Finite Group Databasebeta

← #16857514

Subgroups — #16857514

Order 3968.

444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#14521866C211yesmaximal, characteristic, complemented
2#14521865C212yesmaximal, complemented
3#14521862C211yesmaximal, characteristic, complemented
4#14521427C211yesmaximal, characteristic, complemented
5#14521325C211yesmaximal, characteristic, complemented
6#14521323C212yesmaximal, complemented
7#14521234C212yesmaximal, complemented
8#14521230C212yesmaximal, complemented
9#14521165C211yesmaximal, characteristic, complemented
10#14521164C211yesmaximal, characteristic, complemented
11C31×#473C211yesmaximal, characteristic, complemented
12#11758567C2212yes—
13#11758564C2212yes—
14C31×#137C2212yes—
15C2×Q16×C31C2211yescharacteristic
16C31×#131C2211yescharacteristic
17#11758527C2211yescharacteristic
18#11758521C2212yes—
19C2×#92482C2212yes—
20#11758519C2212yes—
21#11758496—21no—
22#11758495—22no—
23#11758495—22no—
24Q16×D31—22no—
25Q16×D31—21no—
26#11758493—22no—
27#11758492—22no—
28#11758486—22no—
29#11758486C2212yes—
30#11758486C2212yes—
31#11758484C2212yes—
32C2×Dic124—21no—
33C2×Dic124C2211yescharacteristic
34#11758481—21no—
35#11758481C2211yescharacteristic
36#11758478C2211yescharacteristic
37C31×#108C2211yescharacteristic
38C31×#101C2212yes—
39#11758425C2211yescharacteristic
40#11758413C2211yescharacteristic
41#11758413C2212yes—
42#11758412C2212yes—
43#11758410C2211yescharacteristic
44C8×Dic31C2211yescharacteristic
45#41×C31C2311yescharacteristic
46C2×Q8×C31C2312yes—
47#92499—22no—
48#92499—22no—
49Q8×D31—22no—
50Q8×D31—22no—
51Q8×D31—22no—
52#92497—22no—
53#92497—42no—
54#92495—22no—
55#92495—42no—
56#92495C2311yescharacteristic
57#92495C2312yes—
58C2×Dic62—22no—
59C2×Dic62C2312yes—
60Q16×C31—22no—
61Q16×C31—21no—
62Q16×C31—21no—
63SD16×C31—22no—
64M16×C31—21no—
65M16×C31C2311yescharacteristic
66M16×C31C2312yes—
67C2×C8×C31—21no—
68C2×C8×C31C2311yescharacteristic
69#92482—22no—
70#92482—22no—
71#92482—22no—
72#92482D411yescharacteristic
73#92481—22no—
74#92481D411yescharacteristic
75#92480D411yescharacteristic
76#92479D411yescharacteristic
77Dic31⋊C4—42no—
78C4×Dic31C2311yescharacteristic
79#92474C2311yescharacteristic
80C2×C31⋊C8C2311yescharacteristic
81Dic124—22no—
82Dic124—22no—
83Dic124—21no—
84Dic124—21no—
85Dic124D411yescharacteristic
86D248D411yescharacteristic
87#92470—22no—
88#92470—22no—
89#92470D412yes—
90#92469—21no—
91#92469—22no—
92C8×D31—21no—
93C8×D31—22no—
94Q8×C31—22no—
95Q8×C31—22no—
96Q8×C31C2×D411yescharacteristic
97D4×C31—21no—
98D4×C31C2×D411yescharacteristic
99C2×C4×C31—21no—
100C2×C4×C31—22no—
101C2×C4×C31C2411yescharacteristic
102C22⋊D31—21no—
103C22⋊D31—22no—
104C22⋊D31—42no—
105C2×Dic31—21no—
106C2×Dic31—22no—
107C2×Dic31—42no—
108D124—42no—
109D124C2×D411yescharacteristic
110D124C2×D412yes—
111C4×D31—22no—
112C4×D31—21no—
113C4×D31—42no—
114C4×D31—42no—
115C4×D31—42no—
116Dic62—22no—
117Dic62—22no—
118Dic62—42no—
119Dic62—42no—
120Dic62C2×D412yes—
121Dic62C2×D411yescharacteristic
122C8×C31—22no—
123C8×C31—21no—
124C8×C31C2×D411yescharacteristic
125C8×C31C2×D411yescharacteristic
126C31⋊C8—21no—
127C31⋊C8C2×D411yescharacteristic
128C31⋊C8C2×D411yescharacteristic
129#3293—311nomaximal, Sylow
130C22×C31—21no—
131C22×C31H(5,𝔽2)11yescharacteristic
132C2×D31—21no—
133C2×D31—22no—
134C4×C31—21no—
135C4×C31—42no—
136C4×C31C22×D411yescharacteristic
137C4×C31C22×D411yescharacteristic
138Dic31—22no—
139Dic31—21no—
140Dic31—22no—
