesmaximal, characteristic
2C2×C22⋊C4×D31C211yesmaximal, characteristic, complemented
3C2×#11758422C211yesmaximal, characteristic, complemented
4#14520904C211yesmaximal, characteristic, complemented
5#14520815C211yesmaximal, characteristic, complemented
6#14520815C211yesmaximal, characteristic, complemented
7C2×C31×#99C211yesmaximal, characteristic, complemented
8C24×D31C2211yescharacteristic
9C22×D4×C31C2211yescharacteristic
10C22×C22⋊D31C412yescomplemented
11C22×C4×D31—21no—
12C2×C22⋊C4×C31C2211yescharacteristic
13C2×C22⋊C4×C31C2211yescharacteristic
14C2×C22⋊Dic31C2211yescharacteristic
15C2×C22⋊Dic31C2211yescharacteristic
16C2×C22⋊Dic31C2211yescharacteristic
17#11758514—21no—
18#11758514—22no—
19#11758514—21no—
20C2×(C2×D31)⋊C4—21no—
21C2×(C2×D31)⋊C4—22no—
22C2×(C2×D31)⋊C4C412yescomplemented
23C22⋊C4×D31—22no—
24C22⋊C4×D31—22no—
25C31×#99—22no—
26#11758422—22no—
27C24×C31C2×C411yescharacteristic, complemented
28C24×C31C2311yescharacteristic
29C23×D31—21no—
30C23×D31—21no—
31C23×D31—21no—
32C23×D31—21no—
33C23×D31—44no—
34C23×D31C2×C412yes—
35C23×D31D411yescharacteristic
36C23×D31D412yes—
37C23×D31D411yescharacteristic
38C2×D4×C31—21no—
39C2×D4×C31—21no—
40C2×D4×C31—21no—
41C2×D4×C31—21no—
42C2×D4×C31—21no—
43C2×D4×C31—21no—
44C22×C4×C31—21no—
45C22×C4×C31—21no—
46C22×C4×C31C2×C411yescharacteristic, complemented
47C2×C22⋊D31—22no—
48C2×C22⋊D31—22no—
49C2×C22⋊D31—44no—
50C22×Dic31—21no—
51C22×Dic31—21no—
52C22×Dic31C2×C412yescomplemented
53C2×C4×D31—24no—
54C2×C4×D31—44no—
55C22⋊C4×C31—21no—
56C22⋊C4×C31—21no—
57C22⋊C4×C31—21no—
58C22⋊C4×C31D412yescomplemented
59C22⋊Dic31—21no—
60C22⋊Dic31—21no—
61C22⋊Dic31—21no—
62C22⋊Dic31—21no—
63C22⋊Dic31—21no—
64C22⋊Dic31D412yescomplemented
65(C2×D31)⋊C4—24no—
66(C2×D31)⋊C4—22no—
67(C2×D31)⋊C4—22no—
68(C2×D31)⋊C4—44no—
69C23×C31—21no—
70C23×C31—21no—
71C23×C31—21no—
72C23×C31—42no—
73C23×C31—42no—
74C23×C31C22×C411yescharacteristic
75C23×C31C2×D411yescharacteristic
76C23×C31C2×D411yescharacteristic
77C23×C31C2×D411yescharacteristic
78C23×C31C2×D411yescharacteristic
79C23×C31#4111yescharacteristic
80C23×C31#4111yescharacteristic
81C22×D31—21no—
82C22×D31—21no—
83C22×D31—24no—
84C22×D31—22no—
85C22×D31—22no—
86C22×D31—21no—
87C22×D31—22no—
88C22×D31—22no—
89C22×D31—21no—
90C22×D31—24no—
91C22×D31—24no—
92C22×D31—42no—
93C22×D31—42no—
94C22×D31—42no—
95C22×D31—44no—
96C22×D31—44no—
97C22×D31—44no—
98C22×D31—44no—
99C22×D31C22⋊C412yes—
100C22×D31C22⋊C412yes—
101D4×C31—41no—
102D4×C31—41no—
103D4×C31—41no—
104D4×C31—41no—
105C2×C4×C31—21no—
106C2×C4×C31—21no—
107C2×C4×C31—21no—
