Finite Group Databasebeta

← #15760286

Subgroups — #15760286

Order 3328.

506 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 117 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#13123916C211yesmaximal, characteristic
2#13119825C211yesmaximal, characteristic
3#13114829C211yesmaximal, characteristic
4#13113508C211yesmaximal, characteristic
5#13112738C211yesmaximal, characteristic
6#13112737C211yesmaximal, characteristic
7C13×#1546C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×#88198—21no—
10C2×C4×Dic26C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#423C2211yescharacteristic
13#11718891—21no—
14C2×#88064—21no—
15#11718641C414yes—
16#11718634—22no—
17C4×C4⋊Dic13C2211yescharacteristic
18#11718586C2211yescharacteristic
19#11718585C2211yescharacteristic
20#11718491—22no—
21#11718379—22no—
22C8×Dic26—22no—
23C13×#332—22no—
24#11718146—21no—
25#11718139—22no—
26C22×Q8×C13—21no—
27C22×Dic26D411yescharacteristic
28C2×C13×M16—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C412yes—
35C2×C42×C13C2311yescharacteristic
36#88198—42no—
37#88198—42no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13D411yescharacteristic
40C2×#6101—24no—
41C2×#6101C2×C412yes—
42C2×C4×Dic13—21no—
43C2×C4×Dic13D412yes—
44C2×#6099—21no—
45C4×Dic26—21no—
46C4×Dic26—21no—
47C4×Dic26—21no—
48C4×Dic26—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8D412yes—
52C13×C22⋊C8—21no—
53C4×C8×C13—21no—
54#88071—24no—
55#88071C2×C412yes—
56C22⋊#1055—21no—
57#88064—42no—
58#88054—24no—
59C8×Dic13—24no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055D412yes—
63C4×#1055—21no—
64#9394—131nomaximal, Sylow
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C22×C4×C13—22no—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—22no—
76C22×Dic13C22⋊C412yes—
77C22×Dic13C22⋊C412yes—
78C2×Dic26—21no—
79C2×Dic26—21no—
80C2×Dic26—21no—
81C2×Dic26—21no—
82C2×Dic26D812yes—
83C2×Dic26SD1612yes—
84C13×M16—41no—
85C13×M16—41no—
86C2×C8×C13—22no—
87C2×C8×C13—41no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13#4111yescharacteristic
95C42×C13#4111yescharacteristic
96C4⋊Dic13—24no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99#6101—22no—
100#6101—22no—
101#6101—48no—
102C4×Dic13—22no—
103C4×Dic13—22no—
104C4×Dic13—41no—
105C4×Dic13—41no—
106#6099—41no—
107#6099—41no—
108C2×#1055—22no—
109C2×#1055—41no—
110#2982—131no—
111#2546—131no—
112#1801—131no—
113#1546—131no—
114#1546D1311yescharacteristic
115#1303—131no—
116#1303—131no—
117C23×C13C2×C22⋊C411yescharacteristic
118Q8×C13—81no—
119Q8×C13—81no—
120Q8×C13—81no—
121Q8×C13—81no—
122C2×C4×C13—22no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13C4×D411yescharacteristic
128C2×C4×C13C4×D411yescharacteristic
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12111yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12311yescharacteristic
133C2×C4×C13C2×D811yescharacteristic
134C2×C4×C13C2×SD1611yescharacteristic
135C2×C4×C13#13511yescharacteristic
136C2×C4×C13#13511yescharacteristic
137C2×Dic13—22no—
138C2×Dic13—22no—
139C2×Dic13—24no—
140C2×Dic13—22no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13#10214yes—
145Dic26—22no—
146Dic26—22no—
147Dic26—22no—
148Dic26—22no—
149C8×C13—42no—
150C8×C13—81no—
151#1055—42no—
152#1055—81no—
153C2×C4⋊Q8—261no—
154C2×C4⋊Q8C2×D1311yescharacteristic
155C2×C4×Q8—131no—
156C8×Q8—262no—
157C8×Q8—262no—
158#431—131no—
159#431—262no—
160#431C2×D1311yescharacteristic
161#423—131no—
162#423C2×D1311yescharacteristic
163C2×#101—261no—
164#398—134no—
165#391—261no—
166#389—262no—
167C4×C4⋊C4—131no—
168#343—261no—
169#332—22no—
