Finite Group Databasebeta

← #15761960

Subgroups — #15761960

Order 3328.

570 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#13123232C211yesmaximal, characteristic
2#13114987C211yesmaximal, characteristic
3C4⋊C8×Dic13C211yesmaximal, characteristic
4C2×#11718074C211yesmaximal, characteristic
5C2×#11718139C211yesmaximal, characteristic
6C2×#11718078C211yesmaximal, characteristic
7C2×C13×#332C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88198—21no—
10C2×#88198—21no—
11C2×#88123C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×#88054—22no—
15C2×C8×Dic13—21no—
16#11718637—22no—
17#11718637C414yes—
18C42×Dic13C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4⋊#1055C2211yescharacteristic
21C13×#332—22no—
22#11718142—21no—
23#11718139—22no—
24#11718078—22no—
25#11718074—22no—
26C22×Q8×C13—21no—
27C22×Dic26—21no—
28C22×C8×C13—21no—
29C22×C8×C13—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C412yes—
36C2×C42×C13C2311yescharacteristic
37#88198—42no—
38#88198—42no—
39#88198—42no—
40#88198—42no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13C2×C412yes—
43C2×#6101—24no—
44C2×#6101—24no—
45C2×C4×Dic13C2×C412yes—
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13D412yes—
49C22×#1055—21no—
50C22×#1055—21no—
51#88123—21no—
52#88123—21no—
53#88123—21no—
54#88123—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8D412yes—
59#88054—44no—
60C8×Dic13—42no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055D412yes—
65#9694—131nomaximal, Sylow
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C22×C4×C13—22no—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—22no—
77C22×Dic13C22⋊C412yes—
78C22×Dic13C22⋊C412yes—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×C8×C13—22no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C2×C8×C13—42no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13#4111yescharacteristic
97C42×C13#4111yescharacteristic
98C4⋊Dic13—22no—
99C4⋊Dic13—22no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102#6101—48no—
103#6101—48no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13—24no—
107C4×Dic13D812yes—
108C4×Dic13SD1612yes—
109C4×Dic13SD1614yes—
110C4×Dic13Q1614yes—
111C2×#1055—22no—
112C2×#1055—41no—
113C2×#1055—41no—
114C2×#1055—41no—
115C2×#1055—42no—
116#2868—131no—
117#1842—131no—
118C4×C4⋊C8—131no—
119C2×#332—131no—
120C2×#332—131no—
121C2×#332—131no—
122C2×#332D1311yescharacteristic
123C23×C13C2×C22⋊C411yescharacteristic
124Q8×C13—81no—
125Q8×C13—81no—
126Q8×C13—81no—
127Q8×C13—81no—
128C2×C4×C13—22no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13C4×D411yescharacteristic
133C2×C4×C13C4×D411yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12411yescharacteristic
137C2×C4×C13#12711yescharacteristic
138C2×C4×C13C2×D811yescharacteristic
139C2×C4×C13C2×SD1611yescharacteristic
140C2×C4×C13C2×SD1612yes—
141C2×C4×C13C2×Q1612yes—
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13#10114yes—
150C2×Dic13#10214yes—
151C2×Dic13#10314yes—
152C2×Dic13#10314yes—
153Dic26—81no—
154Dic26—81no—
155Dic26—81no—
156Dic26—81no—
157C8×C13—42no—
158C8×C13—81no—
159#1055—42no—
160#1055—81no—
161C2×C4⋊Q8—131no—
162C2×C4⋊Q8—261no—
163C2×C4⋊Q8—261no—
164C2×C4⋊Q8C2×D1311yescharacteristic
165C2×C4⋊C8—131no—
166C2×C4⋊C8—131no—
167C2×C4⋊C8—262no—
168C2×C4⋊C8C2×D1311yescharacteristic
169C2×C4⋊C8C2×D1311yescharacteristic
170C2×C4×C8—261no—
171#384—134no—
172#384—262no—
173C43—131no—
174#336—261no—
175#332—22no—
176#332—262no—
177#332—262no—
178#332—262no—
179C22×C13#39011yescharacteristic
180C22×C13C2×#10112yes—
181C22×C13C2×#10211yescharacteristic
182C22×C13C2×#10312yes—
183C22×C13#41811yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—82no—
187C4×C13#45911yescharacteristic
188C4×C13#45911yescharacteristic
189C4×C13#46011yescharacteristic
