Finite Group Databasebeta

← #15778459

Subgroups — #15778459

Order 3328.

986 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 135 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#13116525C214yesmaximal, complemented
2#13114764C212yesmaximal, complemented
3C13×#3485C211yesmaximal, characteristic
4C2×C13×H(5,𝔽2)C411yescharacteristic
5C22×C13×#41C2211yescharacteristic
6C13×#547—24no—
7C13×#546—24no—
8C13×#536C2212yes—
9C13×#534—22no—
10C13×#525C412yes—
11C2×C13×#123—22no—
12C13×#518C411yescharacteristic
13C2×#88076C2214yescomplemented
14C2×#88073—22no—
15#11718868—22no—
16#11718140—24no—
17#11718134—24no—
18C13×H(5,𝔽2)—44no—
19C2×C13×#41—22no—
20C2×C13×#41—24no—
21C2×C13×#41—44no—
22C2×C13×#41C2×C412yes—
23C22×Q8×C13C2311yescharacteristic
24C22×D4×C13—22no—
25C22×D4×C13—22no—
26C22×D4×C13C2×C411yescharacteristic
27C22×D4×C13D412yes—
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D412yes—
30C13×C4⋊Q8D414yes—
31C13×#124D414yes—
32C13×#123—28no—
33C13×#123—24no—
34C13×#123—22no—
35C13×#123—24no—
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8—24no—
38C13×#121—28no—
39C13×#121—22no—
40C13×#120—24no—
41C13×#120—22no—
42C4×D4×C13—24no—
43C4×D4×C13—24no—
44C13×#117C2×C412yes—
45C2×C13×C4⋊C4—24no—
46C2×C13×C22⋊C4—24no—
47C2×C13×C22⋊C4—22no—
48C2×#6099—24no—
49#88076—28no—
50#88073—44no—
51C22⋊#1055—44no—
52#12709—131nomaximal, Sylow
53C24×C13—22no—
54C24×C13C22⋊C411yescharacteristic
55C24×C13C22⋊C412yes—
56C13×#41—44no—
57C13×#41—416no—
58C13×#41—48no—
59C2×Q8×C13—42no—
60C2×Q8×C13C22⋊C412yes—
61C2×Q8×C13C2×D414yes—
62C2×D4×C13—24no—
63C2×D4×C13—24no—
64C2×D4×C13—24no—
65C2×D4×C13—22no—
66C2×D4×C13—24no—
67C2×D4×C13—22no—
68C2×D4×C13—24no—
69C2×D4×C13—42no—
70C2×D4×C13—48no—
71C2×D4×C13—44no—
72C2×D4×C13—44no—
73C2×D4×C13C22⋊C412yes—
74C22×C4×C13—22no—
75C22×C4×C13—24no—
76C22×C4×C13—24no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—24no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13C22⋊C411yescharacteristic
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D412yes—
85C13×C4⋊C4—24no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—28no—
88C13×C22⋊C4—24no—
89C13×C22⋊C4—24no—
90C13×C22⋊C4—24no—
91C13×C22⋊C4—22no—
92C13×C22⋊C4—28no—
93C42×C13C22⋊C414yes—
94#6099—44no—
95#6099—44no—
96C2×#1055—44no—
97#3485D1311yescharacteristic
98#2133—134no—
99#1785—132no—
100C23×C13—22no—
101C23×C13—22no—
102C23×C13—22no—
103C23×C13—21no—
104C23×C13—22no—
105C23×C13—44no—
106C23×C13—82no—
107C23×C13—81no—
108C23×C13—84no—
109C23×C13#9914yes—
110C23×C13C2×C22⋊C411yescharacteristic
111Q8×C13—44no—
112Q8×C13—42no—
113D4×C13—28no—
114D4×C13—48no—
115D4×C13—42no—
116D4×C13—48no—
117D4×C13—44no—
118D4×C13—84no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—24no—
123C2×C4×C13—21no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—48no—
127C2×C4×C13—44no—
128C2×C4×C13—44no—
129C2×C4×C13—44no—
130C2×C4×C13—84no—
131C2×C4×C13C2×C22⋊C412yes—
132C2×C4×C13#12014yes—
133#1055—84no—
134C2×H(5,𝔽2)Dic1311yescharacteristic
135C22×#41C2×D1311yescharacteristic
136#547—24no—
137#546—24no—
138#536C2×D1312yes—
139#534—22no—
140#525Dic1312yes—
141C2×#123—22no—
142#518Dic1311yescharacteristic
143C2×#101—134no—
144C2×#100—262no—
145#407—262no—
146#356—264no—
147#355—264no—
