Finite Group Databasebeta

← #15758610

Subgroups — #15758610

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718587C211yesmaximal, characteristic
2#13114816C211yesmaximal, characteristic
3C2×#11718139C212yesmaximal, complemented
4#13112719C212yesmaximal, complemented
5C13×#2857C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×C22⋊Q8—21no—
8C22×C42×C13C2211yescharacteristic
9C13×#391—21no—
10C13×#389—21no—
11C13×#389C412yes—
12C13×#384C2211yescharacteristic
13C13×#380—21no—
14C13×#380C412yes—
15C2×C22⋊#1055—21no—
16C2×C22⋊#1055—21no—
17#11718587—24no—
18C2×C4⋊#1055C2212yes—
19C2×C4⋊#1055C2212yes—
20C2×#88043—21no—
21#11718139—24no—
22#11718116—21no—
23C22×Q8×C13—21no—
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C4⋊Q8—22no—
28C13×C4⋊Q8—22no—
29C13×C22⋊Q8—44no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C412yes—
35C2×C13×C4⋊C4C2×C412yes—
36C2×C13×C22⋊C4—22no—
37C2×C42×C13—22no—
38C2×C42×C13—22no—
39C2×C42×C13C2×C411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13C2311yescharacteristic
43C22×#1055—22no—
44C22×#1055—22no—
45C13×#95—22no—
46C13×#95—22no—
47C22⋊#1055—24no—
48C22⋊#1055—42no—
49C4⋊#1055—22no—
50C4⋊#1055—22no—
51C4⋊#1055—22no—
52C4⋊#1055D414yes—
53#88043—24no—
54#9138—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C2×Q8×C13—42no—
57C2×Q8×C13—42no—
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—21no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—41no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C13×C4⋊C4—24no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—44no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—42no—
86C13×C22⋊C4—44no—
87C42×C13—22no—
88C42×C13—21no—
89C42×C13—22no—
90C42×C13—21no—
91C42×C13C2×D412yes—
92C42×C13#4112yes—
93C2×#1055—24no—
94C2×#1055—42no—
95C2×#1055—42no—
96C2×#1055—42no—
97C2×#1055—42no—
98C2×#1055—42no—
99C2×#432—131no—
100#2857D1311yescharacteristic
101#1797—131no—
102C2×#332—132no—
103#1296—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13#10112yes—
111C23×C13C2×C22⋊C411yescharacteristic
112Q8×C13—82no—
113Q8×C13—82no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—44no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13C4×D412yes—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12112yes—
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13#13512yes—
141C2×C4×C13AGL(1,ℤ/8)12yes—
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13712yes—
144C2×C4×C13#13711yescharacteristic
145#1055—44no—
146#1055—82no—
147C2×C4⋊Q8C2×D1311yescharacteristic
148C2×C22⋊Q8—21no—
149C22×C42C2×D1311yescharacteristic
150#432—264no—
151C2×C4⋊C8—132no—
152C2×C4⋊C8—132no—
153C2×C22⋊C8—261no—
154C2×C22⋊C8—261no—
155C2×#97—261no—
156#391—21no—
157#389—21no—
158#389Dic1312yes—
159#384C2×D1311yescharacteristic
160#380—21no—
161#380Dic1312yes—
162#336—261no—
163#332—264no—
164C22×C13—22no—
165C22×C13—22no—
166C22×C13—22no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13#38611yescharacteristic
172C22×C13C2×#10111yescharacteristic
173C22×C13#41311yescharacteristic
174C22×C13#41611yescharacteristic
175C22×C13#41711yescharacteristic
176C22×C13#41811yescharacteristic
177C22×C13#41911yescharacteristic
178C4×C13—22no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—82no—
183C4×C13—82no—
184C4×C13#45212yes—
185C4×C13#46812yes—
186C4×C13#46912yes—
187C4×C13#48512yes—
188C22×Q8—21no—
189C23×C4C2×Dic1311yescharacteristic
190C23×C4C22⋊D1311yescharacteristic
191C23×C4C22⋊D1311yescharacteristic
192C22×C8—262no—
193C22×C8—262no—
194C4⋊Q8—22no—
195C4⋊Q8—22no—
196C22⋊Q8—44no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×Dic1312yes—
202C2×C4⋊C4C2×Dic1312yes—
203C2×C22⋊C4—22no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42C2×Dic1311yescharacteristic
207C2×C42C22⋊D1311yescharacteristic
208C2×C42C22⋊D1311yescharacteristic
209C2×C42C22×D1311yescharacteristic
210C4⋊C8—134no—
211C4⋊C8—262no—
212C4⋊C8—262no—
213C4⋊C8—262no—
214C22⋊C8—264no—
215C22⋊C8—522no—
216#97—264no—
217#95—22no—
218#95—22no—
219C2×C13—42no—
220C2×C13#155211yescharacteristic
221C2×C13#155311yescharacteristic
222C2×C13#155611yescharacteristic
223C2×C13#155911yescharacteristic
224C2×C13#187311yescharacteristic
225C2×C13#189511yescharacteristic
226C2×C13#190111yescharacteristic
227C24C22⋊Dic1311yescharacteristic
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—41no—
245C22×C4C22⋊Dic1311yescharacteristic
246C22×C4C22⋊Dic1311yescharacteristic
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4C22×Dic1311yescharacteristic
249C22×C4C2×C22⋊D1311yescharacteristic
250C22×C4C2×C22⋊D1311yescharacteristic
251C2×C8—264no—
252C2×C8—522no—
253C2×C8—522no—
254C2×C8—522no—
255C2×C8—522no—
256C2×C8—522no—
257C4⋊C4—24no—
258C4⋊C4—42no—
259C4⋊C4—44no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—42no—
264C22⋊C4—44no—
265C42—22no—
266C42—21no—
267C42—21no—
268C42—22no—
269C42D4×D1312yes—
270C42#612912yes—
271C13#913811yescharacteristic, complemented, Sylow
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#8807612yes—
279C23C2×C22⋊Dic1311yescharacteristic
280Q8—82no—
281Q8—82no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—44no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4#8818612yes—
305C2×C4D4×Dic1312yes—
306C2×C4#8818911yescharacteristic
307C2×C4#8819111yescharacteristic
308C2×C4#8819312yes—
309C2×C4#8819612yes—
310C2×C4#8820311yescharacteristic
311C2×C4#8820412yes—
312C2×C4#8820511yescharacteristic
313C8—524no—
314C8—1042no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22#1171887611yescharacteristic
323C22#1171888111yescharacteristic
324C22#1171888611yescharacteristic
325C22C2×#8807611yescharacteristic
326C22#1171889311yescharacteristic
327C22#1171889411yescharacteristic
328C22#1171889811yescharacteristic
329C4—22no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—82no—
334C4—82no—
335C4#1171870012yes—
336C4#1171870312yes—
337C4#1171870612yes—
338C4#1171870812yes—
339C2—42no—
340C2#1311353611yescharacteristic
341C2#1311354111yescharacteristic
342C2#1311355311yescharacteristic
343C2#1311356611yescharacteristic
344C2#1311514911yescharacteristic
345C2#1311527511yescharacteristic
346C2#1311530511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2857C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2857D13
hypocenterC13#9138
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
3. C2×#11718139C2semidirect
4. #13112719C2semidirect
271. C13#9138semidirect

Maximal subgroups

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

subgroupindex
C2×#117185872
#131148162
C2×#117181392
#131127192
C13×#28572
#913813