Finite Group Databasebeta

← #16808139

Subgroups — #16808139

Order 3328.

2738 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719625C212yesmaximal
2#13131484C218yesmaximal, complemented
3#13131482C218yesmaximal, complemented
4#13131480C216yesmaximal, complemented
5D13⋊#423C216yesmaximal, complemented
6C2×C4×#6131C211yesmaximal, characteristic
7C22×#6131C2211yescharacteristic
8#11719625—216no—
9C2×#88240C22116yes—
10C2×D13⋊M16C22112yes—
11C2×C4×Q8×C13C411yescharacteristic
12C2×Q8×Dic13C411yescharacteristic
13C4×#6131C414yes—
14C4×#6131C414yes—
15C4×#6131C2214yes—
16C4×#6131C2214yes—
17C2×#88147C413yes—
18C2×#88146C2213yes—
19C2×C4×D52C413yes—
20C2×C42×D13C2213yes—
21#11719129C2214yes—
22#11719129C22112yes—
23#11719079C22148yescomplemented
24#11719053C22112yescomplemented
25#11719052C22112yescomplemented
26D13⋊(C4⋊C8)C22112yescomplemented
27D13⋊(C4⋊C8)C22112yescomplemented
28C22×Q8×C13C2×C411yescharacteristic
29C2×#6131C2×C414yes—
30C2×#6131D418yes—
31C2×#6131Q818yes—
32C2×#6131C2314yes—
33C22×D52C2×C413yes—
34C22×C4×D13C2×C413yes—
35C22×C4×D13C2×C413yes—
36C22×C4×D13C2313yes—
37C2×#6122C2318yes—
38#88240—264no—
39D13⋊M16—248no—
40C2×#6118C23124yes—
41C2×D13⋊C8C23124yes—
42C4×Q8×C13C2×C414yes—
43C4×Q8×C13C2×C414yes—
44C2×C13×C4⋊C4C2×C413yes—
45C2×C42×C13C2×C413yes—
46Q8×Dic13C2×C414yes—
47Q8×Dic13C2×C414yes—
48C2×#6103C2×C416yes—
49C2×C4⋊Dic13C2×C413yes—
50C2×C4×Dic13C2×C413yes—
51C2×C4×Dic13C2311yescharacteristic
52C2×C4×Dic13C2313yes—
53#88147C2×C4112yes—
54#88147C2×C4112yes—
55#88146C2×C4112yes—
56#88146C23112yes—
57C4×D52C2×C4112yes—
58C4×D52C2×C4112yes—
59C42×D13C2×C416yes—
60C42×D13C2×C416yes—
61C42×D13C2316yes—
62C42×D13C2316yes—
63#88112C2318yes—
64#88112C23124yes—
65C4⋊#1057C2318yes—
66C4⋊#1057C23124yes—
67#60099—131nomaximal, Sylow
68C23×D13C22×C413yes—
69C2×Q8×C13C4⋊C418yes—
70C2×Q8×C13C22×C414yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C22×C413yes—
73C22×C4×C13C22×C413yes—
74C22×Dic13C22×C411yescharacteristic
75C22×Dic13C22×C413yes—
76C22×Dic13C2411yescharacteristic
77#6131C4⋊C4132yes—
78#6131C2×D4116yes—
79#6131C2×Q8116yes—
80C2×D52C4⋊C4124yes—
81C2×D52C22×C4112yes—
82C2×C4×D13—46no—
83C2×C4×D13—46no—
84C2×C4×D13C22×C416yes—
85C2×C4×D13C22×C416yes—
86C2×C4×D13C22×C416yes—
87C2×C4×D13C22×C416yes—
88C2×C4×D13C22×C416yes—
89C2×C4×D13C2×D4112yes—
90C2×C4×D13C2×Q8112yes—
91C2×C4×D13C2416yes—
92#6122—216no—
93C2×#1057C24116yes—
94#6118—248no—
95D13⋊C8—248no—
96C13×C4⋊C4C22×C4112yes—
97C42×C13C22×C416yes—
98C42×C13C22×C416yes—
99#6103C22×C4124yes—
100C4⋊Dic13C22×C4112yes—
101C4×Dic13C22×C411yescharacteristic