141Dic31—42no—
142#578—312no—
143#578—311no—
144#578—311no—
145#494—311no—
146#473—311no—
147#473—312no—
148#473D3111yescharacteristic, complemented
149#456—312no—
150#456—312no—
151#443—311no—
152#443—311no—
153C2×C31—21no—
154C2×C31—41no—
155C2×C31D4211yescharacteristic
156D31—41no—
157D31—42no—
1582−1+4—312no—
1592−1+4—312no—
160#137—312no—
161#137—312no—
162#137—312no—
163#137—622no—
164#137—622no—
165#137—622no—
166#137—622no—
167#137C2×D3112yes—
168#135—311no—
169#135—311no—
170#135—621no—
171#135—622no—
172#135—621no—
173C2×Q16—312no—
174C2×Q16—311no—
175C2×Q16—621no—
176C2×Q16—622no—
177C2×Q16—621no—
178C2×Q16C2×D3111yescharacteristic
179#131—312no—
180#131—311no—
181#131C2×D3111yescharacteristic
182C4⋊Q8—312no—
183#108—311no—
184#108C2×D3111yescharacteristic
185#104—311no—
186#104—312no—
187#104—311no—
188#101—312no—
189#101C2×D3112yes—
190C4×C8—311no—
191C31#329311yescharacteristic, complemented, Sylow
192#41—311no—
193#41—312no—
194#41—622no—
195#41—622no—
196#41—622no—
197#41—622no—
198#41—1242no—
199#41—1242no—
200#41C22×D3111yescharacteristic
201C2×Q8—312no—
202C2×Q8—622no—
203C2×Q8—622no—
204C2×Q8—622no—
205C2×Q8—622no—
206C2×Q8C22×D3112yes—
207Q16—22no—
208Q16—21no—
209Q16—21no—
210Q16—311no—
211Q16—311no—
212Q16—622no—
213Q16—622no—
214Q16—622no—
215Q16—622no—
216Q16—622no—
217Q16—621no—
218Q16—621no—
219SD16—22no—
220SD16—311no—
221SD16—311no—
222SD16—312no—
223SD16—622no—
224SD16—622no—
225SD16—622no—
226D8—311no—
227D8—311no—
228M16—21no—
229M16—311no—
230M16—622no—
231M16—621no—
232M16C22×D3112yes—
233M16C22×D3111yescharacteristic
234C2×C8—21no—
235C2×C8—311no—
236C2×C8—622no—
237C2×C8—621no—
238C2×C8C22×D3111yescharacteristic
239C4⋊C4—1242no—
240C42—311no—
241Q8—22no—
242Q8—22no—
243Q8—311no—
244Q8—312no—
245Q8—622no—
246Q8—622no—
247Q8—1242no—
248Q8—1242no—
249Q8D4×D3111yescharacteristic
250D4—21no—
251D4—311no—
252D4—312no—
253D4—621no—
254D4—622no—
255D4—1242no—
256D4—1242no—
257D4D4×D3111yescharacteristic
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—621no—
261C2×C4—622no—
262C2×C4—621no—
263C2×C4—622no—
264C2×C4—1242no—
265C2×C4—1242no—
266C2×C4—1242no—
267C2×C4—1242no—
268C2×C4C23×D3111yescharacteristic
269C8—21no—
270C8—22no—
271C8—311no—
272C8—311no—
273C8—621no—
274C8D4×D3111yescharacteristic
275C8D4×D3111yescharacteristic
276C22—21no—
277C22—622no—
278C22—621no—
279C22#1175856611yescharacteristic
280C4—21no—
281C4—42no—
282C4—622no—
283C4—621no—
284C4—622no—
285C4—1242no—
286C4C2×D4×D3111yescharacteristic
287C4C2×D4×D3111yescharacteristic
288C2—21no—
289C2—41no—
290C2—1242no—
291C2—1241no—
292C2#1452168311yescharacteristic
subgroupG/H
centerC2#14521683
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#473C2
socleC2×C31D42
hypercenter#473D31
hypocenterC31#3293
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ #473

Complements

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

NH ≅ G/Ntype
1. #14521866C2semidirect
2. #14521865C2semidirect
3. #14521862C2semidirect
4. #14521427C2semidirect
5. #14521325C2semidirect
6. #14521323C2semidirect
7. #14521234C2semidirect
8. #14521230C2semidirect
9. #14521165C2semidirect
10. #14521164C2semidirect
11. C31×#473C2semidirect
148. #473D31semidirect
191. C31#3293semidirect

Maximal subgroups

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

subgroupindex
#145218662
#145218652
#145218622
#145214272
#145213252
#145213232
#145212342
#145212302
#145211652
#145211642
C31×#4732
#329331