Finite Group Databasebeta

← #15768705

Subgroups — #15768705

Order 3328.

1174 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#1055C211yesmaximal, characteristic
2C2×C42×Dic13C211yesmaximal, characteristic
3C2×#11718142C214yesmaximal
4C22×C13×C4⋊C8C211yesmaximal, characteristic
5C23×C8×C13C2212yes—
6C22×C42×C13C2211yescharacteristic
7C22×C4×Dic13C412yes—
8C22×C4×Dic13C412yes—
9C22×C4×Dic13C2212yes—
10C23×#1055C2212yes—
11C2×C13×C4⋊C8—22no—
12C2×C13×C4⋊C8—22no—
13C2×C13×C4⋊C8C414yescomplemented
14C42×Dic13—22no—
15C42×Dic13—22no—
16C2×C4⋊#1055—22no—
17C2×C4⋊#1055—22no—
18C2×C4⋊#1055C414yescomplemented
19#11718142—28no—
20C23×C4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13C2×C414yes—
24C22×C8×C13—22no—
25C22×C8×C13—22no—
26C22×C8×C13—24no—
27C22×C8×C13—24no—
28C22×C8×C13C2×C414yes—
29C2×C42×C13C2×C412yes—
30C2×C42×C13C2×C412yes—
31C2×C42×C13D412yes—
32C2×C42×C13D412yes—
33C2×C42×C13D412yes—
34C2×C42×C13Q812yes—
35C2×C4×Dic13—24no—
36C2×C4×Dic13—24no—
37C2×C4×Dic13—24no—
38C2×C4×Dic13—22no—
39C2×C4×Dic13—22no—
40C2×C4×Dic13—22no—
41C2×C4×Dic13—22no—
42C2×C4×Dic13—28no—
43C2×C4×Dic13C818yescomplemented
44C2×C4×Dic13D414yes—
45C2×C4×Dic13Q814yes—
46C22×#1055—22no—
47C22×#1055—22no—
48C22×#1055—24no—
49C22×#1055—24no—
50C22×#1055C2×C414yes—
51C13×C4⋊C8—28no—
52C4⋊#1055—28no—
53#10832—131nomaximal, Sylow
54C24×C13C22×C411yescharacteristic
55C22×C4×C13—24no—
56C22×C4×C13C4212yes—
57C22×C4×C13C4212yes—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C4⋊C412yes—
61C22×C4×C13C4⋊C412yes—
62C22×C4×C13C2×C814yes—
63C22×C4×C13M1614yes—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×Q811yescharacteristic
71C22×C4×C13C2×Q812yes—
72C22×C4×C13#4112yes—
73C22×C4×C13#4112yes—
74C22×Dic13—24no—
75C22×Dic13—24no—
76C22×Dic13—24no—
77C22×Dic13—24no—
78C22×Dic13C4⋊C418yes—
79C22×Dic13C2×C818yes—
80C22×Dic13M1618yes—
81C2×C8×C13—24no—
82C2×C8×C13—28no—
83C2×C8×C13—44no—
84C2×C8×C13—42no—
85C2×C8×C13—42no—
86C42×C13C22⋊C414yes—
87C42×C13C22⋊C414yes—
88C42×C13C4⋊C414yes—
89C42×C13C4⋊C414yes—
90C4×Dic13—216no—
91C4×Dic13—216no—
92C4×Dic13—24no—
93C4×Dic13—24no—
94C4×Dic13—24no—
95C4×Dic13—24no—
96C2×#1055—24no—
97C2×#1055—28no—
98C2×#1055—44no—
99C2×#1055—42no—
100C2×#1055—42no—
101C22×C4⋊C8—131no—
102C22×C4⋊C8D1311yescharacteristic
103C2×C43—131no—
104C2×#336—134no—
105C23×C13C2×C4211yescharacteristic
106C23×C13C2×C22⋊C411yescharacteristic
107C23×C13C2×C4⋊C411yescharacteristic
108C23×C13C2×C4⋊C412yes—
109C23×C13#11712yes—
110C23×C13C22×C812yes—
111C23×C13C2×M1612yes—
112C23×C13C2×M1614yes—
113C2×C4×C13—24no—
114C2×C4×C13—24no—
115C2×C4×C13—24no—
116C2×C4×C13#9514yes—
117C2×C4×C13#9514yes—
118C2×C4×C13C4×C814yes—
119C2×C4×C13#9714yes—
120C2×C4×C13C22⋊C818yes—
121C2×C4×C13C4⋊C818yes—
122C2×C4×C13C2×C22⋊C411yescharacteristic
123C2×C4×C13C2×C22⋊C411yescharacteristic
124C2×C4×C13C2×C4⋊C411yescharacteristic
125C2×C4×C13C2×C4⋊C411yescharacteristic
126C2×C4×C13C4×D412yes—
127C2×C4×C13C4×D412yes—