102C4×Dic13C22×C411yescharacteristic
103C4×Dic13C22×C416yes—
104C4×Dic13C22×C416yes—
105C4×Dic13C22×C416yes—
106C4×Dic13C2411yescharacteristic
107C4×Dic13C2416yes—
108C4×Dic13C2411yescharacteristic
109C2×#568—132no—
110C2×C4×#41—131no—
111#2906—138no—
112#2906—138no—
113#2905—136no—
114C2×#423—136no—
115C23×C13C23×C411yescharacteristic
116C22×D13—43no—
117C22×D13—43no—
118C22×D13C2×C4⋊C4112yes—
119C22×D13C23×C416yes—
120Q8×C13C2×C4⋊C4116yes—
121C2×C4×C13—22no—
122C2×C4×C13—43no—
123C2×C4×C13C2×C4⋊C4112yes—
124C2×C4×C13C23×C416yes—
125C2×C4×C13C23×C411yescharacteristic
126C2×C4×C13C23×C416yes—
127C2×C4×C13C23×C411yescharacteristic
128C2×Dic13—22no—
129C2×Dic13—43no—
130C2×Dic13C23×C411yescharacteristic
131C2×Dic13C23×C416yes—
132C2×Dic13C23×C411yescharacteristic
133C2×Dic13C23×C411yescharacteristic
134C2×Dic13C22×D412yes—
135C2×Dic13C22×Q812yes—
136C2×Dic13C2511yescharacteristic
137D52C2×C4⋊C4148yes—
138C4×D13—212no—
139C4×D13—212no—
140C4×D13—46no—
141C4×D13—46no—
142C4×D13C2×C4⋊C4124yes—
143C4×D13C22×D4112yes—
144C4×D13C22×Q8112yes—
145#1057—216no—
146C22×#41—131no—
147#568—2616no—
148C2×#131—1316no—
149C22×M16—1312no—
150C4×#41—134no—
151C4×#41—134no—
152C4×#41—134no—
153C4×#41—134no—
154C2×C4×Q8—131no—
155C2×C4×Q8#26111yescharacteristic
156C2×C4×D4—133no—
157C2×C4×D4—133no—
158C2×#117—133no—
159C22×C42—133no—
160#424—1348no—
161#423—134no—
162#423—1312no—
163#423—1312no—
164#423—1312no—
165C2×C4⋊C8—1312no—
166C2×C4⋊C8—1312no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13C22×C4⋊C412yes—
170C22×C13C24×C411yescharacteristic
171C2×D13—26no—
172C2×D13—26no—
173C2×D13—412no—
174C2×D13C22×C4⋊C4112yes—
175C4×C13—26no—
176C4×C13—21no—
177C4×C13C22×C4⋊C4112yes—
178C4×C13#56812yescomplemented
179Dic13—26no—
180Dic13—21no—
181Dic13C22×C4⋊C412yes—
182Dic13#56812yescomplemented
183Dic13C23×D411yescharacteristic
184Dic13C23×Q811yescharacteristic
185C2×#41—138no—
186C2×#41—138no—
187C2×#41—134no—
188C2×#41—134no—
189C22×Q8C2×#26111yescharacteristic
190C22×D4—133no—
191C23×C4—133no—
192C23×C4—133no—
193C23×C4—133no—
194#131—2664no—
195C2×M16—138no—
196C2×M16—1324no—
197C2×M16—2648no—
198C22×C8—1324no—
199C4×Q8—134no—
200C4×Q8—134no—
201C4×Q8C2×#26114yes—
202C4×Q8C2×#26114yes—
203C4×D4—1312no—
204C4×D4—1312no—
205C4×D4—1312no—
206C4×D4—1312no—
207#117—1312no—
208#117—1312no—
209C2×C4⋊C4—133no—
210C2×C4⋊C4C2×#26113yes—
211C2×C22⋊C4—136no—
212C2×C42—133no—
213C2×C42—133no—
214C2×C42—131no—
215C2×C42—136no—
216C2×C42—136no—
217C2×C42—136no—
218C2×C42—136no—
219C2×C42C2×#26113yes—
220C4⋊C8—138no—
221C4⋊C8—1324no—
222C4⋊C8—138no—
223C4⋊C8—1324no—
224C2×C13—22no—
