Finite Group Databasebeta

← #15848271

Subgroups — #15848271

Order 3328.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125959C211yesmaximal, characteristic
2#13124308C211yesmaximal, characteristic
3C2×#11718692C211yesmaximal, characteristic, complemented
4#13114280C214yesmaximal, complemented
5#13114230C214yesmaximal, complemented
6#13113611C211yesmaximal, characteristic, complemented
7#13113507C211yesmaximal, characteristic, complemented
8#13113483C211yesmaximal, characteristic
9C13×#2982C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C13C2211yescharacteristic
11C22×#6107—21no—
12C2×#88196—21no—
13#11719182C2211yescharacteristic
14C2×#88123C2211yescharacteristic
15C8×Q8×C13—22no—
16C8×Q8×C13C2214yes—
17C13×#431—22no—
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718692—22no—
21#11718692C2212yes—
22#11718692C2214yes—
23#11718689—22no—
24#11718688C2212yes—
25C2×#88050—21no—
26#11718627—21no—
27#11718585C2211yescharacteristic
28C2×C4⋊#1055C2211yescharacteristic
29#11718507—22no—
30#11718397—22no—
31#11718355C2212yes—
32#11718343C2212yes—
33#11718078C2212yes—
34#11718078C2214yes—
35#11718077C2212yes—
36#11718050C2214yes—
37C22×Q8×C13D411yescharacteristic
38C2×#6127—21no—
39C22×Dic26—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13D412yes—
43C4×Q8×C13C2312yes—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4D411yescharacteristic
46C2×C42×C13—21no—
47C2×C42×C13C2311yescharacteristic
48C2×#6107—22no—
49C2×#6107—24no—
50C2×#6107—44no—
51#88196—44no—
52C2×#6106—22no—
53#88184—21no—
54#88184—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C2×#6099—21no—
58C22×#1055—21no—
59#88129—21no—
60#88128C2311yescharacteristic
61C4×D52—21no—
62C4×D52—21no—
63#88123—21no—
64#88123—21no—
65#88123—21no—
66#88123C2312yes—
67#88123C2311yescharacteristic
68C13×C4⋊C8—24no—
69C13×C4⋊C8D412yes—
70C13×C4⋊C8C2312yes—
71C13×C22⋊C8—21no—
72C13×C22⋊C8D412yes—
73C4×C8×C13—24no—
74C4×C8×C13—21no—
75C4×C8×C13C2312yes—
76#88061—24no—
77#88058—24no—
78#88050—22no—
79#88050—24no—
80#88049—22no—
81C4⋊#1055—21no—
82C4⋊#1055—21no—
83C4⋊#1055C2312yes—
84C4⋊#1055C2312yes—
85#19404—131nomaximal, Sylow
86C2×Q8×C13—21no—
87C2×Q8×C13—22no—
88C2×Q8×C13D814yes—
89C2×Q8×C13C2×D412yes—
90C22×C4×C13—21no—
91C22×C4×C13—21no—
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C22×C4×C13#4111yescharacteristic
95C2×C22⋊D13—41no—
96C22×Dic13—41no—
97#6127—42no—
98#6127—42no—
99C2×D52—21no—
100C2×D52—21no—
101C2×D52—21no—
102C2×C4×D13—41no—
103C2×Dic26—22no—
104C2×Dic26—21no—
105C2×Dic26—42no—
106C2×Dic26—42no—
107C2×Dic26—41no—
108C2×C8×C13—22no—
109C2×C8×C13C2×D414yes—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—21no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4C2×D412yes—
114C42×C13—22no—
115C42×C13—22no—
116C42×C13C2×D411yescharacteristic
117C42×C13C2×D411yescharacteristic
118C42×C13#4111yescharacteristic
119C42×C13C2411yescharacteristic
120#6107—44no—
