Finite Group Databasebeta

← #15762011

Subgroups — #15762011

Order 3328.

538 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123232C211yesmaximal, characteristic
2#13114952C211yesmaximal, characteristic
3#13114691C211yesmaximal, 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×#88055—21no—
15#11718637—22no—
16#11718637C414yes—
17C42×Dic13C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C13×#332—22no—
21#11718142—21no—
22#11718142—22no—
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×Dic13D412yes—
48C2×C4×Dic13D411yescharacteristic
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#88055—42no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055—21no—
63C4⋊#1055D412yes—
64#9705—131nomaximal, Sylow
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C22×C4×C13—22no—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—22no—
76C22×Dic13C22⋊C412yes—
77C22×Dic13C22⋊C412yes—
78C2×Dic26—41no—
79C2×Dic26—41no—
80C2×Dic26—41no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×C8×C13—22no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—42no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13#4111yescharacteristic
96C42×C13#4111yescharacteristic
97C4⋊Dic13—22no—
98C4⋊Dic13—22no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101#6101—48no—
102#6101—48no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13—22no—
106C4×Dic13—22no—
107C4×Dic13—24no—
108C4×Dic13D812yes—
109C4×Dic13SD1612yes—
110C2×#1055—22no—
111C2×#1055—41no—
112C2×#1055—41no—
113C2×#1055—41no—
114C2×#1055—42no—
115#2868—131no—
116#1831—131no—
117#1767—131no—
118C2×#332—131no—
119C2×#332—131no—
120C2×#332—131no—
121C2×#332D1311yescharacteristic
122C23×C13C2×C22⋊C411yescharacteristic
123Q8×C13—81no—
124Q8×C13—81no—
125Q8×C13—81no—
126Q8×C13—81no—
127C2×C4×C13—22no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13C4×D411yescharacteristic
132C2×C4×C13C4×D411yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12411yescharacteristic
136C2×C4×C13#12711yescharacteristic
137C2×C4×C13C2×D811yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13#13712yes—
142C2×C4×C13#13712yes—
143C2×Dic13—22no—
144C2×Dic13—22no—
145C2×Dic13—22no—
146C2×Dic13—22no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13#10114yes—
151C2×Dic13#10214yes—
152Dic26—81no—
153Dic26—81no—
154Dic26—81no—
155Dic26—81no—
156C8×C13—42no—
157C8×C13—81no—
158#1055—42no—
159#1055—81no—
160C2×C4⋊Q8—131no—
161C2×C4⋊Q8—261no—
162C2×C4⋊Q8—261no—
163C2×C4⋊Q8C2×D1311yescharacteristic
164C2×C4⋊C8—131no—
165C2×C4⋊C8—131no—
166C2×C4⋊C8C2×D1311yescharacteristic
167C2×C4⋊C8C2×D1311yescharacteristic
168C2×#97—261no—
169#384—134no—
170#384—262no—
171C43—131no—
172#336—262no—
173#336—261no—
174#332—22no—
175#332—262no—
176#332—262no—
177#332—262no—
178C22×C13#39011yescharacteristic
179C22×C13C2×#10112yes—
180C22×C13C2×#10211yescharacteristic
181C22×C13#41811yescharacteristic
182C22×C13#41912yes—
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—82no—
186C4×C13#45911yescharacteristic
187C4×C13#45911yescharacteristic
188C4×C13#46011yescharacteristic
189C4×C13#46011yescharacteristic
190C4×C13#49112yes—
191C4×C13#49711yescharacteristic
192C4×C13#49711yescharacteristic
193Dic13—24no—
194Dic13—24no—
195Dic13—82no—
196C22×Q8—21no—
197C22×Q8—261no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—261no—
