Finite Group Databasebeta

← #16785137

Subgroups — #16785137

Order 3328.

450 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#13130769C211yesmaximal, characteristic
2C4×#88112C211yesmaximal, characteristic
3#13129714C212yesmaximal
4#13129714C212yesmaximal
5#13123195C211yesmaximal, characteristic
6C2×#88143—21no—
7C2×#88112—21no—
8C2×#88112C2212yes—
9C2×#88112C2212yes—
10C2×C4⋊#1057—21no—
11C2×C4×#1057—21no—
12C13×#389C411yescharacteristic
13#11718646C411yescharacteristic
14#11718637C2211yescharacteristic
15#11718637C2211yescharacteristic
16#11718634C411yescharacteristic
17#11718633—21no—
18C42×Dic13C2211yescharacteristic
19#11718589C411yescharacteristic
20#11718311—21no—
21#11718308—21no—
22#11718290—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×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44#88143—42no—
45#88143—42no—
46#88112—22no—
47#88112—24no—
48#88112—42no—
49#88112Q814yes—
50C4⋊#1057—42no—
51C4×#1057—42no—
52C13×#95—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#9900—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C2×#1057—24no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—42no—
77C42×C13—41no—
78C4⋊Dic13—42no—
79C4⋊Dic13—41no—
80C4⋊Dic13—41no—
81#6101—42no—
82#6101—42no—
83#6101—41no—
84#6101—41no—
85#6101—41no—
86#6101—41no—
87#6101—42no—
88#6101—41no—
89#6101—41no—
90C4×Dic13—22no—
91C4×Dic13—21no—
92C4×Dic13—21no—
93C4×Dic13—41no—
94C4×Dic13D812yes—
95C4×Dic13SD1612yes—
96C4×Dic13SD1612yes—
97C4×Dic13Q1612yes—
98C4×Dic13C2×Q812yes—
99C4×Dic13#4112yes—
100#2859—131no—
101#1842—131no—
102C4×C4⋊C8—131no—
103#1296—132no—
104#1296—132no—
105C23×C13C2×C22⋊C411yescharacteristic
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13#10212yes—
119C2×C4×C13#10312yes—
120C2×C4×C13C4×Q812yes—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13#10212yes—
132C2×Dic13#10312yes—
133C2×Dic13C22⋊Q812yes—
134C2×Dic13#12411yescharacteristic
135C2×Dic13C4⋊Q811yescharacteristic
136C2×Dic13C2×D811yescharacteristic
137C2×Dic13C2×SD1611yescharacteristic
138C2×Dic13C2×SD1611yescharacteristic
139C2×Dic13C2×Q1611yescharacteristic
140C2×Dic13#13512yes—
141C2×Dic13AGL(1,ℤ/8)11yescharacteristic
142C2×Dic13#13711yescharacteristic
143#1057—44no—
144#1057—82no—
145C2×#125—261no—
146C2×C4⋊C8—132no—
147C2×C4⋊C8—132no—
148C2×C4⋊C8—261no—
149C2×C4⋊C8—261no—
150C2×C4×C8—261no—
151#389—131no—
152#389—131no—
153#389—131no—
154#389—261no—
155#389—261no—
156#389#26111yescharacteristic
157#384—131no—
158#384—131no—
159#382—261no—
160C43—131no—
161#336—261no—
162C22×C13#39111yescharacteristic
163C22×C13#41311yescharacteristic
164C22×C13#41311yescharacteristic
165C22×C13C2×#10211yescharacteristic
166C22×C13C2×#10311yescharacteristic
167C22×C13#41611yescharacteristic
168C22×C13#41711yescharacteristic
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—81no—
173C4×C13—81no—
174Dic13—22no—
175Dic13—22no—
176Dic13—81no—
177Dic13—81no—
178Dic13#47812yes—
179Dic13#47912yes—
180Dic13#48611yescharacteristic
181Dic13#48711yescharacteristic
182Dic13#49811yescharacteristic
183Dic13#50011yescharacteristic
184C22×C8—262no—
185C22×C8—262no—
186#125—522no—
187#125—522no—
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⋊C4—261no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4C2×#26111yescharacteristic
199C2×C4⋊C4C2×#26111yescharacteristic
200C2×C42—131no—
201C2×C42—131no—
202C2×C42—131no—
203C2×C42—131no—
204C2×C42—131no—
205C2×C42—131no—
206C2×C42C2×#26111yescharacteristic
207C4⋊C8—134no—
208C4⋊C8—262no—
209C4⋊C8—264no—
210C4⋊C8—522no—
211C4⋊C8—522no—
212C4×C8—522no—
213#95—21no—
214#95—261no—
215#95—261no—
216#95—261no—
217C2×C13#154011yescharacteristic
218C2×C13#154211yescharacteristic
219C2×C13#154711yescharacteristic
220C2×C13#155011yescharacteristic
221C2×C13#198911yescharacteristic
222C2×C13#199011yescharacteristic
223C2×C13#199811yescharacteristic
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—131no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4C22⋊#26111yescharacteristic
233C22×C4C22⋊#26111yescharacteristic
234C22×C4C22×#26111yescharacteristic
235C2×C8—264no—
236C2×C8—522no—
237C2×C8—522no—
238C2×C8—522no—
239C2×C8—522no—
240C2×C8—522no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—521no—
245C4⋊C4—521no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C4⋊C4—521no—
249C4⋊C4—521no—
250C4⋊C4—522no—
251C4⋊C4—522no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C42—41no—
257C42—132no—
258C42—132no—
259C42—132no—
260C42—132no—
261C42—132no—
262C42—132no—
263C42—261no—
264C42—261no—
265C42—262no—
266C42—521no—
267C13#990011yescharacteristic, complemented, Sylow
268C23C2×C22⋊#26111yescharacteristic
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—132no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—131no—
289C2×C4—131no—
290C2×C4—132no—
291C2×C4—132no—
292C2×C4—132no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4#8811512yes—
304C2×C4#8811712yes—
305C2×C4Q8×#26112yes—
306C8—524no—
307C8—1042no—
308C22#1171913211yescharacteristic
309C22C2×#8811511yescharacteristic
310C22#1171914811yescharacteristic
311C22C2×#8811711yescharacteristic
312C22(C2×#261)⋊Q811yescharacteristic
313C22#1171916411yescharacteristic
314C22#1171916511yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—81no—
319C4—81no—
320C4—132no—
321C4—132no—
322C4—131no—
323C4—131no—
324C4—131no—
325C4—131no—
326C4—262no—
327C4—262no—
328C4—1041no—
329C4—1041no—
330C2#1313033411yescharacteristic
331C2#1313033711yescharacteristic
332C2#1313034711yescharacteristic
333C2#1313035411yescharacteristic
334C2#1313101611yescharacteristic
335C2#1313101711yescharacteristic
336C2#1313103011yescharacteristic
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#9900
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
267. C13#9900semidirect

Maximal subgroups

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

subgroupindex
#131307692
C4×#881122
#131297142
#131231952
#990013