Finite Group Databasebeta

← #15779186

Subgroups — #15779186

Order 3328.

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

normal subgroups only

This group has 642 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#13117327C211yesmaximal, characteristic
2#13114764C211yesmaximal, characteristic
3#13112962C214yesmaximal, complemented
4C13×#1785C211yesmaximal, characteristic
5C22×C13×#41C2211yescharacteristic
6C2×#88180C411yescharacteristic
7C22×C4×Dic13C411yescharacteristic
8C2×C13×#101C2212yes—
9C2×C13×#100—21no—
10C13×#407—21no—
11#11718891C2212yes—
12C2×#88076C2212yes—
13#11718882C412yes—
14#11718881—21no—
15#11718881—21no—
16C2×#88073—21no—
17C4×C22⋊Dic13—21no—
18C4×C22⋊Dic13—21no—
19#11718868—21no—
20C2×C13×#41—24no—
21C2×C13×#41—42no—
22C2×C13×#41—42no—
23C22×Q8×C13C2311yescharacteristic
24C22×D4×C13C2×C411yescharacteristic
25C22×D4×C13D411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C23×Dic13—21no—
31C2×C13×M16—22no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35#88180—42no—
36C2×C4⋊Dic13C2×C412yes—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—42no—
40C2×C4×Dic13C2×C412yes—
41C2×#6099—22no—
42C13×#101—24no—
43C13×#100—42no—
44C13×C22⋊C8—42no—
45#88076—24no—
46#88073—42no—
47#88071—22no—
48#88071—22no—
49C22⋊#1055—42no—
50#12861—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C22⋊C411yescharacteristic
53C24×C13C22⋊C411yescharacteristic
54C13×#41—416no—
55C2×Q8×C13—41no—
56C2×Q8×C13—41no—
57C2×Q8×C13#4114yes—
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—22no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13—44no—
83C22×Dic13—42no—
84C13×M16—42no—
85C13×M16—42no—
86C2×C8×C13—42no—
87C22⋊Dic13—44no—
88C22⋊Dic13—44no—
89C22⋊Dic13—42no—
90C4⋊Dic13—42no—
91C4×Dic13—42no—
92C4×Dic13—42no—
93C4×Dic13—42no—
94#6099—42no—
95#6099—42no—
96C2×#1055—42no—
97#2297—131no—
98#1785—131no—
99#1785D1311yescharacteristic
100#1394—134no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—42no—
110C23×C13—42no—
111C23×C13—42no—
112C23×C13#9912yes—
113C23×C13C2×C22⋊C411yescharacteristic
114Q8×C13—44no—
115D4×C13—44no—
116D4×C13—44no—
117D4×C13—44no—
118C2×C4×C13—28no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—44no—
128C2×C4×C13—44no—
129C2×C4×C13#9912yes—
130C2×C4×C13#11712yes—
131C2×C4×C13#12312yes—
132C2×C4×C13#12312yes—
133C2×Dic13—24no—
134C2×Dic13—42no—
135C2×Dic13—48no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C8×C13—82no—
141#1055—82no—
142C22×#41C2×D1311yescharacteristic
143C2×#117—131no—
144C22×C42—131no—
145C2×#101—132no—
146C2×#101C2×D1312yes—
147C2×#100—21no—
148C2×#100—261no—
149#407—21no—
150#407—261no—
151#391—132no—
152#390—132no—
153#386—261no—
154#386—261no—
155C4×C22⋊C4—261no—
156C4×C22⋊C4—261no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13—42no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—42no—
167C22×C13—42no—
168C22×C13—81no—
169C22×C13—81no—
170C22×C13#38111yescharacteristic
171C22×C13C2×#9911yescharacteristic
172C22×C13C2×#9911yescharacteristic
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—22no—
177Dic13—44no—
178Dic13—82no—
179C2×#41—24no—
180C2×#41—42no—
181C2×#41—42no—
182C22×Q8C22×D1311yescharacteristic
183C22×D4C4×D1311yescharacteristic
184C22×D4D5211yescharacteristic
185C22×D4C22⋊D1311yescharacteristic
186C23×C4—261no—
187C23×C4C4×D1311yescharacteristic
188C23×C4D5211yescharacteristic
189C23×C4C22⋊D1311yescharacteristic
190C2×M16—22no—
191C2×M16—262no—
192#117—522no—
193C2×C4⋊C4—132no—
194C2×C22⋊C4—261no—
195C2×C22⋊C4—262no—
196C2×C22⋊C4—262no—
197C2×C42—132no—
198C2×C42—261no—
199C2×C42—261no—
200C2×C42—522no—
201#101—24no—
202#101—264no—
203#100—42no—
204#100—522no—
205C22⋊C8—42no—
206C22⋊C8—522no—
207#95—262no—
208#95—262no—
209C2×C13—21no—
210C2×C13—21no—
211C2×C13—42no—
212C2×C13—81no—
213C2×C13—81no—
214C2×C13#181911yescharacteristic
215C2×C13#213212yes—
216C24#610311yescharacteristic
217C24#610311yescharacteristic
218C24#610311yescharacteristic
219#41—416no—
220C2×Q8—41no—
221C2×Q8—41no—
222C2×Q8#612914yes—
223C2×D4—22no—
224C2×D4—22no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—262no—
242C22×C4—262no—
243C22×C4—524no—
244C22×C4—522no—
245C22×C4#610311yescharacteristic
246C22×C4C2×C4×D1311yescharacteristic
247C22×C4C2×D5211yescharacteristic
248C22×C4C2×C22⋊D1311yescharacteristic
249M16—42no—
250M16—42no—
251M16—522no—
252M16—522no—
253C2×C8—42no—
254C2×C8—522no—
255C4⋊C4—522no—
256C22⋊C4—524no—
257C22⋊C4—524no—
258C22⋊C4—522no—
259C42—522no—
260C42—522no—
261C42—522no—
262C13#1286111yescharacteristic, complemented, Sylow
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—42no—
272C23—42no—
273C23—42no—
274C23#8804612yes—
275C23C2×#610311yescharacteristic
276Q8—44no—
277D4—44no—
278D4—44no—
279D4—44no—
280C2×C4—28no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—264no—
292C2×C4—522no—
293C2×C4—528no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4#8804612yes—
299C2×C4#8813112yes—
300C2×C4#8814012yes—
301C2×C4#8818912yes—
302C8—82no—
303C8—1042no—
304C22—22no—
305C22—22no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—42no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—81no—
316C22—81no—
317C22#1171860411yescharacteristic
318C22C2×#8804611yescharacteristic
319C22C2×#8804611yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—524no—
325C4—1042no—
326C2—21no—
327C2—21no—
328C2—42no—
329C2—81no—
330C2—81no—
331C2#1311490811yescharacteristic
332C2#1311651912yes—
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×Q8C22×D13
FittingC13×#1785C2
socleC22×C13C2×#99
prime radicalC22×C13×#41C22
cosocleC22×Q8×C13C23
hypercenter#1785D13
hypocenterC13#12861
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1785

Complements

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

NH ≅ G/Ntype
3. #13112962C2semidirect
262. C13#12861semidirect

Maximal subgroups

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

subgroupindex
#131173272
#131147642
#131129622
C13×#17852
#1286113