Finite Group Databasebeta

← #15761951

Subgroups — #15761951

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 334 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—22no—
10C2×#88123C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×C13×C4⋊C8C2211yescharacteristic
13C2×#88054—22no—
14C2×C8×Dic13—21no—
15#11718637—21no—
16#11718637—21no—
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—44no—
38#88198—44no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13C2×C412yes—
41C2×#6101—24no—
42C2×#6101—24no—
43C2×C4×Dic13C2×C412yes—
44C2×C4×Dic13D411yescharacteristic
45C2×C4×Dic13D412yes—
46C2×C4×Dic13D411yescharacteristic
47C22×#1055—21no—
48C22×#1055—21no—
49#88123—21no—
50#88123—21no—
51#88123—21no—
52#88123—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C4⋊C8D412yes—
57#88054—44no—
58C8×Dic13—42no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055D412yes—
63#9692—131nomaximal, Sylow
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C2×Q8×C13—42no—
67C2×Q8×C13—42no—
68C22×C4×C13—22no—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—22no—
73C22×Dic13C22⋊C412yes—
74C22×Dic13C22⋊C412yes—
75C2×Dic26—41no—
76C2×Dic26—41no—
77C2×Dic26—42no—
78C2×Dic26—42no—
79C2×C8×C13—22no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C2×C8×C13—42no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C42×C13C2×D411yescharacteristic
89C42×C13C2×D411yescharacteristic
90C42×C13#4111yescharacteristic
91C42×C13#4111yescharacteristic
92C4⋊Dic13—22no—
93C4⋊Dic13—22no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96#6101—48no—
97#6101—48no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—24no—
101C4×Dic13D814yes—
102C4×Dic13SD1614yes—
103C4×Dic13SD1612yes—
104C4×Dic13Q1612yes—
105C2×#1055—22no—
106C2×#1055—41no—
107C2×#1055—41no—
108C2×#1055—41no—
109C2×#1055—42no—
110#2868—131no—
111#1842—131no—
112C4×C4⋊C8—131no—
113C2×#332—131no—
114C2×#332—131no—
115C2×#332—131no—
116C2×#332D1311yescharacteristic
117C23×C13C2×C22⋊C411yescharacteristic
118Q8×C13—82no—
119Q8×C13—81no—
120Q8×C13—81no—
121C2×C4×C13—22no—
122C2×C4×C13—42no—
123C2×C4×C13—44no—
124C2×C4×C13C4×D411yescharacteristic
125C2×C4×C13C4×D411yescharacteristic
126C2×C4×C13#12111yescharacteristic
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12411yescharacteristic
129C2×C4×C13#12711yescharacteristic
130C2×C4×C13C2×D812yes—
131C2×C4×C13C2×SD1611yescharacteristic
132C2×C4×C13C2×SD1612yes—
133C2×C4×C13C2×Q1611yescharacteristic
134C2×C4×C13#13711yescharacteristic
135C2×C4×C13#13711yescharacteristic
136C2×Dic13—22no—
137C2×Dic13—22no—
138C2×Dic13—42no—
139C2×Dic13—44no—
140C2×Dic13#10114yes—
141C2×Dic13#10214yes—
142C2×Dic13#10214yes—
143C2×Dic13#10314yes—
144Dic26—82no—
145Dic26—81no—
146Dic26—81no—
147C8×C13—42no—
148C8×C13—81no—
149#1055—42no—
150#1055—81no—
151C2×C4⋊Q8—131no—
152C2×C4⋊Q8—262no—
153C2×C4⋊Q8C2×D1311yescharacteristic
154C2×C4⋊C8—131no—
155C2×C4⋊C8—131no—
156C2×C4⋊C8—262no—
157C2×C4⋊C8C2×D1311yescharacteristic
158C2×C4⋊C8C2×D1311yescharacteristic
159C2×C4×C8—261no—
160#384—134no—
161#384—261no—
162#384—261no—
163C43—131no—
164#336—261no—
165#332—22no—
166#332—262no—
167#332—262no—
168#332—262no—
169C22×C13#39011yescharacteristic
170C22×C13C2×#10112yes—
171C22×C13C2×#10212yes—
172C22×C13C2×#10311yescharacteristic
173C22×C13#41911yescharacteristic
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—82no—
177C4×C13#46111yescharacteristic
178C4×C13#46111yescharacteristic
179C4×C13#46211yescharacteristic
