Finite Group Databasebeta

← #16789388

Subgroups — #16789388

Order 3328.

420 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13⋊M32C211yesmaximal, characteristic
2C2×#11718217C211yesmaximal, characteristic, complemented
3C2×#11718218C211yesmaximal, characteristic, complemented
4#13130572C211yesmaximal, characteristic
5#13129876C211yesmaximal, characteristic, complemented
6#13129876C211yesmaximal, characteristic, complemented
7#13116445C211yesmaximal, characteristic
8C22×C8×D13C2211yescharacteristic
9C4×C22⋊#261C411yescharacteristic
10D13⋊(C22⋊C8)C411yescharacteristic
11C2×#88106C412yescomplemented
12C2×#88100C2211yescharacteristic
13C2×#88100C2211yescharacteristic
14D13⋊M32—22no—
15D13⋊M32—22no—
16C2×#88098C2211yescharacteristic
17C2×#88098C2211yescharacteristic
18C2×D13⋊C16C412yescomplemented
19C2×#88038C2211yescharacteristic
20C2×#88038C2211yescharacteristic
21(C2×#261)⋊C8C411yescharacteristic
22(C2×#261)⋊C8C411yescharacteristic
23#11718218—22no—
24#11718217—22no—
25C13×C22⋊C16C411yescharacteristic, complemented
26C22⋊#6090C411yescharacteristic, complemented
27#11718099C411yescharacteristic, complemented
28#11718099C411yescharacteristic, complemented
29C22×C4×D13C2×C411yescharacteristic
30C2×C22⋊#261—21no—
31C2×C4×#261C2×C411yescharacteristic
32C2×C4×#261C2×C411yescharacteristic
33C2×D13⋊C8C2×C411yescharacteristic
34C2×D13⋊C8C2×C411yescharacteristic
35C22×C8×C13C2×C411yescharacteristic
36C22×#1055C2×C411yescharacteristic
37C2×C8×D13—21no—
38C2×C8×D13—21no—
39C2×C8×D13—21no—
40C2×C8×D13—21no—
41C2×C8×D13C2×C411yescharacteristic
42C2×C8×D13C2×C411yescharacteristic
43C2×C8×D13C2×C411yescharacteristic
44C2×C8×D13C2311yescharacteristic
45C22⋊#1057—21no—
46(C2×#261)⋊C4—21no—
47#88111—21no—
48#88106—24no—
49C2×#6092C2×C412yes—
50C2×#6092C2×C412yes—
51#88100—21no—
52#88100—21no—
53#88100—21no—
54#88100—21no—
55#88098—21no—
56#88098—21no—
57#88098D412yes—
58#88098D412yes—
59D13⋊C16—24no—
60C2×C13×C16C2×C411yescharacteristic
61C2×C13×C16C2×C411yescharacteristic
62C2×#6090C2×C411yescharacteristic
63C2×#6090C2×C411yescharacteristic
64#88038—21no—
65#88038—21no—
66#88038—21no—
67#88038—21no—
68#12616—131nomaximal, Sylow
69C23×D13M1611yescharacteristic
70C22×#261—21no—
71C22×#261—21no—
72C22×C4×C13C4211yescharacteristic
73C22×Dic13M1611yescharacteristic
74C2×C4×D13—21no—
75C2×C4×D13—21no—
76C2×C4×D13—21no—
77C2×C4×D13—21no—
78C2×C4×D13C4211yescharacteristic
79C2×C4×D13M1611yescharacteristic
80C2×C4×D13M1611yescharacteristic
81C2×C4×D13C22×C411yescharacteristic
82C22⋊#261—42no—
83C2×#1057—21no—
84C2×#1057—21no—
85C4×#261—21no—
86C4×#261—21no—
87C4×#261—21no—
88C4×#261—21no—
89D13⋊C8—21no—
90D13⋊C8—21no—
91D13⋊C8—21no—
92D13⋊C8—21no—
93C2×C8×C13—21no—
94C2×C8×C13—21no—
95C2×C8×C13C4211yescharacteristic
96C2×C8×C13C22×C411yescharacteristic
97C2×#1055—21no—
98C2×#1055—21no—
99C2×#1055C4211yescharacteristic
