Finite Group Databasebeta

← #16797581

Subgroups — #16797581

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719125C211yesmaximal, characteristic
2C22×C4⋊#1057C211yesmaximal, characteristic
3#13130632C212yesmaximal, complemented
4C4⋊C4×#1057C212yesmaximal, complemented
5#13130624C214yesmaximal, complemented
6#13130573C212yesmaximal
7C22⋊C4×#1057C212yesmaximal
8#13117231C211yesmaximal, characteristic
9C23×#1057C2212yes—
10C22×C4×Dic13C2211yescharacteristic
11C2×C22⋊#1057C2211yescharacteristic
12C2×C22⋊#1057C2211yescharacteristic
13#11719125C418yescomplemented
14C2×#88112C2212yes—
15C2×#88110C2214yes—
16C2×C4⋊#1057C418yescomplemented
17C2×C4⋊#1057C2212yes—
18C2×C4⋊#1057C2211yescharacteristic
19C2×C4⋊#1057C2211yescharacteristic
20C2×C4×#1057C2214yes—
21C2×C4×#1057C2212yes—
22C13×#380C411yescharacteristic
23#11718873C411yescharacteristic
24#11718638C412yes—
25C4⋊C4×Dic13C2212yes—
26#11718604C412yes—
27C22⋊C4×Dic13C2212yes—
28#11718312C412yes—
29#11718309C2212yes—
30#11718290C2214yes—
31#11718290C2214yes—
32C23×C4×C13C2×C411yescharacteristic
33C23×Dic13C2×C411yescharacteristic
34C23×Dic13C2311yescharacteristic
35C22×#1057—44no—
36C22×#1057C2×C418yes—
37C22×#1057C2312yes—
38C22×#1057C2312yes—
39C22×#1057C2312yes—
40C22×#1057C2312yes—
41C2×C13×C4⋊C4C2×C412yes—
42C2×C13×C22⋊C4C2×C412yes—
43C2×C22⋊Dic13C2×C412yes—
44C2×C4⋊Dic13C2×C412yes—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C2×C4×Dic13C2×C414yes—
48C2×C4×Dic13C2×C414yes—
49C2×C4×Dic13C2314yes—
50C2×C4×Dic13C2311yescharacteristic
51C2×C4×Dic13C2311yescharacteristic
52C22⋊#1057C2×C414yes—
53C22⋊#1057C2×C414yes—
54#88112C2×C418yes—
55#88110—44no—
56C4⋊#1057C2×C418yes—
57C4⋊#1057C2×C414yes—
58C4⋊#1057C2×C414yes—
59C4×#1057—44no—
60C4×#1057C2×C418yes—
61C13×#95C2×C412yes—
62#88071C2×C412yes—
63#88071C2×C414yes—
64#88071C2×C414yes—
65#88071C2×C414yes—
66#20545—131nomaximal, Sylow
67C24×C13C22×C411yescharacteristic
68C22×C4×C13—24no—
69C22×C4×C13C4214yes—
70C22×C4×C13C22×C414yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×Dic13—22no—
74C22×Dic13—22no—
75C22×Dic13—22no—
76C22×Dic13—22no—
77C22×Dic13C4214yes—
78C22×Dic13C22×C414yes—
79C22×Dic13C22×C411yescharacteristic
80C22×Dic13C22×C411yescharacteristic
81C22×Dic13C22×C411yescharacteristic
82C22×Dic13C22×C412yes—
83C22×Dic13C22×C412yes—
84C22×Dic13C2411yescharacteristic
85C2×#1057—22no—
86C2×#1057—24no—
87C2×#1057—22no—
88C2×#1057—24no—
89C2×#1057—22no—
90C2×#1057—22no—
91C2×#1057—48no—
92C2×#1057C22×C414yes—
93C2×#1057C22×C414yes—
94C2×#1057C22×C414yes—
95C2×#1057C22×C414yes—
96C13×C4⋊C4—24no—
97C13×C22⋊C4—24no—
98C22⋊Dic13—24no—
99C4⋊Dic13—24no—
100C4×Dic13—24no—
101C4×Dic13—24no—
102C4×Dic13C4214yes—
103C4×Dic13C4214yes—
104C4×Dic13C22×C412yes—
105C4×Dic13C22×C412yes—
106C4×Dic13C22×C412yes—
107C4×Dic13C22×C412yes—
108C2×#431—131no—
109C22×C4⋊C8—131no—
110#2283—131no—
111#1770—132no—
112C8×C4⋊C4—132no—
113#1768—134no—
114#1752—132no—
115C8×C22⋊C4—132no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13C2×C4212yes—
119C23×C13#13112yes—
120C23×C13#13112yes—
121C23×C13C23×C411yescharacteristic
122C2×C4×C13—22no—
123C2×C4×C13—28no—
124C2×C4×C13—24no—
125C2×C4×C13—24no—
126C2×C4×C13—24no—
127C2×C4×C13C2×C4212yes—
128C2×C4×C13C2×C4212yes—
129C2×C4×C13#13114yes—
130C2×Dic13—22no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—28no—
136C2×Dic13—22no—
137C2×Dic13—22no—
138C2×Dic13—24no—
139C2×Dic13—24no—
140C2×Dic13—24no—
141C2×Dic13—24no—
142C2×Dic13C2×C4212yes—
143C2×Dic13C2×C4212yes—
144C2×Dic13C2×C4212yes—
145C2×Dic13C23×C411yescharacteristic
146C2×Dic13C23×C411yescharacteristic
147C2×Dic13H(5,𝔽2)12yes—
148C2×Dic132−1+412yes—
149#1057—24no—
150#1057—24no—
151#1057—24no—
152#1057—24no—
153C23×C8—132no—
154C22×C42—131no—
155#431—138no—
156C2×C4⋊C8—138no—
157C2×C4⋊C8—132no—
158C2×C4⋊C8—131no—
159C2×C4⋊C8—131no—
160C2×C4⋊C8—132no—
161C2×C22⋊C8—131no—
162C2×C22⋊C8—131no—
163C2×#97—134no—
164C2×C4×C8—132no—