121#6107—48no—
122#6106—44no—
123#6103—41no—
124#6103—41no—
125C4⋊Dic13—22no—
126C4⋊Dic13—21no—
127C4⋊Dic13—22no—
128C4⋊Dic13—21no—
129C4⋊Dic13—41no—
130C4⋊Dic13—41no—
131#6099—42no—
132C2×#1055—22no—
133C2×#1055—22no—
134C2×#1055—42no—
135#3226—131no—
136#3037—131no—
137C2×#462—131no—
138#2982D1311yescharacteristic, complemented
139#1682—134no—
140#1674—134no—
141#1571—131no—
142#1546—131no—
143#1540—131no—
144C23×C13#12111yescharacteristic
145C22×D13—41no—
146Q8×C13—22no—
147Q8×C13—24no—
148Q8×C13C2×D814yes—
149C2×C4×C13—22no—
150C2×C4×C13—24no—
151C2×C4×C13—22no—
152C2×C4×C13—22no—
153C2×C4×C13—41no—
154C2×C4×C13—81no—
155C2×C4×C13#12111yescharacteristic
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13C2×D812yes—
159C2×C4×C13#13512yes—
160C2×C4×C13C22×D411yescharacteristic
161C2×C4×C13C22×D411yescharacteristic
162C2×C4×C13C2×#4111yescharacteristic
163C22⋊D13—82no—
164C2×Dic13—42no—
165C2×Dic13—41no—
166C2×Dic13—82no—
167D52—41no—
168D52—41no—
169D52—42no—
170D52—81no—
171C4×D13—82no—
172Dic26—42no—
173Dic26—41no—
174Dic26—42no—
175Dic26—41no—
176Dic26—82no—
177C8×C13—24no—
178C8×C13—42no—
179#1055—42no—
180#1055—42no—
181C2×#137—261no—
182C22×Q16—261no—
183#532—131no—
184C2×C4⋊Q8—131no—
185C2×C4×Q8C2×D1311yescharacteristic
186#500—132no—
187#486—132no—
188#480—262no—
189#474—262no—
190#464—262no—
191#462—132no—
192#462—134no—
193#462—262no—
194#460—132no—
195C8×Q8—22no—
196C8×Q8C2×D1314yes—
197#431—22no—
198#431C2×D1311yescharacteristic
199#431C2×D1311yescharacteristic
200#423—131no—
201C2×C4⋊C8—131no—
202#417—261no—
203C2×#103—261no—
204#335—134no—
205#332—132no—
206#332—134no—
207#331—132no—
208C22×C13—21no—
209C22×C13—21no—
210C22×C13#46612yes—
211C22×C13C2×#12111yescharacteristic
212C2×D13—81no—
213C2×D13—81no—
214C2×D13—81no—
215C4×C13—21no—
216C4×C13—24no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—42no—
220C4×C13#46612yes—
221C4×C13C22×D811yescharacteristic
222C4×C13C2×#13511yescharacteristic
223C4×C13#57812yes—
224Dic13—82no—
225Dic13—81no—
226C2×#41—261no—
227C22×Q8—261no—
228C22×Q8D5211yescharacteristic
229#137—524no—
230C2×Q16—264no—
231C2×Q16—262no—
232C2×Q16—524no—
233C2×SD16—262no—
234C2×M16—261no—
235C22×C8—261no—
236C4⋊Q8—132no—
237C4⋊Q8—131no—
238C4⋊Q8—261no—
239C4⋊Q8—261no—
240C4⋊Q8—261no—
241#127—131no—
242#124—261no—
243#121—261no—
244#121—261no—
245C4×Q8—21no—
246C4×Q8—21no—
247C4×Q8D5212yes—
248C4×Q8C22×D1312yes—
249C4×D4—261no—
250C4×D4—261no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—261no—
253C2×C4⋊C4—261no—
254C2×C4⋊C4D5211yescharacteristic
255C2×C42—21no—
256C2×C42C22×D1311yescharacteristic
257#107—264no—
258C4⋊C8—24no—
259C4⋊C8—132no—
260C4⋊C8—132no—
261C4⋊C8—261no—
262C4⋊C8—261no—
263C4⋊C8C22⋊D1312yes—
264C4⋊C8C22×D1312yes—
265#103—264no—
266#103—262no—
267#102—264no—
268#102—262no—
269C22⋊C8—21no—
270C22⋊C8C22⋊D1312yes—
271C4×C8—24no—
272C4×C8—21no—
273C4×C8C22×D1312yes—
274C2×C13—22no—
