Finite Group Databasebeta

← #15760708

Subgroups — #15760708

Order 3328.

556 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 119 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#13119153C211yesmaximal, characteristic
2#13114927C212yesmaximal, complemented
3#13114824C211yesmaximal, characteristic
4#13112704C212yesmaximal, complemented
5C13×#2973C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C13×#435—24no—
9C13×#432—21no—
10C13×#407—21no—
11C2×C13×C22⋊C8C2212yes—
12#11718881—21no—
13C2×#88074—21no—
14#11718873—21no—
15#11718873C2212yes—
16#11718873C2211yescharacteristic
17#11718647C412yescomplemented
18#11718610C412yescomplemented
19#11718607—21no—
20#11718589—21no—
21#11718143—24no—
22#11718118—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13—21no—
27C2×C13×M16—22no—
28C22×C8×C13D414yes—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—22no—
38C2×C4⋊Dic13—22no—
39C2×C4⋊Dic13—22no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—22no—
43C2×C4⋊Dic13C2×C412yes—
44C2×#6101—22no—
45C13×C4⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—22no—
49C13×#97—22no—
50#88074—42no—
51#88071—22no—
52#88071—22no—
53#88071—22no—
54#88071C2×C412yes—
55#9473—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C2×D411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13—22no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D412yes—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13#4112yes—
73C22×Dic13—22no—
74C22×Dic13—22no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13—82no—
78C13×M16—82no—
79C2×C8×C13—24no—
80C2×C8×C13—44no—
81C13×C4⋊C4—22no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—22no—
84C42×C13—21no—
85C42×C13—21no—
86C22⋊Dic13—41no—
87C22⋊Dic13—41no—
88C22⋊Dic13—42no—
89C22⋊Dic13—42no—
90C22⋊Dic13—82no—
91C4⋊Dic13—24no—
92C4⋊Dic13—42no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13—44no—
96#6101—82no—
97#2973D1311yescharacteristic
98#2487—131no—
99#1824—132no—
100#1799—131no—
101#1289—132no—
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×C13AGL(1,ℤ/8)11yescharacteristic
112C23×C13#13711yescharacteristic
113C23×C13#13712yes—
114D4×C13—42no—
115D4×C13—42no—
116C2×C4×C13—24no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—81no—
129C2×C4×C13C4×D412yes—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12311yescharacteristic
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—84no—
139C2×Dic13—82no—
140C2×Dic13—82no—
141C2×Dic13—82no—
142C8×C13—44no—
143C2×C4×D4C2×D1311yescharacteristic
144C22×C4⋊C4—131no—
145#435—24no—
146#432—21no—
147C2×#99—261no—
148#407—21no—
149C2×C22⋊C8C2×D1312yes—
150#400—132no—
151#399—132no—
152#389—261no—
153#386—261no—
154#385—261no—
155#380—131no—
156#380—132no—
157#380—261no—
158#342—261no—
159#340—264no—
160C22×C13—21no—
161C22×C13—22no—
162C22×C13—21no—
163C22×C13—22no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—42no—
167C22×C13—42no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—81no—
172C22×C13#38611yescharacteristic
173C22×C13#41711yescharacteristic
174C22×C13#41911yescharacteristic
175C22×C13#46812yes—
176C22×C13#47012yes—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13#45812yes—
183Dic13—82no—
184Dic13—82no—
185Dic13—162no—
186C22×D4D5211yescharacteristic
187C23×C4—261no—
188C23×C4C22⋊D1311yescharacteristic
189C23×C4C22×D1311yescharacteristic
190C2×M16—22no—
191C22×C8C22⋊D1314yes—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—132no—
195C2×C4⋊C4—262no—
196C2×C4⋊C4—262no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—262no—
201C2×C4⋊C4C4×D1311yescharacteristic
202C2×C22⋊C4—261no—
203C2×C22⋊C4—262no—
204C2×C22⋊C4—262no—
205C2×C22⋊C4C4×D1311yescharacteristic
206C2×C22⋊C4D5211yescharacteristic
207C2×C42C22⋊D1311yescharacteristic
208C4⋊C8—22no—
209#99—522no—
210C22⋊C8—22no—
211C22⋊C8—22no—
212C22⋊C8—22no—
213#97—22no—
214#95—132no—
215#95—262no—
216#95—262no—
217#95—262no—
218C2×C13—21no—
219C2×C13—22no—
220C2×C13—21no—
221C2×C13—22no—
222C2×C13—81no—
223C2×C13#189011yescharacteristic
224C2×C13#189411yescharacteristic
225C2×C13#191011yescharacteristic
226C24#610311yescharacteristic
227C24C2×D5211yescharacteristic
228C2×D4—21no—
229C2×D4—22no—
230C2×D4—21no—
231C2×D4—22no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—262no—
237C22×C4—262no—
238C22×C4—522no—
239C22×C4—522no—
240C22×C4—1042no—
241C22×C4#610311yescharacteristic
242C22×C4#610311yescharacteristic
243C22×C4#610311yescharacteristic
244C22×C4C2×C4×D1311yescharacteristic
245C22×C4#612712yes—
246C22×C4C2×C22⋊D1312yes—
247C22×C4C2×C22⋊D1311yescharacteristic
248M16—82no—
249C2×C8—24no—
250C2×C8—44no—
251C4⋊C4—22no—
252C4⋊C4—264no—
253C4⋊C4—522no—
254C4⋊C4—524no—
255C4⋊C4—521no—
256C4⋊C4—521no—
257C4⋊C4—1042no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—521no—
261C22⋊C4—521no—
262C22⋊C4—522no—
263C22⋊C4—522no—
264C22⋊C4—1042no—
265C42—21no—
266C42—21no—
267C13#947311yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23#8816211yescharacteristic
276C23#8816312yes—
277C23#8816311yescharacteristic
278C23C2×#610311yescharacteristic
279C23#8818412yes—
280D4—42no—
281D4—42no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—1044no—
302C2×C4—1042no—
303C2×C4—1042no—
304C2×C4—1042no—
305C2×C4C4×C22⋊D1312yes—
306C2×C4#8818311yescharacteristic
307C2×C4#8820711yescharacteristic
308C8—44no—
309C22—21no—
310C22—22no—
311C22—21no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—42no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#1171878111yescharacteristic
322C22#1171879411yescharacteristic
323C22#1171879512yes—
324C22#1171879812yes—
325C22#1171887411yescharacteristic
326C4—21no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—1042no—
332C4—1042no—
333C4—2082no—
334C4#1171890412yes—
335C2—21no—
336C2—22no—
337C2—21no—
338C2—22no—
339C2—81no—
340C2#1311524911yescharacteristic
341C2#1311526911yescharacteristic
342C2#1311536311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2973C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2973D13
hypocenterC13#9473
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13114927C2semidirect
4. #13112704C2semidirect
17. #11718647C4semidirect
18. #11718610C4semidirect
267. C13#9473semidirect

Maximal subgroups

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

subgroupindex
#131191532
#131149272
#131148242
#131127042
C13×#29732
#947313