165C2×C4×C8—134no—
166#383—132no—
167#382—132no—
168#381—132no—
169#380—131no—
170#380#26111yescharacteristic
171C4×C4⋊C4—132no—
172C4×C22⋊C4—132no—
173#376—132no—
174#336—134no—
175#336—134no—
176C22×C13—22no—
177C22×C13—24no—
178C22×C13—24no—
179C22×C13—22no—
180C22×C13#40514yes—
181C22×C13C22×C4211yescharacteristic
182C22×C13#52012yes—
183C22×C13C2×#13111yescharacteristic
184C22×C13C2×#13112yes—
185C22×C13C2×#13111yescharacteristic
186C4×C13—22no—
187C4×C13—44no—
188C4×C13#40514yes—
189Dic13—22no—
190Dic13—22no—
191Dic13—22no—
192Dic13—44no—
193Dic13#51811yescharacteristic
194Dic13#51911yescharacteristic
195Dic13#52012yes—
196C23×C4—131no—
197C23×C4—131no—
198C23×C4C2×#26111yescharacteristic
199C22×C8—132no—
200C22×C8—132no—
201C22×C8—132no—
202C22×C8—132no—
203C22×C8—138no—
204C22×C8—524no—
205C2×C4⋊C4—132no—
206C2×C4⋊C4C2×#26112yes—
207C2×C22⋊C4—132no—
208C2×C22⋊C4C2×#26112yes—
209C2×C42—134no—
210C2×C42—134no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42—131no—
214C2×C42—131no—
215C2×C42—134no—
216C4⋊C8—138no—
217C4⋊C8—134no—
218C4⋊C8—134no—
219C4⋊C8—138no—
220C22⋊C8—134no—
221C22⋊C8—134no—
222#97—524no—
223C4×C8—138no—
224C4×C8—524no—
225#95—132no—
226#95—134no—
227#95—134no—
228#95—134no—
229#95C2×#26112yes—
230C2×C13—24no—
231C2×C13#227411yescharacteristic
232C2×C13C2×#40511yescharacteristic
233C2×C13C2×#40511yescharacteristic
234C2×C13#299412yes—
235C2×C13#299412yes—
236C24C22×#26111yescharacteristic
237C22×C4—24no—
238C22×C4—131no—
239C22×C4—132no—
240C22×C4—132no—
241C22×C4—134no—
242C22×C4—131no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—134no—
246C22×C4—262no—
247C22×C4—262no—
248C22×C4—262no—
249C22×C4—262no—
250C22×C4C4×#26114yes—
251C22×C4C22×#26114yes—
252C22×C4C22×#26111yescharacteristic
253C22×C4C22×#26111yescharacteristic
254C2×C8—134no—
255C2×C8—134no—
256C2×C8—134no—
257C2×C8—134no—
258C2×C8—262no—
259C2×C8—264no—
260C2×C8—262no—
261C2×C8—264no—
262C2×C8—262no—
263C2×C8—262no—
264C2×C8—528no—
265C4⋊C4—24no—
266C4⋊C4—264no—
267C22⋊C4—24no—
268C22⋊C4—264no—
269C42—132no—
270C42—132no—
271C42—132no—
272C42—132no—
273C42—134no—
274C42—134no—
275C42—264no—
276C42—264no—
277C13#2054511yescharacteristic, complemented, Sylow
278C23—22no—
279C23—22no—
280C23C2×C4×#26112yes—
281C23#8823812yes—
282C23#8824012yes—
283C23C23×#26111yescharacteristic
284C2×C4—22no—
285C2×C4—28no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—131no—
290C2×C4—131no—
291C2×C4—132no—
292C2×C4—132no—
293C2×C4—132no—
294C2×C4—132no—
295C2×C4—132no—
296C2×C4—262no—
297C2×C4—262no—
298C2×C4—264no—
299C2×C4—268no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—262no—
305C2×C4—264no—
306C2×C4—264no—
307C2×C4—264no—
308C2×C4C2×C4×#26112yes—
309C2×C4C2×C4×#26112yes—
310C2×C4#8823814yes—
311C8—264no—
312C8—264no—
313C8—264no—
314C8—264no—
315C22—24no—
316C22—22no—
317C22—24no—
318C22—22no—
319C22#1171907214yes—
320C22C22×C4×#26111yescharacteristic
321C22C2×#8823811yescharacteristic
322C22C2×#8823812yes—
323C22C2×#8824011yescharacteristic
324C22#1171963112yes—
325C4—22no—
326C4—44no—
327C4—131no—
328C4—131no—
329C4—132no—
330C4—262no—
331C4—262no—
332C4—262no—
333C4—524no—
334C4#1171906214yes—
335C2—24no—
336C2#1313127311yescharacteristic
337C2C2×#1171906211yescharacteristic
338C2C2×#1171907211yescharacteristic
339C2#1313178312yes—
340C2#1313178712yes—
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C22×C42
FittingC13×#380C4
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenter#380#261
hypocenterC13#20545
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13130632C2semidirect
4. C4⋊C4×#1057C2semidirect
5. #13130624C2semidirect
13. #11719125C4semidirect
16. C2×C4⋊#1057C4semidirect
277. C13#20545semidirect

Maximal subgroups

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

subgroupindex
C2×#117191252
C22×C4⋊#10572
#131306322
C4⋊C4×#10572
#131306242
#131305732
C22⋊C4×#10572
#131172312
#2054513