Finite Group Databasebeta

← #16807004

Subgroups — #16807004

Order 3328.

706 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719096C212yesmaximal
2#13131173C212yesmaximal, complemented
3#13131172C214yesmaximal, complemented
4#13131169C212yesmaximal, complemented
5#13131168C211yesmaximal, characteristic, complemented
6D13⋊(C4⋊C16)C212yesmaximal, complemented
7C2×C4⋊#6092C211yesmaximal, characteristic, complemented
8C4×#88161C211yesmaximal, characteristic
9C2×#88161C411yescharacteristic
10C2×#88161C2211yescharacteristic
11C4×#6127C411yescharacteristic
12C2×#88106C2212yes—
13C22×#6092C2212yes—
14#11719096—28no—
15C2×#88098C2214yes—
16C2×D13⋊C16C2214yes—
17C4×C13×M16C411yescharacteristic
18#11718783C411yescharacteristic
19#11718783C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21#11718369C412yes—
22#11718369C2212yes—
23C4×#6094C412yes—
24C4×C8×D13C2212yes—
25#11718260C2214yes—
26#11718260C2214yes—
27C4⋊#6092C2211yescharacteristic
28C4⋊#6092C2211yescharacteristic
29C4⋊#6092C2212yes—
30C4⋊#6092C2212yes—
31C4⋊#6092C2212yes—
32C2×#6127C2×C411yescharacteristic
33C2×C13×M16C2×C411yescharacteristic
34C2×C13×M16C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C4×C22⋊D13C812yes—
37C4×C22⋊D13C812yes—
38#88180C2×C411yescharacteristic
39C22×#1055C2×C411yescharacteristic
40C22×#1055C2311yescharacteristic
41#88161—24no—
42#88161D414yes—
43#88161Q814yes—
44C2×#6094C2×C412yes—
45C2×#6094C2×C412yes—
46C2×C8×D13C2×C412yes—
47C2×C8×D13C2312yes—
48C4×D52C811yescharacteristic
49C4×D52C811yescharacteristic
50#88126C2×C412yes—
51C42×D13C2×C412yes—
52C4×Dic26C811yescharacteristic
53C4×Dic26C811yescharacteristic
54#88106—24no—
55C2×#6092—24no—
56C2×#6092C2312yes—
57C2×#6092C2314yes—
58C2×#6092C2312yes—
59#88098—28no—
60D13⋊C16—28no—
61C13×#97C2×C412yes—
62C4×C8×C13C2×C412yes—
63#88055C2×C412yes—
64#88055C2×C412yes—
65C8×Dic13C2×C412yes—
66C8×Dic13C2312yes—
67C4×#1055C2×C411yescharacteristic
68C4×#1055C2×C411yescharacteristic
69C4×#1055C2311yescharacteristic
70C4×#1055C2311yescharacteristic
71#33398—131nomaximal, Sylow
72C22×C4×C13C2×C811yescharacteristic
73C22×C4×C13C2×C811yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C2×C22⋊D13C2×C812yes—
76#6127C4⋊C414yes—
77#6127M1614yes—
78C2×D52C2×C811yescharacteristic
79C2×C4×D13C2×C812yes—
80C2×C4×D13C2×C812yes—
81C2×C4×D13C22×C412yes—
82C2×Dic26C2×C811yescharacteristic
83C13×M16—22no—
84C13×M16C4⋊C414yes—
85C2×C8×C13C22×C412yes—
86C2×C8×C13C22×C412yes—
87C42×C13C2×C811yescharacteristic
88C42×C13C2×C811yescharacteristic
89C42×C13C22×C411yescharacteristic
90C42×C13C22×C411yescharacteristic
91C22⋊Dic13C2×C812yes—
92#6103C2×C812yes—
93#6103C2×C812yes—
94C4⋊Dic13C2×C811yescharacteristic
95C4⋊Dic13C2×C811yescharacteristic
96#6101C2×C812yes—
97#6101C2×C812yes—
98C4×Dic13C2×C812yes—
