Finite Group Databasebeta

← #15836842

Subgroups — #15836842

Order 3328.

940 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125608C212yesmaximal
2#13120649C211yesmaximal, characteristic
3#13113878C214yesmaximal, complemented
4#13113810C214yesmaximal, complemented
5#13113408C212yesmaximal
6C2×#11718120C211yesmaximal, characteristic
7C2×C13×#544C211yesmaximal, characteristic
8C13×#544—24no—
9C13×#544—22no—
10C13×#544C2214yes—
11C2×C13×C4⋊Q8—22no—
12C2×C13×#125—22no—
13C2×C13×C22⋊Q8—21no—
14C2×C13×C22⋊Q8C2212yes—
15C2×C13×#117—21no—
16C22×C13×C4⋊C4C2211yescharacteristic
17C2×#88178C2211yescharacteristic
18#11718889—22no—
19#11718873C2211yescharacteristic
20#11718872—21no—
21#11718871—21no—
22C2×C22⋊#1055C2212yes—
23#11718712—24no—
24#11718711C2214yes—
25#11718705C2214yes—
26#11718647C2212yes—
27#11718645—22no—
28#11718640C2212yes—
29#11718631—22no—
30#11718130C2218yes—
31#11718120C2214yes—
32C22×Q8×C13—21no—
33C22×Q8×C13D412yes—
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C22×Dic26C2311yescharacteristic
38C13×C4⋊Q8—28no—
39C13×C4⋊Q8—28no—
40C13×#125—28no—
41C13×#125—28no—
42C13×C22⋊Q8—24no—
43C13×C22⋊Q8—24no—
44C13×C22⋊Q8—22no—
45C13×C22⋊Q8—22no—
46C13×C22⋊Q8D414yes—
47C13×C22⋊Q8C2314yes—
48C13×#117—24no—
49C13×#117—24no—
50C2×C13×C4⋊C4—21no—
51C2×C13×C4⋊C4—21no—
52C2×C13×C4⋊C4—21no—
53C2×C13×C4⋊C4—22no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—22no—
56C2×C13×C4⋊C4—22no—
57C2×C13×C4⋊C4D412yes—
58C2×C13×C4⋊C4D412yes—
59C2×C13×C4⋊C4C2312yes—
60C2×C13×C22⋊C4—22no—
61C2×C42×C13—22no—
62C2×C22⋊Dic13—21no—
63C2×C22⋊Dic13—21no—
64C2×#6107—24no—
65C2×C4⋊Dic13—21no—
66C2×C4⋊Dic13C2311yescharacteristic
67#88178—22no—
68#88178—22no—
69C2×#6101—21no—
70C2×#6101—22no—
71C22×#1055—22no—
72#88075—24no—
73#88071—22no—
74#88071—22no—
75#88071—22no—
76#88071C2312yes—
77C22⋊#1055—22no—
78C22⋊#1055C2314yes—
79#88050—24no—
80#88047—24no—
81#18295—131nomaximal, Sylow
82C24×C13C2×D411yescharacteristic
83C2×Q8×C13—24no—
84C2×Q8×C13—22no—
85C2×Q8×C13—82no—
86C2×Q8×C13—82no—
87C2×Q8×C13C2×D414yes—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—22no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—81no—
96C22×C4×C13—81no—
97C22×C4×C13Q1614yescomplemented
98C22×C4×C13C2×D412yes—
99C22×C4×C13C2×D412yes—
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D412yes—
102C22×C4×C13C2×D412yes—
103C22×C4×C13C2411yescharacteristic
104C22×Dic13—21no—
105C22×Dic13—22no—
106C22×Dic13—21no—
107C2×Dic26—22no—
108C2×Dic26—81no—
109C13×C4⋊C4—24no—
110C13×C4⋊C4—24no—
111C13×C4⋊C4—24no—
112C13×C4⋊C4—28no—
113C13×C4⋊C4—24no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4—24no—
118C13×C4⋊C4C2×D414yes—
119C13×C22⋊C4—24no—
120C13×C22⋊C4—24no—
121C42×C13—28no—
122C22⋊Dic13—41no—
123C22⋊Dic13—41no—
124C22⋊Dic13—42no—
125#6107—84no—
126C4⋊Dic13—22no—
127C4⋊Dic13—81no—
128#6101—42no—
129#6101—82no—
130C2×#1055—24no—
131C2×#1055—82no—
132C2×#544D1311yescharacteristic
133#3189—132no—
134#2627—131no—
135#1617—134no—
136#1605—134no—
137#1520—132no—
138C2×#324—131no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13#12011yescharacteristic
142C23×C13#12011yescharacteristic
143C23×C13C2×Q1612yes—
144C23×C13#13712yes—
145C23×C13C22×D411yescharacteristic
146Q8×C13—44no—
147Q8×C13—82no—
148Q8×C13—84no—
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13—24no—
152C2×C4×C13—24no—
153C2×C4×C13—24no—
154C2×C4×C13—24no—
155C2×C4×C13—22no—
156C2×C4×C13—42no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—42no—
160C2×C4×C13—44no—
161C2×C4×C13—42no—
162C2×C4×C13—44no—
163C2×C4×C13—42no—
164C2×C4×C13—81no—
165C2×C4×C13#12012yes—
166C2×C4×C13C2×Q1614yes—
167C2×C4×C13C22×D412yes—
168C2×Dic13—42no—
169C2×Dic13—42no—
170C2×Dic13—42no—
171C2×Dic13—42no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174C2×Dic13—42no—
175Dic26—44no—
176#1055—44no—
177#544—24no—
178#544—22no—
179#544C2×D1314yes—
180C2×C4⋊Q8—22no—
181C2×#125—22no—
182C2×C22⋊Q8—21no—
183C2×C22⋊Q8—131no—
184C2×C22⋊Q8C2×D1312yes—
185C2×#117—21no—
186C22×C4⋊C4C2×D1311yescharacteristic
187#484—134no—
