Finite Group Databasebeta

← #15751227

Subgroups — #15751227

Order 3328.

500 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88178C211yesmaximal, characteristic
2#13114904C211yesmaximal, characteristic
3#13112661C212yesmaximal, complemented
4#13112658C212yesmaximal, complemented
5C13×#1797C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C2×#88178C411yescharacteristic
8C2×C4×Dic26C411yescharacteristic
9C2×C13×C4⋊C8—21no—
10C2×C13×C22⋊C8—21no—
11#11718873C411yescharacteristic
12#11718871—21no—
13C4×C22⋊Dic13—21no—
14C2×C22⋊#1055—21no—
15C4×C4⋊Dic13C411yescharacteristic
16#11718594—21no—
17C4×#6101—21no—
18#11718590C2211yescharacteristic
19#11718589C2211yescharacteristic
20C13×#336C2212yes—
21#11718116—21no—
22#11718116C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×C8×C13—22no—
28C2×C42×C13—42no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C42×C13C2311yescharacteristic
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13C2×C411yescharacteristic
38#88178—22no—
39#88178—22no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—21no—
45C22×#1055—22no—
46C4×Dic26—42no—
47C13×C4⋊C8—42no—
48C13×C22⋊C8—42no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54C22⋊#1055—42no—
55#7648—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—22no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13SD1612yes—
70C22×C4×C13Q1612yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×Dic26—21no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26M1612yes—
82C2×C8×C13—42no—
83C2×C8×C13—42no—
84C2×C8×C13—42no—
85C42×C13—22no—
86C42×C13—22no—
87C42×C13—41no—
88C42×C13—41no—
89C22⋊Dic13—24no—
90C22⋊Dic13—42no—
91C4⋊Dic13—21no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13M1612yes—
95#6101—24no—
96#6101—42no—
97#6101—42no—
98C4×Dic13—42no—
99C4×Dic13—42no—
100C2×#1055—42no—
101C2×#1055—42no—
102C2×#1055—42no—
103C4×C22⋊Q8—131no—
104#1817—131no—
105#1797D1311yescharacteristic
106#1272—132no—
107#1271—132no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13#10312yes—
115C23×C13C2×C22⋊C411yescharacteristic
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—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—44no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13#9912yes—
135C2×C4×C13#10312yes—
136C2×C4×C13C2×M1611yescharacteristic
137C2×C4×C13C2×M1611yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13C2×Q1611yescharacteristic
140C2×C4×C13#13512yes—
141C2×Dic13—22no—
142C2×Dic13—22no—
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—42no—
154Dic26—42no—
155C8×C13—82no—
156#1055—82no—
157C2×C22⋊Q8—131no—
158C2×C4×Q8—131no—
159C22×C42C2×D1311yescharacteristic
160C2×C4⋊C8—21no—
161C2×C22⋊C8—21no—
162C2×C22⋊C8—261no—
163#391—131no—
164#389—131no—
165#387—261no—
166#385—261no—
167#380—131no—
168C4×C4⋊C4—131no—
169C4×C4⋊C4—261no—
170C4×C22⋊C4—261no—
171#336—132no—
172#336—261no—
173#336C2×D1312yes—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13#40711yescharacteristic
182C22×C13C2×#9911yescharacteristic
183C22×C13#41311yescharacteristic
184C22×C13C2×#10311yescharacteristic
185C22×C13#41611yescharacteristic
186C22×C13#42111yescharacteristic
187C22×C13#42111yescharacteristic
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—22no—
191C4×C13—22no—
192C4×C13—21no—
193C4×C13—22no—
194C4×C13—21no—
195C4×C13—41no—
196Dic13—42no—
197Dic13—42no—
198Dic13—81no—
199Dic13—81no—
200C22×Q8—131no—
201C23×C4C4×D1311yescharacteristic
202C23×C4D5211yescharacteristic
203C23×C4C22⋊D1311yescharacteristic
204C22×C8—22no—
205C22×C8—262no—
206C22⋊Q8—262no—
207C22⋊Q8—262no—
208C4×Q8—522no—
209C2×C4⋊C4—131no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C22⋊C4—261no—
216C2×C22⋊C4—261no—
217C2×C42—42no—
218C2×C42—261no—
219C2×C42—261no—
220C2×C42C4×D1311yescharacteristic
221C2×C42D5211yescharacteristic
222C2×C42C22⋊D1311yescharacteristic
223C2×C42C22×D1311yescharacteristic
224C4⋊C8—42no—
225C22⋊C8—42no—
226C22⋊C8—522no—
227#95—261no—
228#95—261no—
229#95—261no—
230#95—261no—
231#95—261no—
232C2×C13—42no—
233C2×C13#146511yescharacteristic
234C2×C13#148711yescharacteristic
235C2×C13#148811yescharacteristic
236C2×C13#151611yescharacteristic
237C2×C13#152011yescharacteristic
238C2×C13#153511yescharacteristic
239C2×C13#154211yescharacteristic
240C24#610311yescharacteristic
241C2×Q8—132no—
242C2×Q8—261no—
243C2×Q8—521no—
244C2×Q8—521no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4#610311yescharacteristic
259C22×C4#610311yescharacteristic
260C22×C4#610311yescharacteristic
261C22×C4#610512yes—
262C22×C4#610712yes—
263C22×C4C2×C4×D1311yescharacteristic
264C22×C4C2×D5211yescharacteristic
265C22×C4C2×C22⋊D1311yescharacteristic
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—42no—
269C2×C8—522no—
270C2×C8—522no—
271C2×C8—522no—
272C4⋊C4—132no—
273C4⋊C4—264no—
274C4⋊C4—261no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—522no—
278C4⋊C4—522no—
279C22⋊C4—264no—
280C22⋊C4—522no—
281C42—22no—
282C42—22no—
283C42—41no—
284C42—41no—
285C42—522no—
286C42—522no—
287C13#764811yescharacteristic, complemented, Sylow
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23#8805012yes—
295C23C2×#610311yescharacteristic
296Q8—522no—
297Q8—522no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
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—42no—
312C2×C4—42no—
313C2×C4—44no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—262no—
317C2×C4—262no—
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—521no—
327C2×C4—521no—
328C2×C4#8804612yes—
329C2×C4#8805012yes—
330C2×C4#8815812yes—
331C2×C4M16×D1311yescharacteristic
332C2×C4M16×D1311yescharacteristic
333C2×C4C2×#610511yescharacteristic
334C2×C4C2×#610711yescharacteristic
335C8—82no—
336C8—1042no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22C2×#8804611yescharacteristic
345C22C2×#8805011yescharacteristic
346C22#1171866611yescharacteristic
347C22#1171877411yescharacteristic
348C22#1171878711yescharacteristic
349C22#1171879311yescharacteristic
350C22#1171880011yescharacteristic
351C4—22no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—22no—
356C4—21no—
357C4—21no—
358C4—41no—
359C4—522no—
360C4—522no—
361C4—1041no—
362C4—1041no—
363C2—42no—
364C2#1311317211yescharacteristic
365C2#1311326411yescharacteristic
366C2#1311327111yescharacteristic
367C2#1311339311yescharacteristic
368C2#1311340711yescharacteristic
369C2#1311346511yescharacteristic
370C2#1311349411yescharacteristic
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#7648
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. #13112661C2semidirect
4. #13112658C2semidirect
287. C13#7648semidirect

Maximal subgroups

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

subgroupindex
C4×#881782
#131149042
#131126612
#131126582
C13×#17972
#764813