Finite Group Databasebeta

← #15837672

Subgroups — #15837672

Order 3328.

978 conjugacy classes of subgroups; only the 207 normal subgroups are shown.

normal subgroups only

This group has 978 conjugacy classes of subgroups — too many to draw. Only its 207 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125781C212yesmaximal, complemented
2#13120009C211yesmaximal, characteristic
3#13113793C218yesmaximal, complemented
4#13113335C212yesmaximal, complemented
5#13113157C211yesmaximal, characteristic
6C13×#3501C211yesmaximal, characteristic
7C13×#554—22no—
8C13×#554—24no—
9D4×Q8×C13—22no—
10C13×#544—21no—
11C13×#543C2214yes—
12C13×#533C2212yes—
13C2×C13×C22⋊Q8—22no—
14C13×#518—21no—
15C2×C4×D4×C13C2211yescharacteristic
16C2×#88123C2211yescharacteristic
17#11718882—21no—
18#11718873—22no—
19#11718754—22no—
20#11718753—22no—
21#11718711C2218yes—
22#11718692—24no—
23#11718638—21no—
24#11718608C2214yes—
25C4×C4⋊Dic13C2211yescharacteristic
26#11718586C2212yes—
27#11718130C2218yes—
28#11718117C2214yes—
29C22×Q8×C13—22no—
30C22×D4×C13D411yescharacteristic
31C23×C4×C13D412yes—
32C22×Dic26C2312yes—
33C13×C4⋊Q8—24no—
34C13×C4⋊Q8D412yes—
35C13×C4⋊Q8D412yes—
36C13×#125—24no—
37C13×#125—22no—
38C13×C22⋊Q8—24no—
39C13×C22⋊Q8—24no—
40C13×C22⋊Q8—28no—
41C13×C22⋊Q8—22no—
42C13×C22⋊Q8—24no—
43C13×C22⋊Q8—28no—
44C13×C22⋊Q8C2314yes—
45C4×Q8×C13—22no—
46C4×Q8×C13D414yes—
47C4×D4×C13—24no—
48C4×D4×C13—24no—
49C4×D4×C13—22no—
50C4×D4×C13—22no—
51C13×#117—22no—
52C2×C13×C4⋊C4—22no—
53C2×C13×C4⋊C4—24no—
54C2×C13×C4⋊C4D411yescharacteristic
55C2×C13×C22⋊C4—24no—
56C2×C13×C22⋊C4C2312yes—
57C2×C42×C13C2311yescharacteristic
58C2×C22⋊Dic13—24no—
59C2×#6107—28no—
60C2×C4⋊Dic13—21no—
61C2×C4⋊Dic13—21no—
62C2×C4⋊Dic13—21no—
63C2×C4×Dic13—21no—
64#88123—22no—
65#88123—22no—
66#88071—24no—
67#88071C2312yes—
68C22⋊#1055C2314yes—
69#88050—28no—
70C4⋊#1055—22no—
71C4×#1055—22no—
72#18390—131nomaximal, Sylow
73C24×C13C2×D412yes—
74C2×Q8×C13—24no—
75C2×Q8×C13—22no—
76C2×Q8×C13—84no—
77C2×Q8×C13C2×D414yes—
78C2×D4×C13—22no—
79C2×D4×C13—22no—
80C2×D4×C13Q1614yescomplemented
81C22×C4×C13—24no—
82C22×C4×C13—24no—
83C22×C4×C13—22no—
84C22×C4×C13—22no—
85C22×C4×C13—44no—
86C22×C4×C13C2×D411yescharacteristic
87C22×C4×C13C2×D412yes—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2411yescharacteristic
90C22×Dic13—22no—
91C22×Dic13—22no—
92C2×Dic26—24no—
93C2×Dic26—82no—
94C13×C4⋊C4—24no—
95C13×C4⋊C4—28no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—24no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—22no—
100C13×C4⋊C4—22no—
101C13×C4⋊C4—24no—
102C13×C4⋊C4C2×D414yes—