180C4×C13#46211yescharacteristic
181C4×C13#48612yes—
182C4×C13#49211yescharacteristic
183C4×C13#49311yescharacteristic
184Dic13—24no—
185Dic13—82no—
186Dic13#33218yescomplemented
187C22×Q8—21no—
188C22×Q8—261no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—261no—
192C22×C8—261no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—261no—
198C4⋊Q8—261no—
199C4⋊Q8—261no—
200C4⋊Q8—261no—
201C4⋊Q8—524no—
202C4⋊Q8—524no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—132no—
205C2×C4⋊C4—264no—
206C2×C4⋊C4—264no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C4×D1312yes—
209C2×C42—132no—
210C2×C42—131no—
211C2×C42—132no—
212C2×C42—131no—
213C2×C42C22×D1311yescharacteristic
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—132no—
218C4⋊C8—261no—
219C4⋊C8—261no—
220C4⋊C8—261no—
221C4⋊C8—524no—
222C4⋊C8C22⋊D1312yes—
223C4×C8—522no—
224C2×C13C2×#33212yes—
225C2×C13#154612yes—
226C2×C13#195711yescharacteristic
227C2×C13#196611yescharacteristic
228C2×C13#198111yescharacteristic
229C2×Q8—41no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—41no—
233C2×Q8—521no—
234C2×Q8—522no—
235C2×Q8—522no—
236C2×Q8—521no—
237C22×C4—22no—
238C22×C4—132no—
239C22×C4—132no—
240C22×C4—262no—
241C22×C4C2×C4×D1311yescharacteristic
242C22×C4D4×D1311yescharacteristic
243C22×C4D4×D1311yescharacteristic
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—42no—
248C2×C8—41no—
249C2×C8—262no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8—522no—
253C2×C8—521no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—262no—
259C4⋊C4—262no—
260C4⋊C4—528no—
261C4⋊C4—528no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C42—134no—
265C42—132no—
266C42—134no—
267C42—132no—
268C42—264no—
269C42—261no—
270C42—261no—
271C42#612711yescharacteristic
272C42D4×D1311yescharacteristic
273C42#612911yescharacteristic
274C42C2×C22⋊D1311yescharacteristic
275C13#969211yescharacteristic, complemented, Sylow
276C23C22⋊C4×D1311yescharacteristic
277Q8—82no—
278Q8—81no—
279Q8—81no—
280Q8—1042no—
281Q8—1041no—
282Q8—1041no—
283C2×C4—22no—
284C2×C4—44no—
285C2×C4—42no—
286C2×C4—134no—
287C2×C4—134no—
288C2×C4—134no—
289C2×C4—134no—
290C2×C4—262no—
291C2×C4—262no—
292C2×C4—524no—
293C2×C4—522no—
294C2×C4#8813511yescharacteristic
295C2×C4#8813811yescharacteristic
296C2×C4#8813911yescharacteristic
297C2×C4D8×D1312yes—
298C2×C4SD16×D1312yes—
299C2×C4SD16×D1311yescharacteristic
300C2×C4#8816911yescharacteristic
301C2×C4Q16×D1311yescharacteristic
302C2×C4#8817211yescharacteristic
303C2×C4C4×C22⋊D1311yescharacteristic
304C2×C4#8819311yescharacteristic
305C2×C4#8819411yescharacteristic
306C8—42no—
307C8—81no—
308C8—522no—
309C8—1041no—
310C22D13×#10112yes—
311C22D13×#10212yes—
312C22D13×#10311yescharacteristic
313C22#1171846311yescharacteristic
314C22#1171861811yescharacteristic
315C4—21no—
316C4—21no—
317C4—82no—
318C4—138no—
319C4—264no—
320C4—1042no—
321C4#1171842112yes—
322C4#1171845411yescharacteristic
323C4#1171847911yescharacteristic
324C4#1171881211yescharacteristic
325C4#1171882311yescharacteristic
326C4#1171883611yescharacteristic
327C4#1171884311yescharacteristic
328C2D13×#33212yes—
329C2#1311350612yes—
330C2#1311564011yescharacteristic
331C2#1311567811yescharacteristic
332C2#1311575711yescharacteristic
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#9692
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
186. Dic13#332semidirect
275. C13#9692semidirect

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
#969213