148C22×C13—24no—
149C22×C13—41no—
150C22×C13—44no—
151C22×C13—44no—
152C22×C13—42no—
153C22×C13—44no—
154C22×C13—41no—
155C22×C13—42no—
156C22×C13—82no—
157C22×C13—82no—
158C22×C13—164no—
159C22×C13#37911yescharacteristic
160C22×C13C2×#9912yes—
161C4×C13—24no—
162C4×C13—22no—
163C4×C13—44no—
164C4×C13—41no—
165C4×C13—42no—
166H(5,𝔽2)—44no—
167C2×#41—22no—
168C2×#41—24no—
169C2×#41—44no—
170C2×#41C2×Dic1312yes—
171C22×Q8C22×D1311yescharacteristic
172C22×D4—22no—
173C22×D4—22no—
174C22×D4C2×Dic1311yescharacteristic
175C22×D4C22⋊D1312yes—
176C23×C4C2×Dic1311yescharacteristic
177C23×C4C22⋊D1312yes—
178C2×M16—264no—
179C4⋊Q8C22⋊D1314yes—
180#124C22⋊D1314yes—
181#123—28no—
182#123—24no—
183#123—22no—
184#123—24no—
185C22⋊Q8—22no—
186C22⋊Q8—24no—
187#121—28no—
188#121—22no—
189#120—24no—
190#120—22no—
191C4×D4—24no—
192C4×D4—24no—
193#117C2×Dic1312yes—
194C2×C4⋊C4—24no—
195C2×C22⋊C4—24no—
196C2×C22⋊C4—22no—
197#101—268no—
198#100—524no—
199C22⋊C8—524no—
200C2×C13—21no—
201C2×C13—22no—
202C2×C13—44no—
203C2×C13—81no—
204C2×C13—82no—
205C2×C13#178111yescharacteristic
206C24—22no—
207C24C22⋊Dic1311yescharacteristic
208C24C22⋊Dic1312yes—
209#41—44no—
210#41—416no—
211#41—48no—
212C2×Q8—42no—
213C2×Q8C22⋊Dic1312yes—
214C2×Q8C2×C22⋊D1314yes—
215C2×D4—24no—
216C2×D4—24no—
217C2×D4—24no—
218C2×D4—22no—
219C2×D4—24no—
220C2×D4—22no—
221C2×D4—24no—
222C2×D4—42no—
223C2×D4—48no—
224C2×D4—44no—
225C2×D4—44no—
226C2×D4C22⋊Dic1312yes—
227C22×C4—22no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—24no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4C22⋊Dic1311yescharacteristic
236C22×C4C22×Dic1311yescharacteristic
237C22×C4C2×C22⋊D1312yes—
238M16—524no—
239M16—524no—
240C2×C8—524no—
241C4⋊C4—24no—
242C4⋊C4—22no—
243C4⋊C4—28no—
244C22⋊C4—24no—
245C22⋊C4—24no—
246C22⋊C4—24no—
247C22⋊C4—22no—
248C22⋊C4—28no—
249C42C22⋊Dic1314yes—
250C13#1270911yescharacteristic, complemented, Sylow
251C23—22no—
252C23—22no—
253C23—22no—
254C23—21no—
255C23—22no—
256C23—44no—
257C23—82no—
258C23—81no—
259C23—84no—
260C23#8807414yes—
261C23C2×C22⋊Dic1311yescharacteristic
262Q8—44no—
263Q8—42no—
264D4—28no—
265D4—48no—
266D4—42no—
267D4—48no—
268D4—44no—
269D4—84no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—48no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—84no—
282C2×C4C2×C22⋊Dic1312yes—
283C2×C4#8820714yes—
284C8—1044no—
285C22—24no—
286C22—41no—
287C22—44no—
288C22—44no—
289C22—42no—
290C22—44no—
291C22—41no—
292C22—42no—
293C22—82no—
294C22—82no—
295C22—164no—
296C22C2×#8807412yes—
297C22#1171890811yescharacteristic
298C4—24no—
299C4—22no—
300C4—44no—
301C4—41no—
302C4—42no—
303C2—21no—
304C2—22no—
305C2—44no—
306C2—81no—
307C2—82no—
308C2#1311475111yescharacteristic
subgroupG/H
centerC2#13114751
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
Fitting, prime radicalC13×#3485C2
socleC2×C13#1781
cosocleC22×Q8×C13C23
hypercenter#3485D13
hypocenterC13#12709
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×#41 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. #13116525C2semidirect
2. #13114764C2semidirect
13. C2×#88076C22semidirect
250. C13#12709semidirect

Maximal subgroups

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

subgroupindex
#131165252
#131147642
C13×#34852
#1270913