Finite Group Databasebeta

← #16789099

Subgroups — #16789099

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊M32C211yesmaximal, characteristic
2C2×#11719092C211yesmaximal, characteristic
3#13129893C214yesmaximal, complemented
4C2×D13×#107C211yesmaximal, characteristic
5C2×#88237—21no—
6C22×C8×D13C2211yescharacteristic
7C2×C4⋊C4×D13—21no—
8C2×#88106—21no—
9#11719092—22no—
10#11719092C414yescomplemented
11C2×#88102C2212yes—
12C2×#88101—21no—
13D13⋊M32—22no—
14D13⋊M32C414yescomplemented
15C2×#88098—21no—
16C2×D13⋊C16C2212yes—
17C2×C13×#107C411yescharacteristic, complemented
18C2×#88058C411yescharacteristic, complemented
19C2×#88047—21no—
20D13×#107—21no—
21D13×#107—21no—
22D13×#107C412yescomplemented
23D13×#107C2212yes—
24C22×C4×D13—41no—
25C22×C4×D13D411yescharacteristic
26C2×C22⋊#261—41no—
27#88237—24no—
28#88237—42no—
29C2×C4⋊#261—22no—
30C2×C4×#261—41no—
31C22×C8×C13C2×C411yescharacteristic
32C2×C13×C4⋊C4—21no—
33C2×C4⋊Dic13—21no—
34C2×#6101—41no—
35C22×#1055D411yescharacteristic
36C2×C8×D13C2×C411yescharacteristic
37C2×C8×D13C2×C412yes—
38C2×C8×D13C2×C412yes—
39C2×C8×D13D411yescharacteristic
40C2×C8×D13D411yescharacteristic
41C2×C8×D13D412yes—
42C2×C8×D13Q812yes—
43C2×C8×D13C2311yescharacteristic
44C4⋊C4×D13—22no—
45C4⋊C4×D13—22no—
46C4⋊C4×D13—41no—
47C4⋊C4×D13—41no—
48#88106—24no—
49C2×#6092—22no—
50#88102—22no—
51#88102C2×C414yescomplemented
52#88101—24no—
53#88098—24no—
54D13⋊C16—22no—
55D13⋊C16C2×C414yescomplemented
56C13×#107—21no—
57C13×#107C2×C412yes—
58#88058—21no—
59#88058C2×C412yes—
60#88047—22no—
61#88047—22no—
62#12557—131nomaximal, Sylow
63C23×D13D811yescharacteristic
64C22×#261—42no—
65C22×C4×C13—41no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×Dic13—41no—
68C22×Dic13SD1611yescharacteristic
69C2×C4×D13—42no—
70C2×C4×D13—42no—
71C2×C4×D13—84no—
72C2×C4×D13C22⋊C411yescharacteristic
73C2×C4×D13C22⋊C412yes—
74C2×C4×D13C4⋊C412yes—
75C2×C4×D13D811yescharacteristic
76C2×C4×D13SD1612yes—
77C2×C4×D13SD1611yescharacteristic
78C2×C4×D13Q1612yes—
79C2×C4×D13C2×D411yescharacteristic
80C22⋊#261—44no—
81C4⋊#261—24no—
82C4⋊#261—42no—
83C4×#261—44no—
84C2×C8×C13C4212yes—
85C2×C8×C13C22⋊C411yescharacteristic
86C2×C8×C13C4⋊C412yes—
87C2×C8×C13C22×C411yescharacteristic
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C4⋊Dic13—22no—
91C4⋊Dic13—41no—
92#6101—42no—
93#6101—42no—
94C2×#1055C22⋊C411yescharacteristic
95C2×#1055C22⋊C412yes—
96C2×#1055C4⋊C412yes—
97C2×#1055C2×D411yescharacteristic
98C8×D13C4212yes—
99C8×D13C22⋊C412yes—
100C8×D13C22⋊C412yes—
101C8×D13C4⋊C412yes—
102C8×D13C4⋊C412yes—
103C8×D13C4⋊C412yes—
104C8×D13C22×C411yescharacteristic
105C8×D13C22×C411yescharacteristic
106C8×D13C2×D411yescharacteristic
107C8×D13C2×Q811yescharacteristic
108#6092—24no—
109C22×M32—131no—
110C2×#427—131no—
111C22×#107—131no—
112#1380—134no—
