Finite Group Databasebeta

← #16788236

Subgroups — #16788236

Order 3328.

334 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 86 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#13131196C211yesmaximal, characteristic
2#13130757C211yesmaximal, characteristic
3#13129825C212yesmaximal
4#13129824C212yesmaximal
5#13125419C211yesmaximal, characteristic
6#11719283—21no—
7#11719059—21no—
8C4×C13×Q16C411yescharacteristic, complemented
9#11718849C2211yescharacteristic
10#11718842C411yescharacteristic, complemented
11C4×#6107—21no—
12#11718548C2211yescharacteristic
13#11718535C411yescharacteristic, complemented
14#11718474—21no—
15#11718453—21no—
16C4×Dic52C411yescharacteristic, complemented
17C4×C8×D13C2211yescharacteristic
18#11718265—21no—
19#11718265C2212yes—
20#11718259C2212yes—
21#11718257—21no—
22C4⋊#6092—21no—
23C2×C4⋊#261—22no—
24C2×C4⋊#261—41no—
25C2×C4⋊#261—41no—
26C2×C13×Q16C2×C411yescharacteristic
27C4×Q8×C13—21no—
28#88200—21no—
29#88198—21no—
30C2×#6107—21no—
31C2×Dic52C2×C411yescharacteristic
32C2×C8×D13D411yescharacteristic
33C2×C8×D13C2311yescharacteristic
34#88151—21no—
35#88150—41no—
36#88143—41no—
37#88142—21no—
38#88126—41no—
39C42×D13D411yescharacteristic
40C4×Dic26—21no—
41C4×Dic26—41no—
42C2×#6092—22no—
43C13×#107C2×C411yescharacteristic
44C13×#103—21no—
45C4×C8×C13C2×C411yescharacteristic
46#88075—21no—
47#88058C2×C411yescharacteristic
48#88056—21no—
49C8×Dic13C2×C411yescharacteristic
50C8×Dic13D411yescharacteristic
51#88050—21no—
52#88047—21no—
53C4×#1055D411yescharacteristic
54#11857—131nomaximal, Sylow
55C22×#261—42no—
56C2×Q8×C13—21no—
57C2×C4×D13D811yescharacteristic
58C2×C4×D13D811yescharacteristic
59C2×C4×D13C2×D411yescharacteristic
60C2×Dic26—21no—
61C2×Dic26—41no—
62C4⋊#261—42no—
63C4⋊#261—42no—
64C4⋊#261—82no—
65C4⋊#261—82no—
66C13×Q16—41no—
67C2×C8×C13C22⋊C411yescharacteristic
68C2×C8×C13C22×C411yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—41no—
71C42×C13—41no—
72C42×C13C22⋊C411yescharacteristic
73#6107—42no—
74#6103—41no—
75#6103—41no—
76C4⋊Dic13—21no—
77C4⋊Dic13—41no—
78#6101—41no—
79#6101—41no—
80#6101—41no—
81#6101—41no—
82#6101—41no—
83C4×Dic13—41no—
84C4×Dic13C22⋊C411yescharacteristic
85C4×Dic13SD1611yescharacteristic
86C4×Dic13SD1611yescharacteristic
87C2×#1055C22⋊C411yescharacteristic
88C2×#1055C2×D411yescharacteristic
89Dic52—41no—
90C8×D13—41no—
91C8×D13—41no—
92#6092—42no—
93#3170—131no—
94#2162—131no—
95#1834—131no—
96#1348—132no—
97#1348—132no—
98C22×D13C2×D811yescharacteristic
99C2×#261—82no—
100C2×#261—82no—
101C2×#261—82no—
102Q8×C13—41no—
103Q8×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13#10211yescharacteristic
107C2×C4×C13#10211yescharacteristic
108C2×C4×C13C2×C22⋊C411yescharacteristic
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13#10211yescharacteristic
112C2×Dic13#10211yescharacteristic
113C2×Dic13C2×SD1611yescharacteristic
114C4×D13—21no—
115C4×D13—21no—
116C4×D13—22no—
117C4×D13SD3212yes—
118C4×D13Q3212yes—
119Dic26—41no—
120Dic26—41no—
121Dic26—82no—
122C8×C13—21no—
123C8×C13—21no—
124#1055—21no—
125#1055—21no—
126#533—261no—
127#500—131no—
128#494—131no—
129#487—261no—
130#467—131no—
131#467—131no—
132#467—261no—
133C4×Q16—131no—
134C4×Q16—261no—
135C4×Q16#26111yescharacteristic, complemented
136C2×C4×C8—131no—
137#384—261no—
138C4⋊C16—261no—
