Finite Group Databasebeta

← #15848259

Subgroups — #15848259

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#13125964C211yesmaximal, characteristic
2#13124308C211yesmaximal, characteristic
3#13123917C211yesmaximal, characteristic, complemented
4#13114254C214yesmaximal, complemented
5#13114220C214yesmaximal, complemented
6#13113606C211yesmaximal, characteristic, complemented
7#13113517C211yesmaximal, characteristic, complemented
8#13113486C211yesmaximal, characteristic
9C2×C13×#477C211yesmaximal, characteristic, complemented
10C2×C13×C4⋊Q8C2211yescharacteristic
11C2×C4×Q8×C13C2211yescharacteristic
12C2×#88196—21no—
13#11719182C2211yescharacteristic
14C13×#477—22no—
15C13×#477C2214yes—
16C2×C13×#107—21no—
17C2×C13×C4⋊C8C2211yescharacteristic
18C2×C13×#103—21no—
19#11718749C2212yes—
20#11718745—22no—
21#11718740C2212yes—
22#11718692C2212yes—
23#11718689—22no—
24#11718688C2212yes—
25Q8×#1055—22no—
26Q8×#1055C2214yes—
27#11718629—22no—
28#11718627—21no—
29#11718586—22no—
30#11718586C2211yescharacteristic
31#11718586C2211yescharacteristic
32#11718585C2211yescharacteristic
33#11718138C2214yes—
34#11718077C2212yes—
35#11718074C2212yes—
36#11718072C2214yes—
37C22×Q8×C13—21no—
38C22×Q8×C13D411yescharacteristic
39C2×#6127—21no—
40C22×C8×C13—21no—
41C13×C4⋊Q8—21no—
42C13×C4⋊Q8—21no—
43C13×C4⋊Q8—21no—
44C13×C4⋊Q8C2312yes—
45C4×Q8×C13—21no—
46C4×Q8×C13—21no—
47C4×Q8×C13D412yes—
48C4×Q8×C13C2312yes—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4D411yescharacteristic
53C2×C42×C13—21no—
54C2×C42×C13C2311yescharacteristic
55C2×#6107—22no—
56#88196—44no—
57C2×#6106—22no—
58#88184—21no—
59#88184—21no—
60C2×#6099—21no—
61#88129—21no—
62#88128C2311yescharacteristic
63C4×D52—21no—
64C4×D52—21no—
65#88123C2311yescharacteristic
66C13×#107—24no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8C2312yes—
69C13×#103—24no—
70C22⋊#1055—21no—
71C22⋊#1055D412yes—
72#88050—22no—
73#88049—22no—
74#88049—24no—
75#88048—24no—
76C4⋊#1055—21no—
77C4⋊#1055—24no—
78C4⋊#1055D412yes—
79C4⋊#1055C2312yes—
80C4⋊#1055C2312yes—
81C4×#1055—21no—
82C4×#1055—24no—
83C4×#1055C2312yes—
84#19403—131nomaximal, Sylow
85C2×Q8×C13—21no—
86C2×Q8×C13—22no—
87C2×Q8×C13—22no—
88C2×Q8×C13—41no—
89C2×Q8×C13—82no—
90C2×Q8×C13SD1614yes—
91C2×Q8×C13C2×D412yes—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—41no—
95C22×C4×C13C2×D411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C2×C22⋊D13—41no—
99#6127—42no—
100#6127—42no—
101C2×D52—21no—
102C2×D52—21no—
103C2×D52—21no—
104C2×C4×D13—41no—
105C2×Dic26—21no—
106C2×C8×C13—22no—
107C2×C8×C13—42no—
108C13×C4⋊C4—22no—
109C13×C4⋊C4—21no—
110C13×C4⋊C4—22no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—22no—
113C13×C4⋊C4—41no—
114C13×C4⋊C4—41no—
115C13×C4⋊C4C2×D412yes—
116C42×C13—22no—
117C42×C13—22no—
118C42×C13C2×D411yescharacteristic
119C42×C13C2×D411yescharacteristic
120C42×C13#4111yescharacteristic
121C42×C13C2411yescharacteristic
122#6107—44no—
123#6106—44no—
124#6103—41no—
125#6103—41no—
126C4⋊Dic13—21no—
127C4⋊Dic13—21no—
128#6099—42no—
129C2×#1055—22no—
130C2×#1055—22no—
131C2×#1055C2×D414yes—
132#3227—131no—
133C2×#477D1311yescharacteristic, complemented
134#3037—131no—
135#2982—131no—
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×C13—82no—
146Q8×C13—82no—
147Q8×C13C2×SD1614yes—
148C2×C4×C13—22no—
149C2×C4×C13—24no—
150C2×C4×C13—22no—
151C2×C4×C13—22no—
152C2×C4×C13—41no—
153C2×C4×C13—42no—
154C2×C4×C13—81no—
155C2×C4×C13—82no—
156C2×C4×C13#12111yescharacteristic
157C2×C4×C13#12111yescharacteristic
158C2×C4×C13#12111yescharacteristic
159C2×C4×C13C2×SD1612yes—
160C2×C4×C13#13512yes—
161C2×C4×C13C22×D411yescharacteristic
162C2×C4×C13C22×D411yescharacteristic
163C2×C4×C13C2×#4111yescharacteristic
164C22⋊D13—82no—
165C2×Dic13—41no—
166D52—41no—
167D52—41no—
168D52—42no—
169D52—81no—
170C4×D13—82no—
171Dic26—41no—
172Dic26—41no—
173C8×C13—42no—
174#1055—24no—
175#1055—42no—
176#1055—42no—
177C2×#137—261no—
178#532—131no—
179C2×C4⋊Q8C2×D1311yescharacteristic
180C2×C4×Q8C2×D1311yescharacteristic
181#498—132no—
182#486—132no—
183#481—262no—
184#477—22no—
185#477C2×D1314yes—
