Finite Group Databasebeta

← #15866519

Subgroups — #15866519

Order 3328.

1642 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719182C211yesmaximal, characteristic
2C22×C4⋊#1055C211yesmaximal, characteristic, complemented
3C2×#11718790C214yesmaximal, complemented
4#13115634C214yesmaximal, complemented
5#13115630C214yesmaximal, complemented
6C2×C4×C13×M16C211yesmaximal, characteristic, complemented
7C22×#6127C2212yes—
8C22×C13×M16C2212yes—
9C22×C42×C13C2211yescharacteristic
10C2×#88184C412yes—
11C2×#88184C412yes—
12C23×#1055C2212yes—
13#11719182—24no—
14#11719182—24no—
15C2×#88129C412yes—
16C2×#88128C411yescharacteristic
17C2×C4×D52C2212yes—
18C2×C4×D52C2212yes—
19C2×#88123C411yescharacteristic
20C4×C13×M16—24no—
21C2×C13×#97C2212yes—
22C2×C4×C8×C13C2212yes—
23#11718790—216no—
24C2×#88060C22116yes—
25C2×C4⋊#1055—24no—
26C2×C4⋊#1055C2212yes—
27C2×C4⋊#1055C2212yes—
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13C2311yescharacteristic
31C22×C22⋊D13C2×C414yes—
32C2×#6127—24no—
33C2×#6127—24no—
34C2×#6127—28no—
35C2×#6127—28no—
36C22×D52C2×C412yes—
37C22×D52C2×C412yes—
38C22×D52C2×C412yes—
39C22×C4×D13C2314yes—
40C22×Dic26C2×C412yes—
41C2×C13×M16—24no—
42C2×C13×M16—24no—
43C2×C13×M16D418yescomplemented
44C22×C8×C13C2314yes—
45C2×C42×C13C2×C411yescharacteristic
46C2×C42×C13C2×C411yescharacteristic
47C2×C42×C13D414yes—
48C2×C42×C13D414yes—
49C2×C42×C13C2311yescharacteristic
50C2×C42×C13C2311yescharacteristic
51#88184—28no—
52#88184—28no—
53C2×#6103C2×C414yes—
54C2×#6103C2×C414yes—
55C2×C4⋊Dic13C2×C412yes—
56C2×C4⋊Dic13C2×C412yes—
57C22×#1055—28no—
58C22×#1055—24no—
59C22×#1055C2314yes—
60#88129—28no—
61#88128—24no—
62C4×D52—24no—
63C4×D52—24no—
64C4×D52—24no—
65C4×D52—24no—
66#88123—24no—
67C13×#97—24no—
68C4×C8×C13—24no—
69#88060—232no—
70C4⋊#1055—24no—
71C4⋊#1055—24no—
72#21189—131nomaximal, Sylow
73C24×C13C22×C411yescharacteristic
74C23×D13C22×C414yes—
75C22×C4×C13—24no—
76C22×C4×C13—42no—
77C22×C4×C13C22⋊C414yes—
78C22×C4×C13C22⋊C414yes—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D412yes—
85C22×C4×C13C2×D414yes—
86C22×C4×C13C2×D412yes—
87C22×C4×C13#4114yes—
88C22×C4×C13C2411yescharacteristic
89C2×C22⋊D13—28no—
90C2×C22⋊D13—216no—
91C22×Dic13C22×C414yes—
92#6127—416no—
93#6127—48no—
94#6127—48no—
95C2×D52—24no—
96C2×D52—24no—
97C2×D52—24no—
98C2×D52—28no—
99C2×D52—28no—
100C2×D52—44no—
101C2×C4×D13—24no—
102C2×C4×D13—24no—
103C2×C4×D13—28no—
104C2×C4×D13—28no—
105C2×Dic26—24no—
106C2×Dic26—28no—
107C13×M16—216no—
108C2×C8×C13—24no—
109C2×C8×C13—24no—
110C2×C8×C13C2×D418yes—
111C42×C13C22⋊C414yes—
112C42×C13C22⋊C414yes—
113C42×C13C2×D412yes—
114C42×C13C2×D412yes—
115C42×C13C2×D412yes—
116C42×C13C2×D412yes—
117#6103—28no—
118#6103—28no—
119C4⋊Dic13—24no—
120C4⋊Dic13—24no—
121C2×#1055—24no—
122C2×#1055—28no—
123C2×#1055—48no—
124C2×#532—131no—
125C22×C4⋊C8—131no—
126C2×#408—134no—
127C2×C4×M16D1311yescharacteristic, complemented
128#1955—134no—
