Finite Group Databasebeta

← #15780741

Subgroups — #15780741

Order 3328.

324 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718085C211yesmaximal, characteristic, complemented
2C2×#11718159C211yesmaximal, characteristic
3#13116543C211yesmaximal, characteristic
4#13114715C211yesmaximal, characteristic, complemented
5#13112933C211yesmaximal, characteristic, complemented
6#13112914C211yesmaximal, characteristic, complemented
7C13×#1974C211yesmaximal, characteristic
8C2×C13×#135C2211yescharacteristic
9C2×C13×#108C2211yescharacteristic
10C2×C13×#104—21no—
11C13×#408—21no—
12C2×C4×C8×C13C2211yescharacteristic
13C2×#88059C2211yescharacteristic
14#11718767C2211yescharacteristic
15#11718762—21no—
16C22×#6090C2211yescharacteristic
17C22×#6090C2211yescharacteristic
18#11718159—22no—
19#11718156C411yescharacteristic, complemented
20#11718156C411yescharacteristic, complemented
21#11718154C411yescharacteristic, complemented
22#11718154C411yescharacteristic, complemented
23#11718115—21no—
24#11718085—22no—
25C2×C13×#41—21no—
26C13×#135—21no—
27C13×#135—21no—
28C13×#135—21no—
29C13×#135—21no—
30C2×C13×Q16C2×C411yescharacteristic
31C2×C13×SD16—21no—
32C2×C13×D8C2×C411yescharacteristic
33C2×C13×M16—21no—
34C22×C8×C13D411yescharacteristic
35C22×C8×C13C2311yescharacteristic
36C2×C42×C13D411yescharacteristic
37#88180—21no—
38C2×#6099—21no—
39C13×#108—21no—
40C13×#108—21no—
41C13×#104—42no—
42C13×C22⋊C8—41no—
43C13×C22⋊C8—41no—
44C4×C8×C13—21no—
45C4×C8×C13—21no—
46#88059—21no—
47#88059D412yes—
48#88058C2×C411yescharacteristic
49#88058C2×C411yescharacteristic
50#88057—21no—
51#88055—41no—
52C8×Dic13—41no—
53C2×#6090—21no—
54C2×#6090—21no—
55C2×#6090—21no—
56C2×#6090—21no—
57C2×#6090—21no—
58C2×#6090C2×C411yescharacteristic
59C2×#6090C2×C411yescharacteristic
60#13134—131nomaximal, Sylow
61C13×#41—41no—
62C13×#41—41no—
63C13×#41—41no—
64C13×#41—41no—
65C2×Q8×C13—21no—
66C2×D4×C13—21no—
67C2×D4×C13—41no—
68C22×C4×C13—21no—
69C22×C4×C13—41no—
70C22×C4×C13C2×D411yescharacteristic
71C13×Q16—21no—
72C13×Q16—21no—
73C13×SD16—41no—
74C13×SD16—41no—
75C13×D8—21no—
76C13×D8—21no—
77C13×M16—41no—
78C13×M16—41no—
79C2×C8×C13—21no—
80C2×C8×C13—21no—
81C2×C8×C13—41no—
82C2×C8×C13D811yescharacteristic
83C2×C8×C13D811yescharacteristic
84C2×C8×C13C22×C411yescharacteristic
85C2×C8×C13C2×D411yescharacteristic
86C2×C8×C13#4111yescharacteristic
87C2×C8×C13#4111yescharacteristic
88C2×C8×C13#4111yescharacteristic
89C2×C8×C13#4111yescharacteristic
90C42×C13—21no—
91C42×C13—21no—
92C22⋊Dic13—41no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4×Dic13—41no—
96#6099—22no—
97#6099—41no—
98C2×#1055—41no—
99#6090—21no—
100#6090—21no—
101#6090—41no—
102C2×#368—131no—
103C2×#359—131no—
104#2138—131no—
105#1974D1311yescharacteristic
106#1772—131no—
107#1382—131no—
108#1374—131no—
109C23×C13—41no—
110C23×C13#13511yescharacteristic
111Q8×C13—41no—
112Q8×C13—41no—
113D4×C13—41no—
114D4×C13—41no—
115D4×C13—81no—
116D4×C13—81no—
117C2×C4×C13—22no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—81no—
122C2×C4×C13—81no—
123C2×C4×C13C4×D411yescharacteristic
124C2×C4×C13#12111yescharacteristic
125C2×C4×C13#12311yescharacteristic
126C2×C4×C13C2×D811yescharacteristic
127C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C13#13711yescharacteristic
129C2×Dic13—41no—
130C2×Dic13—41no—
131C8×C13—21no—
132C8×C13—21no—
133C8×C13—81no—
134C8×C13#11711yescharacteristic
135C8×C13C4×D411yescharacteristic
136C8×C13#12411yescharacteristic
137C8×C13#12611yescharacteristic
138#1055—42no—
139C2×#135C2×D1311yescharacteristic
140C22×C16—131no—
141C22×C16—131no—
142C2×#108—131no—
143C2×#108C2×D1311yescharacteristic
144#427—131no—
145C2×#104—21no—
146#408—21no—
147#405—261no—
148C2×C4×C8C2×D1311yescharacteristic
149#368—262no—
150#359—262no—
151#358—131no—
