Finite Group Databasebeta

← #15846051

Subgroups — #15846051

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13126152C212yesmaximal
2#13125350C211yesmaximal, characteristic, complemented
3#13114335C214yesmaximal, complemented
4#13114235C212yesmaximal, complemented
5#13114225C212yesmaximal, complemented
6C2×#11718050C211yesmaximal, characteristic, complemented
7#13113527C212yesmaximal, complemented
8C13×#2931C211yesmaximal, characteristic
9C2×C13×#131—21no—
10C13×#532C2211yescharacteristic
11#11719175C2212yes—
12C13×#436—21no—
13C13×#436C2212yes—
14C8×D4×C13—21no—
15C8×D4×C13C2212yes—
16C13×#423C2211yescharacteristic
17C13×#408—21no—
18C2×C4×C8×C13C2211yescharacteristic
19#11718767—21no—
20#11718767—21no—
21#11718755—22no—
22#11718736—22no—
23#11718702—24no—
24#11718680C2214yes—
25#11718669C2214yes—
26C2×C4⋊#1055C2212yes—
27#11718344—21no—
28#11718344—21no—
29#11718343C2211yescharacteristic
30#11718343C2211yescharacteristic
31#11718341C2212yes—
32#11718078C2214yes—
33#11718073C2214yes—
34#11718050C2212yes—
35#11718050C2212yes—
36C2×C13×#41—21no—
37C13×#131—44no—
38C2×C13×M16—21no—
39C2×C13×M16—22no—
40C22×C8×C13—22no—
41C22×C8×C13D411yescharacteristic
42C22×C8×C13D411yescharacteristic
43C13×C4⋊Q8D411yescharacteristic
44C13×#127D411yescharacteristic
45C13×#124—21no—
46C13×#121—21no—
47C13×#121D412yes—
48C4×D4×C13—21no—
49C4×D4×C13C2312yes—
50C2×C42×C13C2311yescharacteristic
51C2×#6105—24no—
52#88180—22no—
53#88178—22no—
54#88178—22no—
55C22×#1055—22no—
56#88124—22no—
57#88123C2312yes—
58#88123C2312yes—
59C4×Dic26—22no—
60C4×Dic26—22no—
61C13×C4⋊C8—21no—
62C13×C4⋊C8C2312yes—
63C13×C22⋊C8—22no—
64C13×C22⋊C8—22no—
65C4×C8×C13D411yescharacteristic
66C4×C8×C13D411yescharacteristic
67C4×C8×C13C2311yescharacteristic
68C4×C8×C13C2311yescharacteristic
69#88072—24no—
70#88058—21no—
71#88058—21no—
72#88058—21no—
73#88058—21no—
74#88057—22no—
75#88057—22no—
76#88050—24no—
77#88048—24no—
78C4⋊#1055—22no—
79C4⋊#1055C2314yes—
80#19195—131nomaximal, Sylow
81C13×#41—42no—
82C13×#41—42no—
83C2×Q8×C13—21no—
84C2×D4×C13—22no—
85C2×D4×C13—21no—
86C2×D4×C13—21no—
87C2×D4×C13C2×D412yes—
88C22×C4×C13—22no—
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13#4111yescharacteristic
92C2×Dic26—22no—
93C2×Dic26—22no—
94C13×M16—42no—
95C13×M16—44no—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—44no—
99C2×C8×C13SD1614yescomplemented
100C2×C8×C13C2×D411yescharacteristic
101C2×C8×C13C2×D411yescharacteristic
102C2×C8×C13C2×D411yescharacteristic
103C2×C8×C13C2×D411yescharacteristic
104C13×C4⋊C4—21no—
105C13×C4⋊C4C2×D412yes—
106C13×C22⋊C4—22no—
107C13×C22⋊C4—22no—
108C42×C13C2×D411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13#4111yescharacteristic
111C42×C13C2411yescharacteristic
112C22⋊Dic13—42no—
113#6105—84no—
114C4⋊Dic13—22no—
115C4⋊Dic13—22no—
116C4⋊Dic13—22no—
117C4⋊Dic13—22no—
118#6101—42no—
119#6101—42no—
120C4×Dic13—42no—
121C2×#1055—24no—
122C2×#1055—82no—
123#3246—132no—
124#3160—131no—
125#2931D1311yescharacteristic
126#1691—134no—
127#1675—132no—
128#1673—132no—
129C2×#335—131no—
130#1550—132no—
131C23×C13—22no—
132C23×C13#12111yescharacteristic
133Q8×C13—42no—
134D4×C13—22no—
135D4×C13—22no—
136D4×C13—42no—
137D4×C13—44no—
138D4×C13—42no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—22no—
142C2×C4×C13—41no—
143C2×C4×C13—42no—
144C2×C4×C13—42no—
145C2×C4×C13#12111yescharacteristic
146C2×C4×C13#12111yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13C2×SD1612yes—
149C2×C4×C13#13712yes—
150C2×C4×C13C22×D411yescharacteristic
151C2×C4×C13C22×D411yescharacteristic
152C2×C4×C13C2×#4111yescharacteristic
153C2×Dic13—42no—
154C2×Dic13—42no—
155Dic26—42no—
156Dic26—42no—
157Dic26—82no—
158C8×C13—21no—
159C8×C13—21no—
160C8×C13—42no—
161C8×C13C2×SD1612yes—
162C8×C13C2×SD1612yes—
163#1055—44no—
164C2×#131—21no—
165#533—132no—
166#532C2×D1311yescharacteristic
167#500—131no—
168#500—131no—
169#499—261no—
170#499—261no—
171#498—132no—
172#476—134no—
173#475—262no—
174#465—264no—
175#461—134no—
176#460—262no—
177#436—21no—
178#436C2×D1312yes—
179C8×D4—21no—
180C8×D4C2×D1312yes—
181#427—261no—
182#427—261no—
183#423C2×D1311yescharacteristic
184C2×C4⋊C8—132no—
185#408—21no—
186C2×C4×C8C2×D1311yescharacteristic