100C2×#1055C22×C411yescharacteristic
101C8×D13—21no—
102C8×D13—21no—
103C8×D13—21no—
104C8×D13—21no—
105C8×D13—21no—
106C8×D13—21no—
107C8×D13C2×D411yescharacteristic
108C8×D13C2×D411yescharacteristic
109C8×D13#4111yescharacteristic
110C8×D13#4111yescharacteristic
111#6092—22no—
112#6092C22⋊C414yescomplemented
113C13×C16—21no—
114C13×C16—21no—
115#6090—21no—
116#6090—21no—
117C22×M32—131no—
118#2112—131no—
119C2×#347—131no—
120C2×#347—131no—
121#1752—131no—
122#1375—131no—
123#1375—131no—
124C23×C13#9711yescharacteristic
125C22×D13—22no—
126C22×D13—21no—
127C22×D13—21no—
128C22×D13—41no—
129C22×D13#9711yescharacteristic
130C22×D13C2×M1611yescharacteristic
131C2×#261—41no—
132C2×#261—41no—
133C2×#261—41no—
134C2×#261—41no—
135C2×#261—41no—
136C2×#261—41no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13#9711yescharacteristic
140C2×C4×C13C2×C4211yescharacteristic
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13#9711yescharacteristic
144C2×Dic13C2×M1611yescharacteristic
145C4×D13—21no—
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—21no—
149C4×D13—21no—
150C4×D13—21no—
151C4×D13C4×D411yescharacteristic
152C4×D13C4×D411yescharacteristic
153C4×D13#13111yescharacteristic
154C4×D13#13111yescharacteristic
155#1057—41no—
156#1057—41no—
157C8×C13—21no—
158C8×C13C4×D411yescharacteristic
159C8×C13C4×D411yescharacteristic
160#1055—21no—
161#1055C2×C22⋊C411yescharacteristic
162#1055#11711yescharacteristic
163C23×C8—131no—
164C2×M32—131no—
165C2×M32—131no—
166C2×M32—132no—
167C2×M32—131no—
168C2×M32—131no—
169C2×M32—262no—
170C2×M32—262no—
171C22×C16—132no—
172C2×C22⋊C8—131no—
173C2×#97—131no—
174C2×#97—131no—
175C4×C22⋊C4—131no—
176C22⋊C16—131no—
177C22⋊C16—131no—
178C22⋊C16—131no—
179C22⋊C16#26111yescharacteristic, complemented
180#347—262no—
181#347—262no—
182#336—131no—
183#336—131no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13C2×#9711yescharacteristic
188C2×D13—21no—
189C2×D13—21no—
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—42no—
193C2×D13—42no—
194C2×D13#34712yescomplemented
195C2×D13#43511yescharacteristic
196C2×D13#43511yescharacteristic
197#261—81no—
198#261—81no—
199C4×C13—21no—
200C4×C13C4×C22⋊C411yescharacteristic
201C4×C13#40511yescharacteristic
202Dic13—21no—
203Dic13#43511yescharacteristic
204Dic13#43511yescharacteristic
205C23×C4—131no—
206C22×C8—131no—
207C22×C8—131no—
208C22×C8—131no—
209C22×C8—131no—
210C22×C8—131no—
211C22×C8—131no—
212C22×C8—131no—
213C22×C8—261no—
214C22×C8—261no—
215C22×C8—261no—
216C22×C8—261no—
217C22×C8C2×#26111yescharacteristic
218C2×C22⋊C4—261no—
219C2×C42—131no—
220C2×C42—131no—
221M32—132no—
222M32—132no—
223M32—261no—
224M32—261no—
225M32—261no—
226M32—261no—
227M32—264no—
228M32—261no—
229M32—261no—
230C2×C16—132no—
231C2×C16—132no—
232C2×C16—131no—
233C2×C16—131no—
234C2×C16—264no—
235C2×C16C2×#26111yescharacteristic
