Finite Group Databasebeta

← #16789387

Subgroups — #16789387

Order 3328.

420 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
2#13131065C211yesmaximal, characteristic
3C2×#11718262C211yesmaximal, characteristic, complemented
4C2×#11718232C211yesmaximal, characteristic, complemented
5#13129878C211yesmaximal, characteristic, complemented
6#13129877C211yesmaximal, characteristic, complemented
7#13114611C211yesmaximal, characteristic
8C22×C8×D13C2211yescharacteristic
9C2×#88106C2211yescharacteristic
10C2×#88106C2211yescharacteristic
11C2×#88106C2211yescharacteristic
12C2×#88106C2211yescharacteristic
13D13⋊M32—22no—
14D13⋊M32—22no—
15C2×#88098C412yescomplemented
16C2×D13⋊C16C412yescomplemented
17C2×#88060C411yescharacteristic
18C2×#88055C2211yescharacteristic
19C4×#6103C411yescharacteristic
20C2×#88043C2211yescharacteristic
21#11718262—22no—
22#11718259C412yescomplemented
23#11718259C412yescomplemented
24#11718232—22no—
25C13×#336C411yescharacteristic
26#11718142C411yescharacteristic
27C22×C4×D13C2×C411yescharacteristic
28C22×C8×C13C2×C411yescharacteristic
29C22×C8×C13C2×C411yescharacteristic
30C2×C42×C13C2×C411yescharacteristic
31C2×#6103—21no—
32C2×C4×Dic13C2×C411yescharacteristic
33C22×#1055C2×C411yescharacteristic
34C22×#1055C2311yescharacteristic
35C2×C8×D13—21no—
36C2×C8×D13—21no—
37C2×C8×D13—21no—
38C2×C8×D13—21no—
39C2×C8×D13C2×C411yescharacteristic
40C2×C8×D13C2×C411yescharacteristic
41C2×C8×D13C2×C411yescharacteristic
42C2×C8×D13C2×C411yescharacteristic
43#88106—21no—
44#88106—21no—
45#88106—21no—
46#88106—21no—
47#88106—21no—
48#88106—21no—
49#88106D412yes—
50#88106D412yes—
51C2×#6092C2×C412yes—
52C2×#6092C2×C412yes—
53C2×#6092C2×C412yes—
54C2×#6092C2×C412yes—
55#88098—24no—
56D13⋊C16—24no—
57#88071—21no—
58#88060—21no—
59#88060—21no—
60#88055—21no—
61#88055—21no—
62#88043—21no—
63#88043—21no—
64#12616—131nomaximal, Sylow
65C23×D13M1611yescharacteristic
66C22×C4×C13—21no—
67C22×C4×C13C22×C411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13M1611yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13—21no—
74C2×C4×D13C4211yescharacteristic
75C2×C4×D13C4211yescharacteristic
76C2×C4×D13M1611yescharacteristic
77C2×C4×D13M1611yescharacteristic
78C2×C8×C13—21no—
79C2×C8×C13—21no—
80C2×C8×C13—21no—
81C2×C8×C13—21no—
82C2×C8×C13—21no—
83C2×C8×C13C4211yescharacteristic
84C2×C8×C13C4211yescharacteristic
85C42×C13—21no—
86C42×C13—21no—
87#6103—42no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C2×#1055—21no—
91C2×#1055—21no—
92C2×#1055—21no—
93C2×#1055C22×C411yescharacteristic
94C2×#1055C22×C411yescharacteristic
95C2×#1055C2×D411yescharacteristic
96C2×#1055C2×D411yescharacteristic
97C2×#1055#4111yescharacteristic
98C2×#1055#4111yescharacteristic
99C8×D13—21no—
100C8×D13—21no—
101C8×D13—21no—
102C8×D13—21no—
103C8×D13—21no—
104C8×D13—21no—
105C8×D13—21no—
106C8×D13—21no—
107#6092—22no—
108#6092—22no—
109#6092—22no—
110#6092C22⋊C414yescomplemented
111C22×M32—131no—
112#2112—131no—
113C2×#347—131no—
114C2×#347—131no—
115#1752—131no—
116#1375—131no—
117#1375—131no—
118C23×C13C2×M1611yescharacteristic
119C22×D13—21no—
120C22×D13—21no—
121C22×D13—22no—
122C22×D13—41no—
123C22×D13#9711yescharacteristic
124C22×D13#9711yescharacteristic
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13C2×C4211yescharacteristic
129C2×C4×C13C4×D411yescharacteristic
130C2×C4×C13C4×D411yescharacteristic
131C2×C4×C13C2×M1611yescharacteristic
132C2×C4×C13#13111yescharacteristic
133C2×C4×C13#13111yescharacteristic
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13#9711yescharacteristic
140C2×Dic13#9711yescharacteristic
141C4×D13—21no—
142C4×D13—21no—
143C4×D13—21no—
144C4×D13—21no—
145C4×D13—21no—
146C4×D13—21no—
147C4×D13—21no—
148C4×D13—21no—
149C8×C13—21no—
150C8×C13—21no—
151C8×C13—41no—
152#1055—41no—
153#1055C2×C22⋊C411yescharacteristic
154#1055#11711yescharacteristic
155#1055C4×D411yescharacteristic
156#1055C4×D411yescharacteristic
157C23×C8—131no—
158C2×M32—131no—
159C2×M32—131no—
160C2×M32—131no—
