Finite Group Databasebeta

← #15773448

Subgroups — #15773448

Order 3328.

462 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 87 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#13120216C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic
3#13112865C212yesmaximal, complemented
4#13112841C212yesmaximal, complemented
5C2×C13×#343C211yesmaximal, characteristic
6C22×C13×M16—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88178C411yescharacteristic
9#11718871—21no—
10#11718871—21no—
11C4×C22⋊Dic13C411yescharacteristic
12#11718868—21no—
13#11718644C411yescharacteristic
14#11718644C2211yescharacteristic
15#11718640C411yescharacteristic
16#11718640C2211yescharacteristic
17#11718633—21no—
18#11718633—21no—
19C13×#343—21no—
20C13×#343C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C2×C13×M16—24no—
28C2×C13×M16—22no—
29C2×C13×M16—41no—
30C2×C13×M16—42no—
31C22×C8×C13—41no—
32C2×C13×C4⋊C4—41no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4C2311yescharacteristic
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41#88178—41no—
42#88178—41no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×#6101—21no—
48C2×C4×Dic13—21no—
49C2×#6099—41no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56C22⋊#1055—22no—
57C22⋊#1055—41no—
58#11768—131nomaximal, Sylow
59C24×C13C22⋊C411yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—81no—
70C22×C4×C13—81no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C2×Dic26—41no—
82C2×Dic26—81no—
83C13×M16—24no—
84C13×M16—44no—
85C13×M16—42no—
86C2×C8×C13—44no—
87C2×C8×C13—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C22⋊Dic13—24no—
93C22⋊Dic13—41no—
94C22⋊Dic13—41no—
95C4⋊Dic13—41no—
96#6101—42no—
97#6101—42no—
98#6101—41no—
99#6101—41no—
100#6101—81no—
101#6101—81no—
102C4×Dic13—81no—
103#6099—82no—
104C2×#1055—42no—
105#2583—131no—
106C2×#343D1311yescharacteristic
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
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
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—21no—
129C2×C4×C13—42no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—81no—
135C2×C4×C13—81no—
136C2×C4×C13—81no—
137C2×C4×C13#10412yes—
138C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—22no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152Dic26—82no—
153C8×C13—44no—
154#1055—82no—
155C22×M16—21no—
156C2×C22⋊Q8—131no—
157C22×C4⋊C4C2×D1311yescharacteristic
158#407—261no—
159#398—131no—
160#398—131no—
161#395—131no—
162#395—131no—
163#389—261no—
164#389—261no—
165#385—261no—
166#385—261no—
167C4×C22⋊C4—131no—
168#343—21no—
169#343C2×D1312yes—
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—41no—
189C4×C13—41no—
190C4×C13—41no—
191C4×C13—41no—
192Dic13—42no—
193Dic13—42no—
194Dic13—81no—
195Dic13—81no—
196C22×Q8—131no—
197C23×C4C4×D1311yescharacteristic
198C23×C4D5211yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C2×M16—24no—
201C2×M16—22no—
202C2×M16—41no—
203C2×M16—42no—
204C2×M16—521no—
205C22×C8—41no—
206C22⋊Q8—521no—
207C22⋊Q8—521no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4C4×D1311yescharacteristic
217C2×C4⋊C4D5211yescharacteristic
218C2×C4⋊C4C22⋊D1311yescharacteristic
219C2×C4⋊C4C22×D1311yescharacteristic
220C2×C22⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C42—261no—
223C22⋊C8—262no—
224C22⋊C8—521no—
225#95—131no—
226#95—131no—
227#95—261no—
228#95—261no—
229#95—261no—
230#95—261no—
231C2×C13—21no—
232C2×C13—21no—
233C2×C13—22no—
234C2×C13—41no—
235C2×C13#150411yescharacteristic
236C2×C13#212111yescharacteristic
237C2×C13C2×#35611yescharacteristic
238C24#610311yescharacteristic
239C2×Q8—521no—
240C2×Q8—1041no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4#610311yescharacteristic
257C22×C4#610311yescharacteristic
258C22×C4#610311yescharacteristic
259C22×C4C2×C4×D1311yescharacteristic
260C22×C4C2×D5211yescharacteristic
261C22×C4C2×C22⋊D1311yescharacteristic
262M16—24no—
263M16—44no—
264M16—42no—
265M16—1042no—
266C2×C8—44no—
267C2×C8—42no—
268C2×C8—522no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—521no—
274C4⋊C4—522no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4—522no—
278C4⋊C4—1041no—
279C4⋊C4—1041no—
280C22⋊C4—264no—
281C22⋊C4—521no—
282C22⋊C4—521no—
283C42—1041no—
284C13#1176811yescharacteristic, complemented, Sylow
285C23—22no—
286C23—21no—
287C23—21no—
288C23—41no—
289C23#8804611yescharacteristic
290C23#8804611yescharacteristic
291C23C2×#610311yescharacteristic
292Q8—1042no—
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—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—262no—
314C2×C4—262no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4#8804512yes—
326C2×C4#8818611yescharacteristic
327C2×C4#8819611yescharacteristic
328C8—44no—
329C8—1042no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—42no—
338C22—42no—
339C22#1171807012yes—
340C22C2×#8804511yescharacteristic
341C22C2×#8804611yescharacteristic
342C22#1171862711yescharacteristic
343C4—21no—
344C4—21no—
345C4—22no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—522no—
351C4—522no—
352C4—1041no—
353C4—1041no—
354C2—21no—
355C2—21no—
356C2—22no—
357C2—41no—
358C2#1311333811yescharacteristic
359C2#1311648311yescharacteristic
360C2C2×#1171807011yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC2×C13×#343C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenterC2×#343D13
hypocenterC13#11768
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
3. #13112865C2semidirect
4. #13112841C2semidirect
284. C13#11768semidirect

Maximal subgroups

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

subgroupindex
#131202162
#131131662
#131128652
#131128412
C2×C13×#3432
#1176813