139C22⋊C16—132no—
140C4×C16—261no—
141#340—132no—
142#340—261no—
143C22×C13C2×#10211yescharacteristic
144C2×D13—21no—
145C2×D13—21no—
146C2×D13C2×SD3211yescharacteristic
147C2×D13C2×Q3211yescharacteristic
148#261—162no—
149C4×C13—21no—
150C4×C13—81no—
151C4×C13—81no—
152C4×C13#35812yes—
153C4×C13#41011yescharacteristic
154C4×C13#42111yescharacteristic
155Dic13—21no—
156Dic13—81no—
157Dic13—81no—
158Dic13#35812yes—
159Dic13#36012yes—
160C2×Q16—131no—
161C2×Q16—261no—
162C2×Q16C2×#26111yescharacteristic
163C22×C8—131no—
164C22×C8—131no—
165C4⋊Q8—261no—
166C4⋊Q8—261no—
167#125—521no—
168C22⋊Q8—261no—
169C22⋊Q8—261no—
170C22⋊Q8—521no—
171C4×Q8—21no—
172C4×Q8—261no—
173C4×Q8—521no—
174#117—521no—
175C2×C4⋊C4—262no—
176C2×C4⋊C4—521no—
177C2×C4⋊C4—521no—
178C2×C42—131no—
179C2×C16—262no—
180#107—131no—
181#107—261no—
182#107C2×#26111yescharacteristic
183#103—21no—
184#103—261no—
185#103—261no—
186#103—261no—
187C4×C8—131no—
188C4×C8—131no—
189C4×C8—131no—
190C4×C8C2×#26111yescharacteristic
191C2×C13#151711yescharacteristic
192C2×C13C2×#35811yescharacteristic
193C2×C13C2×#36011yescharacteristic
194D13—21no—
195D13—21no—
196C2×Q8—21no—
197C2×Q8—261no—
198C2×Q8—521no—
199C22×C4—131no—
200C22×C4—131no—
201C22×C4—131no—
202C22×C4—522no—
203Q16—41no—
204Q16—521no—
205Q16—522no—
206C2×C8—131no—
207C2×C8—131no—
208C2×C8—521no—
209C2×C8—521no—
210C2×C8C22⋊#26111yescharacteristic
211C2×C8C22×#26111yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—41no—
214C4⋊C4—261no—
215C4⋊C4—521no—
216C4⋊C4—521no—
217C4⋊C4—521no—
218C4⋊C4—521no—
219C4⋊C4—521no—
220C4⋊C4—522no—
221C4⋊C4—522no—
222C4⋊C4—521no—
223C4⋊C4—1042no—
224C4⋊C4—1042no—
225C22⋊C4—521no—
226C22⋊C4—521no—
227C42—41no—
228C42—131no—
229C42—131no—
230C42—131no—
231C42—521no—
232C42C22⋊#26111yescharacteristic
233C16—522no—
234C13#1185711yescharacteristic, complemented, Sylow
235C23—131no—
236Q8—41no—
237Q8—41no—
238Q8—521no—
239Q8—521no—
240Q8—1042no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—131no—
244C2×C4—131no—
245C2×C4—132no—
246C2×C4—132no—
247C2×C4—131no—
248C2×C4—262no—
249C2×C4—261no—
250C2×C4—261no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4—1042no—
254C2×C4—1042no—
255C2×C4—1042no—
256C2×C4#8811511yescharacteristic
257C2×C4#8811511yescharacteristic
258C2×C4C2×C22⋊#26111yescharacteristic
259C8—21no—
260C8—21no—
261C8—261no—
262C8—261no—
263C22—131no—
264C22—131no—
265C22—261no—
266C22—261no—
267C22C2×#8811511yescharacteristic
268C4—21no—
269C4—81no—
270C4—81no—
271C4—132no—
272C4—132no—
273C4—261no—
274C4—1041no—
275C4—1041no—
276C4—2082no—
277C4#1171828012yes—
278C4#1171911611yescharacteristic
279C4#1171916611yescharacteristic
280C2—261no—
281C2—261no—
282C2#1313026611yescharacteristic
283C2C2×#1171828011yescharacteristic
284C2D13⋊#36011yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC4×C13×Q16C4
socleC22×C13C2×#102
prime radicalC22×D13C2×D8
cosocleC2×C8×D13C23
hypercenterC4×Q16#261
hypocenterC13#11857
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
8. C4×C13×Q16C4semidirect
10. #11718842C4semidirect
13. #11718535C4semidirect
16. C4×Dic52C4semidirect
135. C4×Q16#261semidirect
234. C13#11857semidirect

Maximal subgroups

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

subgroupindex
#131311962
#131307572
#131298252
#131298242
#131254192
#1185713