Finite Group Databasebeta

← #15848262

Subgroups — #15848262

Order 3328.

644 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125966C211yesmaximal, characteristic
2C2×#11718682C211yesmaximal, characteristic, complemented
3#13124308C211yesmaximal, characteristic
4#13114252C214yesmaximal, complemented
5#13114218C214yesmaximal, complemented
6#13113607C211yesmaximal, characteristic, complemented
7#13113516C211yesmaximal, characteristic, complemented
8#13113483C211yesmaximal, characteristic
9C13×#2982C211yesmaximal, characteristic, complemented
10C2×C4×Q8×C13C2211yescharacteristic
11C2×#88196—21no—
12#11719182C2211yescharacteristic
13C2×#88123C2211yescharacteristic
14C8×Q8×C13—22no—
15C8×Q8×C13C2214yes—
16C13×#431—22no—
17C13×#431C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C2×#88075—21no—
20#11718692C2212yes—
21#11718689—22no—
22#11718688C2212yes—
23#11718682—22no—
24#11718682C2214yes—
25#11718627—21no—
26C2×#88047—21no—
27#11718585C2211yescharacteristic
28C2×C4⋊#1055C2211yescharacteristic
29#11718503—22no—
30#11718396—22no—
31#11718355C2212yes—
32#11718341C2212yes—
33#11718078C2212yes—
34#11718077C2212yes—
35#11718073C2214yes—
36#11718049C2214yes—
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—
49#88196—44no—
50C2×#6106—22no—
51#88184—21no—
52#88184—21no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×#6099—21no—
56C22×#1055—21no—
57#88129—21no—
58#88128C2311yescharacteristic
59C4×D52—21no—
60C4×D52—21no—
61#88123—21no—
62#88123—21no—
63#88123—21no—
64#88123C2312yes—
65#88123C2311yescharacteristic
66C13×C4⋊C8—24no—
67C13×C4⋊C8D412yes—
68C13×C4⋊C8C2312yes—
69C13×C22⋊C8—21no—
70C13×C22⋊C8D412yes—
71C4×C8×C13—24no—
72C4×C8×C13—21no—
73C4×C8×C13C2312yes—
74#88075—24no—
75#88061—24no—
76#88057—24no—
77#88050—22no—
78#88049—22no—
79#88047—24no—
80C4⋊#1055—21no—
81C4⋊#1055—21no—
82C4⋊#1055C2312yes—
83C4⋊#1055C2312yes—
84#19403—131nomaximal, Sylow
85C2×Q8×C13—21no—
86C2×Q8×C13—22no—
87C2×Q8×C13SD1614yes—
88C2×Q8×C13C2×D412yes—
89C22×C4×C13—21no—
90C22×C4×C13—21no—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D411yescharacteristic
93C22×C4×C13#4111yescharacteristic
94C2×C22⋊D13—41no—
95C22×Dic13—41no—
96#6127—42no—
97#6127—42no—
98C2×D52—21no—
99C2×D52—21no—
100C2×D52—21no—
101C2×C4×D13—41no—
102C2×Dic26—21no—
103C2×Dic26—22no—
104C2×Dic26—41no—
105C2×Dic26—82no—
106C2×C8×C13—22no—
107C2×C8×C13C2×D414yes—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4C2×D412yes—
112C42×C13—22no—
113C42×C13—22no—
114C42×C13C2×D411yescharacteristic
115C42×C13C2×D411yescharacteristic
116C42×C13#4111yescharacteristic
117C42×C13C2411yescharacteristic
118#6107—44no—
119#6106—44no—
120#6103—41no—
121#6103—41no—
122C4⋊Dic13—22no—
123C4⋊Dic13—22no—
124C4⋊Dic13—21no—
125C4⋊Dic13—21no—
126C4⋊Dic13—41no—
127C4⋊Dic13—41no—
128#6099—42no—
129C2×#1055—22no—
130C2×#1055—22no—
131C2×#1055—42no—
132#3227—131no—
133C2×#477—131no—
134#3037—131no—
135#2982D1311yescharacteristic, complemented
136#1678—134no—
137#1672—134no—
138#1570—131no—
139#1548—131no—
140#1540—131no—
141C23×C13#12111yescharacteristic
142C22×D13—41no—
143Q8×C13—22no—
144Q8×C13—24no—
145Q8×C13C2×SD1614yes—
146C2×C4×C13—22no—
147C2×C4×C13—24no—
148C2×C4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—41no—
151C2×C4×C13—81no—
152C2×C4×C13#12111yescharacteristic
153C2×C4×C13#12111yescharacteristic
154C2×C4×C13#12111yescharacteristic
155C2×C4×C13C2×SD1612yes—
156C2×C4×C13#13512yes—
157C2×C4×C13C22×D411yescharacteristic
158C2×C4×C13C22×D411yescharacteristic
159C2×C4×C13C2×#4111yescharacteristic
160C22⋊D13—82no—
161C2×Dic13—42no—
162C2×Dic13—41no—
163C2×Dic13—82no—
164D52—41no—
165D52—41no—
166D52—42no—
167D52—81no—
168C4×D13—82no—
169Dic26—41no—
170Dic26—41no—
171Dic26—82no—
172Dic26—82no—
173C8×C13—24no—
174C8×C13—42no—
175#1055—42no—
176#1055—42no—
177C2×#137—261no—
178#532—131no—
179C2×C4⋊Q8—131no—
180C2×C4×Q8C2×D1311yescharacteristic
181#498—132no—
182#486—132no—
183#481—262no—
184#477—134no—
185#477—262no—
186#476—262no—
187#464—262no—
188#462—132no—
189#460—132no—
190C8×Q8—22no—
191C8×Q8C2×D1314yes—
192#431—22no—
193#431C2×D1311yescharacteristic
194#431C2×D1311yescharacteristic
195C2×#107—261no—
196#423—131no—
197C2×C4⋊C8—131no—
198#417—261no—
