Finite Group Databasebeta

← #15779540

Subgroups — #15779540

Order 3328.

398 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718556C211yesmaximal, characteristic
2C2×#11718085C211yesmaximal, characteristic, complemented
3C2×#11718102C211yesmaximal, characteristic
4#13116541C211yesmaximal, characteristic
5#13115585C211yesmaximal, characteristic, complemented
6#13112913C211yesmaximal, characteristic, complemented
7C13×#1382C211yesmaximal, characteristic, complemented
8C2×#88161—21no—
9C2×#88158C2211yescharacteristic
10C22×C13×C16C2211yescharacteristic
11C2×C13×#108C2211yescharacteristic
12C13×#427C2211yescharacteristic
13C2×#88065—21no—
14C2×#88059C2211yescharacteristic
15C2×C8×Dic13C2211yescharacteristic
16C22×#6090C2211yescharacteristic
17#11718660—21no—
18#11718556—22no—
19#11718556—22no—
20#11718124—21no—
21#11718102—22no—
22#11718085—22no—
23#11718084C411yescharacteristic, complemented
24#11718084C411yescharacteristic, complemented
25#11718083C411yescharacteristic, complemented
26#11718083C411yescharacteristic, complemented
27C2×#6127—21no—
28C2×C13×M16—21no—
29C22×C8×C13C2311yescharacteristic
30C13×#117—21no—
31C2×C4×Dic13D411yescharacteristic
32C2×#6099—21no—
33C22×#1055D411yescharacteristic
34#88161—24no—
35#88161—42no—
36C2×Dic52C2×C411yescharacteristic
37#88158—21no—
38#88158—21no—
39#88158D412yes—
40#88158Q812yes—
41C2×D104C2×C411yescharacteristic
42C2×#6095—21no—
43C2×#6094—41no—
44C2×C8×D13—41no—
45C2×C13×C16—21no—
46C2×C13×C16—21no—
47C2×C13×C16—21no—
48C13×#108—21no—
49C13×#108D412yes—
50C13×#107C2×C411yescharacteristic
51C13×#107C2×C411yescharacteristic
52C13×#106—21no—
53#88065—24no—
54#88059—21no—
55#88059—21no—
56C8×Dic13—21no—
57C8×Dic13—21no—
58C2×#6090—21no—
59C2×#6090—21no—
60C2×#6090C2×C411yescharacteristic
61C2×#6090C2×C411yescharacteristic
62C4⋊#1055—41no—
63C4⋊#1055—41no—
64#12939—131nomaximal, Sylow
65C22×C4×C13C2×D411yescharacteristic
66C2×C22⋊D13—41no—
67C22×Dic13—21no—
68#6127—22no—
69#6127—22no—
70#6127—41no—
71#6127—41no—
72C2×D52—21no—
73C2×C4×D13—41no—
74C2×Dic26—21no—
75C13×M16—22no—
76C13×M16—41no—
77C2×C8×C13—41no—
78C2×C8×C13C22×C411yescharacteristic
79C2×C8×C13C2×D411yescharacteristic
80C2×C8×C13C2×D411yescharacteristic
81C2×C8×C13C2×Q811yescharacteristic
82C2×C8×C13#4111yescharacteristic
83C2×C8×C13#4111yescharacteristic
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C22⋊C4—41no—
87C42×C13—41no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90#6099—41no—
91#6099—41no—
92C2×#1055—21no—
93C2×#1055—21no—
94C2×#1055—41no—
95C2×#1055D811yescharacteristic
96C2×#1055D811yescharacteristic
97Dic52—21no—
98Dic52C4⋊C412yes—
99D104—21no—
100D104C4⋊C412yes—
101#6095—22no—
102#6095—22no—
103#6094—44no—
104C8×D13—44no—
105C13×C16—41no—
106#6090—21no—
107#6090—21no—
108C2×#443—131no—
109C2×#368—131no—
110C2×#359—131no—
111#2138—131no—
112#1945—131no—
113#1382D1311yescharacteristic, complemented
114#1374—131no—
115C23×C13#13511yescharacteristic
116C22×D13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13C4×D411yescharacteristic
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13C22⋊Q811yescharacteristic
122C2×C4×C13C2×D811yescharacteristic
123C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C13#13711yescharacteristic
125C22⋊D13—42no—
126C22⋊D13—42no—
127C2×Dic13—22no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131D52—22no—
132D52—41no—
133C4×D13—42no—
134C4×D13—42no—
135Dic26—22no—
136Dic26—41no—
137C8×C13—42no—
138C8×C13C2×C4⋊C411yescharacteristic
139C8×C13C4×D411yescharacteristic
140C8×C13C22⋊Q811yescharacteristic
141C8×C13#12311yescharacteristic
142#1055—21no—
143#1055—21no—
144#1055—81no—
145C2×#135—131no—
146C2×#131—261no—
147C22×C16—131no—
148C22×C16C2×D1311yescharacteristic
149#443—262no—
150#443—262no—
151C2×#108—131no—
152C2×#108C2×D1311yescharacteristic
153#427C2×D1311yescharacteristic
154#424—261no—
155C2×#104—261no—
156C2×C4×C8—131no—
157#368—262no—
158#359—262no—
159#358—131no—
160#358—131no—
161#357—131no—