152#358—131no—
153#357—131no—
154#357—131no—
155#339—261no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—81no—
159C22×C13—81no—
160C22×C13—81no—
161C22×C13C4×D811yescharacteristic
162C22×C13#46411yescharacteristic
163C22×C13#48211yescharacteristic
164C4×C13—42no—
165C4×C13—81no—
166C4×C13#38811yescharacteristic
167C4×C13#44011yescharacteristic
168C4×C13#45911yescharacteristic
169C4×C13#48011yescharacteristic
170Dic13—81no—
171Dic13—81no—
172C2×#41—21no—
173#135—21no—
174#135—21no—
175#135—21no—
176#135—21no—
177C2×Q16C4×D1311yescharacteristic
178C2×SD16—21no—
179C2×D8C4×D1311yescharacteristic
180C2×M16—21no—
181C2×M16—261no—
182C22×C8C22⋊D1311yescharacteristic
183C22×C8C22×D1311yescharacteristic
184#117—261no—
185C2×C42C22⋊D1311yescharacteristic
186C2×C16—131no—
187C2×C16—131no—
188C2×C16—261no—
189C2×C16—261no—
190C2×C16—261no—
191C2×C16—261no—
192C2×C16—261no—
193#108—21no—
194#108—21no—
195#108—132no—
196#108—261no—
197#107—131no—
198#107—131no—
199#106—261no—
200#104—42no—
201C22⋊C8—41no—
202C22⋊C8—41no—
203#97—521no—
204C4×C8—21no—
205C4×C8—21no—
206C4×C8—521no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—161no—
210C2×C13#192511yescharacteristic
211C2×C13#217811yescharacteristic
212C2×C13#217911yescharacteristic
213#41—41no—
214#41—41no—
215#41—41no—
216#41—41no—
217C2×Q8—21no—
218C2×D4—21no—
219C2×D4—41no—
220C22×C4—21no—
221C22×C4—41no—
222C22×C4C2×C22⋊D1311yescharacteristic
223Q16—21no—
224Q16—21no—
225SD16—41no—
226SD16—41no—
227D8—21no—
228D8—21no—
229M16—41no—
230M16—41no—
231M16—262no—
232M16—521no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—521no—
237C2×C8#610411yescharacteristic
238C2×C8#610411yescharacteristic
239C2×C8C2×C4×D1311yescharacteristic
240C2×C8#612711yescharacteristic
241C2×C8D4×D1311yescharacteristic
242C2×C8#612911yescharacteristic
243C2×C8#612911yescharacteristic
244C2×C8#612911yescharacteristic
245C4⋊C4—261no—
246C4⋊C4—261no—
247C22⋊C4—521no—
248C42—21no—
249C42—21no—
250C42—521no—
251C16—261no—
252C16—261no—
253C16—521no—
254C13#1313411yescharacteristic, complemented, Sylow
255C23—41no—
256C23#8820411yescharacteristic
257Q8—41no—
258Q8—41no—
259D4—41no—
260D4—41no—
261D4—81no—
262D4—81no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4C4×C22⋊D1311yescharacteristic
272C2×C4C2×#610411yescharacteristic
273C2×C4#8818611yescharacteristic
274C2×C4#8818911yescharacteristic
275C2×C4#8819211yescharacteristic
276C2×C4#8820511yescharacteristic
277C8—21no—
278C8—21no—
279C8—81no—
280C8—522no—
281C8#8813111yescharacteristic
282C8#8813311yescharacteristic
283C8#8813511yescharacteristic
284C8#8813911yescharacteristic
285C22—21no—
286C22—21no—
287C22—81no—
288C22—81no—
289C22—81no—
290C22C4×#610411yescharacteristic
291C22#1171869611yescharacteristic
292C22#1171871511yescharacteristic
293C4—42no—
294C4—81no—
295C4—1041no—
296C4—1041no—
297C4#1171860511yescharacteristic
298C4#1171867911yescharacteristic
299C4#1171869411yescharacteristic
300C4#1171873311yescharacteristic
301C2—21no—
302C2—21no—
303C2—161no—
304C2#1311545311yescharacteristic
305C2#1311671511yescharacteristic
306C2#1311672011yescharacteristic
subgroupG/H
centerC2×C4C2×#6104
commutatorC2×C8×C13C22×C4
FrattiniC22×C8C22×D13
FittingC13×#1974C2
socleC22×C13C4×D8
prime radicalC2×C13×#135C22
cosocleC22×C8×C13C23
hypercenter#1974D13
hypocenterC13#13134
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
1. C2×#11718085C2semidirect
4. #13114715C2semidirect
5. #13112933C2semidirect
6. #13112914C2semidirect
19. #11718156C4semidirect
20. #11718156C4semidirect
21. #11718154C4semidirect
22. #11718154C4semidirect
254. C13#13134semidirect

Maximal subgroups

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

subgroupindex
C2×#117180852
C2×#117181592
#131165432
#131147152
#131129332
#131129142
C13×#19742
#1313413