199C2×#103—261no—
200#334—134no—
201#333—134no—
202#332—132no—
203#331—132no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13#46512yes—
207C22×C13C2×#12111yescharacteristic
208C2×D13—81no—
209C2×D13—81no—
210C2×D13—81no—
211C4×C13—21no—
212C4×C13—24no—
213C4×C13—21no—
214C4×C13—21no—
215C4×C13—42no—
216C4×C13#46512yes—
217C4×C13C22×SD1611yescharacteristic
218C4×C13C2×#13511yescharacteristic
219C4×C13#57812yes—
220Dic13—81no—
221Dic13—82no—
222C2×#41—261no—
223C22×Q8—261no—
224C22×Q8D5211yescharacteristic
225#137—524no—
226C2×Q16—262no—
227C2×SD16—262no—
228C2×M16—261no—
229C22×C8—261no—
230C4⋊Q8—132no—
231C4⋊Q8—131no—
232C4⋊Q8—261no—
233C4⋊Q8—261no—
234C4⋊Q8—261no—
235#127—131no—
236#124—261no—
237#121—261no—
238#121—261no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8D5212yes—
242C4×Q8C22×D1312yes—
243C4×D4—261no—
244C4×D4—261no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—261no—
247C2×C4⋊C4—261no—
248C2×C4⋊C4D5211yescharacteristic
249C2×C42—21no—
250C2×C42C22×D1311yescharacteristic
251#107—264no—
252#106—264no—
253C4⋊C8—24no—
254C4⋊C8—132no—
255C4⋊C8—132no—
256C4⋊C8—261no—
257C4⋊C8—261no—
258C4⋊C8C22⋊D1312yes—
259C4⋊C8C22×D1312yes—
260#103—264no—
261#103—262no—
262#102—264no—
263#102—262no—
264C22⋊C8—21no—
265C22⋊C8C22⋊D1312yes—
266C4×C8—24no—
267C4×C8—21no—
268C4×C8C22×D1312yes—
269C2×C13—22no—
270C2×C13#304411yescharacteristic
271C2×C13C2×#46511yescharacteristic
272C2×C13#306811yescharacteristic
273D13—161no—
274#41—522no—
275#41—522no—
276C2×Q8—22no—
277C2×Q8—21no—
278C2×Q8—261no—
279C2×Q8—262no—
280C2×Q8—521no—
281C2×Q8—1042no—
282C2×Q8#609514yes—
283C2×Q8C2×D5212yes—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—521no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—521no—
291C22×C4—521no—
292C22×C4C2×D5211yescharacteristic
293C22×C4#612711yescharacteristic
294C22×C4C2×C22⋊D1311yescharacteristic
295Q16—524no—
296SD16—524no—
297M16—522no—
298C2×C8—22no—
299C2×C8—262no—
300C2×C8—262no—
301C2×C8—522no—
302C2×C8C2×C22⋊D1314yes—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—262no—
307C4⋊C4—261no—
308C4⋊C4—262no—
309C4⋊C4—261no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C4⋊C4C2×D5212yes—
313C22⋊C4—521no—
314C22⋊C4—521no—
315C42—22no—
316C42—22no—
317C42C2×D5211yescharacteristic
318C42#612711yescharacteristic
319C42C2×C22⋊D1311yescharacteristic
320C42C23×D1311yescharacteristic
321C13#1940311yescharacteristic, complemented, Sylow
322C23—521no—
323C23#8818411yescharacteristic
324Q8—22no—
325Q8—24no—
326Q8—521no—
327Q8—521no—
328Q8—1042no—
329Q8—1042no—
330Q8C2×#609514yes—
331D4—521no—
332D4—521no—
333D4—522no—
334D4—1041no—
335D4—1042no—
336C2×C4—22no—
337C2×C4—24no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—81no—
342C2×C4—521no—
343C2×C4—522no—
344C2×C4—1042no—
345C2×C4—1042no—
346C2×C4C2×#609512yes—
347C2×C4#8815812yes—
348C2×C4#8818411yescharacteristic
349C2×C4#8818411yescharacteristic
350C2×C4#8818411yescharacteristic
351C2×C4C22×D5211yescharacteristic
352C2×C4C2×#612711yescharacteristic
353C2×C4C22×C22⋊D1311yescharacteristic
354C8—24no—
355C8—42no—
356C8—522no—
357C8—522no—
358C22—21no—
359C22—21no—
360C22—1041no—
361C22—1041no—
362C22—1041no—
363C22#1171877512yes—
364C22C2×#8818411yescharacteristic
365C4—21no—
366C4—24no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—1041no—
371C4—1042no—
372C4#1171877512yes—
373C4C22×#609511yescharacteristic
374C4C2×#8815811yescharacteristic
375C4#1171954312yes—
376C2—22no—
377C2—2081no—
378C2#1312436611yescharacteristic
379C2C2×#1171877511yescharacteristic
380C2#1312456411yescharacteristic
subgroupG/H
centerC22C2×#88184
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#2982C2
socleC22×C13C2×#121
prime radical#11719182C22
hypercenter#2982D13
hypocenterC13#19403
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
2. C2×#11718682C2semidirect
4. #13114252C2semidirect
5. #13114218C2semidirect
6. #13113607C2semidirect
7. #13113516C2semidirect
9. C13×#2982C2semidirect
135. #2982D13semidirect
321. C13#19403semidirect

Maximal subgroups

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

subgroupindex
#131259662
C2×#117186822
#131243082
#131142522
#131142182
#131136072
#131135162
#131134832
C13×#29822
#1940313