201C22×C8—261no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—261no—
207C4⋊Q8—261no—
208C4⋊Q8—261no—
209C4⋊Q8—261no—
210C4⋊Q8—522no—
211C4⋊Q8—522no—
212C4⋊Q8—522no—
213C4⋊Q8—522no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—132no—
216C2×C4⋊C4—264no—
217C2×C4⋊C4—264no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4C4×D1312yes—
220C2×C42—131no—
221C2×C42—132no—
222C2×C42—131no—
223C2×C42—132no—
224C2×C42C22×D1311yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—132no—
229C4⋊C8—261no—
230C4⋊C8—261no—
231C4⋊C8—261no—
232C4⋊C8C22⋊D1312yes—
233#97—522no—
234C2×C13#154612yes—
235C2×C13#155612yes—
236C2×C13#196011yescharacteristic
237C2×C13#196611yescharacteristic
238C2×C13#198211yescharacteristic
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—521no—
246C2×Q8—521no—
247C2×Q8—521no—
248C2×Q8—521no—
249C2×Q8—521no—
250C2×Q8—521no—
251C22×C4—22no—
252C22×C4—132no—
253C22×C4—132no—
254C22×C4—262no—
255C22×C4C2×C4×D1311yescharacteristic
256C22×C4D4×D1311yescharacteristic
257C22×C4D4×D1311yescharacteristic
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—42no—
262C2×C8—41no—
263C2×C8—262no—
264C2×C8—521no—
265C2×C8—521no—
266C2×C8—522no—
267C2×C8—521no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—262no—
273C4⋊C4—262no—
274C4⋊C4—528no—
275C4⋊C4—528no—
276C4⋊C4—521no—
277C4⋊C4—521no—
278C42—132no—
279C42—132no—
280C42—264no—
281C42—261no—
282C42—261no—
283C42—262no—
284C42—262no—
285C42#612711yescharacteristic
286C42D4×D1311yescharacteristic
287C42#612911yescharacteristic
288C42C2×C22⋊D1311yescharacteristic
289C13#970511yescharacteristic, complemented, Sylow
290C23C22⋊C4×D1311yescharacteristic
291Q8—81no—
292Q8—81no—
293Q8—81no—
294Q8—81no—
295Q8—1041no—
296Q8—1041no—
297Q8—1041no—
298Q8—1041no—
299C2×C4—22no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—134no—
304C2×C4—134no—
305C2×C4—262no—
306C2×C4—262no—
307C2×C4—262no—
308C2×C4—262no—
309C2×C4—522no—
310C2×C4—522no—
311C2×C4—522no—
312C2×C4#8813511yescharacteristic
313C2×C4#8813811yescharacteristic
314C2×C4#8813911yescharacteristic
315C2×C4D8×D1311yescharacteristic
316C2×C4#8816511yescharacteristic
317C2×C4SD16×D1311yescharacteristic
318C2×C4#8816811yescharacteristic
319C2×C4#8816912yes—
320C2×C4#8817212yes—
321C2×C4C4×C22⋊D1311yescharacteristic
322C2×C4#8819311yescharacteristic
323C2×C4#8819411yescharacteristic
324C8—42no—
325C8—81no—
326C8—522no—
327C8—1041no—
328C22D13×#10112yes—
329C22D13×#10211yescharacteristic
330C22#1171843111yescharacteristic
331C22#1171846312yes—
332C22#1171861811yescharacteristic
333C4—21no—
334C4—21no—
335C4—82no—
336C4—264no—
337C4—264no—
338C4—1042no—
339C4#1171842311yescharacteristic
340C4#1171844711yescharacteristic
341C4#1171845812yes—
342C4#1171881111yescharacteristic
343C4#1171882411yescharacteristic
344C4#1171882811yescharacteristic
345C4#1171885111yescharacteristic
346C2#1311350612yes—
347C2#1311355112yes—
348C2#1311565411yescharacteristic
349C2#1311567811yescharacteristic
350C2#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#9705
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
289. C13#9705semidirect

Maximal subgroups

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

subgroupindex
#131232322
#131149522
#131146912
C2×#117180742
C2×#117181392
C2×#117180782
C2×C13×#3322
#970513