99C4×Dic13C2×C812yes—
100C4×Dic13C22×C412yes—
101C2×#1055—22no—
102C2×#1055C22×C411yescharacteristic
103C2×#1055C22×C411yescharacteristic
104C2×#1055C22×C411yescharacteristic
105C2×#1055C2×D412yes—
106C2×#1055C2×Q812yes—
107C2×#1055C2411yescharacteristic
108#6094—24no—
109#6094C4⋊C418yes—
110C8×D13—24no—
111C8×D13C2×D414yes—
112C8×D13C2×Q814yes—
113#6092—22no—
114#6092—24no—
115#6092—22no—
116C2×#504—132no—
117C4×#131—131no—
118#2151—134no—
119#2151—132no—
120#2150—131no—
121#2150—132no—
122C2×C4⋊C16—131no—
123C2×C4⋊C16—132no—
124C23×C13C22×C811yescharacteristic
125C22×D13C22×C812yes—
126C2×C4×C13—22no—
127C2×C4×C13—41no—
128C2×C4×C13C2×C4⋊C412yes—
129C2×C4×C13C22×C811yescharacteristic
130C2×C4×C13C22×C811yescharacteristic
131C2×C4×C13C22×C811yescharacteristic
132C2×C4×C13C22×C811yescharacteristic
133C2×C4×C13C22×C811yescharacteristic
134C2×C4×C13C2×M1612yes—
135C2×C4×C13C23×C411yescharacteristic
136C22⋊D13C4⋊C818yes—
137C2×Dic13C22×C812yes—
138C2×Dic13C22×C812yes—
139C2×Dic13C22×C812yes—
140D52C4⋊C814yes—
141C4×D13—24no—
142C4×D13—42no—
143C4×D13C2×C4⋊C414yes—
144C4×D13C2×M1614yes—
145Dic26C4⋊C814yes—
146C8×C13—22no—
147C8×C13C2×C4⋊C414yes—
148#1055—21no—
149#1055—21no—
150#1055C2×C4⋊C412yes—
151#1055C22×D411yescharacteristic
152#1055C22×Q811yescharacteristic
153C2×#131—131no—
154C2×#131—131no—
155C4×#41—131no—
156#504—268no—
157C2×M32—134no—
158C2×M32—132no—
159C22×C16—134no—
160C22×C16—132no—
161#405—131no—
162#405—131no—
163#405—132no—
164#405—132no—
165C4×M16—132no—
166C4×M16#26111yescharacteristic
167C2×C4×C8—131no—
168C2×C4×C8—132no—
169C4⋊C16—131no—
170C4⋊C16—131no—
171C4⋊C16—132no—
172C4⋊C16—132no—
173C4⋊C16—132no—
174C4⋊C16—134no—
175C4⋊C16—134no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13C2×C4⋊C812yes—
179C22×C13C23×C811yescharacteristic
180C2×D13—22no—
181C2×D13—22no—
182C2×D13C2×C4⋊C814yes—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13C2×C4⋊C812yes—
187C4×C13#50412yescomplemented
188C4×C13C22×C4⋊C411yescharacteristic
189C4×C13C22×M1611yescharacteristic
190Dic13—22no—
191Dic13—22no—
192Dic13C2×C4⋊C814yes—
193C2×#41—131no—
194#131—134no—
195#131—134no—
196#131—264no—
197C2×M16—132no—
198C2×M16—132no—
199C2×M16C2×#26111yescharacteristic
200C2×M16C2×#26111yescharacteristic
201C22×C8—131no—
202C22×C8—132no—
203C22×C8—131no—
204C22×C8—132no—
205C4×Q8—131no—
206C4×Q8—131no—
207C4×D4—132no—
208C4×D4—132no—
209C4×D4—131no—
210C4×D4—131no—
211#117—131no—
212#117—132no—
213C2×C42—132no—
214C2×C42C2×#26111yescharacteristic
215M32—268no—
216M32—264no—
217C2×C16—132no—
218C2×C16—134no—
219C2×C16—132no—
220C2×C16—268no—
221C2×C16—264no—
222#97—132no—
223#97—132no—
224#97C2×#26112yes—
225C4×C8—132no—
226C4×C8—132no—
227C4×C8—131no—
228C4×C8—131no—
229C4×C8—131no—
230C4×C8—131no—
231C4×C8C2×#26112yes—
