Finite Group Databasebeta

← #15781233

Subgroups — #15781233

Order 3328.

552 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 111 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
1C2×#11718133C214yesmaximal
2#13114824C211yesmaximal, characteristic
3C4×#88074C211yesmaximal, characteristic
4C13×#2547C211yesmaximal, characteristic
5C2×C13×C4⋊Q8C411yescharacteristic, complemented
6C2×C13×#124C2212yes—
7C2×C4×D4×C13C2211yescharacteristic
8C13×#397—21no—
9C13×#397—21no—
10C13×#391C412yescomplemented
11C13×#380—21no—
12C13×#380—21no—
13C4×C13×C4⋊C4C411yescharacteristic, complemented
14C2×#88074C2212yes—
15C2×#88074C2212yes—
16#11718873—21no—
17C4×C22⋊Dic13—21no—
18#11718133—28no—
19#11718118—21no—
20#11718118—21no—
21C22×Q8×C13C2×C412yes—
22C22×D4×C13C2311yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C13×C4⋊Q8—41no—
26C13×C4⋊Q8—41no—
27C13×#124—24no—
28C13×#124—24no—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C42×C13C2×C412yes—
40C2×C42×C13C2×C411yescharacteristic
41C2×C22⋊Dic13—22no—
42C2×C22⋊Dic13—22no—
43C2×C4⋊Dic13—41no—
44C2×C4×Dic13—41no—
45C13×#95—21no—
46C13×#95—22no—
47C13×#95—22no—
48#88074—22no—
49#88074—24no—
50#88074D414yes—
51#88071—41no—
52#88071—41no—
53#13224—131nomaximal, Sylow
54C24×C13C2×D411yescharacteristic
55C24×C13C2×D411yescharacteristic
56C2×Q8×C13—24no—
57C2×Q8×C13—42no—
58C2×Q8×C13—42no—
59C2×D4×C13—41no—
60C2×D4×C13—41no—
61C2×D4×C13C2×D412yes—
62C2×D4×C13#4112yes—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×Dic13—42no—
77C22×Dic13—42no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—44no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—24no—
91C22⋊Dic13—24no—
92C22⋊Dic13—42no—
93C22⋊Dic13—42no—
94C22⋊Dic13—42no—
95C4⋊Dic13—82no—
96C4×Dic13—82no—
97#2547D1311yescharacteristic
98C2×#354—134no—
99#1799—131no—
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
113Q8×C13—84no—
114D4×C13—42no—
115D4×C13—42no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13#9911yescharacteristic
136C2×C4×C13#9911yescharacteristic
137C2×C4×C13C4×D412yes—
138C2×Dic13—44no—
139C2×Dic13—82no—
140C2×Dic13—82no—
141C2×Dic13—82no—
142C2×Dic13—82no—
143C2×Dic13—82no—
144C2×C4⋊Q8Dic1311yescharacteristic, complemented
145C2×#124C2×D1312yes—
146C2×C4×D4C2×D1311yescharacteristic
147C2×#99—132no—
148C2×#99—132no—
149#397—21no—
150#397—21no—
151#391Dic1312yescomplemented
152#380—21no—
153#380—21no—
154#380—261no—
155C4×C4⋊C4Dic1311yescharacteristic, complemented
156C4×C22⋊C4—261no—
157#354—268no—
158#342—261no—
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—82no—
183C4×C13—82no—
184C4×C13#35412yescomplemented
185Dic13—84no—
186Dic13—162no—
187C22×Q8C2×Dic1312yes—
188C22×D4C22×D1311yescharacteristic
189C23×C4C22⋊D1311yescharacteristic
190C23×C4C22⋊D1311yescharacteristic
191C4⋊Q8—41no—
192C4⋊Q8—41no—
193#124—24no—
194#124—24no—
195C4×D4—41no—
196C4×D4—41no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—521no—
201C2×C4⋊C4C2×Dic1311yescharacteristic
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—262no—
205C2×C22⋊C4—262no—
206C2×C22⋊C4C22⋊D1311yescharacteristic
207C2×C22⋊C4C22⋊D1311yescharacteristic
208C2×C42—521no—
209C2×C42C2×Dic1312yes—
210C2×C42C2×Dic1311yescharacteristic
211#99—134no—
212#99—262no—
213#99—264no—
214#95—21no—
215#95—22no—
216#95—22no—
217#95—521no—
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×C22⋊D1311yescharacteristic
228C24C2×C22⋊D1311yescharacteristic
229C2×Q8—24no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4D4×D1312yes—
235C2×D4#612912yes—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—522no—
245C22×C4—522no—
246C22×C4C22⋊Dic1311yescharacteristic
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4C22⋊Dic1311yescharacteristic
249C22×C4C22⋊Dic1311yescharacteristic
250C22×C4C22×Dic1311yescharacteristic
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—1042no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—44no—
261C22⋊C4—42no—
262C22⋊C4—264no—
263C22⋊C4—522no—
264C22⋊C4—522no—
265C22⋊C4—522no—
266C42—21no—
267C42—21no—
268C42—24no—
269C42—1042no—
270C13#1322411yescharacteristic, complemented, Sylow
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23#8819011yescharacteristic
280C23#8819212yes—
281C23#8819411yescharacteristic
282C23C2×C22⋊Dic1311yescharacteristic
283Q8—84no—
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—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—524no—
306C2×C4—1042no—
307C2×C4—1042no—
308C2×C4—1042no—
309C2×C4—1042no—
310C2×C4—1042no—
311C2×C4#8807411yescharacteristic
312C2×C4#8807411yescharacteristic
313C2×C4D4×Dic1312yes—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—21no—
319C22—41no—
320C22—42no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22—81no—
328C22C2×#8807411yescharacteristic
329C22#1171888211yescharacteristic
330C22#1171890111yescharacteristic
331C4—22no—
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—82no—
337C4—82no—
338C4—1044no—
339C4—2082no—
340C4#1171813312yescomplemented
341C2—21no—
342C2—21no—
343C2—42no—
344C2—41no—
345C2—41no—
346C2#1311567311yescharacteristic
347C2C2×#1171813311yescharacteristic
348C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2547C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#2547D13
hypocenterC13#13224
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2547

Complements

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

NH ≅ G/Ntype
5. C2×C13×C4⋊Q8C4semidirect
10. C13×#391C4semidirect
13. C4×C13×C4⋊C4C4semidirect
144. C2×C4⋊Q8Dic13semidirect
151. #391Dic13semidirect
155. C4×C4⋊C4Dic13semidirect
184. C4×C13#354semidirect
270. C13#13224semidirect
340. C4#11718133semidirect

Maximal subgroups

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

subgroupindex
C2×#117181332
#131148242
C4×#880742
C13×#25472
#1322413