170#332—262no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13#38611yescharacteristic
174C22×C13C2×#10211yescharacteristic
175C22×C13#41611yescharacteristic
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—21no—
179C4×C13—82no—
180C4×C13#45612yes—
181C4×C13#46511yescharacteristic
182C4×C13#46511yescharacteristic
183C4×C13#46611yescharacteristic
184C4×C13#46611yescharacteristic
185Dic13—24no—
186Dic13—44no—
187Dic13—42no—
188C22×Q8—21no—
189C22×Q8—131no—
190C2×M16—21no—
191C2×M16—261no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—522no—
197C4⋊Q8—522no—
198C4×Q8—261no—
199C4×Q8—261no—
200C4×Q8—261no—
201C4×Q8—261no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—132no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—264no—
207C2×C4⋊C4C4×D1312yes—
208C2×C42—132no—
209C2×C42—261no—
210C2×C42C22×D1311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—132no—
214C4⋊C8—264no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217C4⋊C8C22⋊D1312yes—
218#101—522no—
219C22⋊C8—21no—
220C22⋊C8—261no—
221C4×C8—21no—
222C4×C8—264no—
223C4×C8—261no—
224#95—132no—
225#95—264no—
226C2×C13—21no—
227C2×C13—21no—
228C2×C13#188611yescharacteristic
229C2×C13#189311yescharacteristic
230C2×C13#191511yescharacteristic
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—132no—
238C2×Q8—132no—
239C2×Q8—261no—
240C2×Q8—261no—
241C2×Q8—261no—
242C2×Q8—261no—
243C22×C4—22no—
244C22×C4—132no—
245C22×C4—132no—
246C22×C4—262no—
247C22×C4C2×C4×D1311yescharacteristic
248C22×C4D4×D1311yescharacteristic
249C22×C4D4×D1311yescharacteristic
250M16—41no—
251M16—41no—
252M16—521no—
253M16—521no—
254C2×C8—22no—
255C2×C8—41no—
256C2×C8—262no—
257C2×C8—521no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—264no—
263C4⋊C4—262no—
264C4⋊C4—261no—
265C4⋊C4—262no—
266C4⋊C4—261no—
267C4⋊C4—528no—
268C42—262no—
269C42—262no—
270C42—521no—
271C42—521no—
272C42#612711yescharacteristic
273C42D4×D1311yescharacteristic
274C42#612911yescharacteristic
275C42C2×C22⋊D1311yescharacteristic
276C13#939411yescharacteristic, complemented, Sylow
277C23C22⋊C4×D1311yescharacteristic
278Q8—81no—
279Q8—81no—
280Q8—81no—
281Q8—81no—
282Q8—262no—
283Q8—262no—
284Q8—262no—
285Q8—262no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—134no—
292C2×C4—262no—
293C2×C4—262no—
294C2×C4—264no—
295C2×C4—262no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4#8813511yescharacteristic
300C2×C4#8813711yescharacteristic
301C2×C4#8813811yescharacteristic
302C2×C4D8×D1311yescharacteristic
303C2×C4#8816611yescharacteristic
304C2×C4SD16×D1311yescharacteristic
305C2×C4#8817011yescharacteristic
306C2×C4C4×C22⋊D1311yescharacteristic
307C2×C4#8819111yescharacteristic
308C2×C4#8819211yescharacteristic
309C8—42no—
310C8—81no—
311C8—522no—
312C8—1041no—
313C22—21no—
314C22—21no—
315C22D13×#10211yescharacteristic
316C22#1171843311yescharacteristic
317C22#1171861711yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—264no—
323C4—524no—
324C4—522no—
325C4#1171843611yescharacteristic
326C4#1171843911yescharacteristic
327C4#1171881811yescharacteristic
328C4#1171883211yescharacteristic
329C4#1171886612yes—
330C2—21no—
331C2—21no—
332C2#1311522611yescharacteristic
333C2#1311526111yescharacteristic
334C2#1311538511yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1546C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1546D13
hypocenterC13#9394
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
276. C13#9394semidirect

Maximal subgroups

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

subgroupindex
#131239162
#131198252
#131148292
#131135082
#131127382
#131127372
C13×#15462
#939413