129#1954—134no—
130C23×C13—22no—
131C23×C13—22no—
132C23×C13C2×C22⋊C412yes—
133C23×C13C4×D414yes—
134C23×C13C23×C411yescharacteristic
135C22×D13—24no—
136C22×D13—28no—
137C22×D13—28no—
138C22×D13—28no—
139C2×C4×C13—22no—
140C2×C4×C13—22no—
141C2×C4×C13—22no—
142C2×C4×C13—28no—
143C2×C4×C13—44no—
144C2×C4×C13C2×C22⋊C412yes—
145C2×C4×C13C2×C22⋊C412yes—
146C2×C4×C13C2×C22⋊C412yes—
147C2×C4×C13C2×C22⋊C412yes—
148C2×C4×C13C2×C22⋊C412yes—
149C2×C4×C13C4×D414yes—
150C2×C4×C13#12118yes—
151C2×C4×C13#12414yes—
152C2×C4×C13#12714yes—
153C2×C4×C13#13114yes—
154C2×C4×C13C22×D411yescharacteristic
155C2×C4×C13C22×D412yes—
156C2×C4×C13C22×D411yescharacteristic
157C2×C4×C13C2×#4112yes—
158C22⋊D13—416no—
159C2×Dic13—24no—
160C2×Dic13—28no—
161D52—48no—
162D52—48no—
163D52—48no—
164C4×D13—48no—
165C4×D13—44no—
166C4×D13—44no—
167Dic26—48no—
168C8×C13—28no—
169#1055—44no—
170C22×#41—132no—
171C22×M16C2×D1312yes—
172C23×C8—132no—
173#532—264no—
174#532—264no—
175C2×C4⋊Q8—131no—
176C2×#127—131no—
177C2×#124—132no—
178C2×#121—132no—
179C2×#121—132no—
180C2×C4×D4—132no—
181C2×C4×D4—132no—
182C22×C42C2×D1311yescharacteristic
183C2×C4⋊C8—132no—
184C2×C4⋊C8—132no—
185C2×C4⋊C8—264no—
186#408—2616no—
187C2×C22⋊C8—1316no—
188C4×M16—24no—
189C2×#97C2×D1312yes—
190C2×C4×C8C2×D1312yes—
191C22×C13—22no—
192C22×C13—22no—
193C22×C13—28no—
194C22×C13#39014yes—
195C22×C13C22×C22⋊C411yescharacteristic
196C22×C13C2×C4×D412yes—
197C22×C13C2×#13112yes—
198C22×C13#56812yes—
199C2×D13—44no—
200C2×D13—44no—
201C2×D13—416no—
202C2×D13—44no—
203C4×C13—22no—
204C4×C13—22no—
205C4×C13—22no—
206C4×C13#39014yes—
207C4×C13#40814yescomplemented
208C4×C13C2×#12112yes—
209C4×C13C2×#12411yescharacteristic
210C4×C13C2×#12711yescharacteristic
211Dic13—44no—
212C2×#41—264no—
213C2×#41—268no—
214C2×#41—268no—
215C2×#41—264no—
216C22×Q8—132no—
217C22×D4—134no—
218C22×D4—132no—
219C22×D4—132no—
220C22×D4—132no—
221C23×C4—134no—
222C23×C4C4×D1311yescharacteristic
223C23×C4C4×D1311yescharacteristic
224C23×C4C22×D1311yescharacteristic
225C2×M16—24no—
226C2×M16—24no—
227C2×M16D5218yescomplemented
228C22×C8—134no—
229C22×C8—268no—
230C22×C8—264no—
231C22×C8C22×D1314yes—
232C4⋊Q8—264no—
233#127—264no—
234#124—268no—
235#121—268no—
236#121—268no—
237C4×D4—264no—
238C4×D4—264no—
239C4×D4—264no—
240C4×D4—264no—
241C2×C4⋊C4—132no—
242C2×C4⋊C4—132no—
243C2×C22⋊C4—134no—
244C2×C22⋊C4—134no—
245C2×C42C4×D1311yescharacteristic
246C2×C42C4×D1311yescharacteristic
247C2×C42D5214yes—
248C2×C42C22⋊D1314yes—
249C2×C42C22×D1311yescharacteristic
250C2×C42C22×D1311yescharacteristic
251C4⋊C8—264no—
252C4⋊C8—264no—
253C22⋊C8—2632no—
254#97—24no—
255C4×C8—24no—
256C2×C13—24no—
257C2×C13C2×#39011yescharacteristic
258C2×C13C2×#40811yescharacteristic
259C2×C13#287911yescharacteristic
260C2×C13#293514yes—
261D13—84no—
262C24—134no—
263C24C2×C4×D1311yescharacteristic
264#41—528no—
265#41—528no—
266#41—5216no—
267C2×Q8—268no—
268C2×Q8—264no—
269C2×D4—2616no—
