Finite Group Databasebeta

← #16015509

Subgroups — #16015509

Order 3328.

806 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
1C2×#11718539C212yesmaximal
2C2×#11718519C212yesmaximal
3#13123198C211yesmaximal, characteristic
4#13123197C211yesmaximal, characteristic
5#13115005C211yesmaximal, characteristic
6#13115004C211yesmaximal, characteristic
7#13115003C212yesmaximal
8#13115002C211yesmaximal, characteristic
9#13115001C212yesmaximal
10#97×Dic13C211yesmaximal, characteristic
11C13×#1847C211yesmaximal, characteristic
12C2×#88144C2212yes—
13C2×#88144C2211yescharacteristic
14C2×#88144C2211yescharacteristic
15C2×C13×#107C2212yes—
16C2×C13×#106C2212yes—
17C2×C13×#97C2211yescharacteristic
18C13×#384C2211yescharacteristic
19C13×#382C2211yescharacteristic
20C2×#88058C2212yes—
21C2×#88057C2212yes—
22C2×#88055C2212yes—
23C2×C8×Dic13C2212yes—
24#11718646—22no—
25#11718638C2212yes—
26#11718637C2211yescharacteristic
27#11718637C2211yescharacteristic
28#11718634—22no—
29C2×#88048C2212yes—
30C2×#88048C2212yes—
31C2×#88047C2212yes—
32C2×#88047C2212yes—
33#11718597C2211yescharacteristic
34#11718596C2211yescharacteristic
35C42×Dic13C2211yescharacteristic
36C2×#88043C2211yescharacteristic
37#11718539—28no—
38#11718519—28no—
39#11718308—22no—
40#11718308—22no—
41C22×C8×C13C2312yes—
42C2×C13×C4⋊C4—22no—
43C2×C13×C4⋊C4C2311yescharacteristic
44C2×C13×C4⋊C4C2311yescharacteristic
45C2×C13×C4⋊C4C2312yes—
46C2×C42×C13C2311yescharacteristic
47C2×C4⋊Dic13—22no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50C2×C4⋊Dic13—22no—
51C2×C4⋊Dic13C2311yescharacteristic
52C2×C4⋊Dic13C2312yes—
53C2×C4⋊Dic13C2311yescharacteristic
54C2×#6101—21no—
55C2×#6101—21no—
56C2×#6101—22no—
57C2×#6101—22no—
58C2×#6101—22no—
59C2×C4×Dic13D412yes—
60C2×C4×Dic13D412yes—
61C2×C4×Dic13C2311yescharacteristic
62C2×C4×Dic13C2311yescharacteristic
63C22×#1055C2312yes—
64#88144—24no—
65#88144—24no—
66#88144—24no—
67#88144—24no—
68C13×#107—24no—
69C13×#106—24no—
70C13×#97Q814yes—
71C13×#95—22no—
72#88071—22no—
73#88071—24no—
74#88058—24no—
75#88057—24no—
76#88055Q818yes—
77C8×Dic13D418yes—
78#88048—24no—
79#88048—24no—
80#88047—24no—
81#88047—24no—
82#88043Q814yes—
83#33315—131nomaximal, Sylow
84C22×C4×C13—22no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13C2×D412yes—
88C22×C4×C13C2411yescharacteristic
89C22×Dic13—21no—
90C22×Dic13—21no—
91C22×Dic13—22no—
92C22×Dic13C2×D411yescharacteristic
93C22×Dic13C2×D411yescharacteristic
94C22×Dic13C2×D412yes—
95C2×C8×C13C2×D414yes—
96C2×C8×C13C2×Q814yes—
97C2×C8×C13C2×Q814yes—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—44no—
103C42×C13C2×Q812yes—
104C42×C13C2×Q812yes—
105C4⋊Dic13—22no—
106C4⋊Dic13—22no—
107C4⋊Dic13—22no—
108C4⋊Dic13—22no—
109C4⋊Dic13—44no—
110C4⋊Dic13—42no—
111C4⋊Dic13—44no—
112C4⋊Dic13—42no—
113#6101—44no—
114#6101—44no—
115#6101—44no—
116#6101—42no—
117#6101—42no—
118C4×Dic13—42no—
119C4×Dic13—42no—
120C4×Dic13C2×D414yes—
121C4×Dic13C2×Q814yes—
122C2×#1055C2×D414yes—
123C2×#1055C2×Q814yes—
124C2×#1055C2×Q814yes—
125C2×#499—132no—
126C2×#499—132no—
127#2859—131no—
128#2859—131no—
129#1847—132no—
130#1847—132no—
131#1847—131no—
132#1847—131no—
133#1847—131no—
134#1847D1311yescharacteristic
135C4×#97—131no—
136C23×C13C22×D411yescharacteristic
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—41no—
140C2×C4×C13—42no—
141C2×C4×C13—41no—
142C2×C4×C13—42no—
143C2×C4×C13—42no—
144C2×C4×C13—44no—
145C2×C4×C13C4⋊Q814yes—
146C2×C4×C13C22×D412yes—
147C2×C4×C13C22×Q811yescharacteristic
148C2×C4×C13C22×Q811yescharacteristic
149C2×C4×C13C22×Q812yes—
150C2×Dic13—22no—
151C2×Dic13—22no—
152C2×Dic13—22no—
153C2×Dic13—22no—
154C2×Dic13—41no—
155C2×Dic13—42no—
156C2×Dic13—41no—
157C2×Dic13—42no—
158C2×Dic13—42no—
159C2×Dic13—44no—
160C2×Dic13#12712yes—
161C2×Dic13#12712yes—
162C2×Dic13C4⋊Q814yes—
163C8×C13C4⋊Q818yes—
164#1055C4⋊Q818yes—
165C2×#125—132no—
166C2×#125—131no—
167C2×#125—131no—
168#499—268no—
169#499—268no—