162#357—131no—
163#339—261no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13C4×D811yescharacteristic
167C22×C13#45211yescharacteristic
168C22×C13#47811yescharacteristic
169C2×D13—42no—
170C2×D13—81no—
171C2×D13—81no—
172C4×C13—81no—
173C4×C13—81no—
174C4×C13#38511yescharacteristic
175C4×C13#44011yescharacteristic
176C4×C13#44711yescharacteristic
177C4×C13#47411yescharacteristic
178Dic13—42no—
179Dic13—42no—
180C2×#41—261no—
181#135—132no—
182#135—132no—
183#135—261no—
184#135—261no—
185C2×Q16—131no—
186C2×SD16—261no—
187C2×D8—131no—
188#131—264no—
189#131—522no—
190C2×M16—21no—
191C2×M16—261no—
192C2×M16—521no—
193C22×C8—131no—
194C22×C8—521no—
195C22×C8C22×D1311yescharacteristic
196#117—21no—
197C2×C42—131no—
198C2×C16—21no—
199C2×C16—21no—
200C2×C16—21no—
201C2×C16—131no—
202C2×C16—131no—
203C2×C16—261no—
204C2×C16—261no—
205#108—21no—
206#108—261no—
207#108—261no—
208#108D5212yes—
209#107C4×D1311yescharacteristic
210#107C4×D1311yescharacteristic
211#106—21no—
212C4⋊C8—521no—
213C4⋊C8—521no—
214#104—264no—
215C4×C8—261no—
216C4×C8—261no—
217C2×C13—21no—
218C2×C13—21no—
219C2×C13#186211yescharacteristic
220C2×C13#217811yescharacteristic
221C2×C13#217911yescharacteristic
222D13—82no—
223#41—262no—
224#41—262no—
225#41—521no—
226#41—521no—
227C2×Q8—261no—
228C2×D4—261no—
229C2×D4—521no—
230C22×C4—261no—
231C22×C4—521no—
232C22×C4D4×D1311yescharacteristic
233Q16—132no—
234Q16—261no—
235SD16—262no—
236SD16—262no—
237D8—132no—
238D8—261no—
239M16—22no—
240M16—41no—
241M16—524no—
242M16—521no—
243M16—521no—
244C2×C8—41no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8—261no—
248C2×C8—261no—
249C2×C8—524no—
250C2×C8—521no—
251C2×C8C2×C4×D1311yescharacteristic
252C2×C8C2×D5211yescharacteristic
253C2×C8#612711yescharacteristic
254C2×C8D4×D1311yescharacteristic
255C2×C8#612911yescharacteristic
256C2×C8Q8×D1311yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C22⋊C4—41no—
260C42—41no—
261C42—261no—
262C42—261no—
263C16—41no—
264C16—261no—
265C16—261no—
266C13#1293911yescharacteristic, complemented, Sylow
267C23—521no—
268C23#8817011yescharacteristic
269Q8—262no—
270Q8—521no—
271D4—262no—
272D4—522no—
273D4—522no—
274D4—521no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—262no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—522no—
282C2×C4—522no—
283C2×C4#8813511yescharacteristic
284C2×C4#8813611yescharacteristic
285C2×C4#8815011yescharacteristic
286C2×C4D8×D1311yescharacteristic
287C2×C4#8816811yescharacteristic
288C2×C4#8817211yescharacteristic
289C8—42no—
290C8—261no—
291C8—261no—
292C8—1041no—
293C8C4×D5211yescharacteristic
294C8#8813711yescharacteristic
295C8C4⋊C4×D1311yescharacteristic
296C8#8815111yescharacteristic
297C22—21no—
298C22—21no—
299C22—522no—
300C22—1041no—
301C22—1041no—
302C22#1171841711yescharacteristic
303C22#1171847111yescharacteristic
304C22#1171853211yescharacteristic
305C4—81no—
306C4—81no—
307C4—522no—
308C4—522no—
309C4#1171832911yescharacteristic
310C4#1171843411yescharacteristic
311C4#1171847811yescharacteristic
312C4#1171855111yescharacteristic
313C2—21no—
314C2—21no—
315C2—1042no—
316C2#1311508411yescharacteristic
317C2#1311671411yescharacteristic
318C2#1311671911yescharacteristic
subgroupG/H
centerC2×C4D8×D13
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1382C2
socleC22×C13C4×D8
prime radicalC2×#88158C22
cosocleC22×C8×C13C23
hypercenter#1382D13
hypocenterC13#12939
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ #1382

Complements

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

NH ≅ G/Ntype
2. C2×#11718085C2semidirect
5. #13115585C2semidirect
6. #13112913C2semidirect
7. C13×#1382C2semidirect
23. #11718084C4semidirect
24. #11718084C4semidirect
25. #11718083C4semidirect
26. #11718083C4semidirect
113. #1382D13semidirect
266. C13#12939semidirect

Maximal subgroups

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

subgroupindex
C2×#117185562
C2×#117180852
C2×#117181022
#131165412
#131155852
#131129132
C13×#13822
#1293913