275C2×C13#304411yescharacteristic
276C2×C13C2×#46611yescharacteristic
277C2×C13#306911yescharacteristic
278D13—161no—
279#41—522no—
280#41—522no—
281C2×Q8—22no—
282C2×Q8—21no—
283C2×Q8—261no—
284C2×Q8—262no—
285C2×Q8—521no—
286C2×Q8—522no—
287C2×Q8—522no—
288C2×Q8D10414yes—
289C2×Q8C2×D5212yes—
290C2×D4—261no—
291C2×D4—261no—
292C2×D4—261no—
293C2×D4—521no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—521no—
297C22×C4—521no—
298C22×C4C2×D5211yescharacteristic
299C22×C4#612711yescharacteristic
300C22×C4C2×C22⋊D1311yescharacteristic
301Q16—528no—
302Q16—524no—
303SD16—524no—
304M16—522no—
305C2×C8—22no—
306C2×C8—262no—
307C2×C8—262no—
308C2×C8—522no—
309C2×C8C2×C22⋊D1314yes—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—262no—
314C4⋊C4—261no—
315C4⋊C4—262no—
316C4⋊C4—261no—
317C4⋊C4—521no—
318C4⋊C4—521no—
319C4⋊C4C2×D5212yes—
320C22⋊C4—521no—
321C22⋊C4—521no—
322C42—22no—
323C42—22no—
324C42C2×D5211yescharacteristic
325C42#612711yescharacteristic
326C42C2×C22⋊D1311yescharacteristic
327C42C23×D1311yescharacteristic
328C13#1940411yescharacteristic, complemented, Sylow
329C23—521no—
330C23#8818411yescharacteristic
331Q8—22no—
332Q8—24no—
333Q8—522no—
334Q8—521no—
335Q8—522no—
336Q8—521no—
337Q8—1042no—
338Q8C2×D10414yes—
339D4—521no—
340D4—521no—
341D4—522no—
342D4—1041no—
343D4—1042no—
344C2×C4—22no—
345C2×C4—24no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—521no—
351C2×C4—522no—
352C2×C4—1042no—
353C2×C4—1042no—
354C2×C4C2×D10412yes—
355C2×C4#8815812yes—
356C2×C4#8818411yescharacteristic
357C2×C4#8818411yescharacteristic
358C2×C4#8818411yescharacteristic
359C2×C4C22×D5211yescharacteristic
360C2×C4C2×#612711yescharacteristic
361C2×C4C22×C22⋊D1311yescharacteristic
362C8—24no—
363C8—42no—
364C8—522no—
365C8—522no—
366C22—21no—
367C22—21no—
368C22—1041no—
369C22—1041no—
370C22—1041no—
371C22#1171877612yes—
372C22C2×#8818411yescharacteristic
373C4—21no—
374C4—24no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—1041no—
379C4—1042no—
380C4#1171877612yes—
381C4C22×D10411yescharacteristic
382C4C2×#8815811yescharacteristic
383C4#1171954312yes—
384C2—22no—
385C2—2081no—
386C2#1312436611yescharacteristic
387C2C2×#1171877611yescharacteristic
388C2#1312457311yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2982C2
socleC22×C13C2×#121
prime radical#11719182C22
hypercenter#2982D13
hypocenterC13#19404
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2982

Complements

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

NH ≅ G/Ntype
3. C2×#11718692C2semidirect
4. #13114280C2semidirect
5. #13114230C2semidirect
6. #13113611C2semidirect
7. #13113507C2semidirect
9. C13×#2982C2semidirect
138. #2982D13semidirect
328. C13#19404semidirect

Maximal subgroups

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

subgroupindex
#131259592
#131243082
C2×#117186922
#131142802
#131142302
#131136112
#131135072
#131134832
C13×#29822
#1940413