Finite Group Databasebeta

← #15773450

Subgroups — #15773450

Order 3328.

462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#11718122C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic
3#13112866C212yesmaximal, complemented
4#13112842C212yesmaximal, complemented
5C13×#2583C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C22×#6099—21no—
9C13×#398C411yescharacteristic
10C13×#398C2211yescharacteristic
11C13×#395C411yescharacteristic
12C13×#395C2211yescharacteristic
13C13×#389—21no—
14C13×#389—21no—
15C13×#385—21no—
16C13×#385—21no—
17C4×C13×C22⋊C4C411yescharacteristic
18#11718868—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—41no—
28C13×C22⋊Q8—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4C2311yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C42×C13—21no—
44C2×#6099—24no—
45C2×#6099—22no—
46C2×#6099—41no—
47C2×#6099—42no—
48C2×#6099—41no—
49C22×#1055—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95C2×C411yescharacteristic
55C13×#95C2×C411yescharacteristic
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11768—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C2×Q8×C13—41no—
61C2×Q8×C13—81no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
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—21no—
74C22×C4×C13—21no—
75C22×C4×C13—81no—
76C22×C4×C13—81no—
77C22×C4×C13C22⋊C411yescharacteristic
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—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—42no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—81no—
93C13×C4⋊C4—81no—
94C13×C22⋊C4—24no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C42×C13—81no—
98#6099—24no—
99#6099—44no—
100#6099—42no—
101#6099—82no—
102C2×#1055—44no—
103C2×#1055—42no—
104C2×#1055—42no—
105#2583D1311yescharacteristic
106C2×#343—131no—
107#1463—131no—
108#1354—132no—
109#1346—132no—
110C23×C13—22no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—41no—
114C23×C13#9911yescharacteristic
115C23×C13#9911yescharacteristic
116C23×C13C2×C22⋊C411yescharacteristic
117Q8×C13—82no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—42no—
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—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—81no—
148C2×C4×C13—81no—
149C2×C4×C13—81no—
150C2×C4×C13#10412yes—
151C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C13#13711yescharacteristic
153#1055—44no—
154#1055—82no—
155C22×M16—261no—
156C2×C22⋊Q8Dic1311yescharacteristic
157C22×C4⋊C4C2×D1311yescharacteristic
158#407—261no—
159#398Dic1311yescharacteristic
160#398C2×D1311yescharacteristic
161#395Dic1311yescharacteristic
162#395C2×D1311yescharacteristic
163#389—21no—
164#389—21no—
165#385—21no—
166#385—21no—
167C4×C22⋊C4Dic1311yescharacteristic
168#343—132no—
169#343—261no—
170#324—132no—
171#324—261no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—42no—
180C22×C13—42no—
181C22×C13#35612yes—
182C22×C13C2×#9911yescharacteristic
183C22×C13#41711yescharacteristic
184C22×C13C2×#10411yescharacteristic
185C4×C13—21no—
186C4×C13—22no—
187C4×C13—21no—
188C4×C13—42no—
189C4×C13—42no—
190C4×C13—41no—
191C4×C13—41no—
192C4×C13—41no—
193C4×C13—41no—
194C4×C13—81no—
195C4×C13—81no—
196C22×Q8C2×Dic1311yescharacteristic
197C23×C4C2×Dic1311yescharacteristic
198C23×C4C22⋊D1311yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C2×M16—264no—
201C2×M16—262no—
202C2×M16—521no—
203C2×M16—522no—
204C2×M16—521no—
205C22×C8—521no—
206C22⋊Q8—41no—
207C22⋊Q8—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4C2×Dic1311yescharacteristic
216C2×C4⋊C4C2×Dic1311yescharacteristic
217C2×C4⋊C4C22⋊D1311yescharacteristic
218C2×C4⋊C4C22⋊D1311yescharacteristic
219C2×C4⋊C4C22×D1311yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C42—21no—
223C22⋊C8—262no—
224C22⋊C8—521no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95C2×Dic1311yescharacteristic
230#95C2×Dic1311yescharacteristic
231C2×C13—21no—
232C2×C13—21no—
233C2×C13—22no—
234C2×C13—41no—
235C2×C13#150411yescharacteristic
236C2×C13#212111yescharacteristic
237C2×C13C2×#35611yescharacteristic
238C24C22⋊Dic1311yescharacteristic
239C2×Q8—41no—
240C2×Q8—81no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—21no—
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—21no—
254C22×C4—81no—
255C22×C4—81no—
256C22×C4C22⋊Dic1311yescharacteristic
257C22×C4C22⋊Dic1311yescharacteristic
258C22×C4C22⋊Dic1311yescharacteristic
259C22×C4C22×Dic1311yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261C22×C4C2×C22⋊D1311yescharacteristic
262M16—264no—
263M16—524no—
264M16—522no—
265M16—1042no—
266C2×C8—524no—
267C2×C8—522no—
268C2×C8—522no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—42no—
275C4⋊C4—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C22⋊C4—24no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—81no—
284C13#1176811yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—22no—
288C23—41no—
289C23#8807411yescharacteristic
290C23#8807411yescharacteristic
291C23C2×C22⋊Dic1311yescharacteristic
292Q8—82no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—42no—
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—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4#8807712yes—
326C2×C4#8820311yescharacteristic
327C2×C4#8820511yescharacteristic
328C8—524no—
329C8—1042no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22#1171814012yes—
340C22C2×#8807411yescharacteristic
341C22#1171889311yescharacteristic
342C22C2×#8807711yescharacteristic
343C4—21no—
344C4—22no—
345C4—21no—
346C4—42no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—81no—
353C4—81no—
354C2—21no—
355C2—21no—
356C2—22no—
357C2—41no—
358C2#1311334011yescharacteristic
359C2#1311648211yescharacteristic
360C2C2×#1171814011yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2583C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2583D13
hypocenterC13#11768
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2583

Complements

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

NH ≅ G/Ntype
3. #13112866C2semidirect
4. #13112842C2semidirect
284. C13#11768semidirect

Maximal subgroups

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

subgroupindex
C2×#117181222
#131131662
#131128662
#131128422
C13×#25832
#1176813