103C13×C22⋊C4—28no—
104C13×C22⋊C4—24no—
105C13×C22⋊C4—24no—
106C42×C13—24no—
107C42×C13C2×D412yes—
108C42×C13C2×D412yes—
109C22⋊Dic13—84no—
110#6107—88no—
111C4⋊Dic13—42no—
112C4⋊Dic13—41no—
113C4⋊Dic13—42no—
114C4⋊Dic13—41no—
115C4×Dic13—42no—
116C2×#1055—24no—
117#3501D1311yescharacteristic
118#3209—132no—
119#2563—131no—
120#1602—138no—
121#1503—132no—
122#1460—131no—
123C23×C13—22no—
124C23×C13—22no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13C2×Q1614yes—
128C23×C13C22×D411yescharacteristic
129Q8×C13—44no—
130Q8×C13—44no—
131Q8×C13—84no—
132D4×C13—28no—
133C2×C4×C13—22no—
134C2×C4×C13—24no—
135C2×C4×C13—24no—
136C2×C4×C13—22no—
137C2×C4×C13—41no—
138C2×C4×C13—44no—
139C2×C4×C13—42no—
140C2×C4×C13—82no—
141C2×C4×C13—84no—
142C2×C4×C13—84no—
143C2×C4×C13#12011yescharacteristic
144C2×C4×C13#12012yes—
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13C2×Q1612yes—
147C2×C4×C13#13712yes—
148C2×C4×C13C22×D412yes—
149C2×Dic13—42no—
150C2×Dic13—42no—
151C2×Dic13—44no—
152C2×Dic13—42no—
153C2×Dic13—42no—
154Dic26—48no—
155#1055—44no—
156#554—22no—
157#554—24no—
158D4×Q8—22no—
159#544—21no—
160#543C2×D1314yes—
161#533C2×D1312yes—
162C2×C4⋊Q8—131no—
163C2×C22⋊Q8—22no—
164#518—21no—
165C2×C4×D4C2×D1311yescharacteristic
166#494—262no—
167#487—262no—
168#462—264no—
169#451—138no—
170#431—132no—
171#393—134no—
172#390—261no—
173#382—261no—
174#380—262no—
175C4×C4⋊C4—131no—
176#328—138no—
177#323—134no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—24no—
181C22×C13—44no—
182C22×C13—42no—
183C22×C13—42no—
184C22×C13—82no—
185C22×C13C2×#12011yescharacteristic
186C22×C13C22×Q1611yescharacteristic
187C22×C13C2×#13711yescharacteristic
188C4×C13—21no—
189C4×C13—22no—
190C4×C13—42no—
191C4×C13—44no—
192C4×C13—44no—
193C4×C13#45114yes—
194C4×C13#45512yes—
195Dic13—82no—
196Dic13—82no—
197C22×Q8—22no—
198C22×Q8—132no—
199C22×D4C22⋊D1311yescharacteristic
200C23×C4C22⋊D1312yes—
201C2×Q16—268no—
202C4⋊Q8—24no—
203C4⋊Q8—262no—
204C4⋊Q8—262no—
205C4⋊Q8C22⋊D1312yes—
206C4⋊Q8C22⋊D1312yes—
207#125—24no—
208#125—22no—
209C22⋊Q8—24no—
210C22⋊Q8—24no—
211C22⋊Q8—28no—
212C22⋊Q8—22no—
213C22⋊Q8—24no—
214C22⋊Q8—28no—
215C22⋊Q8C22×D1314yes—
216C4×Q8—22no—
217C4×Q8C22⋊D1314yes—
218C4×D4—24no—
219C4×D4—24no—
220C4×D4—22no—
221C4×D4—22no—
222#117—22no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4—261no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4C22⋊D1311yescharacteristic
229C2×C22⋊C4—24no—
230C2×C22⋊C4—264no—
231C2×C22⋊C4C22×D1312yes—
232C2×C42—261no—
233C2×C42C22×D1311yescharacteristic
234C4⋊C8—262no—
235#103—268no—
236C22⋊C8—134no—