113C23×C13#10211yescharacteristic
114C22×D13—22no—
115C22×D13—22no—
116C22×D13#10211yescharacteristic
117C22×D13#10212yes—
118C22×D13#10712yes—
119C22×D13C2×D811yescharacteristic
120C2×#261—44no—
121C2×#261—82no—
122C2×#261—82no—
123C2×C4×C13—42no—
124C2×C4×C13—82no—
125C2×C4×C13#9512yes—
126C2×C4×C13#10211yescharacteristic
127C2×C4×C13#10312yes—
128C2×C4×C13C2×C22⋊C411yescharacteristic
129C2×Dic13—42no—
130C2×Dic13—82no—
131C2×Dic13#10211yescharacteristic
132C2×Dic13#10312yes—
133C2×Dic13#10612yes—
134C2×Dic13C2×SD1611yescharacteristic
135C4×D13—84no—
136C4×D13—84no—
137C4×D13#9512yes—
138C4×D13#10212yes—
139C4×D13#10312yes—
140C4×D13#10312yes—
141C4×D13#10612yes—
142C4×D13#10712yes—
143C4×D13C2×C22⋊C411yescharacteristic
144C4×D13C2×C4⋊C411yescharacteristic
145C4×D13C2×SD1611yescharacteristic
146C4×D13C2×Q1611yescharacteristic
147C8×C13#9512yes—
148C8×C13C2×C4211yescharacteristic
149C8×C13C2×C4⋊C411yescharacteristic
150#1055#9512yes—
151#1055C2×C22⋊C411yescharacteristic
152#1055C2×C4⋊C411yescharacteristic
153C23×C8—131no—
154C2×#117—261no—
155C22×C4⋊C4—261no—
156C2×M32—134no—
157C2×M32—261no—
158C2×M32—262no—
159C2×M32—261no—
160C22×C16—132no—
161#427—134no—
162#427—262no—
163C2×#107—132no—
164C2×#107—131no—
165C2×#107—132no—
166C2×#107—132no—
167C2×#107—261no—
168C2×#107—261no—
169C2×#107—261no—
170C2×#107#26111yescharacteristic, complemented
171C2×#106—261no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13#34012yes—
175C22×C13C2×#10211yescharacteristic
176C2×D13—21no—
177C2×D13—21no—
178C2×D13—24no—
179C2×D13—24no—
180C2×D13#34012yes—
181C2×D13C2×#10211yescharacteristic
182C2×D13C2×#10711yescharacteristic
183C2×D13#50912yes—
184C2×D13#51012yes—
185#261—84no—
186C4×C13—82no—
187C4×C13#34012yes—
188C4×C13C2×#9511yescharacteristic
189C4×C13C2×#10311yescharacteristic
190Dic13—82no—
191Dic13#34012yes—
192Dic13C2×#10311yescharacteristic
193Dic13C2×#10611yescharacteristic
194C23×C4—131no—
195C23×C4—521no—
196C22×C8—131no—
197C22×C8—132no—
198C22×C8—132no—
199C22×C8—132no—
200C22×C8—132no—
201C22×C8—131no—
202C22×C8—131no—
203C22×C8—131no—
204C22×C8—131no—
205C22×C8C2×#26111yescharacteristic
206#117—264no—
207#117—522no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—262no—
210C2×C4⋊C4—262no—
211C2×C4⋊C4—262no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—521no—
214C2×C4⋊C4—521no—
215C2×C4⋊C4—521no—
216C2×C22⋊C4—521no—
217C2×C42—521no—
218M32—264no—
219M32—264no—
220C2×C16—134no—
221C2×C16—262no—
222C2×C16—262no—
223#107—21no—
224#107—134no—
225#107—132no—
226#107—262no—
227#107—262no—
228#107—262no—
229#107—261no—
230#107C2×#26112yes—
231#106—264no—
232C2×C13—22no—
233C2×C13C2×#34011yescharacteristic
234C2×C13#214011yescharacteristic
235C2×C13#214111yescharacteristic
236D13—22no—
237D13#213912yes—
238D13#215912yes—
239C24—131no—
240C22×C4—41no—
