Finite Group Databasebeta

← #15774078

Subgroups — #15774078

Order 3328.

440 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 103 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#13114828C211yesmaximal, characteristic
2#13113154C211yesmaximal, characteristic
3#13112866C212yesmaximal, complemented
4#13112863C212yesmaximal, complemented
5C13×#2564C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#400C2211yescharacteristic
9C13×#399C411yescharacteristic
10C13×#395C2211yescharacteristic
11C13×#393C411yescharacteristic
12C13×#387—21no—
13C13×#386—21no—
14C13×#385—21no—
15C13×#380—21no—
16C2×C13×#95C411yescharacteristic
17C2×#88073—21no—
18C2×C22⋊#1055—21no—
19#11718585—21no—
20#11718122C2212yes—
21#11718120C2212yes—
22#11718117—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13D411yescharacteristic
25C23×C4×C13—21no—
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×C22⋊Q8—41no—
29C13×C22⋊Q8—41no—
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2311yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×#6099—22no—
44C22×#1055—41no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88073—42no—
53C22⋊#1055—22no—
54C22⋊#1055—41no—
55C4⋊#1055—41no—
56C4⋊#1055—41no—
57#11906—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C22⋊C411yescharacteristic
60C2×Q8×C13—41no—
61C2×Q8×C13—81no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13SD1612yes—
65C2×D4×C13Q1612yes—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13—81no—
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—81no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—81no—
95C42×C13—21no—
96C42×C13—21no—
97#6099—42no—
98#6099—42no—
99C2×#1055—42no—
100C2×#1055—42no—
101C2×#1055—82no—
102#2564D1311yescharacteristic
103#1800—131no—
104#1459—131no—
105#1354—132no—
106#1353—132no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13#10312yes—
116C23×C13#10312yes—
117C23×C13C2×C22⋊C411yescharacteristic
118Q8×C13—82no—
119D4×C13—42no—
120D4×C13—42no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—22no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13—84no—
147C2×C4×C13#9911yescharacteristic
148C2×C4×C13#9911yescharacteristic
149C2×C4×C13C2×SD1611yescharacteristic
150C2×C4×C13C2×Q1611yescharacteristic
151#1055—82no—
152#1055—82no—
153C2×C22⋊Q8Dic1311yescharacteristic
154C2×C4×D4C2×D1311yescharacteristic
155#423—261no—
156C2×#100—261no—
157C2×C22⋊C8—261no—
158#400C2×D1311yescharacteristic
159#399Dic1311yescharacteristic
160#395C2×D1311yescharacteristic
161#393Dic1311yescharacteristic
162#387—21no—
163#386—21no—
164#385—21no—
165#380—21no—
166C2×#95Dic1311yescharacteristic
167#343—132no—
168#324—132no—
169#323—261no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—42no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—81no—
182C22×C13C2×#9911yescharacteristic
183C22×C13C2×#10311yescharacteristic
184C22×C13#42111yescharacteristic
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—42no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—81no—
194C4×C13—81no—
195C4×C13—81no—
196C22×Q8C2×Dic1311yescharacteristic
197C22×D4C22⋊D1311yescharacteristic
198C23×C4—21no—
199C23×C4C2×Dic1311yescharacteristic
200C23×C4C22⋊D1311yescharacteristic
201C2×M16—262no—
202C22×C8—521no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×Dic1311yescharacteristic
211C2×C4⋊C4C22×D1311yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4C2×Dic1311yescharacteristic
216C2×C22⋊C4C22⋊D1311yescharacteristic
217C2×C42C22⋊D1311yescharacteristic
218C4⋊C8—521no—
219C4⋊C8—521no—
220#100—522no—
221C22⋊C8—262no—
222C22⋊C8—521no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95C2×Dic1311yescharacteristic
229#95C2×Dic1311yescharacteristic
230C2×C13—21no—
231C2×C13—21no—
232C2×C13—42no—
233C2×C13—42no—
234C2×C13#152011yescharacteristic
235C2×C13#212111yescharacteristic
236C2×C13#213211yescharacteristic
237C24C22⋊Dic1311yescharacteristic
238C24C22⋊Dic1311yescharacteristic
239C2×Q8—41no—
240C2×Q8—81no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4#610612yes—
244C2×D4#610712yes—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—81no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4C22⋊Dic1311yescharacteristic
259C22×C4C22⋊Dic1311yescharacteristic
260C22×C4C22×Dic1311yescharacteristic
261C22×C4C2×C22⋊D1311yescharacteristic
262C22×C4C2×C22⋊D1311yescharacteristic
263M16—522no—
264M16—522no—
265C2×C8—522no—
266C2×C8—522no—
267C2×C8—1042no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—42no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—81no—
274C22⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—81no—
279C42—21no—
280C42—21no—
281C13#1190611yescharacteristic, complemented, Sylow
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23#8807512yes—
291C23#8807512yes—
292C23C2×C22⋊Dic1311yescharacteristic
293Q8—82no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—84no—
322C2×C4#8807411yescharacteristic
323C2×C4#8807411yescharacteristic
324C2×C4C2×#610611yescharacteristic
325C2×C4C2×#610711yescharacteristic
326C8—1042no—
327C8—1042no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—81no—
340C22C2×#8807411yescharacteristic
341C22C2×#8807511yescharacteristic
342C22#1171889711yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—81no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—42no—
358C2#1311340811yescharacteristic
359C2#1311648211yescharacteristic
360C2#1311652111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2564C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenter#2564D13
hypocenterC13#11906
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2564

Complements

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

NH ≅ G/Ntype
3. #13112866C2semidirect
4. #13112863C2semidirect
281. C13#11906semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131131542
#131128662
#131128632
C13×#25642
#1190613