Finite Group Databasebeta

← #15774069

Subgroups — #15774069

Order 3328.

568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 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#13118201C211yesmaximal, characteristic
2#13114828C211yesmaximal, characteristic
3#13112867C214yesmaximal, complemented
4C13×#1459C211yesmaximal, characteristic
5C23×Dic26C411yescharacteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178—21no—
8C2×C13×C22⋊C8—21no—
9#11718881—21no—
10C2×#88073—21no—
11#11718873C411yescharacteristic
12#11718640C2212yes—
13#11718608C412yes—
14#11718607—21no—
15#11718590—21no—
16#11718585—21no—
17C13×#324C2212yes—
18C13×#323—21no—
19#11718122C2212yes—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13—21no—
24C22×Dic26—21no—
25C22×Dic26—44no—
26C22×Dic26—41no—
27C22×Dic26—41no—
28C22×Dic26C2×C412yes—
29C22×C8×C13—41no—
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C2×C13×C4⋊C4C2311yescharacteristic
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39#88178—44no—
40C2×#6101—22no—
41C2×#6099—22no—
42C13×C22⋊C8—22no—
43C13×C22⋊C8—41no—
44#88073—42no—
45#88071—22no—
46#88071—22no—
47#88071C2×C412yes—
48C4⋊#1055—41no—
49C4⋊#1055—41no—
50#11904—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C22⋊C411yescharacteristic
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13SD1612yes—
56C2×D4×C13Q1612yes—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22×C411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—44no—
71C22×Dic13—42no—
72C2×Dic26—24no—
73C2×Dic26—42no—
74C2×Dic26—48no—
75C2×Dic26—44no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26—42no—
79C2×Dic26—44no—
80C2×Dic26—44no—
81C2×C8×C13—42no—
82C2×C8×C13—82no—
83C13×C4⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—21no—
87C42×C13—21no—
88C22⋊Dic13—44no—
89C22⋊Dic13—42no—
90C4⋊Dic13—42no—
91#6101—44no—
92#6099—42no—
93#6099—42no—
94C2×#1055—42no—
95#2409—131no—
96#1800—131no—
97#1459D1311yescharacteristic
98#1354—134no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13#10312yes—
108C23×C13#10312yes—
109C23×C13C2×C22⋊C411yescharacteristic
110D4×C13—42no—
111D4×C13—42no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—81no—
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13C2×SD1611yescharacteristic
128C2×C4×C13C2×Q1611yescharacteristic
129C2×Dic13—24no—
130C2×Dic13—42no—
131C2×Dic13—48no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136Dic26—44no—
137Dic26—44no—
138Dic26—44no—
139Dic26—44no—
140C8×C13—82no—
141#1055—82no—
142C23×Q8—131no—
143C2×C22⋊Q8—261no—
144C2×C4×D4C2×D1311yescharacteristic
145#423—261no—
146C2×#100—261no—
147C2×C22⋊C8—21no—
148#395—132no—
149#393—132no—
150#391—261no—
151#386—261no—
152#385—261no—
153#380—131no—
154#343—132no—
155#324C2×D1312yes—
156#323—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13—42no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—81no—
169C22×C13C2×#9911yescharacteristic
170C22×C13C2×#10311yescharacteristic
171C22×C13#42111yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13AΣL(1,𝔽16)12yes—
179Dic13—44no—
180Dic13—82no—
181C22×Q8—132no—
182C22×Q8—261no—
183C22×Q8—521no—
184C22×Q8—521no—
185C22×Q8—524no—
186C22×D4D5211yescharacteristic
187C23×C4—261no—
188C23×C4C4×D1311yescharacteristic
189C23×C4C22⋊D1311yescharacteristic
190C2×M16—262no—
191C22×C8—41no—
192C22⋊Q8—524no—
193C4×D4—41no—
194C4×D4—41no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—262no—
197C2×C4⋊C4C22×D1311yescharacteristic
198C2×C22⋊C4—262no—
199C2×C22⋊C4—261no—
200C2×C22⋊C4C4×D1311yescharacteristic
201C2×C22⋊C4C22⋊D1311yescharacteristic
202C2×C42D5211yescharacteristic
203C4⋊C8—521no—
204C4⋊C8—521no—
205#100—522no—
206C22⋊C8—22no—
207C22⋊C8—41no—
208#95—132no—
209#95—262no—
210#95—262no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—42no—
214C2×C13—42no—
215C2×C13#152011yescharacteristic
216C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
217C2×C13#213511yescharacteristic
218C24#610311yescharacteristic
219C24#610311yescharacteristic
220C2×Q8—264no—
221C2×Q8—522no—
222C2×Q8—522no—
223C2×Q8—524no—
224C2×Q8—524no—
225C2×Q8—528no—
226C2×Q8—524no—
227C2×Q8—521no—
228C2×Q8—521no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4#609512yes—
232C2×D4Dic5212yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—262no—
240C22×C4—262no—
241C22×C4—524no—
242C22×C4—522no—
243C22×C4#610311yescharacteristic
244C22×C4#610311yescharacteristic
245C22×C4C2×C4×D1311yescharacteristic
246C22×C4C2×D5211yescharacteristic
247C22×C4C2×C22⋊D1311yescharacteristic
248M16—522no—
249M16—522no—
250C2×C8—42no—
251C2×C8—82no—
252C2×C8—522no—
253C4⋊C4—41no—
254C4⋊C4—522no—
255C4⋊C4—524no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—524no—
259C22⋊C4—522no—
260C42—21no—
261C42—21no—
262C13#1190411yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23#8805612yes—
272C23#8805612yes—
273C23C2×#610311yescharacteristic
274Q8—524no—
275Q8—524no—
276Q8—524no—
277Q8—524no—
278D4—42no—
279D4—42no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—264no—
294C2×C4—522no—
295C2×C4—528no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4#8804611yescharacteristic
301C2×C4#8804611yescharacteristic
302C2×C4C2×#609511yescharacteristic
303C2×C4C2×Dic5211yescharacteristic
304C8—82no—
305C8—1042no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—22no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×#8804611yescharacteristic
319C22C2×#8805611yescharacteristic
320C22#1171880011yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—524no—
328C4—1042no—
329C4#1171806312yes—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2#1311340911yescharacteristic
335C2C2×#1171806311yescharacteristic
336C2#1311653011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1459C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenter#1459D13
hypocenterC13#11904
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13112867C2semidirect
262. C13#11904semidirect

Maximal subgroups

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

subgroupindex
#131182012
#131148282
#131128672
C13×#14592
#1190413