108C2×C4×C31—22no—
109C2×C4×C31—42no—
110C2×C4×C31—42no—
111C2×C4×C31—41no—
112C22⋊D31—44no—
113C22⋊D31—44no—
114C2×Dic31—22no—
115C2×Dic31—22no—
116C2×Dic31—42no—
117C2×Dic31—42no—
118C2×Dic31—42no—
119C2×Dic31—41no—
120C4×D31—48no—
121#1898—311nomaximal, Sylow
122C22×C31—22no—
123C22×C31—22no—
124C22×C31—22no—
125C22×C31—41no—
126C22×C31—41no—
127C22×C31—41no—
128C22×C31—41no—
129C22×C31—41no—
130C22×C31—42no—
131C22×C31—81no—
132C22×C31—81no—
133C22×C31C2×C22⋊C411yescharacteristic
134C22×C31C4×D411yescharacteristic
135C22×C31C4×D411yescharacteristic
136C22×C31#12011yescharacteristic
137C22×C31#12111yescharacteristic
138C22×C31#12111yescharacteristic
139C22×C31#12311yescharacteristic
140C2×D31—24no—
141C2×D31—24no—
142C2×D31—22no—
143C2×D31—22no—
144C2×D31—22no—
145C2×D31—22no—
146C2×D31—22no—
147C2×D31—44no—
148C2×D31—44no—
149C2×D31—44no—
150C2×D31—44no—
151C2×D31—42no—
152C2×D31—42no—
153C2×D31#9914yescomplemented
154C4×C31—42no—
155C4×C31—41no—
156C4×C31—81no—
157Dic31—42no—
158Dic31—42no—
159Dic31—81no—
160C2×#120—311no—
161C22×C22⋊C4—311no—
162C2×#99—311no—
163C2×#99D3111yescharacteristic, complemented
164#379—311no—
165#342—311no—
166#342—311no—
167C2×C31—21no—
168C2×C31—21no—
169C2×C31—21no—
170C2×C31—21no—
171C2×C31—21no—
172C2×C31—21no—
173C2×C31—81no—
174C2×C31#38611yescharacteristic
175C2×C31C2×#9912yes—
176D31—24no—
177D31—42no—
178C25—311no—
179C22×D4—312no—
180C22×D4C2×D3111yescharacteristic
181C23×C4—621no—
182#120—621no—
183#120—622no—
184#120—621no—
185C2×C22⋊C4—311no—
186C2×C22⋊C4—311no—
187C2×C22⋊C4—312no—
188C2×C22⋊C4—311no—
189C2×C22⋊C4—622no—
190C2×C22⋊C4—621no—
191C2×C22⋊C4—622no—
192C2×C22⋊C4—622no—
193C2×C22⋊C4C2×D3111yescharacteristic
194C2×C22⋊C4C2×D3111yescharacteristic
195#99—22no—
196#99—622no—
197C31#189811yescharacteristic, complemented, Sylow
198C24—311no—
199C24—312no—
200C24—312no—
201C24—311no—
202C24—621no—
203C24—621no—
204C24—621no—
205C24—621no—
206C24—1244no—
207C24C4×D3111yescharacteristic, complemented
208C24C22×D3111yescharacteristic
209C2×D4—21no—
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—21no—
213C2×D4—21no—
214C2×D4—21no—
215C2×D4—622no—
216C2×D4—622no—
217C2×D4—1244no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—312no—
221C22×C4—624no—
222C22×C4—621no—
223C22×C4—621no—
224C22×C4—1244no—
225C22×C4C4×D3111yescharacteristic, complemented
226C22⋊C4—21no—
227C22⋊C4—21no—
228C22⋊C4—21no—
229C22⋊C4—312no—
230C22⋊C4—622no—
231C22⋊C4—622no—
232C22⋊C4—624no—
233C22⋊C4—621no—
234C22⋊C4—621no—
235C22⋊C4—621no—
236C22⋊C4—621no—
237C22⋊C4—621no—
238C22⋊C4—1244no—
