Finite Group Databasebeta

← #15756395

Subgroups — #15756395

Order 3328.

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

normal subgroups only

This group has 656 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#13114754C211yesmaximal, characteristic
3#13112690C214yesmaximal, complemented
4C13×#1785C211yesmaximal, characteristic
5C22×C13×#41C2211yescharacteristic
6C2×#88180C411yescharacteristic, complemented
7C22×C4×Dic13C411yescharacteristic, complemented
8C2×C13×#101—21no—
9C2×C13×#100—21no—
10C13×#407C2212yes—
11#11718891—21no—
12#11718882—21no—
13#11718881—21no—
14#11718881—21no—
15C2×#88074—21no—
16C2×#88074—21no—
17#11718872C2212yes—
18C4×C22⋊Dic13C412yescomplemented
19C4×C22⋊Dic13C2212yes—
20C2×C13×#41—24no—
21C2×C13×#41—42no—
22C2×C13×#41—42no—
23C22×Q8×C13D411yescharacteristic
24C22×D4×C13D411yescharacteristic
25C22×D4×C13D411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2311yescharacteristic
30C23×Dic13—21no—
31C2×C13×M16—22no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13—22no—
36#88180—42no—
37C2×C4⋊Dic13—21no—
38C2×C4×Dic13—21no—
39C2×C4×Dic13—42no—
40C2×C4×Dic13C2×C412yes—
41C2×C4×Dic13C2×C412yes—
42C13×#101—42no—
43C13×#100—42no—
44C13×C22⋊C8—24no—
45#88074—42no—
46#88074—42no—
47#88071—22no—
48#88071—22no—
49#88071—24no—
50#8739—131nomaximal, Sylow
51C24×C13C22⋊C411yescharacteristic
52C24×C13C22⋊C411yescharacteristic
53C24×C13C2×D411yescharacteristic
54C13×#41—416no—
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13—41no—
58C2×D4×C13—22no—
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—22no—
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—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4114yes—
80C22×Dic13—22no—
81C22×Dic13—22no—
82C22×Dic13—44no—
83C22×Dic13—42no—
84C22×Dic13—42no—
85C13×M16—42no—
86C13×M16—42no—
87C2×C8×C13—42no—
88C22⋊Dic13—44no—
89C22⋊Dic13—44no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C4⋊Dic13—42no—
94C4×Dic13—42no—
95C4×Dic13—42no—
96C4×Dic13—42no—
97#2297—131no—
98#1785D1311yescharacteristic
99#1782—131no—
100#1284—134no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—42no—
111C23×C13#9912yes—
112C23×C13C2×C22⋊C411yescharacteristic
113C23×C13#12312yes—
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—21no—
128C2×C4×C13—44no—
129C2×C4×C13—44no—
130C2×C4×C13#9912yes—
131C2×C4×C13#11712yes—
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—
140C2×Dic13—82no—
141C2×Dic13—84no—
142C8×C13—82no—
143C22×#41C2×D1311yescharacteristic
144C2×#117—131no—
145C22×C42—131no—
146C2×#101—21no—
147C2×#100—21no—
148C2×#99—261no—
149C2×#99—261no—
150#407C2×D1312yes—
151#391—261no—
152#390—261no—
153#386—261no—
154#386—261no—
155#381—132no—
156C4×C22⋊C4—132no—
157C4×C22⋊C4—132no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—24no—
162C22×C13—42no—
163C22×C13—42no—
164C22×C13—42no—
165C22×C13—41no—
166C22×C13—42no—
167C22×C13—81no—
168C22×C13—81no—
169C22×C13—81no—
170C22×C13—81no—
171C22×C13#38111yescharacteristic
172C22×C13C2×#9911yescharacteristic
173C22×C13C2×#9911yescharacteristic
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—41no—
178Dic13—44no—
179Dic13—82no—
180Dic13—162no—
181C2×#41—24no—
182C2×#41—42no—
183C2×#41—42no—
184C22×Q8C22⋊D1311yescharacteristic
185C22×D4D5211yescharacteristic
186C22×D4D5211yescharacteristic
187C22×D4C22⋊D1311yescharacteristic
188C23×C4—261no—
189C23×C4C4×D1311yescharacteristic
190C23×C4C4×D1311yescharacteristic
191C23×C4C22×D1311yescharacteristic
192C2×M16—22no—
193#117—522no—
194C2×C4⋊C4—261no—
195C2×C22⋊C4—261no—
196C2×C22⋊C4—262no—
197C2×C22⋊C4—262no—
198C2×C22⋊C4—262no—
199C2×C42—132no—
200C2×C42—132no—
201C2×C42—261no—
202C2×C42—522no—
203#101—42no—
204#100—42no—
205#99—522no—
206#99—522no—
207C22⋊C8—24no—
208#95—262no—
209#95—262no—
210#95—264no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—42no—
214C2×C13—42no—
215C2×C13—81no—
216C2×C13#181911yescharacteristic
217C2×C13#182712yes—
218C24#610311yescharacteristic
219C24#610311yescharacteristic
220C24C2×D5211yescharacteristic
221#41—416no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—41no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—262no—
243C22×C4—262no—
244C22×C4—524no—
245C22×C4—522no—
246C22×C4—522no—
247C22×C4#610311yescharacteristic
248C22×C4#610311yescharacteristic
249C22×C4C2×C4×D1311yescharacteristic
250C22×C4#612914yes—
251C22×C4C2×C22⋊D1311yescharacteristic
252M16—42no—
253M16—42no—
254C2×C8—42no—
255C4⋊C4—522no—
256C22⋊C4—524no—
257C22⋊C4—524no—
258C22⋊C4—522no—
259C22⋊C4—522no—
260C22⋊C4—522no—
261C42—522no—
262C42—522no—
263C42—522no—
264C13#873911yescharacteristic, complemented, Sylow
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23#8804612yes—
276C23#8814012yes—
277C23C2×#610311yescharacteristic
278Q8—44no—
279D4—44no—
280D4—44no—
281D4—44no—
282C2×C4—28no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—264no—
295C2×C4—522no—
296C2×C4—528no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—1042no—
302C2×C4—1044no—
303C2×C4#8804612yes—
304C2×C4#8813112yes—
305C2×C4#8818912yes—
306C8—82no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—24no—
311C22—42no—
312C22—42no—
313C22—42no—
314C22—41no—
315C22—42no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22#1171860411yescharacteristic
321C22C2×#8804611yescharacteristic
322C22C2×#8804611yescharacteristic
323C4—22no—
324C4—22no—
325C4—22no—
326C4—41no—
327C4—524no—
328C4—1042no—
329C4—2082no—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2—81no—
335C2#1311490811yescharacteristic
336C2#1311494112yes—
subgroupG/H
centerC22#11718604
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1785C2
socleC22×C13#381
prime radicalC22×C13×#41C22
cosocleC23×C4×C13C23
hypercenter#1785D13
hypocenterC13#8739
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1785

Complements

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

NH ≅ G/Ntype
3. #13112690C2semidirect
6. C2×#88180C4semidirect
7. C22×C4×Dic13C4semidirect
18. C4×C22⋊Dic13C4semidirect
264. C13#8739semidirect

Maximal subgroups

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

subgroupindex
#131173272
#131147542
#131126902
C13×#17852
#873913