188#484—262no—
189#467—264no—
190#451—134no—
191#451—262no—
192C2×C22⋊C8—132no—
193#400—132no—
194#398—262no—
195#395—132no—
196#385—261no—
197#381—261no—
198#380—131no—
199#328—138no—
200#324—134no—
201C22×C13—21no—
202C22×C13—21no—
203C22×C13—21no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—21no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13#45112yes—
210C22×C13#45112yes—
211C22×C13C2×#12011yescharacteristic
212C22×C13C22×Q1611yescharacteristic
213C22×C13C2×#13711yescharacteristic
214C4×C13—24no—
215C4×C13—22no—
216C4×C13—22no—
217C4×C13—44no—
218C4×C13—42no—
219C4×C13—44no—
220Dic13—82no—
221Dic13—81no—
222Dic13—81no—
223C22×Q8—21no—
224C22×Q8—131no—
225C22×Q8C22⋊D1312yes—
226C23×C4C22⋊D1311yescharacteristic
227C23×C4C22⋊D1311yescharacteristic
228C23×C4C22×D1311yescharacteristic
229C2×Q16—264no—
230C22×C8—262no—
231C4⋊Q8—28no—
232C4⋊Q8—28no—
233#125—28no—
234#125—28no—
235C22⋊Q8—24no—
236C22⋊Q8—24no—
237C22⋊Q8—22no—
238C22⋊Q8—22no—
239C22⋊Q8—262no—
240C22⋊Q8—262no—
241C22⋊Q8C22⋊D1314yes—
242C22⋊Q8C22×D1314yes—
243#117—24no—
244#117—24no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—131no—
253C2×C4⋊C4—261no—
254C2×C4⋊C4—262no—
255C2×C4⋊C4—261no—
256C2×C4⋊C4C22⋊D1312yes—
257C2×C4⋊C4C22⋊D1312yes—
258C2×C4⋊C4C22×D1312yes—
259C2×C22⋊C4—22no—
260C2×C22⋊C4—261no—
261C2×C22⋊C4—261no—
262C2×C42—22no—
263#107—264no—
264#103—264no—
265#103—264no—
266C22⋊C8—134no—
267C22⋊C8—262no—
268#95—132no—
269#95—262no—
270#95—262no—
271#95—262no—
272C2×C13—21no—
273C2×C13—21no—
274C2×C13—22no—
275C2×C13—22no—
276C2×C13C2×#45111yescharacteristic
277C2×C13#302011yescharacteristic
278C2×C13#302611yescharacteristic
279C24C2×C22⋊D1311yescharacteristic
280C2×Q8—24no—
281C2×Q8—22no—
282C2×Q8—82no—
283C2×Q8—82no—
284C2×Q8—262no—
285C2×Q8—1041no—
286C2×Q8C2×C22⋊D1314yes—
287C22×C4—22no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—81no—
295C22×C4—81no—
296C22×C4—262no—
297C22×C4—261no—
298C22×C4—261no—
299C22×C4#610714yescomplemented
300C22×C4C2×C22⋊D1312yes—
301C22×C4C2×C22⋊D1312yes—
302C22×C4C2×C22⋊D1311yescharacteristic
303C22×C4C2×C22⋊D1312yes—
304C22×C4C2×C22⋊D1312yes—
305C22×C4C23×D1311yescharacteristic
306Q16—1044no—
307C2×C8—264no—
308C2×C8—1042no—
309C4⋊C4—24no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—28no—
313C4⋊C4—24no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—24no—
318C4⋊C4—262no—
319C4⋊C4—522no—
320C4⋊C4—1042no—
321C4⋊C4—1041no—
322C4⋊C4C2×C22⋊D1314yes—
323C22⋊C4—24no—
324C22⋊C4—24no—
325C22⋊C4—522no—
326C22⋊C4—521no—
327C22⋊C4—521no—
328C42—28no—
329C13#1829511yescharacteristic, complemented, Sylow
330C23—41no—
331C23—41no—
332C23#8819612yes—
333C23C2×#610712yes—
334C23#8820711yescharacteristic
335C23#8820711yescharacteristic
336C23C22×C22⋊D1311yescharacteristic
337Q8—44no—
338Q8—82no—
339Q8—84no—
340Q8—524no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—81no—
357C2×C4—522no—
358C2×C4—522no—
359C2×C4—522no—
360C2×C4—522no—
361C2×C4—522no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4C2×#610714yes—
365C2×C4#8820712yes—
366C2×C4C22×C22⋊D1312yes—
367C8—524no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#1171888912yes—
377C22#1171888912yes—
378C22C2×#8819611yescharacteristic
379C22C22×#610711yescharacteristic
380C22C2×#8820711yescharacteristic
381C4—22no—
382C4—22no—
383C4—24no—
384C4—44no—
385C4—42no—
386C4—44no—
387C4—1042no—
388C4—1041no—
389C4—1041no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—22no—
394C2C2×#1171888911yescharacteristic
395C2#1312420011yescharacteristic
396C2#1312423311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#544C2
socleC22×C13C2×#120
prime radicalC24×C13C2×D4
hypercenterC2×#544D13
hypocenterC13#18295
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
3. #13113878C2semidirect
4. #13113810C2semidirect
97. C22×C4×C13Q16semidirect
299. C22×C4#6107semidirect
329. C13#18295semidirect

Maximal subgroups

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

subgroupindex
#131256082
#131206492
#131138782
#131138102
#131134082
C2×#117181202
C2×C13×#5442
#1829513