Finite Group Databasebeta

← #15759611

Subgroups — #15759611

Order 3328.

490 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125774C211yesmaximal, characteristic
2#13115660C211yesmaximal, characteristic
3#13113505C211yesmaximal, characteristic
4#13113400C211yesmaximal, characteristic, complemented
5#13112696C211yesmaximal, characteristic, complemented
6#13112667C211yesmaximal, characteristic, complemented
7C13×#2961C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C2×#88128C2211yescharacteristic
10C13×#446—22no—
11C13×#446—22no—
12C13×#424—21no—
13C13×#423C2211yescharacteristic
14C13×#405—21no—
15C2×C13×#97C2211yescharacteristic
16C2×#88061—21no—
17C2×#88061—21no—
18#11718749C412yescomplemented
19#11718746C412yescomplemented
20#11718707—22no—
21#11718688—22no—
22#11718597C2211yescharacteristic
23#11718586C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718130—22no—
26#11718077—22no—
27C22×D52—21no—
28C22×D52—21no—
29C22×D52—21no—
30C2×C13×M16—21no—
31C22×C8×C13D411yescharacteristic
32C22×C8×C13D411yescharacteristic
33C13×C4⋊Q8C2×C411yescharacteristic
34C13×C4⋊Q8C2×C411yescharacteristic
35C13×#125—21no—
36C13×C22⋊Q8—21no—
37C13×C22⋊Q8D412yes—
38C4×Q8×C13—21no—
39C4×Q8×C13D412yes—
40C13×#117—21no—
41C2×C42×C13C2311yescharacteristic
42C2×#6106—24no—
43C2×C4⋊Dic13—21no—
44#88128—21no—
45#88128—21no—
46#88128—21no—
47#88128C2×C412yes—
48C13×C4⋊C8—24no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8D412yes—
51C13×#97—22no—
52C13×#97—21no—
53C13×#97—21no—
54C4×C8×C13—22no—
55#88071—21no—
56#88071—21no—
57C22⋊#1055—21no—
58C22⋊#1055—21no—
59#88061—42no—
60#88061—42no—
61#88049—24no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4×#1055—21no—
65C4×#1055C2×C412yes—
66#9294—131nomaximal, Sylow
67C23×D13—41no—
68C2×Q8×C13—21no—
69C2×Q8×C13C22⋊C412yes—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13#4111yescharacteristic
73C22×Dic13—41no—
74C2×D52—22no—
75C2×D52—22no—
76C2×D52—22no—
77C2×D52—41no—
78C2×D52—41no—
79C2×D52—41no—
80C2×D52—41no—
81C2×D52—41no—
82C2×D52—41no—
83C2×D52—41no—
84C2×D52—82no—
85C2×D52—82no—
86C13×M16—41no—
87C13×M16—41no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—22no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13SD1612yescomplemented
95C13×C4⋊C4—21no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4C22⋊C412yes—
101C13×C22⋊C4—22no—
102C42×C13—22no—
103C42×C13C22×C411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13#4111yescharacteristic
107#6106—84no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C2×#1055—22no—
111C2×#1055—41no—
112#3208—131no—
113#2961D1311yescharacteristic, complemented
114#1961—131no—
115#1545—131no—
116#1518—131no—
117#1286—131no—
118#1275—131no—
119C23×C13#12111yescharacteristic
120C22×D13—42no—
121C22×D13—82no—
122C22×D13—82no—
123C22×D13—81no—
124C22×D13—81no—
125Q8×C13—42no—
126Q8×C13—81no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13C2×C22⋊C411yescharacteristic
132C2×C4×C13C4×D411yescharacteristic
133C2×C4×C13C4×D411yescharacteristic
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12311yescharacteristic
137C2×C4×C13C2×SD1611yescharacteristic
138C2×C4×C13#13511yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×Dic13—81no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144D52—44no—
145D52—42no—
146D52—42no—
147D52—82no—
148D52—82no—
149D52—82no—
150D52—81no—
151D52—81no—
152C8×C13—22no—
153C8×C13—41no—
154C8×C13—42no—
155#1055—42no—
156#1055—81no—
157#533C2×D1311yescharacteristic
158C2×#127—131no—
159#492—132no—
160#486—132no—
161#460—262no—
162#450—262no—
163#446—22no—
164#446—22no—
165#431—131no—
166#431—131no—
167#424—21no—
168#423C2×D1311yescharacteristic
169C2×#102—261no—
170C2×#102—261no—
171#405—21no—
172C2×#97C2×D1311yescharacteristic
173#382—131no—
174#331—262no—
175#328—262no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13#38611yescharacteristic
179C22×C13#46011yescharacteristic
180C22×C13#46411yescharacteristic
181C2×D13—82no—
182C2×D13—82no—