232C2×C13—22no—
233C2×C13C22×C4⋊C811yescharacteristic
234C2×C13C2×#50411yescharacteristic
235C2×C13#340711yescharacteristic
236D13—24no—
237#41—134no—
238#41—134no—
239C2×Q8—131no—
240C2×D4—132no—
241C2×D4—131no—
242C22×C4—132no—
243C22×C4—132no—
244C22×C4—132no—
245C22×C4D13⋊C811yescharacteristic
246C22×C4D13⋊C811yescharacteristic
247C22×C4C22×#26111yescharacteristic
248M16—22no—
249M16—138no—
250M16—264no—
251M16C4⋊#26114yes—
252C2×C8—132no—
253C2×C8—132no—
254C2×C8—131no—
255C2×C8—131no—
256C2×C8—134no—
257C2×C8—134no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—264no—
261C2×C8—262no—
262C2×C8C22×#26112yes—
263C2×C8C22×#26112yes—
264C4⋊C4—132no—
265C4⋊C4—132no—
266C4⋊C4—131no—
267C4⋊C4—131no—
268C22⋊C4—132no—
269C22⋊C4—132no—
270C22⋊C4—132no—
271C42—132no—
272C42—132no—
273C42—132no—
274C42D13⋊C811yescharacteristic
275C42D13⋊C811yescharacteristic
276C42C22×#26111yescharacteristic
277C42C22×#26111yescharacteristic
278C16—262no—
279C16—264no—
280C16—262no—
281C13#3339811yescharacteristic, complemented, Sylow
282C23—132no—
283C23C2×D13⋊C811yescharacteristic
284Q8—134no—
285D4—138no—
286D4—134no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—132no—
290C2×C4—134no—
291C2×C4—134no—
292C2×C4—132no—
293C2×C4—132no—
294C2×C4—264no—
295C2×C4—522no—
296C2×C4C2×D13⋊C811yescharacteristic
297C2×C4C2×D13⋊C811yescharacteristic
298C2×C4C2×D13⋊C811yescharacteristic
299C2×C4C2×D13⋊C811yescharacteristic
300C2×C4C2×D13⋊C811yescharacteristic
301C2×C4D13⋊M1612yes—
302C2×C4C2×C4⋊#26112yes—
303C2×C4C23×#26111yescharacteristic
304C8—22no—
305C8—131no—
306C8—132no—
307C8—131no—
308C8—261no—
309C8—261no—
310C8C2×C4⋊#26114yes—
311C22—21no—
312C22—21no—
313C22—134no—
314C22—262no—
315C22—262no—
316C22D13⋊(C4⋊C8)12yes—
317C22C22×D13⋊C811yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—134no—
322C4—262no—
323C4—262no—
324C4D13⋊(C4⋊C8)12yes—
325C4#1171909612yescomplemented
326C4C2×D13⋊M1611yescharacteristic
327C4C22×C4⋊#26111yescharacteristic
328C2—22no—
329C2—264no—
330C2C2×D13⋊(C4⋊C8)11yescharacteristic
331C2C2×#1171909611yescharacteristic
332C2#1313180511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#261
commutator, socleC22×C13C23×C8
FittingC4×C13×M16C4
prime radicalC2×#6127C2×C4
cosocleC2×#1055C24
hypercenterC4×M16#261
hypocenterC13#33398
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
2. #13131173C2semidirect
3. #13131172C2semidirect
4. #13131169C2semidirect
5. #13131168C2semidirect
6. D13⋊(C4⋊C16)C2semidirect
7. C2×C4⋊#6092C2semidirect
187. C4×C13#504semidirect
281. C13#33398semidirect
325. C4#11719096semidirect

Maximal subgroups

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

subgroupindex
C2×#117190962
#131311732
#131311722
#131311692
#131311682
D13⋊(C4⋊C16)2
C2×C4⋊#60922
C4×#881612
#3339813