128C2×C4×C13C4×Q812yes—
129C2×C4×C13C4×Q812yes—
130C2×C4×C13#12112yes—
131C2×C4×C13#12112yes—
132C2×C4×C13C22⋊Q812yes—
133C2×C4×C13C22⋊Q812yes—
134C2×C4×C13#12411yescharacteristic
135C2×C4×C13#12411yescharacteristic
136C2×C4×C13#12512yes—
137C2×C4×C13#12711yescharacteristic
138C2×C4×C13C4⋊Q812yes—
139C2×C4×C13C4⋊Q811yescharacteristic
140C2×Dic13—28no—
141C2×Dic13—28no—
142C2×Dic13—28no—
143C2×Dic13—28no—
144C2×Dic13—28no—
145C2×Dic13—28no—
146C2×Dic13C4⋊C8116yescomplemented
147C8×C13—44no—
148#1055—44no—
149C23×C8—132no—
150C23×C8C2×D1312yes—
151C22×C42—132no—
152C22×C42—132no—
153C22×C42—132no—
154C22×C42C2×D1311yescharacteristic
155C2×C4⋊C8—22no—
156C2×C4⋊C8—22no—
157C2×C4⋊C8—134no—
158C2×C4⋊C8—262no—
159C2×C4⋊C8—262no—
160C2×C4⋊C8Dic1314yescomplemented
161C43—262no—
162C43—262no—
163#336—268no—
164C22×C13C2×#9511yescharacteristic
165C22×C13C4×C4⋊C412yes—
166C22×C13#38012yes—
167C22×C13#38211yescharacteristic
168C22×C13#38411yescharacteristic
169C22×C13C2×C4×C811yescharacteristic
170C22×C13C2×#9711yescharacteristic
171C22×C13C4×M1612yes—
172C22×C13C2×C22⋊C812yes—
173C22×C13#40712yes—
174C22×C13C2×C4⋊C814yes—
175C22×C13C2×C4⋊C812yes—
176C22×C13#42314yes—
177C22×C13#42312yes—
178C22×C13#43114yes—
179C22×C13#43214yes—
180C4×C13—24no—
181C4×C13#33618yescomplemented
182C4×C13#38912yes—
183C4×C13#38912yes—
184C4×C13#39011yescharacteristic
185C4×C13#39011yescharacteristic
186C4×C13#39111yescharacteristic
187C4×C13#39111yescharacteristic
188Dic13—216no—
189C23×C4—134no—
190C23×C4C4×D1311yescharacteristic
191C23×C4C4×D1311yescharacteristic
192C23×C4C22×D1311yescharacteristic
193C22×C8—24no—
194C22×C8—24no—
195C22×C8—22no—
196C22×C8—22no—
197C22×C8—134no—
198C22×C8—262no—
199C22×C8—264no—
200C22×C8—264no—
201C22×C8—262no—
202C22×C8C2×Dic1314yes—
203C2×C42—138no—
204C2×C42—134no—
205C2×C42—134no—
206C2×C42—268no—
207C2×C42—264no—
208C2×C42—264no—
209C2×C42—264no—
210C2×C42—262no—
211C2×C42—262no—
212C2×C42—262no—
213C2×C42—262no—
214C2×C42Dic2612yes—
215C2×C42C4×D1312yes—
216C2×C42D5212yes—
217C2×C42C2×Dic1312yes—
218C2×C42C22⋊D1312yes—
219C2×C42C22⋊D1312yes—
220C4⋊C8—28no—
221C4⋊C8—268no—
222C2×C13C4⋊#9511yescharacteristic
223C2×C13C2×#33611yescharacteristic
224C2×C13#172811yescharacteristic
225C2×C13C4×C4⋊C812yes—
226C2×C13#176712yes—
227C2×C13#179714yes—
228C2×C13#183112yes—
229C2×C13#184212yes—
230C24C2×C4×D1311yescharacteristic
231C22×C4—24no—
232C22×C4—138no—
233C22×C4—138no—
234C22×C4—138no—
235C22×C4—264no—
236C22×C4—264no—
237C22×C4—264no—
238C22×C4—264no—
239C22×C4C8×D1314yes—
240C22×C4#609414yes—
241C22×C4C4×Dic1312yes—
242C22×C4C4×Dic1312yes—
243C22×C4#610112yes—
244C22×C4#610112yes—
245C22×C4#610312yes—
246C22×C4#610312yes—
247C22×C4C2×Dic2611yescharacteristic
248C22×C4C2×C4×D1311yescharacteristic
249C22×C4C2×D5211yescharacteristic
250C22×C4D4×D1312yes—
251C22×C4#612912yes—
252C22×C4Q8×D1312yes—
253C22×C4#613112yes—
254C22×C4C22×Dic1311yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257C2×C8—28no—
