Finite Group Databasebeta

← #15760686

Subgroups — #15760686

Order 3328.

578 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 131 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#13123860C211yesmaximal, characteristic
2#13119153C211yesmaximal, characteristic
3#13114924C212yesmaximal, complemented
4#13112703C212yesmaximal, complemented
5C13×#1799C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C2×C13×#99—21no—
9C13×#380C2212yes—
10#11718881—21no—
11#11718873—21no—
12#11718873C2211yescharacteristic
13C2×C22⋊#1055—21no—
14C2×C22⋊#1055C2212yes—
15D4×#1055—24no—
16#11718647C412yescomplemented
17#11718610C412yescomplemented
18#11718607—21no—
19#11718589—21no—
20#11718586—21no—
21C13×#342—21no—
22#11718121—24no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13—21no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—22no—
37C2×C4⋊Dic13—22no—
38C2×C4⋊Dic13—22no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C412yes—
42C2×#6101—22no—
43C22×#1055—22no—
44C22×#1055D414yes—
45C13×#99—42no—
46C13×#95—22no—
47#88071—22no—
48#88071—22no—
49#88071C2×C412yes—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53C4⋊#1055—22no—
54C4×#1055—22no—
55#9469—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C2×D411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13SD1612yes—
61C2×D4×C13Q1612yes—
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×C13C2×D411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×C4×C13#4112yes—
74C22×Dic13—22no—
75C22×Dic13—22no—
76C22×Dic13—42no—
77C22×Dic13—82no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—44no—
80C13×C22⋊C4—22no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C42×C13—21no—
85C42×C13—21no—
86C22⋊Dic13—42no—
87C22⋊Dic13—82no—
88C4⋊Dic13—24no—
89C4⋊Dic13—42no—
90C4⋊Dic13—41no—
91C4⋊Dic13—41no—
92#6101—82no—
93C2×#1055—24no—
94C2×#1055—44no—
95C2×#1055—82no—
96#2972—131no—
97#2487—131no—
98#1824—132no—
99#1799D1311yescharacteristic
100#1289—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13#10312yes—
108C23×C13C2×C22⋊C411yescharacteristic
109C23×C13#12112yes—
110C23×C13C2×SD1611yescharacteristic
111C23×C13C2×Q1611yescharacteristic
112C23×C13#13512yes—
113D4×C13—24no—
114D4×C13—24no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—24no—
118C2×C4×C13—22no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—81no—
127C2×C4×C13—82no—
128C2×C4×C13—82no—
129C2×C4×C13—82no—
130C2×C4×C13#10312yes—
131C2×C4×C13C4×D412yes—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12311yescharacteristic
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—84no—
141#1055—44no—
142C2×C4×D4C2×D1311yescharacteristic
143C22×C4⋊C4—131no—
144C8×D4—264no—
145#431—261no—
146C2×#99—21no—
147C2×C22⋊C8—132no—
148C2×C22⋊C8—261no—
149#400—132no—
150#399—132no—
151#389—261no—
152#386—261no—
153#385—261no—
154#380—131no—
155#380—261no—
156#380C2×D1312yes—
157#342—21no—
158#340—264no—
159C22×C13—21no—
160C22×C13—22no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—42no—
167C22×C13—42no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—81no—
171C22×C13#38611yescharacteristic
172C22×C13C2×#10311yescharacteristic
173C22×C13#41611yescharacteristic
174C22×C13#46512yes—
175C22×C13#46712yes—
176C4×C13—21no—
177C4×C13—22no—
178C4×C13—22no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—162no—
182C4×C13#45812yes—
183Dic13—82no—
184Dic13—82no—
185C22×D4C22⋊D1311yescharacteristic
186C23×C4—261no—
187C23×C4D5211yescharacteristic
188C23×C4C22×D1311yescharacteristic
189C22×C8—134no—
190C22×C8—262no—
191C4×D4—22no—
192C4×D4—22no—
193C2×C4⋊C4—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⋊C4C4×D1311yescharacteristic
201C2×C22⋊C4—22no—
202C2×C22⋊C4—261no—
203C2×C22⋊C4—262no—
204C2×C22⋊C4C4×D1311yescharacteristic
205C2×C22⋊C4C22⋊D1311yescharacteristic
206C2×C42D5211yescharacteristic
207C4⋊C8—262no—
208#99—42no—
209C22⋊C8—262no—
210C22⋊C8—262no—
211C22⋊C8—262no—
212C4×C8—262no—
213#95—22no—
214#95—132no—
215#95—262no—
216#95—262no—
217C2×C13—21no—
218C2×C13—22no—
219C2×C13—21no—
220C2×C13—22no—
221C2×C13—42no—
222C2×C13#189011yescharacteristic
223C2×C13#189211yescharacteristic
224C2×C13#191011yescharacteristic
225C24#610311yescharacteristic
226C24C2×C22⋊D1311yescharacteristic
227C2×D4—22no—
228C2×D4—22no—
229C2×D4#610512yes—
230C2×D4#610712yes—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—262no—
237C22×C4—262no—
238C22×C4—522no—
239C22×C4—1042no—
240C22×C4#610311yescharacteristic
241C22×C4#610311yescharacteristic
242C22×C4#610311yescharacteristic
243C22×C4C2×C4×D1311yescharacteristic
244C22×C4C2×D5211yescharacteristic
245C22×C4D4×D1312yes—
246C22×C4#612912yes—
247C2×C8—264no—
248C2×C8—524no—
249C2×C8—1042no—
250C4⋊C4—22no—
251C4⋊C4—44no—
252C4⋊C4—264no—
253C4⋊C4—522no—
254C4⋊C4—521no—
255C4⋊C4—521no—
256C4⋊C4—1042no—
257C22⋊C4—22no—
258C22⋊C4—22no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—522no—
262C22⋊C4—1042no—
263C42—21no—
264C42—21no—
265C13#946911yescharacteristic, complemented, Sylow
266C23—21no—
267C23—21no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23—41no—
272C23#8805012yes—
273C23C2×#610311yescharacteristic
274C23C2×#610511yescharacteristic
275C23#8819312yes—
276C23C2×#610711yescharacteristic
277C23#8820412yes—
278D4—24no—
279D4—24no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—81no—
292C2×C4—82no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—1044no—
302C2×C4#8805012yes—
303C2×C4#8813512yes—
304C2×C4#8813611yescharacteristic
305C2×C4#8814011yescharacteristic
306C8—524no—
307C22—21no—
308C22—22no—
309C22—21no—
310C22—22no—
311C22—22no—
312C22—41no—
313C22—41no—
314C22—42no—
315C22—42no—
316C22—41no—
317C22—41no—
318C22—81no—
319C22#1171861911yescharacteristic
320C22C2×#8805011yescharacteristic
321C22#1171866311yescharacteristic
322C22#1171870212yes—
323C22#1171871212yes—
324C4—21no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4—162no—
330C4—1042no—
331C4—1042no—
332C4#1171840312yes—
333C2—22no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—42no—
338C2#1311524711yescharacteristic
339C2#1311525711yescharacteristic
340C2#1311536111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1799C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#1799D13
hypocenterC13#9469
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13114924C2semidirect
4. #13112703C2semidirect
16. #11718647C4semidirect
17. #11718610C4semidirect
265. C13#9469semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131191532
#131149242
#131127032
C13×#17992
#946913