183C2×D13—82no—
184C2×D13—162no—
185C2×D13—162no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—42no—
191C4×C13—42no—
192C4×C13C4×SD1611yescharacteristic
193C4×C13#44011yescharacteristic
194C4×C13#44811yescharacteristic
195C4×C13#44911yescharacteristic
196Dic13—161no—
197C22×D4—261no—
198C22×D4—261no—
199C22×D4—261no—
200C2×SD16—264no—
201C2×M16—21no—
202C22×C8C22⋊D1311yescharacteristic
203C22×C8C22⋊D1311yescharacteristic
204C4⋊Q8C4×D1311yescharacteristic
205C4⋊Q8C4×D1311yescharacteristic
206#127—132no—
207#127—261no—
208#127—261no—
209#127—261no—
210#125—21no—
211C22⋊Q8—21no—
212C22⋊Q8D5212yes—
213C4×Q8—21no—
214C4×Q8C22⋊D1312yes—
215#117—21no—
216C2×C4⋊C4—261no—
217C2×C42C22×D1311yescharacteristic
218C4⋊C8—24no—
219C4⋊C8—21no—
220C4⋊C8—261no—
221C4⋊C8—261no—
222C4⋊C8C22⋊D1312yes—
223#102—264no—
224#102—522no—
225#102—522no—
226C22⋊C8—261no—
227C22⋊C8—261no—
228#97—22no—
229#97—21no—
230#97—21no—
231C4×C8—22no—
232C4×C8—132no—
233C4×C8—261no—
234#95—261no—
235#95—261no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13#188011yescharacteristic
239C2×C13#190311yescharacteristic
240C2×C13#191011yescharacteristic
241D13—162no—
242C24—521no—
243C2×Q8—21no—
244C2×Q8#610312yes—
245C2×D4—262no—
246C2×D4—262no—
247C2×D4—262no—
248C2×D4—521no—
249C2×D4—521no—
250C2×D4—521no—
251C2×D4—521no—
252C2×D4—521no—
253C2×D4—521no—
254C2×D4—521no—
255C2×D4—1042no—
256C2×D4—1042no—
257C22×C4—521no—
258C22×C4C2×D5211yescharacteristic
259C22×C4#612711yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261SD16—1044no—
262M16—41no—
263M16—41no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—22no—
269C2×C8—21no—
270C2×C8—262no—
271C2×C8—521no—
272C2×C8#610612yescomplemented
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C4⋊C4#610312yes—
281C22⋊C4—22no—
282C42—22no—
283C42C2×C4×D1311yescharacteristic
284C42#612711yescharacteristic
285C42C2×C22⋊D1311yescharacteristic
286C42C2×C22⋊D1311yescharacteristic
287C13#929411yescharacteristic, complemented, Sylow
288C23—522no—
289C23—1042no—
290C23—1042no—
291C23—1041no—
292C23—1041no—
293C23#8818411yescharacteristic
294Q8—42no—
295Q8—81no—
296D4—524no—
297D4—522no—
298D4—522no—
299D4—1042no—
300D4—1042no—
301D4—1042no—
302D4—1041no—
303D4—1041no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—1041no—
309C2×C4—1041no—
310C2×C4—1041no—
311C2×C4C2×#610311yescharacteristic
312C2×C4C4×C22⋊D1311yescharacteristic
313C2×C4C4×C22⋊D1311yescharacteristic
314C2×C4#8818311yescharacteristic
315C2×C4#8818411yescharacteristic
316C2×C4C2×#610611yescharacteristic
317C2×C4#8819611yescharacteristic
318C2×C4#8820311yescharacteristic
319C2×C4#8820411yescharacteristic
320C2×C4#8820711yescharacteristic
321C8—22no—
322C8—41no—
323C8—42no—
324C8—522no—
325C8—1041no—
326C22—21no—
327C22—21no—
328C22—1042no—
329C22—1042no—
330C22—1042no—
331C22—2082no—
332C22—2082no—
333C22#1171868811yescharacteristic
334C22#1171868911yescharacteristic
335C22#1171887411yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—2081no—
343C4C4×#610611yescharacteristic
344C4#1171868711yescharacteristic
345C4#1171888811yescharacteristic
346C4#1171889911yescharacteristic
347C2—21no—
348C2—21no—
349C2—2082no—
350C2#1311519111yescharacteristic
351C2#1311531611yescharacteristic
352C2#1311536311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2961C2
socleC22×C13#386
prime radicalC2×#88128C22
cosocleC2×C42×C13C23
hypercenter#2961D13
hypocenterC13#9294
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2961

Complements

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

NH ≅ G/Ntype
4. #13113400C2semidirect
5. #13112696C2semidirect
6. #13112667C2semidirect
7. C13×#2961C2semidirect
18. #11718749C4semidirect
19. #11718746C4semidirect
94. C2×C8×C13SD16semidirect
113. #2961D13semidirect
272. C2×C8#6106semidirect
287. C13#9294semidirect

Maximal subgroups

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

subgroupindex
#131257742
#131156602
#131135052
#131134002
#131126962
#131126672
C13×#29612
#929413