270C2×D4—268no—
271C2×D4—268no—
272C2×D4—268no—
273C2×D4—264no—
274C2×D4—264no—
275C2×D4—264no—
276C2×D4—524no—
277C22×C4—24no—
278C22×C4—42no—
279C22×C4—134no—
280C22×C4—268no—
281C22×C4—264no—
282C22×C4—268no—
283C22×C4—264no—
284C22×C4#610314yes—
285C22×C4#610314yes—
286C22×C4C2×C4×D1311yescharacteristic
287C22×C4C2×C4×D1311yescharacteristic
288C22×C4C2×C4×D1311yescharacteristic
289C22×C4C2×C4×D1311yescharacteristic
290C22×C4C2×C4×D1311yescharacteristic
291C22×C4C2×D5214yes—
292C22×C4C2×D5212yes—
293C22×C4#612714yes—
294C22×C4C2×C22⋊D1312yes—
295C22×C4C23×D1311yescharacteristic
296M16—216no—
297C2×C8—24no—
298C2×C8—24no—
299C2×C8—268no—
300C2×C8—264no—
301C2×C8—528no—
302C2×C8C2×D5218yes—
303C4⋊C4—264no—
304C4⋊C4—264no—
305C22⋊C4—268no—
306C22⋊C4—268no—
307C42#610314yes—
308C42#610314yes—
309C42C2×D5212yes—
310C42C2×D5212yes—
311C42C2×C22⋊D1312yes—
312C42C2×C22⋊D1312yes—
313C13#2118911yescharacteristic, complemented, Sylow
314C23—22no—
315C23—22no—
316C23—268no—
317C23—268no—
318C23—268no—
319C23—264no—
320C23C4×D5214yes—
321C23C2×#610312yes—
322C23C22×C4×D1311yescharacteristic
323Q8—528no—
324D4—528no—
325D4—5216no—
326D4—528no—
327D4—528no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—28no—
332C2×C4—44no—
333C2×C4—268no—
334C2×C4—264no—
335C2×C4—524no—
336C2×C4—524no—
337C2×C4—528no—
338C2×C4C4×D5214yes—
339C2×C4#8812814yes—
340C2×C4#8812914yes—
341C2×C4#8816114yes—
342C2×C4C2×#610312yes—
343C2×C4C2×#610312yes—
344C2×C4C2×#610312yes—
345C2×C4C2×#610312yes—
346C2×C4C2×#610312yes—
347C2×C4#8818418yes—
348C2×C4C22×D5211yescharacteristic
349C2×C4C22×D5212yes—
350C2×C4C2×#612712yes—
351C2×C4C22×C22⋊D1311yescharacteristic
352C8—28no—
353C8—524no—
354C22—22no—
355C22—22no—
356C22—28no—
357C22—524no—
358C22—524no—
359C22—524no—
360C22—5216no—
361C22#1171860014yes—
362C22C2×C4×D5212yes—
363C22C2×#8816112yes—
364C22#1171945012yes—
365C22C22×#610311yescharacteristic
366C4—22no—
367C4—22no—
368C4—22no—
369C4—524no—
370C4#1171860014yes—
371C4#1171879014yescomplemented
372C4C2×#8812811yescharacteristic
373C4C2×#8812911yescharacteristic
374C4C2×#8818412yes—
375C2—24no—
376C2—1044no—
377C2C2×#1171860011yescharacteristic
378C2C2×#1171879011yescharacteristic
379C2#1312328011yescharacteristic
380C2#1312358214yes—
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C4×C13×M16C2
prime radicalC2×#11719182C2
cosocleC22×C4×C13C24
hypercenterC2×C4×M16D13
hypocenterC13#21189
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊#1055C2semidirect
3. C2×#11718790C2semidirect
4. #13115634C2semidirect
5. #13115630C2semidirect
6. C2×C4×C13×M16C2semidirect
43. C2×C13×M16D4semidirect
127. C2×C4×M16D13semidirect
207. C4×C13#408semidirect
227. C2×M16D52semidirect
313. C13#21189semidirect
371. C4#11718790semidirect

Maximal subgroups

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

subgroupindex
C2×#117191822
C22×C4⋊#10552
C2×#117187902
#131156342
#131156302
C2×C4×C13×M162
#2118913