Finite Group Databasebeta

← #15751377

Subgroups — #15751377

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123175C211yesmaximal, characteristic
2C2×#11718116C211yesmaximal, characteristic
3#13112661C212yesmaximal, complemented
4#13112658C212yesmaximal, complemented
5C13×#1728C211yesmaximal, characteristic
6C22×C13×M16—21no—
7C22×C42×C13C2211yescharacteristic
8C2×#88178C411yescharacteristic
9C23×#1055—21no—
10#11718873C411yescharacteristic
11#11718872—21no—
12#11718871—21no—
13#11718594—21no—
14#11718594—21no—
15#11718590C411yescharacteristic
16#11718590C2211yescharacteristic
17#11718589C411yescharacteristic
18#11718589C2211yescharacteristic
19C13×#336—21no—
20C13×#336C2212yes—
21#11718116—21no—
22#11718116C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C2×C13×M16—24no—
28C2×C13×M16—42no—
29C2×C13×M16—42no—
30C22×C8×C13—22no—
31C2×C42×C13—42no—
32C2×C42×C13C2×C411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41#88178—42no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C22×#1055—24no—
46C22×#1055—22no—
47C22×#1055—42no—
48C22×#1055—42no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#7681—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13SD1612yes—
71C22×C4×C13Q1612yes—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C2×Dic26—22no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C13×M16—48no—
83C2×C8×C13—24no—
84C2×C8×C13—42no—
85C2×C8×C13—42no—
86C42×C13—41no—
87C42×C13—41no—
88C42×C13—41no—
89C42×C13—41no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C4⋊Dic13—22no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95#6101—42no—
96#6101—42no—
97#6101—41no—
98#6101—41no—
99C2×#1055—24no—
100C2×#1055—48no—
101C2×#1055—42no—
102C2×#1055—42no—
103#2855—131no—
104#1728D1311yescharacteristic
105C2×#336—131no—
106#1272—132no—
107#1271—132no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13#9912yes—
113C23×C13#10312yes—
114C23×C13#10412yes—
115C23×C13C2×C22⋊C411yescharacteristic
116C2×C4×C13—24no—
117C2×C4×C13—24no—
118C2×C4×C13—24no—
119C2×C4×C13—24no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—44no—
134C2×C4×C13#10312yes—
135C2×C4×C13#10412yes—
136C2×C4×C13#13112yes—
137C2×C4×C13C2×SD1611yescharacteristic
138C2×C4×C13C2×Q1611yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153Dic26—82no—
154C8×C13—44no—
155#1055—44no—
156C22×M16—21no—
157C23×C8—261no—
158C2×C22⋊Q8—131no—
159C22×C42C2×D1311yescharacteristic
160#391—131no—
161#391—131no—
162#389—131no—
163#389—131no—
164#387—261no—
165#387—261no—
166#385—261no—
167#381—261no—
168#380—131no—
169#336—21no—
170#336—132no—
171#336—261no—
172#336C2×D1312yes—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13#32814yes—
180C22×C13#40811yescharacteristic
181C22×C13C2×#9911yescharacteristic
182C22×C13#41311yescharacteristic
183C22×C13C2×#10311yescharacteristic
184C22×C13#41711yescharacteristic
185C22×C13C2×#10411yescharacteristic
186C22×C13C2×#10411yescharacteristic
187C4×C13—22no—
188C4×C13—21no—
189C4×C13—22no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—22no—
193C4×C13—21no—
194C4×C13—41no—
195Dic13—81no—
196Dic13—81no—
197Dic13—81no—
198Dic13—81no—
199C22×Q8—131no—
200C23×C4C4×D1311yescharacteristic
201C23×C4D5211yescharacteristic
202C23×C4C22⋊D1311yescharacteristic
203C2×M16—24no—
204C2×M16—42no—
205C2×M16—42no—
206C22×C8—22no—
207C22×C8—264no—
208C22×C8—262no—
209C22×C8—522no—
210C22×C8—522no—
211C22⋊Q8—522no—
212C2×C4⋊C4—131no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C42—42no—
221C2×C42C4×D1311yescharacteristic
222C2×C42D5211yescharacteristic
223C2×C42C22⋊D1311yescharacteristic
224C2×C42C22×D1311yescharacteristic
225#95—261no—
226#95—261no—
227#95—261no—
228#95—261no—
229#95—261no—
230#95—261no—
231#95—261no—
232C2×C13—24no—
233C2×C13#146811yescharacteristic
234C2×C13#148311yescharacteristic
235C2×C13#149311yescharacteristic
236C2×C13C2×#32811yescharacteristic
237C2×C13#150411yescharacteristic
238C2×C13#152411yescharacteristic
239C2×C13#155011yescharacteristic
240C24#610311yescharacteristic
241C2×Q8—262no—
242C2×Q8—521no—
243C2×Q8—521no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—41no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4#610311yescharacteristic
258C22×C4#610311yescharacteristic
259C22×C4#610311yescharacteristic
260C22×C4#610512yes—
261C22×C4#610712yes—
262C22×C4C2×C4×D1311yescharacteristic
263C22×C4C2×D5211yescharacteristic
264C22×C4C2×C22⋊D1311yescharacteristic
265M16—48no—
266C2×C8—24no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—264no—
270C2×C8—528no—
271C2×C8—522no—
272C2×C8—522no—
273C4⋊C4—262no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C4⋊C4—522no—
277C4⋊C4—522no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C22⋊C4—522no—
281C22⋊C4—522no—
282C42—41no—
283C42—41no—
284C42—41no—
285C42—41no—
286C13#768111yescharacteristic, complemented, Sylow
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23#8804512yes—
292C23#8804612yes—
293C23#8805012yes—
294C23C2×#610311yescharacteristic
295Q8—1042no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—44no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4#8805012yes—
327C2×C4#8806512yes—
328C2×C4#8816112yes—
329C2×C4#8816211yescharacteristic
330C2×C4#8816311yescharacteristic
331C2×C4C2×#610511yescharacteristic
332C2×C4C2×#610711yescharacteristic
333C8—44no—
334C8—524no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22#1171804414yes—
342C22C2×#8804511yescharacteristic
343C22C2×#8804611yescharacteristic
344C22C2×#8805011yescharacteristic
345C22#1171879011yescharacteristic
346C22#1171879311yescharacteristic
347C22#1171879411yescharacteristic
348C22C2×#8806511yescharacteristic
349C4—22no—
350C4—21no—
351C4—21no—
352C4—22no—
353C4—21no—
354C4—22no—
355C4—21no—
356C4—41no—
357C4—1041no—
358C4—1041no—
359C4—1041no—
360C4—1041no—
361C2—24no—
362C2#1311318511yescharacteristic
363C2#1311325011yescharacteristic
364C2#1311329011yescharacteristic
365C2C2×#1171804411yescharacteristic
366C2#1311334111yescharacteristic
367C2#1311342511yescharacteristic
368C2#1311352711yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1728C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1728D13
hypocenterC13#7681
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1728

Complements

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

NH ≅ G/Ntype
3. #13112661C2semidirect
4. #13112658C2semidirect
286. C13#7681semidirect

Maximal subgroups

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

subgroupindex
#131231752
C2×#117181162
#131126612
#131126582
C13×#17282
#768113