236C2×C16C2×#26111yescharacteristic
237C22⋊C8—261no—
238C22⋊C8—261no—
239#97—261no—
240#97—261no—
241#97—261no—
242#97—261no—
243#95—261no—
244C2×C13—41no—
245C2×C13#175211yescharacteristic
246C2×C13C2×#34711yescharacteristic
247C2×C13#211011yescharacteristic
248D13—21no—
249D13—21no—
250D13—22no—
251C24—131no—
252C22×C4—131no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4C4×#26111yescharacteristic
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—131no—
267C2×C8—131no—
268C2×C8—131no—
269C2×C8—131no—
270C2×C8—131no—
271C2×C8—131no—
272C2×C8—261no—
273C2×C8—261no—
274C2×C8—261no—
275C2×C8—261no—
276C2×C8—261no—
277C2×C8—261no—
278C2×C8—261no—
279C2×C8—261no—
280C2×C8—261no—
281C2×C8—261no—
282C2×C8—261no—
283C2×C8—261no—
284C2×C8—261no—
285C2×C8—261no—
286C2×C8C4×#26111yescharacteristic
287C2×C8C22×#26111yescharacteristic
288C22⋊C4—522no—
289C42—261no—
290C42—261no—
291C42—261no—
292C42—261no—
293C16—21no—
294C16—21no—
295C16—134no—
296C16—262no—
297C16—261no—
298C16—261no—
299C13#1261611yescharacteristic, complemented, Sylow
300C23—131no—
301C23—131no—
302C23—262no—
303C23—261no—
304C23—261no—
305C23—521no—
306C23#8810011yescharacteristic
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—131no—
312C2×C4—131no—
313C2×C4—131no—
314C2×C4—131no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4#8810011yescharacteristic
330C2×C4C2×C4×#26111yescharacteristic
331C8—21no—
332C8—131no—
333C8—131no—
334C8—261no—
335C8—521no—
336C8—521no—
337C8D4×#26111yescharacteristic
338C8D4×#26111yescharacteristic
339C22—21no—
340C22—21no—
341C22—21no—
342C22—132no—
343C22—131no—
344C22—131no—
345C22—261no—
346C22—261no—
347C22—261no—
348C22—261no—
349C22—522no—
350C22—522no—
351C22C2×#8810011yescharacteristic
352C4—21no—
353C4—131no—
354C4—131no—
355C4—261no—
356C4—1041no—
357C4—1041no—
358C4C22⋊C4×#26111yescharacteristic
359C4#1171909911yescharacteristic
360C2—41no—
361C2—261no—
362C2—261no—
363C2—262no—
364C2#1313057511yescharacteristic
365C2#1313105111yescharacteristic
366C2#1313105511yescharacteristic
subgroupG/H
centerC2×C4C2×C4×#261
commutatorC2×C4×C13C2×C42
FrattiniC2×C8C22×#261
FittingC13×C22⋊C16C4
socleC22×C13C2×#97
prime radicalC23×D13M16
cosocleC2×C8×D13C23
hypercenterC22⋊C16#261
hypocenterC13#12616
LCSG ▷ C2×C4×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#11718217C2semidirect
3. C2×#11718218C2semidirect
5. #13129876C2semidirect
6. #13129876C2semidirect
11. C2×#88106C4semidirect
18. C2×D13⋊C16C4semidirect
25. C13×C22⋊C16C4semidirect
26. C22⋊#6090C4semidirect
27. #11718099C4semidirect
28. #11718099C4semidirect
112. #6092C22⋊C4semidirect
179. C22⋊C16#261semidirect
194. C2×D13#347semidirect
299. C13#12616semidirect

Maximal subgroups

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

subgroupindex
C2×D13⋊M322
C2×#117182172
C2×#117182182
#131305722
#131298762
#131164452
#1261613