225C2×C13C23×C4⋊C411yescharacteristic
226C2×C13C2×#56811yescharacteristic
227C2×C13C2×#56811yescharacteristic
228D13—212no—
229C24—133no—
230#41—1316no—
231#41—1332no—
232#41—1316no—
233C2×Q8C4⋊#26118yes—
234C2×Q8C22×#26114yes—
235C2×D4—1324no—
236C2×D4—1312no—
237C22×C4—131no—
238C22×C4—1312no—
239C22×C4—1312no—
240C22×C4—136no—
241C22×C4—136no—
242C22×C4—131no—
243C22×C4—133no—
244C22×C4—136no—
245C22×C4—136no—
246C22×C4—136no—
247C22×C4—136no—
248C22×C4—526no—
249C22×C4—526no—
250C22×C4C22×#26111yescharacteristic
251C22×C4C22×#26113yes—
252C22×C4C22×#26113yes—
253M16—2616no—
254M16—2648no—
255C2×C8—1316no—
256C2×C8—2648no—
257C4⋊C4—1312no—
258C4⋊C4C22×#261112yes—
259C22⋊C4—1324no—
260C42—131no—
261C42—131no—
262C42—136no—
263C42—131no—
264C42—131no—
265C42—136no—
266C42—136no—
267C42—136no—
268C42C22×#26116yes—
269C42C22×#26116yes—
270C13#6009911yescharacteristic, complemented, Sylow
271C23—136no—
272C23—1312no—
273C23—523no—
274C23—523no—
275C23C23×#26111yescharacteristic
276Q8C2×C4⋊#261116yes—
277D4—1348no—
278C2×C4—22no—
279C2×C4—43no—
280C2×C4—132no—
281C2×C4—132no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—1312no—
286C2×C4—1324no—
287C2×C4—1312no—
288C2×C4—131no—
289C2×C4—136no—
290C2×C4—2612no—
291C2×C4—262no—
292C2×C4—2612no—
293C2×C4—526no—
294C2×C4—526no—
295C2×C4—523no—
296C2×C4C2×C4⋊#261112yes—
297C2×C4C23×#26111yescharacteristic
298C2×C4C23×#26116yes—
299C2×C4C23×#26116yes—
300C2×C4C23×#26111yescharacteristic
301C8—2616no—
302C22—21no—
303C22—21no—
304C22—1312no—
305C22—266no—
306C22—266no—
307C22—5212no—
308C22C22×C4⋊#26112yes—
309C22C24×#26111yescharacteristic
310C4—26no—
311C4—21no—
312C4—132no—
313C4—131no—
314C4—131no—
315C4—132no—
316C4—261no—
317C4—266no—
318C4C22×C4⋊#261112yes—
319C4#1171962512yescomplemented
320C2—22no—
321C2—2612no—
322C2C23×C4⋊#26111yescharacteristic
323C2D13⋊#56811yescharacteristic
324C2C2×#1171962511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC2×C4×Q8×C13C4
prime radicalC22×#6131C22
cosocleC2×Dic13C25
hypercenterC2×C4×Q8#261
hypocenterC13#60099
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13131484C2semidirect
3. #13131482C2semidirect
4. #13131480C2semidirect
5. D13⋊#423C2semidirect
23. #11719079C22semidirect
24. #11719053C22semidirect
25. #11719052C22semidirect
26. D13⋊(C4⋊C8)C22semidirect
27. D13⋊(C4⋊C8)C22semidirect
178. C4×C13#568semidirect
182. Dic13#568semidirect
270. C13#60099semidirect
319. C4#11719625semidirect

Maximal subgroups

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

subgroupindex
C2×#117196252
#131314842
#131314822
#131314802
D13⋊#4232
C2×C4×#61312
#6009913