187#335—132no—
188#335—132no—
189#333—134no—
190#332—134no—
191C22×C13—21no—
192C22×C13—21no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13#46112yes—
197C22×C13C2×#12111yescharacteristic
198C4×C13—21no—
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—42no—
202C4×C13#46112yes—
203C4×C13C22×SD1611yescharacteristic
204C4×C13C2×#13711yescharacteristic
205C4×C13#57611yescharacteristic
206C4×C13#57811yescharacteristic
207Dic13—82no—
208Dic13—82no—
209C2×#41—21no—
210C2×SD16—264no—
211#131—44no—
212C2×M16—21no—
213C2×M16—22no—
214C22×C8—22no—
215C22×C8—262no—
216C22×C8C22⋊D1311yescharacteristic
217C22×C8C22⋊D1311yescharacteristic
218C4⋊Q8—132no—
219C4⋊Q8—132no—
220C4⋊Q8D5211yescharacteristic
221#127D5211yescharacteristic
222#125—262no—
223#124—21no—
224C22⋊Q8—262no—
225C22⋊Q8—262no—
226#121—21no—
227#121D5212yes—
228C4×Q8—262no—
229C4×Q8—262no—
230C4×D4—21no—
231C4×D4C22×D1312yes—
232#117—262no—
233C2×C42C22×D1311yescharacteristic
234#107—261no—
235#107—261no—
236#107—261no—
237#107—261no—
238#106—262no—
239#106—262no—
240#106—264no—
241C4⋊C8—21no—
242C4⋊C8—134no—
243C4⋊C8—262no—
244C4⋊C8C22×D1312yes—
245#103—264no—
246#102—264no—
247C22⋊C8—22no—
248C22⋊C8—22no—
249C4×C8C22⋊D1311yescharacteristic
250C4×C8C22⋊D1311yescharacteristic
251C4×C8C22×D1311yescharacteristic
252C4×C8C22×D1311yescharacteristic
253C2×C13—22no—
254C2×C13—82no—
255C2×C13C2×#46111yescharacteristic
256C2×C13#306111yescharacteristic
257C2×C13#306711yescharacteristic
258#41—42no—
259#41—42no—
260C2×Q8—21no—
261C2×Q8—262no—
262C2×Q8—262no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4C2×D5212yes—
267C22×C4—22no—
268C22×C4C2×D5211yescharacteristic
269C22×C4#612711yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271SD16—1044no—
272M16—42no—
273M16—44no—
274C2×C8—22no—
275C2×C8—22no—
276C2×C8—44no—
277C2×C8—264no—
278C2×C8—1042no—
279C2×C8#610514yescomplemented
280C2×C8C2×C22⋊D1311yescharacteristic
281C2×C8C2×C22⋊D1311yescharacteristic
282C2×C8C2×C22⋊D1311yescharacteristic
283C2×C8C2×C22⋊D1311yescharacteristic
284C4⋊C4—21no—
285C4⋊C4—262no—
286C4⋊C4—262no—
287C4⋊C4—262no—
288C4⋊C4—262no—
289C4⋊C4—522no—
290C4⋊C4—522no—
291C4⋊C4C2×D5212yes—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—522no—
295C42—522no—
296C42C2×D5211yescharacteristic
297C42#612711yescharacteristic
298C42C2×C22⋊D1311yescharacteristic
299C42C23×D1311yescharacteristic
300C13#1919511yescharacteristic, complemented, Sylow
301C23—22no—
302C23#8818411yescharacteristic
303Q8—42no—
304Q8—522no—
305Q8—522no—
306Q8—1042no—
307D4—22no—
308D4—22no—
309D4—42no—
310D4—44no—
311D4—42no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—522no—
319C2×C4—522no—
320C2×C4#8818411yescharacteristic
321C2×C4#8818411yescharacteristic
322C2×C4#8818411yescharacteristic
323C2×C4C2×#610512yes—
324C2×C4#8820512yes—
325C2×C4C22×D5211yescharacteristic
326C2×C4C2×#612711yescharacteristic
327C2×C4C22×C22⋊D1311yescharacteristic
328C8—21no—
329C8—21no—
330C8—42no—
331C8—524no—
332C8C2×#610512yes—
333C8C2×#610512yes—
334C22—21no—
335C22—21no—
336C22—42no—
337C22—42no—
338C22—42no—
339C22#1171868012yes—
340C22C2×#8818411yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—42no—
345C4—1042no—
346C4—1042no—
347C4#1171868012yes—
348C4#1171945711yescharacteristic
349C4#1171945811yescharacteristic
350C4C22×#610511yescharacteristic
351C4C2×#8820511yescharacteristic
352C2—22no—
353C2—82no—
354C2C2×#1171868011yescharacteristic
355C2#1312450611yescharacteristic
356C2#1312455611yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2931C2
socleC22×C13C2×#121
prime radicalC13×#532C22
hypercenter#2931D13
hypocenterC13#19195
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2931

Complements

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

NH ≅ G/Ntype
2. #13125350C2semidirect
3. #13114335C2semidirect
4. #13114235C2semidirect
5. #13114225C2semidirect
6. C2×#11718050C2semidirect
7. #13113527C2semidirect
99. C2×C8×C13SD16semidirect
279. C2×C8#6105semidirect
300. C13#19195semidirect

Maximal subgroups

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

subgroupindex
#131261522
#131253502
#131143352
#131142352
#131142252
C2×#117180502
#131135272
C13×#29312
#1919513