Finite Group Databasebeta

← #15773563

Subgroups — #15773563

Order 3328.

444 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#88073C211yesmaximal, characteristic
2#13113174C211yesmaximal, 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—
18#11718868—21no—
19C4×#6099—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—
44C2×#6099—41no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88073—24no—
53C22⋊#1055—22no—
54C22⋊#1055—41no—
55#88043—41no—
56C4×#1055—41no—
57#11793—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C22⋊C411yescharacteristic
60C2×Q8×C13—41no—
61C2×Q8×C13—81no—
62C2×D4×C13—22no—
63C2×D4×C13—22no—
64C2×D4×C13—41no—
65C22×C4×C13—21no—
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—42no—
74C22×C4×C13—42no—
75C22×C4×C13—81no—
76C22×C4×C13—81no—
77C22×C4×C13—81no—
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—81no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C13×C22⋊C4—81no—
94C42×C13—21no—
95C42×C13—21no—
96#6099—24no—
97#6099—42no—
98#6099—82no—
99C2×#1055—42no—
100C2×#1055—42no—
101#2564D1311yescharacteristic
102C4×#100—131no—
103#1465—131no—
104#1354—132no—
105#1353—132no—
106C23×C13—21no—
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#10412yes—
116C23×C13C2×C22⋊C411yescharacteristic
117Q8×C13—82no—
118D4×C13—44no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
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—81no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—84no—
145C2×C4×C13#9911yescharacteristic
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13#13712yes—
148#1055—44no—
149#1055—82no—
150C2×C22⋊Q8Dic1311yescharacteristic
151C2×C4×D4C2×D1311yescharacteristic
152C2×#100—261no—
153#407—261no—
154C4×M16—261no—
155#400C2×D1311yescharacteristic
156#399Dic1311yescharacteristic
157#395C2×D1311yescharacteristic
158#393Dic1311yescharacteristic
159#387—21no—
160#386—21no—
161#385—21no—
162#380—21no—
163C2×#95Dic1311yescharacteristic
164#343—132no—
165#324—132no—
166#323—261no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—22no—
170C22×C13—42no—
171C22×C13—42no—
172C22×C13—42no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—81no—
179C22×C13C2×#9911yescharacteristic
180C22×C13#41911yescharacteristic
181C22×C13C2×#10411yescharacteristic
182C4×C13—21no—
183C4×C13—21no—
184C4×C13—22no—
185C4×C13—42no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13—81no—
192C22×Q8C2×Dic1311yescharacteristic
193C22×D4C22⋊D1311yescharacteristic
194C23×C4—21no—
195C23×C4C2×Dic1311yescharacteristic
196C23×C4C22⋊D1311yescharacteristic
197C2×M16—262no—
198C2×M16—521no—
199C22⋊Q8—41no—
200C22⋊Q8—41no—
201C4×D4—41no—
202C4×D4—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4C2×Dic1311yescharacteristic
207C2×C4⋊C4C22×D1311yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4C2×Dic1311yescharacteristic
212C2×C22⋊C4C22⋊D1311yescharacteristic
213C2×C42C22⋊D1311yescharacteristic
214#100—264no—
215C22⋊C8—262no—
216C22⋊C8—521no—
217#97—521no—
218C4×C8—521no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95C2×Dic1311yescharacteristic
225#95C2×Dic1311yescharacteristic
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—42no—
229C2×C13—81no—
230C2×C13#150811yescharacteristic
231C2×C13#212111yescharacteristic
232C2×C13#213211yescharacteristic
233C24C22⋊Dic1311yescharacteristic
234C24C22⋊Dic1311yescharacteristic
235C2×Q8—41no—
236C2×Q8—81no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—41no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—42no—
249C22×C4—42no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22⋊Dic1311yescharacteristic
255C22×C4C22×Dic1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258M16—264no—
259M16—522no—
260M16—1042no—
261C2×C8—522no—
262C2×C8—522no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—81no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—81no—
274C42—21no—
275C42—21no—
276C13#1179311yescharacteristic, complemented, Sylow
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23#8807712yes—
287C23C2×C22⋊Dic1311yescharacteristic
288Q8—82no—
289D4—44no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—42no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
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—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—84no—
316C2×C4#8807411yescharacteristic
317C2×C4#8807411yescharacteristic
318C2×C4#8819612yes—
319C8—524no—
320C8—1042no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22C2×#8807411yescharacteristic
334C22#1171888611yescharacteristic
335C22C2×#8807711yescharacteristic
336C4—22no—
337C4—21no—
338C4—21no—
339C4—42no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—81no—
344C4—81no—
345C4—81no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2#1311335611yescharacteristic
351C2#1311648211yescharacteristic
352C2#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#11793
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
276. C13#11793semidirect

Maximal subgroups

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

subgroupindex
C4×#880732
#131131742
#131128662
#131128632
C13×#25642
#1179313