Finite Group Databasebeta

← #16785066

Subgroups — #16785066

Order 3328.

486 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130768C211yesmaximal, characteristic
2C4×#88110C211yesmaximal, characteristic
3#13129672C212yesmaximal
4#13129672C212yesmaximal
5#13117395C211yesmaximal, characteristic
6C2×#88144C411yescharacteristic
7C2×#88110—21no—
8C2×#88110—21no—
9C2×C4⋊#1057—21no—
10C2×C4⋊#1057—21no—
11C2×C4⋊#1057C2212yes—
12C2×C4×#1057C2212yes—
13C13×#389C411yescharacteristic
14#11718639—21no—
15#11718638C411yescharacteristic
16C4⋊C4×Dic13—21no—
17C4⋊C4×Dic13C2211yescharacteristic
18C4⋊C4×Dic13C2211yescharacteristic
19C42×Dic13C2211yescharacteristic
20#11718589C411yescharacteristic
21#11718314—21no—
22#11718310—21no—
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13C2311yescharacteristic
42#88144—22no—
43#88144—22no—
44#88110—24no—
45#88110—24no—
46C4⋊#1057—24no—
47C4⋊#1057—42no—
48C4⋊#1057—42no—
49C4×#1057—22no—
50C4×#1057Q814yes—
51C13×#95—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#9876—131nomaximal, Sylow
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C22×Dic13C2×D411yescharacteristic
69C2×#1057—24no—
70C2×#1057—24no—
71C2×#1057—24no—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4M1612yes—
79C42×C13—22no—
80C4⋊Dic13—24no—
81C4⋊Dic13—21no—
82C4⋊Dic13—22no—
83C4⋊Dic13M1612yes—
84#6101—24no—
85#6101—42no—
86C4×Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—21no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98C4×Dic13C2×Q812yes—
99C4×Dic13#4112yes—
100C4×#125—131no—
101#1842—131no—
102C4×#97—131no—
103#1279—132no—
104#1279—132no—
105C23×C13C2×C22⋊C411yescharacteristic
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13#10412yes—
117C2×C4×C13#10412yes—
118C2×C4×C13C4×Q812yes—
119C2×C4×C13C2×M1611yescharacteristic
120C2×C4×C13C2×M1611yescharacteristic
121C2×C4×C13#13112yes—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—22no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13C22⋊Q812yes—
137C2×Dic13#12411yescharacteristic
138C2×Dic13C4⋊Q811yescharacteristic
139C2×Dic13AGL(1,ℤ/8)11yescharacteristic
140C2×Dic13AGL(1,ℤ/8)11yescharacteristic
141C2×Dic13#13711yescharacteristic
142C2×Dic13#13711yescharacteristic
143#1057—28no—
144#1057—82no—
145C2×#125—131no—
146C2×C4⋊C8—132no—
147C2×C4⋊C8—261no—
148C2×C4⋊C8—261no—
149C2×#97—261no—
150C2×#97—261no—
151C2×C4×C8—132no—
152#389—131no—
153#389#26111yescharacteristic
154#387—261no—
155#387—261no—
156#382—131no—
157C4×C4⋊C4—131no—
158C4×C4⋊C4—131no—
159C4×C4⋊C4—261no—
160C4×C4⋊C4—261no—
161C43—131no—
162C22×C13#39111yescharacteristic
163C22×C13#40711yescharacteristic
164C22×C13#40811yescharacteristic
165C22×C13#41711yescharacteristic
166C22×C13#41711yescharacteristic
167C22×C13C2×#10411yescharacteristic
168C22×C13C2×#10411yescharacteristic
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—42no—
172C4×C13—81no—
173C4×C13#44612yes—
174C4×C13#44612yes—
175Dic13—22no—
176Dic13—41no—
177Dic13—41no—
178Dic13—42no—
179Dic13—81no—
180Dic13#49011yescharacteristic
181Dic13#49111yescharacteristic
182Dic13#50111yescharacteristic
183Dic13#50111yescharacteristic
184C22×C8—262no—
185C22×C8—262no—
186#125—262no—
187#125—262no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—131no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4C2×#26111yescharacteristic
195C2×C4⋊C4C2×#26111yescharacteristic
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—131no—
202C2×C42—261no—
203C2×C42—261no—
204C2×C42C2×#26111yescharacteristic
205C4⋊C8—264no—
206C4⋊C8—522no—
207C4⋊C8—522no—
208#97—264no—
209#97—264no—
210C4×C8—134no—
211C4×C8—262no—
212#95—21no—
213#95—261no—
214#95—261no—
215#95—261no—
216#95—261no—
217#95—261no—
218C2×C13#148311yescharacteristic
219C2×C13#148311yescharacteristic
220C2×C13#148911yescharacteristic
221C2×C13#148911yescharacteristic
222C2×C13#198511yescharacteristic
223C2×C13#199211yescharacteristic
224C2×C13#199411yescharacteristic
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—131no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4C22⋊#26111yescharacteristic
234C22×C4C22⋊#26111yescharacteristic
235C22×C4C22×#26111yescharacteristic
236C2×C8—264no—
237C2×C8—264no—
238C2×C8—264no—
239C2×C8—522no—
240C2×C8—522no—
241C2×C8—522no—
242C4⋊C4—21no—
243C4⋊C4—22no—
244C4⋊C4—42no—
245C4⋊C4—132no—
246C4⋊C4—264no—
247C4⋊C4—264no—
248C4⋊C4—261no—
249C4⋊C4—262no—
250C4⋊C4—522no—
251C4⋊C4#611812yes—
252C42—22no—
253C42—132no—
254C42—132no—
255C42—261no—
256C42—261no—
257C42—261no—
258C42—261no—
259C42—262no—
260C42—262no—
261C42—261no—
262C42—261no—
263C42—521no—
264C42—521no—
265C42—521no—
266C42—521no—
267C13#987611yescharacteristic, complemented, Sylow
268C23C2×C22⋊#26111yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—132no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—262no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4#8811612yes—
301C2×C4#8811812yes—
302C2×C4C2×#611811yescharacteristic
303C2×C4D13⋊M1611yescharacteristic
304C2×C4#8823812yes—
305C2×C4Q8×#26112yes—
306C8—268no—
307C8—1042no—
308C22#1171912711yescharacteristic
309C22C2×#8811611yescharacteristic
310C22#1171914611yescharacteristic
311C22C2×#8811811yescharacteristic
312C22(C2×#261)⋊Q811yescharacteristic
313C22#1171916411yescharacteristic
314C22#1171916411yescharacteristic
315C4—22no—
316C4—22no—
317C4—42no—
318C4—81no—
319C4—131no—
320C4—131no—
321C4—131no—
322C4—131no—
323C4—262no—
324C4—521no—
325C4—521no—
326C4—522no—
327C4—1041no—
328C4#1171907812yes—
329C4#1171908012yes—
330C2#1313015111yescharacteristic
331C2#1313015311yescharacteristic
332C2#1313017211yescharacteristic
333C2#1313017411yescharacteristic
334C2#1313100911yescharacteristic
335C2#1313101911yescharacteristic
336C2#1313102111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#9876
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
267. C13#9876semidirect

Maximal subgroups

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

subgroupindex
#131307682
C4×#881102
#131296722
#131173952
#987613