161C2×M32—131no—
162C2×M32—132no—
163C2×M32—262no—
164C2×M32—262no—
165C22×C16—132no—
166C2×C22⋊C8—131no—
167C2×#97—131no—
168C2×#97—131no—
169C4×C22⋊C4—131no—
170C22⋊C16—132no—
171C22⋊C16—132no—
172#347—262no—
173#347—262no—
174#336—131no—
175#336#26111yescharacteristic
176C22×C13—21no—
177C22×C13—21no—
178C22×C13C2×#9711yescharacteristic
179C22×C13#43511yescharacteristic
180C22×C13#43511yescharacteristic
181C2×D13—21no—
182C2×D13—21no—
183C2×D13—21no—
184C2×D13—21no—
185C2×D13—21no—
186C2×D13—42no—
187C2×D13—42no—
188C2×D13#34712yescomplemented
189C4×C13—81no—
190C4×C13C4×C22⋊C411yescharacteristic
191C4×C13#40511yescharacteristic
192C4×C13#43511yescharacteristic
193C4×C13#43511yescharacteristic
194Dic13—21no—
195Dic13—21no—
196Dic13—81no—
197C23×C4—131no—
198C22×C8—131no—
199C22×C8—131no—
200C22×C8—131no—
201C22×C8—131no—
202C22×C8—131no—
203C22×C8—131no—
204C22×C8—261no—
205C22×C8—261no—
206C22×C8—261no—
207C22×C8—261no—
208C22×C8C2×#26111yescharacteristic
209C22×C8C2×#26111yescharacteristic
210C2×C22⋊C4—261no—
211C2×C42—131no—
212C2×C42C2×#26111yescharacteristic
213M32—132no—
214M32—132no—
215M32—264no—
216M32—261no—
217M32—261no—
218M32—261no—
219M32—261no—
220M32—261no—
221M32—261no—
222C2×C16—132no—
223C2×C16—132no—
224C2×C16—132no—
225C2×C16—132no—
226C2×C16—264no—
227C22⋊C8—261no—
228C22⋊C8—261no—
229#97—261no—
230#97—261no—
231#97—261no—
232#97—261no—
233#95—261no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13#175211yescharacteristic
237C2×C13C2×#34711yescharacteristic
238C2×C13#211011yescharacteristic
239D13—22no—
240D13—41no—
241C24—131no—
242C22×C4—21no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4C22×#26111yescharacteristic
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—131no—
260C2×C8—131no—
261C2×C8—131no—
262C2×C8—131no—
263C2×C8—131no—
264C2×C8—131no—
265C2×C8—261no—
266C2×C8—261no—
267C2×C8—261no—
268C2×C8—261no—
269C2×C8—261no—
270C2×C8—261no—
271C2×C8—261no—
272C2×C8—261no—
273C2×C8—261no—
274C2×C8—261no—
275C2×C8—261no—
276C2×C8C4×#26111yescharacteristic
277C2×C8C4×#26111yescharacteristic
278C22⋊C4—522no—
279C42—21no—
280C42—21no—
281C42—261no—
282C42—261no—
283C16—134no—
284C16—262no—
285C16—262no—
286C16—262no—
287C13#1261611yescharacteristic, complemented, Sylow
288C23—131no—
289C23—131no—
290C23—262no—
291C23—261no—
292C23—261no—
293C23—521no—
294C23D13⋊M1611yescharacteristic
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4D13⋊M1611yescharacteristic
314C2×C4C2×C4×#26111yescharacteristic
315C2×C4#8823811yescharacteristic
316C2×C4D4×#26111yescharacteristic
317C2×C4D4×#26111yescharacteristic
318C2×C4#8824011yescharacteristic
319C8—21no—
320C8—21no—
321C8—41no—
322C8—131no—
323C8—131no—
324C8—131no—
325C8—131no—
326C8—521no—
327C22—21no—
328C22—21no—
329C22—132no—
330C22—261no—
331C22—261no—
332C22—261no—
333C22—261no—
334C22—261no—
335C22—522no—
336C22—522no—
337C22#1171904711yescharacteristic
338C22#1171906511yescharacteristic
339C22#1171907511yescharacteristic
340C4—81no—
341C4—261no—
342C4—261no—
343C4—1041no—
344C4#1171906511yescharacteristic
345C4C22⋊C4×#26111yescharacteristic
346C4#1171907211yescharacteristic
347C4#1171907511yescharacteristic
348C2—21no—
349C2—21no—
350C2—262no—
351C2—521no—
352C2#1313057411yescharacteristic
353C2#1313105311yescharacteristic
354C2#1313105811yescharacteristic
subgroupG/H
centerC2×C4C2×C4×#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#336C4
socleC22×C13C2×#97
prime radicalC23×D13M16
cosocleC22×#1055C23
hypercenter#336#261
hypocenterC13#12616
LCSG ▷ C2×C4×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
3. C2×#11718262C2semidirect
4. C2×#11718232C2semidirect
5. #13129878C2semidirect
6. #13129877C2semidirect
15. C2×#88098C4semidirect
16. C2×D13⋊C16C4semidirect
22. #11718259C4semidirect
23. #11718259C4semidirect
110. #6092C22⋊C4semidirect
188. C2×D13#347semidirect
287. 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
#131310652
C2×#117182622
C2×#117182322
#131298782
#131298772
#131146112
#1261613