186#476—262no—
187#464—262no—
188#462—132no—
189#460—132no—
190C8×Q8—134no—
191C8×Q8—262no—
192#431—131no—
193#431—131no—
194#431—262no—
195C2×#107—21no—
196#423—131no—
197C2×C4⋊C8C2×D1311yescharacteristic
198#417—261no—
199C2×#103—21no—
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—82no—
217C4×C13#46512yes—
218C4×C13C22×SD1611yescharacteristic
219C4×C13C2×#13511yescharacteristic
220C4×C13#57812yes—
221Dic13—81no—
222C2×#41—261no—
223C22×Q8—21no—
224C22×Q8C22⋊D1311yescharacteristic
225#137—524no—
226C2×Q16—262no—
227C2×SD16—262no—
228C2×M16—261no—
229C22×C8—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—131no—
234C4⋊Q8C22×D1312yes—
235#127—131no—
236#124—261no—
237#121—261no—
238#121—261no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×Q8C22⋊D1312yes—
242C4×Q8C22×D1312yes—
243C4×D4—261no—
244C4×D4—261no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4C22⋊D1311yescharacteristic
249C2×C42—21no—
250C2×C42C22×D1311yescharacteristic
251#107—24no—
252#106—264no—
253C4⋊C8—21no—
254C4⋊C8—132no—
255C4⋊C8—132no—
256C4⋊C8—132no—
257C4⋊C8—264no—
258C4⋊C8—261no—
259C4⋊C8C22×D1312yes—
260#103—24no—
261#103—262no—
262#102—264no—
263#102—262no—
264C22⋊C8—132no—
265C22⋊C8—261no—
266C4×C8—132no—
267C4×C8—264no—
268C4×C8—261no—
269C2×C13—22no—
270C2×C13#304411yescharacteristic
271C2×C13C2×#46511yescharacteristic
272C2×C13#306811yescharacteristic
273D13—161no—
274#41—522no—
275#41—522no—
276C2×Q8—21no—
277C2×Q8—22no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—82no—
281C2×Q8—261no—
282C2×Q8#610614yes—
283C2×Q8C2×C22⋊D1312yes—
284C2×D4—261no—
285C2×D4—261no—
286C2×D4—261no—
287C2×D4—521no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—41no—
291C22×C4—521no—
292C22×C4D4×D1311yescharacteristic
293C22×C4#612911yescharacteristic
294C22×C4C2×C22⋊D1311yescharacteristic
295Q16—524no—
296SD16—524no—
297M16—522no—
298C2×C8—22no—
299C2×C8—42no—
300C2×C8—134no—
301C2×C8—262no—
302C2×C8—262no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—22no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—261no—
311C4⋊C4—261no—
312C4⋊C4C2×C22⋊D1312yes—
313C22⋊C4—521no—
314C22⋊C4—521no—
315C42—22no—
316C42—22no—
317C42D4×D1311yescharacteristic
318C42#612911yescharacteristic
319C42C2×C22⋊D1311yescharacteristic
320C42C23×D1311yescharacteristic
321C13#1940311yescharacteristic, complemented, Sylow
322C23—521no—
323C23#8819311yescharacteristic
324Q8—24no—
325Q8—22no—
326Q8—82no—
327Q8—82no—
328Q8—521no—
329Q8—521no—
330Q8C2×#610614yes—
331D4—522no—
332D4—521no—
333D4—521no—
334D4—1041no—
335D4—1042no—
336C2×C4—24no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—82no—
344C2×C4—521no—
345C2×C4—1042no—
346C2×C4#8819311yescharacteristic
347C2×C4#8819311yescharacteristic
348C2×C4#8819311yescharacteristic
349C2×C4C2×#610612yes—
350C2×C4#8820412yes—
351C2×C4C2×D4×D1311yescharacteristic
352C2×C4C2×#612911yescharacteristic
353C2×C4C22×C22⋊D1311yescharacteristic
354C8—42no—
355C8—264no—
356C8—522no—
357C8—522no—
358C22—21no—
359C22—21no—
360C22—1041no—
361C22—1041no—
362C22—1041no—
363C22#1171870912yes—
364C22C2×#8819311yescharacteristic
365C4—21no—
366C4—24no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—82no—
371C4—1041no—
372C4#1171870912yes—
373C4#1171947112yes—
374C4C22×#610611yescharacteristic
375C4C2×#8820411yescharacteristic
376C2—22no—
377C2—2081no—
378C2#1312436311yescharacteristic
379C2C2×#1171870911yescharacteristic
380C2#1312456111yescharacteristic
subgroupG/H
centerC22C2×#88193
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#477C2
socleC22×C13C2×#121
prime radical#11719182C22
hypercenterC2×#477D13
hypocenterC13#19403
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13123917C2semidirect
4. #13114254C2semidirect
5. #13114220C2semidirect
6. #13113606C2semidirect
7. #13113517C2semidirect
9. C2×C13×#477C2semidirect
133. C2×#477D13semidirect
321. C13#19403semidirect

Maximal subgroups

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

subgroupindex
#131259642
#131243082
#131239172
#131142542
#131142202
#131136062
#131135172
#131134862
C2×C13×#4772
#1940313