241C22×C4—131no—
242C22×C4—132no—
243C22×C4—132no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—132no—
247C22×C4—132no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—522no—
251C22×C4—522no—
252C22×C4—522no—
253C22×C4—521no—
254C22×C4—1044no—
255C22×C4C22⋊#26111yescharacteristic
256C2×C8—132no—
257C2×C8—132no—
258C2×C8—131no—
259C2×C8—131no—
260C2×C8—132no—
261C2×C8—132no—
262C2×C8—132no—
263C2×C8—132no—
264C2×C8—131no—
265C2×C8—131no—
266C2×C8—132no—
267C2×C8—131no—
268C2×C8—132no—
269C2×C8—131no—
270C2×C8C4×#26112yes—
271C2×C8C4⋊#26112yes—
272C2×C8C22⋊#26111yescharacteristic
273C2×C8C22×#26111yescharacteristic
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—264no—
277C4⋊C4—262no—
278C4⋊C4—522no—
279C4⋊C4—522no—
280C4⋊C4—522no—
281C4⋊C4—521no—
282C22⋊C4—524no—
283C42—524no—
284C16—264no—
285C13#1255711yescharacteristic, complemented, Sylow
286C23—131no—
287C23—132no—
288C23—132no—
289C23—131no—
290C23—262no—
291C23—262no—
292C23#8811511yescharacteristic
293C2×C4—42no—
294C2×C4—82no—
295C2×C4—132no—
296C2×C4—132no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—132no—
300C2×C4—132no—
301C2×C4—132no—
302C2×C4—132no—
303C2×C4—131no—
304C2×C4—132no—
305C2×C4—131no—
306C2×C4—131no—
307C2×C4—132no—
308C2×C4—131no—
309C2×C4—524no—
310C2×C4—522no—
311C2×C4—1044no—
312C2×C4—1044no—
313C2×C4—1042no—
314C2×C4—1042no—
315C2×C4—1042no—
316C2×C4(C2×#261)⋊C412yes—
317C2×C4#8811511yescharacteristic
318C2×C4#8811712yes—
319C2×C4C2×C22⋊#26111yescharacteristic
320C8—131no—
321C8—132no—
322C8—131no—
323C8(C2×#261)⋊C412yes—
324C8C2×C4×#26111yescharacteristic
325C8C2×C4⋊#26111yescharacteristic
326C22—21no—
327C22—21no—
328C22—131no—
329C22—131no—
330C22—132no—
331C22—132no—
332C22—132no—
333C22—264no—
334C22—264no—
335C22—261no—
336C22—261no—
337C22#1171824612yes—
338C22C2×#8811511yescharacteristic
339C4—82no—
340C4—132no—
341C4—131no—
342C4—131no—
343C4—1044no—
344C4—1042no—
345C4#1171824612yes—
346C4C2×(C2×#261)⋊C411yescharacteristic
347C4C2×#8811711yescharacteristic
348C2—22no—
349C2—132no—
350C2—132no—
351C2—262no—
352C2C2×#1171824611yescharacteristic
353C2#1313114511yescharacteristic
354C2#1313114611yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC8×C13C2×C42
FrattiniC2×C8C22×#261
FittingC2×C13×#107C4
socleC22×C13C2×#102
prime radicalC23×D13D8
cosocleC2×C8×D13C23
hypercenterC2×#107#261
hypocenterC13#12557
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #13129893C2semidirect
10. #11719092C4semidirect
14. D13⋊M32C4semidirect
17. C2×C13×#107C4semidirect
18. C2×#88058C4semidirect
22. D13×#107C4semidirect
51. #88102C2×C4semidirect
55. D13⋊C16C2×C4semidirect
170. C2×#107#261semidirect
285. C13#12557semidirect

Maximal subgroups

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

subgroupindex
C2×D13⋊M322
C2×#117190922
#131298932
C2×D13×#1072
#1255713