Finite Group Databasebeta

← #15781231

Subgroups — #15781231

Order 3328.

552 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 103 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#13119828C211yesmaximal, characteristic
2C2×#11718065C214yesmaximal
3C4×#88074C211yesmaximal, characteristic
4C13×#1799C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C2×#88190C2212yes—
7C2×#88123C411yescharacteristic, complemented
8C2×C13×#99C2212yes—
9C13×#380—21no—
10C2×#88074C2212yes—
11#11718873—21no—
12#11718873—21no—
13C4×C22⋊Dic13—21no—
14#11718635C412yescomplemented
15#11718614—21no—
16#11718614—21no—
17C4×C4⋊Dic13C411yescharacteristic, complemented
18C13×#342—21no—
19#11718118—21no—
20#11718065—28no—
21C22×D4×C13C2311yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C22×Dic26C2×C412yes—
25C4×D4×C13—41no—
26C4×D4×C13—41no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—22no—
36#88190—24no—
37#88190—24no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4×Dic13—41no—
42C2×C4×Dic13C2×C412yes—
43#88123—41no—
44#88123—41no—
45C13×#99—24no—
46C13×#95—41no—
47#88074—22no—
48#88074D414yes—
49#88071—21no—
50#88071—22no—
51#88071—22no—
52#88071—41no—
53#13224—131nomaximal, Sylow
54C24×C13C2×D411yescharacteristic
55C24×C13C2×D411yescharacteristic
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13C2×D412yes—
59C2×D4×C13#4112yes—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—42no—
75C2×Dic26—24no—
76C2×Dic26—42no—
77C2×Dic26—42no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—82no—
80C13×C22⋊C4—41no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C42×C13—21no—
85C42×C13—21no—
86C22⋊Dic13—24no—
87C22⋊Dic13—42no—
88C22⋊Dic13—44no—
89C22⋊Dic13—42no—
90C22⋊Dic13—42no—
91C4⋊Dic13—42no—
92C4⋊Dic13—42no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4×Dic13—24no—
96C4×Dic13—82no—
97#2547—131no—
98C2×#354—134no—
99#1799D1311yescharacteristic
100C4×#99—131no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13#12112yes—
111C23×C13#12411yescharacteristic
112C23×C13#12711yescharacteristic
113D4×C13—42no—
114D4×C13—42no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13—82no—
129C2×C4×C13—82no—
130C2×C4×C13—82no—
131C2×C4×C13#9911yescharacteristic
132C2×C4×C13#9911yescharacteristic
133C2×C4×C13C4×D412yes—
134C2×Dic13—42no—
135C2×Dic13—44no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—82no—
142C2×Dic13—82no—
143Dic26—84no—
144C2×C4⋊Q8—131no—
145C2×#124—132no—
146C2×C4×D4C2×D1311yescharacteristic
147C2×#99—132no—
148C2×#99C2×D1312yes—
149#397—261no—
150#397—261no—
151#391—132no—
152#380—21no—
153#380—261no—
154#380—261no—
155C4×C4⋊C4—131no—
156C4×C22⋊C4—261no—
157#354—268no—
158#342—21no—
159#342—261no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—42no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13#39011yescharacteristic
175C22×C13C2×#9911yescharacteristic
176C22×C13#41011yescharacteristic
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—162no—
183C4×C13#35412yescomplemented
184Dic13—82no—
185Dic13—84no—
186Dic13—82no—
187C22×Q8—132no—
188C22×D4C22×D1311yescharacteristic
189C23×C4D5211yescharacteristic
190C23×C4C22⋊D1311yescharacteristic
191C4⋊Q8—521no—
192C4⋊Q8—521no—
193#124—264no—
194#124—264no—
195C4×D4—41no—
196C4×D4—41no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4C4×D1311yescharacteristic
202C2×C22⋊C4—22no—
203C2×C22⋊C4—262no—
204C2×C22⋊C4—262no—
205C2×C22⋊C4—262no—
206C2×C22⋊C4D5211yescharacteristic
207C2×C22⋊C4C22⋊D1311yescharacteristic
208C2×C42—132no—
209C2×C42—521no—
210C2×C42C4×D1311yescharacteristic
211#99—24no—
212#99—134no—
213#99—262no—
214#95—41no—
215#95—261no—
216#95—262no—
217#95—262no—
218#95—521no—
219C2×C13—21no—
220C2×C13—21no—
221C2×C13—42no—
222C2×C13—41no—
223C2×C13—41no—
224C2×C13#196411yescharacteristic
225C2×C13C2×#35411yescharacteristic
226C2×C13#212911yescharacteristic
227C24C2×D5211yescharacteristic
228C24C2×C22⋊D1311yescharacteristic
229C2×Q8—264no—
230C2×Q8—522no—
231C2×Q8—522no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4D4×D1312yes—
235C2×D4#613112yes—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—262no—
244C22×C4—262no—
245C22×C4—522no—
246C22×C4#610311yescharacteristic
247C22×C4#610311yescharacteristic
248C22×C4#610311yescharacteristic
249C22×C4#610311yescharacteristic
250C22×C4C2×C4×D1311yescharacteristic
251C4⋊C4—41no—
252C4⋊C4—82no—
253C4⋊C4—522no—
254C4⋊C4—522no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—264no—
262C22⋊C4—522no—
263C22⋊C4—524no—
264C22⋊C4—522no—
265C22⋊C4—522no—
266C42—21no—
267C42—21no—
268C42—264no—
269C42—1042no—
270C13#1322411yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23#8814912yes—
280C23C2×#610311yescharacteristic
281C23#8819411yescharacteristic
282C23#8820111yescharacteristic
283Q8—1044no—
284D4—42no—
285D4—42no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—524no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—522no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4—1042no—
310C2×C4—1042no—
311C2×C4#8804611yescharacteristic
312C2×C4#8804611yescharacteristic
313C2×C4#8814712yes—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—21no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22—81no—
328C22C2×#8804611yescharacteristic
329C22#1171864911yescharacteristic
330C22#1171866711yescharacteristic
331C4—22no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—162no—
337C4—1042no—
338C4—1044no—
339C4—1042no—
340C4#1171806512yescomplemented
341C2—21no—
342C2—21no—
343C2—41no—
344C2—42no—
345C2—41no—
346C2#1311567111yescharacteristic
347C2C2×#1171806511yescharacteristic
348C2#1311651011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#1799C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#1799D13
hypocenterC13#13224
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1799

Complements

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

NH ≅ G/Ntype
7. C2×#88123C4semidirect
14. #11718635C4semidirect
17. C4×C4⋊Dic13C4semidirect
183. C4×C13#354semidirect
270. C13#13224semidirect
340. C4#11718065semidirect

Maximal subgroups

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

subgroupindex
#131198282
C2×#117180652
C4×#880742
C13×#17992
#1322413