239C22⋊C4C22⋊D3112yescomplemented
240C23—21no—
241C23—21no—
242C23—21no—
243C23—42no—
244C23—42no—
245C23—312no—
246C23—312no—
247C23—624no—
248C23—624no—
249C23—624no—
250C23—621no—
251C23—621no—
252C23—622no—
253C23—621no—
254C23—622no—
255C23—622no—
256C23—621no—
257C23—622no—
258C23—1242no—
259C23—1242no—
260C23—1242no—
261C23—1244no—
262C23—1244no—
263C23—1244no—
264C23—1244no—
265C23C2×C4×D3111yescharacteristic
266C23#9249511yescharacteristic
267C23D4×D3111yescharacteristic
268C23D4×D3111yescharacteristic
269C23D4×D3111yescharacteristic
270C23#9249711yescharacteristic
271C23C2×C22⋊D3111yescharacteristic
272D4—41no—
273D4—41no—
274D4—41no—
275D4—41no—
276D4—1244no—
277D4—1244no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—622no—
286C2×C4—622no—
287C2×C4—1248no—
288C2×C4—1242no—
289C2×C4—1242no—
290C2×C4—1242no—
291C2×C4—1241no—
292C22—22no—
293C22—22no—
294C22—22no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22—42no—
301C22—81no—
302C22—81no—
303C22—314no—
304C22—624no—
305C22—624no—
306C22—622no—
307C22—622no—
308C22—622no—
309C22—622no—
310C22—622no—
311C22—1244no—
312C22—1244no—
313C22—1244no—
314C22—1244no—
315C22—1242no—
316C22—1242no—
317C22C22⋊C4×D3111yescharacteristic
318C22(C22⋊D31)⋊C411yescharacteristic
319C22#1175846011yescharacteristic
320C22#1175846111yescharacteristic
321C22C4×C22⋊D3111yescharacteristic
322C22#1175851411yescharacteristic
323C22#1175851511yescharacteristic
324C4—42no—
325C4—41no—
326C4—81no—
327C4—1242no—
328C4—1242no—
329C4—2481no—
330C2—21no—
331C2—21no—
332C2—21no—
333C2—21no—
334C2—21no—
335C2—21no—
336C2—81no—
337C2—624no—
338C2—1242no—
339C2#1452092511yescharacteristic
340C2#99×D3112yes—
subgroupG/H
centerC22C22⋊C4×D31
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC2×C31×#99C2
socleC22×C31C2×C22⋊C4
prime radicalC2×#11758514C2
cosocleC24×C31C23
hypercenterC2×#99D31
hypocenterC31#1898
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D31C2semidirect
3. C2×#11758422C2semidirect
4. #14520904C2semidirect
5. #14520815C2semidirect
6. #14520815C2semidirect
7. C2×C31×#99C2semidirect
10. C22×C22⋊D31C4semidirect
22. C2×(C2×D31)⋊C4C4semidirect
27. C24×C31C2×C4semidirect
46. C22×C4×C31C2×C4semidirect
52. C22×Dic31C2×C4semidirect
58. C22⋊C4×C31D4semidirect
64. C22⋊Dic31D4semidirect
153. C2×D31#99semidirect
163. C2×#99D31semidirect
197. C31#1898semidirect
207. C24C4×D31semidirect
225. C22×C4C4×D31semidirect
239. C22⋊C4C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
C2×#117585142
C2×C22⋊C4×D312
C2×#117584222
#145209042
#145208152
C2×C31×#992
#189831