237C4×C8—262no—
238#95—132no—
239#95—264no—
240C2×C13—21no—
241C2×C13—21no—
242C2×C13—44no—
243C2×C13C2×#45111yescharacteristic
244C2×C13C2×#45511yescharacteristic
245C2×C13#302711yescharacteristic
246C24C2×C22⋊D1312yes—
247C2×Q8—24no—
248C2×Q8—22no—
249C2×Q8—84no—
250C2×Q8—264no—
251C2×Q8—1042no—
252C2×Q8C2×C22⋊D1314yes—
253C2×D4—22no—
254C2×D4—22no—
255C2×D4#610714yescomplemented
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—44no—
261C22×C4—262no—
262C22×C4—262no—
263C22×C4C2×C22⋊D1311yescharacteristic
264C22×C4C2×C22⋊D1312yes—
265C22×C4C2×C22⋊D1311yescharacteristic
266C22×C4C23×D1311yescharacteristic
267Q16—1048no—
268C2×C8—264no—
269C4⋊C4—24no—
270C4⋊C4—28no—
271C4⋊C4—22no—
272C4⋊C4—24no—
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—24no—
277C4⋊C4—522no—
278C4⋊C4—521no—
279C4⋊C4—522no—
280C4⋊C4—521no—
281C4⋊C4C2×C22⋊D1314yes—
282C22⋊C4—28no—
283C22⋊C4—24no—
284C22⋊C4—24no—
285C22⋊C4—1044no—
286C42—24no—
287C42—522no—
288C42C2×C22⋊D1312yes—
289C42C2×C22⋊D1312yes—
290C13#1839011yescharacteristic, complemented, Sylow
291C23—22no—
292C23—22no—
293C23—42no—
294C23—42no—
295C23C2×#610714yes—
296C23C22×C22⋊D1311yescharacteristic
297Q8—44no—
298Q8—44no—
299Q8—84no—
300Q8—528no—
301D4—28no—
302C2×C4—22no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—41no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—84no—
311C2×C4—84no—
312C2×C4—522no—
313C2×C4—524no—
314C2×C4—522no—
315C2×C4—522no—
316C2×C4—522no—
317C2×C4#8819612yes—
318C2×C4C2×#610712yes—
319C2×C4#8820711yescharacteristic
320C2×C4#8820712yes—
321C2×C4#8820711yescharacteristic
322C2×C4C22×C22⋊D1312yes—
323C8—524no—
324C22—21no—
325C22—21no—
326C22—24no—
327C22—44no—
328C22—42no—
329C22—42no—
330C22—82no—
331C22C2×#8819611yescharacteristic
332C22C22×#610711yescharacteristic
333C22C2×#8820711yescharacteristic
334C4—21no—
335C4—22no—
336C4—42no—
337C4—44no—
338C4—44no—
339C4—1042no—
340C4—1042no—
341C4#1171888914yes—
342C4#1171890312yes—
343C2—21no—
344C2—21no—
345C2—44no—
346C2C2×#1171888911yescharacteristic
347C2C2×#1171890311yescharacteristic
348C2#1312423811yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#3501C2
socleC22×C13C2×#120
prime radicalC22×D4×C13D4
hypercenter#3501D13
hypocenterC13#18390
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13125781C2semidirect
3. #13113793C2semidirect
4. #13113335C2semidirect
80. C2×D4×C13Q16semidirect
255. C2×D4#6107semidirect
290. C13#18390semidirect

Maximal subgroups

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

subgroupindex
#131257812
#131200092
#131137932
#131133352
#131131572
C13×#35012
#1839013