Finite Group Databasebeta

← #15758607

Subgroups — #15758607

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#13123188C211yesmaximal, characteristic
3C2×#11718074C212yesmaximal, complemented
4#13112720C212yesmaximal, complemented
5C13×#1797C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C2×#88178—21no—
8C2×#88123C2211yescharacteristic
9C2×C13×C4⋊C8C2212yes—
10C2×C13×C22⋊C8—21no—
11#11718873—21no—
12#11718873C412yes—
13C2×C22⋊#1055—21no—
14#11718596C2211yescharacteristic
15#11718590—21no—
16#11718589—21no—
17#11718589C412yes—
18#11718587—24no—
19C2×C4⋊#1055C2212yes—
20C2×#88043—21no—
21C13×#336—21no—
22#11718074—24no—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26—21no—
27C22×C8×C13—22no—
28C2×C42×C13—22no—
29C2×C42×C13—22no—
30C2×C42×C13C2×C411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C22⋊Dic13—22no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13C2×C412yes—
39C2×C4⋊Dic13C2×C412yes—
40#88178—44no—
41C2×#6101—22no—
42C22×#1055—22no—
43#88123—22no—
44#88123—22no—
45C13×C4⋊C8—22no—
46C13×C4⋊C8—22no—
47C13×C22⋊C8—42no—
48#88071—22no—
49#88071—22no—
50C22⋊#1055—24no—
51C4⋊#1055—22no—
52C4⋊#1055D414yes—
53#88043—24no—
54#9138—131nomaximal, Sylow
55C24×C13C22⋊C411yescharacteristic
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—22no—
74C22×Dic13—22no—
75C2×Dic26—42no—
76C2×Dic26—42no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×C8×C13—42no—
80C2×C8×C13—42no—
81C2×C8×C13—42no—
82C42×C13—22no—
83C42×C13—21no—
84C42×C13—22no—
85C42×C13—21no—
86C42×C13C2×D412yes—
87C42×C13#4112yes—
88C22⋊Dic13—44no—
89C4⋊Dic13—24no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92C4⋊Dic13—42no—
93C4⋊Dic13—42no—
94C4⋊Dic13—42no—
95#6101—44no—
96C2×#1055—24no—
97C2×#1055—42no—
98C2×#1055—42no—
99C2×#432—131no—
100#2857—131no—
101#1797D1311yescharacteristic
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
112C2×C4×C13—21no—
113C2×C4×C13—21no—
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—44no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13C4×D412yes—
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12112yes—
131C2×C4×C13#12311yescharacteristic
132C2×C4×C13#13512yes—
133C2×C4×C13AGL(1,ℤ/8)12yes—
134C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C13#13712yes—
136C2×C4×C13#13711yescharacteristic
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143Dic26—82no—
144Dic26—82no—
145C8×C13—82no—
146#1055—44no—
147C2×C4⋊Q8—131no—
148C2×C22⋊Q8—261no—
149C22×C42C2×D1311yescharacteristic
150#432—264no—
151C2×C4⋊C8—132no—
152C2×C4⋊C8C2×D1312yes—
153C2×C22⋊C8—21no—
154C2×C22⋊C8—261no—
155C2×#97—261no—
156#391—261no—
157#389—132no—
158#389—261no—
159#384—131no—
160#380—132no—
161#380—261no—
162#336—21no—
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#45212yes—
183C4×C13#46812yes—
184C4×C13#46912yes—
185C4×C13#48512yes—
186Dic13—82no—
187Dic13—82no—
188C22×Q8—261no—
189C23×C4C4×D1311yescharacteristic
190C23×C4D5211yescharacteristic
191C23×C4C22⋊D1311yescharacteristic
192C22×C8—22no—
193C22×C8—262no—
194C4⋊Q8—262no—
195C4⋊Q8—262no—
196C22⋊Q8—524no—
197C2×C4⋊C4—132no—
198C2×C4⋊C4—132no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C22⋊C4—262no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42C4×D1311yescharacteristic
207C2×C42D5211yescharacteristic
208C2×C42C22⋊D1311yescharacteristic
209C2×C42C22×D1311yescharacteristic
210C4⋊C8—22no—
211C4⋊C8—22no—
212C4⋊C8—134no—
213C4⋊C8—262no—
214C22⋊C8—42no—
215C22⋊C8—264no—
216#97—264no—
217#95—262no—
218#95—262no—
219C2×C13—42no—
220C2×C13#155211yescharacteristic
221C2×C13#155311yescharacteristic
222C2×C13#155611yescharacteristic
223C2×C13#155911yescharacteristic
224C2×C13#187311yescharacteristic
225C2×C13#189511yescharacteristic
226C2×C13#190111yescharacteristic
227C24#610311yescharacteristic
228C2×Q8—521no—
229C2×Q8—522no—
230C2×Q8—521no—
231C2×Q8—522no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4—262no—
244C22×C4—262no—
245C22×C4#610311yescharacteristic
246C22×C4#610311yescharacteristic
247C22×C4#610311yescharacteristic
248C22×C4C2×C4×D1311yescharacteristic
249C22×C4C2×D5211yescharacteristic
250C22×C4C2×C22⋊D1311yescharacteristic
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—264no—
255C2×C8—522no—
256C2×C8—522no—
257C4⋊C4—264no—
258C4⋊C4—522no—
259C4⋊C4—524no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—522no—
263C4⋊C4—522no—
264C22⋊C4—524no—
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#8806412yes—
279C23C2×#610311yescharacteristic
280Q8—1042no—
281Q8—1042no—
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—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4—522no—
303C2×C4—522no—
304C2×C4#8813512yes—
305C2×C4#8813611yescharacteristic
306C2×C4#8814011yescharacteristic
307C2×C4#8815812yes—
308C2×C4#8816312yes—
309C2×C4#8818611yescharacteristic
310C2×C4#8819312yes—
311C2×C4#8819611yescharacteristic
312C2×C4#8820312yes—
313C8—82no—
314C8—524no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22#1171861911yescharacteristic
323C22#1171862711yescharacteristic
324C22#1171866211yescharacteristic
325C22#1171877411yescharacteristic
326C22#1171878111yescharacteristic
327C22#1171879311yescharacteristic
328C22C2×#8806411yescharacteristic
329C4—22no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—1042no—
334C4—1042no—
335C4#1171838412yes—
336C4#1171839412yes—
337C4#1171870012yes—
338C4#1171871012yes—
339C2—42no—
340C2#1311353411yescharacteristic
341C2#1311353911yescharacteristic
342C2#1311355411yescharacteristic
343C2#1311356411yescharacteristic
344C2#1311514611yescharacteristic
345C2#1311527211yescharacteristic
346C2#1311530211yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1797C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1797D13
hypocenterC13#9138
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
3. C2×#11718074C2semidirect
4. #13112720C2semidirect
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
#131231882
C2×#117180742
#131127202
C13×#17972
#913813