258C2×C8—24no—
259C2×C8—42no—
260C2×C8—44no—
261C2×C8—42no—
262C2×C8—268no—
263C2×C8—264no—
264C2×C8—524no—
265C2×C8—522no—
266C2×C8—522no—
267C42—2616no—
268C42—264no—
269C42—264no—
270C42—264no—
271C42—264no—
272C42—2616no—
273C42#610114yes—
274C42C4⋊Dic1314yes—
275C42#610314yes—
276C42C22⋊Dic1314yes—
277C13#1083211yescharacteristic, complemented, Sylow
278C23C4⋊C4×D1312yes—
279C23#8814612yes—
280C23C2×C8×D1312yes—
281C23C2×#609412yes—
282C23M16×D1314yes—
283C23C2×C4×Dic1311yescharacteristic
284C23C2×#610111yescharacteristic
285C23C2×#610311yescharacteristic
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—1316no—
290C2×C4—268no—
291C2×C4—268no—
292C2×C4—268no—
293C2×C4—268no—
294C2×C4—268no—
295C2×C4—268no—
296C2×C4C8×Dic1314yes—
297C2×C4#8805418yes—
298C2×C4#8805514yes—
299C2×C4#8806018yes—
300C2×C4#8807114yes—
301C2×C4#8807114yes—
302C2×C4#8814112yes—
303C2×C4#8814212yes—
304C2×C4#8814412yes—
305C2×C4#8814712yes—
306C2×C4#8814912yes—
307C2×C4#8815112yes—
308C2×C4C2×#610111yescharacteristic
309C2×C4C2×C4⋊Dic1311yescharacteristic
310C2×C4C2×#610311yescharacteristic
311C2×C4D4×Dic1312yes—
312C2×C4#8819011yescharacteristic
313C2×C4#8819212yes—
314C2×C4#8819411yescharacteristic
315C2×C4#8819811yescharacteristic
316C2×C4Q8×Dic1312yes—
317C2×C4#8820012yes—
318C2×C4#8820111yescharacteristic
319C2×C4C2×C22⋊Dic1311yescharacteristic
320C8—44no—
321C8—524no—
322C22D13×C4⋊C814yes—
323C22#1171849414yes—
324C22#1171849614yes—
325C22#1171849814yes—
326C22C4⋊C4×Dic1312yes—
327C22#1171863711yescharacteristic
328C22#1171863811yescharacteristic
329C22#1171864812yes—
330C22C2×C8×Dic1311yescharacteristic
331C22C2×#8805412yes—
332C22C2×#8805511yescharacteristic
333C22C2×#8806012yes—
334C22M16×Dic1312yes—
335C22#1171877912yes—
336C22#1171878712yes—
337C22C2×#8807111yescharacteristic
338C4—24no—
339C4—2616no—
340C4#1171814218yescomplemented
341C4#1171863412yes—
342C4#1171863511yescharacteristic
343C4#1171864612yes—
344C4#1171864911yescharacteristic
345C4#1171888211yescharacteristic
346C4#1171889111yescharacteristic
347C2#1311306511yescharacteristic
348C2C2×#1171814211yescharacteristic
349C2#1311452911yescharacteristic
350C2C4⋊C8×Dic1312yes—
351C2#1311469112yes—
352C2#1311481314yes—
353C2#1311495212yes—
354C2#1311498712yes—
subgroupG/H
center, FrattiniC23×C4C22×D13
commutatorC22×C13C2×C4×C8
FittingC22×C13×C4⋊C8C2
socle, prime radicalC24×C13C22×C4
cosocleC23×C4×C13C23
hypercenterC22×C4⋊C8D13
hypocenterC13#10832
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23×C4 ◁ C22×C4⋊C8

Complements

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

NH ≅ G/Ntype
13. C2×C13×C4⋊C8C4semidirect
18. C2×C4⋊#1055C4semidirect
43. C2×C4×Dic13C8semidirect
146. C2×Dic13C4⋊C8semidirect
160. C2×C4⋊C8Dic13semidirect
181. C4×C13#336semidirect
277. C13#10832semidirect
340. C4#11718142semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#10552
C2×C42×Dic132
C2×#117181422
C22×C13×C4⋊C82
#1083213