170C2×#107—132no—
171C2×#107—132no—
172C2×#107—132no—
173C2×#107C2×D1312yes—
174C2×#106—132no—
175C2×#106—132no—
176C2×#106—132no—
177C2×#106C2×D1312yes—
178C2×#97—132no—
179C2×#97—131no—
180C2×#97C2×D1311yescharacteristic
181C2×C4×C8—132no—
182#389—262no—
183#389—262no—
184#389—262no—
185#389—262no—
186#384—131no—
187#384—131no—
188#384—131no—
189#384C2×D1311yescharacteristic
190#382—132no—
191#382—131no—
192#382C2×D1311yescharacteristic
193C43—131no—
194C22×C13C2×#12711yescharacteristic
195C22×C13C2×C4⋊Q811yescharacteristic
196C22×C13C2×C4⋊Q811yescharacteristic
197C22×C13#57512yes—
198C22×C13#57512yes—
199C4×C13—24no—
200C4×C13—81no—
201C4×C13—82no—
202C4×C13—81no—
203C4×C13C2×C4⋊Q812yes—
204C4×C13C2×C4⋊Q812yes—
205Dic13—22no—
206Dic13—22no—
207Dic13—24no—
208Dic13—81no—
209Dic13—81no—
210Dic13—82no—
211C22×C8—132no—
212C22×C8C22×D1312yes—
213#125—264no—
214#125—264no—
215#125—264no—
216#125—264no—
217C2×C4⋊C4—22no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—132no—
220C2×C4⋊C4—131no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—262no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4—262no—
227C2×C4⋊C4—262no—
228C2×C4⋊C4—262no—
229C2×C4⋊C4—262no—
230C2×C4⋊C4C22×D1312yes—
231C2×C4⋊C4C22×D1311yescharacteristic
232C2×C4⋊C4C22×D1311yescharacteristic
233C2×C42—131no—
234C2×C42—131no—
235C2×C42—132no—
236C2×C42—132no—
237C2×C42C22×D1311yescharacteristic
238#107—24no—
239#107—264no—
240#107—264no—
241#107—264no—
242#106—24no—
243#106—264no—
244#106—264no—
245#106—264no—
246#97—138no—
247#97—134no—
248#97Dic2614yes—
249C4×C8—138no—
250#95—22no—
251#95—264no—
252#95—262no—
253C2×C13#286811yescharacteristic
254C2×C13#315011yescharacteristic
255C2×C13#315011yescharacteristic
256C2×C13#316612yes—
257C2×C13#316612yes—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—22no—
261C22×C4—132no—
262C22×C4—131no—
263C22×C4—131no—
264C22×C4—261no—
265C22×C4—262no—
266C22×C4—261no—
267C22×C4D4×D1312yes—
268C22×C4C23×D1311yescharacteristic
269C2×C8—134no—
270C2×C8—134no—
271C2×C8—134no—
272C2×C8C2×Dic2614yes—
273C2×C8D4×D1314yes—
274C2×C8Q8×D1314yes—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—22no—
279C4⋊C4—44no—
280C4⋊C4—262no—
281C4⋊C4—262no—
282C4⋊C4—262no—
283C4⋊C4—262no—
284C4⋊C4—524no—
285C4⋊C4—524no—
286C4⋊C4—522no—
287C4⋊C4—522no—
288C4⋊C4—524no—
289C4⋊C4—522no—
290C4⋊C4—522no—
291C4⋊C4—524no—
292C4⋊C4—524no—
293C42—134no—
294C42—134no—
295C42—522no—
296C42—522no—
297C42C2×Dic2612yes—
298C42Q8×D1312yes—
299C13#3331511yescharacteristic, complemented, Sylow
300C23C2×D4×D1311yescharacteristic
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—134no—
310C2×C4—132no—
311C2×C4—132no—
312C2×C4—262no—
313C2×C4—262no—
314C2×C4—262no—
315C2×C4—262no—
316C2×C4—522no—
317C2×C4—524no—
318C2×C4—522no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—522no—
322C2×C4#8814214yes—
323C2×C4C22×Dic2611yescharacteristic
324C2×C4C2×D4×D1312yes—
325C2×C4C2×Q8×D1311yescharacteristic
326C2×C4C2×Q8×D1312yes—
327C8—138no—
328C8#8814218yes—
329C22C2×#8814211yescharacteristic
330C22D13×#12711yescharacteristic
331C22D13×C4⋊Q811yescharacteristic
332C22#1171947812yes—
333C22#1171948212yes—
334C4—24no—
335C4—82no—
336C4—81no—
337C4—81no—
338C4—264no—
339C4—262no—
340C4—262no—
341C4—1041no—
342C4—1041no—
343C4—1042no—
344C4C2×#8814212yes—
345C4D13×C4⋊Q812yes—
346C2#1312323311yescharacteristic
347C2#1312527811yescharacteristic
348C2#1312528011yescharacteristic
349C2#1312538612yes—
350C2#1312538712yes—
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1847C2
socle, prime radicalC23×C13C22×D4
hypercenter#1847D13
hypocenterC13#33315
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
299. C13#33315semidirect

Maximal subgroups

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

subgroupindex
C2×#117185392
C2×#117185192
#131231982
#131231972
#131150052
#131150042
#131150032
#131150022
#131150012
#97×Dic132
C13×#18472
#3331513