190C4×C13#46011yescharacteristic
191C4×C13#48712yes—
192C4×C13#49211yescharacteristic
193C4×C13#49411yescharacteristic
194Dic13—24no—
195Dic13—82no—
196Dic13#33218yescomplemented
197C22×Q8—21no—
198C22×Q8—261no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—261no—
202C22×C8—261no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—21no—
207C4⋊Q8—261no—
208C4⋊Q8—261no—
209C4⋊Q8—261no—
210C4⋊Q8—261no—
211C4⋊Q8—522no—
212C4⋊Q8—522no—
213C4⋊Q8—522no—
214C4⋊Q8—522no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—132no—
217C2×C4⋊C4—264no—
218C2×C4⋊C4—264no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4C4×D1312yes—
221C2×C42—131no—
222C2×C42—132no—
223C2×C42—132no—
224C2×C42—131no—
225C2×C42C22×D1311yescharacteristic
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—132no—
230C4⋊C8—261no—
231C4⋊C8—261no—
232C4⋊C8—261no—
233C4⋊C8—524no—
234C4⋊C8C22⋊D1312yes—
235C4×C8—522no—
236C2×C13C2×#33212yes—
237C2×C13#154912yes—
238C2×C13#195611yescharacteristic
239C2×C13#196611yescharacteristic
240C2×C13#198211yescharacteristic
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—521no—
248C2×Q8—521no—
249C2×Q8—521no—
250C2×Q8—521no—
251C2×Q8—521no—
252C2×Q8—521no—
253C22×C4—22no—
254C22×C4—132no—
255C22×C4—132no—
256C22×C4—262no—
257C22×C4C2×C4×D1311yescharacteristic
258C22×C4D4×D1311yescharacteristic
259C22×C4D4×D1311yescharacteristic
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—42no—
264C2×C8—41no—
265C2×C8—262no—
266C2×C8—521no—
267C2×C8—521no—
268C2×C8—522no—
269C2×C8—521no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—262no—
275C4⋊C4—262no—
276C4⋊C4—528no—
277C4⋊C4—528no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C42—132no—
281C42—134no—
282C42—132no—
283C42—134no—
284C42—264no—
285C42—261no—
286C42—261no—
287C42#612711yescharacteristic
288C42D4×D1311yescharacteristic
289C42#612911yescharacteristic
290C42C2×C22⋊D1311yescharacteristic
291C13#969411yescharacteristic, complemented, Sylow
292C23C22⋊C4×D1311yescharacteristic
293Q8—81no—
294Q8—81no—
295Q8—81no—
296Q8—81no—
297Q8—1041no—
298Q8—1041no—
299Q8—1041no—
300Q8—1041no—
301C2×C4—22no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—134no—
306C2×C4—134no—
307C2×C4—134no—
308C2×C4—134no—
309C2×C4—262no—
310C2×C4—262no—
311C2×C4—522no—
312C2×C4—522no—
313C2×C4—522no—
314C2×C4#8813511yescharacteristic
315C2×C4#8813811yescharacteristic
316C2×C4#8813911yescharacteristic
317C2×C4D8×D1311yescharacteristic
318C2×C4#8816511yescharacteristic
319C2×C4SD16×D1311yescharacteristic
320C2×C4SD16×D1312yes—
321C2×C4#8816811yescharacteristic
322C2×C4Q16×D1312yes—
323C2×C4C4×C22⋊D1311yescharacteristic
324C2×C4#8819311yescharacteristic
325C2×C4#8819411yescharacteristic
326C8—42no—
327C8—81no—
328C8—522no—
329C8—1041no—
330C22D13×#10112yes—
331C22D13×#10211yescharacteristic
332C22#1171843111yescharacteristic
333C22D13×#10312yes—
334C22#1171861811yescharacteristic
335C4—21no—
336C4—21no—
337C4—82no—
338C4—138no—
339C4—264no—
340C4—1042no—
341C4#1171842311yescharacteristic
342C4#1171844711yescharacteristic
343C4#1171845312yes—
344C4#1171881111yescharacteristic
345C4#1171882411yescharacteristic
346C4#1171883611yescharacteristic
347C4#1171884211yescharacteristic
348C2D13×#33212yes—
349C2#1311351912yes—
350C2#1311563611yescharacteristic
351C2#1311567811yescharacteristic
352C2#1311576111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D13
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#332C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenterC2×#332D13
hypocenterC13#9694
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
196. Dic13#332semidirect
291. C13#9694semidirect

Maximal subgroups

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

subgroupindex
#131232322
#131149872
C4⋊C8×Dic132
C2×#117180742
C2×#117181392
C2×#117180782
C2×C13×#3322
#969413