Finite Group Databasebeta

← #15758003

Subgroups — #15758003

Order 3328.

516 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 107 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#13118119C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic, complemented
3#13113278C212yesmaximal
4#13112728C212yesmaximal, complemented
5C13×#2983C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×D52C2211yescharacteristic
8C13×#446—24no—
9C13×#432—21no—
10C13×#432C2212yes—
11C13×#431—21no—
12#11718892—21no—
13C2×#88076—21no—
14#11718654—21no—
15#11718652C411yescharacteristic
16#11718652C411yescharacteristic
17#11718647C411yescharacteristic
18#11718647C411yescharacteristic
19C4×#6103—21no—
20C4×#6103—21no—
21#11718593C2211yescharacteristic
22C4×#6099C2212yes—
23#11718122—21no—
24#11718075—24no—
25C22×Q8×C13D411yescharacteristic
26C22×D52C2×C411yescharacteristic
27C22×C4×D13—21no—
28C4×Q8×C13—22no—
29C4×Q8×C13—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×#6103—21no—
37C2×#6103—21no—
38C2×#6103—21no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×C4×Dic13—21no—
43C2×#6099—22no—
44C4×D52—22no—
45C4×D52—22no—
46C13×C4⋊C8—22no—
47C13×C4⋊C8—22no—
48C13×C4⋊C8D414yes—
49C13×C22⋊C8—22no—
50C13×#97—22no—
51C13×#97—22no—
52C4×C8×C13—22no—
53#88076—24no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071C2×C411yescharacteristic
60#88071C2×C411yescharacteristic
61#88043—22no—
62C4×#1055—22no—
63#9032—131nomaximal, Sylow
64C23×D13—21no—
65C2×Q8×C13—22no—
66C2×Q8×C13—22no—
67C2×Q8×C13—41no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×D52—22no—
79C2×D52—42no—
80C2×C4×D13—42no—
81C2×C4×D13—42no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C8×C13—24no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13C2×D412yes—
93C42×C13#4112yes—
94#6103—42no—
95#6103—42no—
96#6103—42no—
97#6103—42no—
98#6103—42no—
99C4⋊Dic13—22no—
100C4×Dic13—42no—
101#6099—24no—
102#6099—42no—
103C2×#1055—42no—
104#2983D1311yescharacteristic, complemented
105#2398—131no—
106C4×#101—131no—
107#1490—132no—
108#1300—132no—
109C23×C13C2×C22⋊C411yescharacteristic
110C22×D13—22no—
111C22×D13—41no—
112C22×D13—41no—
113C22×D13—41no—
114C22×D13—41no—
115C22×D13—41no—
116C22×D13—41no—
117Q8×C13—44no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—22no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13#10412yes—
132C2×C4×C13C4×D412yes—
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13#12112yes—
135C2×C4×C13#12311yescharacteristic
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145D52—24no—
146D52—42no—
147C4×D13—82no—
148C4×D13—82no—
149C8×C13—44no—
150#1055—44no—
151C2×C4×Q8C2×D1311yescharacteristic
152C2×C4×D4—131no—
153#446—24no—
154#432—21no—
155#432C2×D1312yes—
156#431—21no—
157C2×#101—261no—
158C4×M16—132no—
159#400—131no—
160#400—131no—
161#397—261no—
162#394—131no—
163#394—131no—
164#393—261no—
165C4×C22⋊C4—261no—
166C4×C22⋊C4—261no—
167#376—131no—
168#343—261no—
169D4⋊C8—264no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13#38611yescharacteristic
173C22×C13C2×#10411yescharacteristic
174C22×C13#42111yescharacteristic
175C2×D13—42no—
176C2×D13—42no—
177C2×D13—42no—
178C2×D13—81no—
179C2×D13—81no—
180C2×D13—81no—
181C2×D13—81no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—21no—
185C4×C13—22no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13#45412yes—
190Dic13—81no—
191Dic13—81no—
192Dic13—81no—
193C22×Q8D5211yescharacteristic
194C22×D4—131no—
195C23×C4—261no—
196C2×M16—262no—
197C4×Q8—22no—
198C4×Q8—22no—
199C4×D4—262no—
200C4×D4—262no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4C4×D1311yescharacteristic
203C2×C4⋊C4C4×D1311yescharacteristic
204C2×C4⋊C4D5211yescharacteristic
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C22⋊C4—261no—
208C2×C22⋊C4—261no—
209C2×C22⋊C4—261no—
210C2×C42—261no—
211C2×C42C22⋊D1311yescharacteristic
212C2×C42C22⋊D1311yescharacteristic
213C2×C42C22×D1311yescharacteristic
214C4⋊C8—22no—
215C4⋊C8—22no—
216C4⋊C8C22⋊D1314yes—
217#101—264no—
218C22⋊C8—22no—
219#97—22no—
220#97—22no—
221#97—262no—
222C4×C8—22no—
223C4×C8—262no—
224#95—131no—
225#95—131no—
226#95—261no—
227#95—261no—
228#95—261no—
229#95—261no—
230#95—261no—
231C2×C13—21no—
232C2×C13—21no—
233C2×C13#187111yescharacteristic
234C2×C13#188811yescharacteristic
235C2×C13#189111yescharacteristic
236D13—82no—
237C24—261no—
238C2×Q8—22no—
239C2×Q8—22no—
240C2×Q8—41no—
241C2×D4—262no—
242C2×D4—522no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—522no—
247C22×C4—522no—
248C22×C4—521no—
249C22×C4—521no—
250C22×C4#610311yescharacteristic
251C22×C4#610311yescharacteristic
252C22×C4#610311yescharacteristic
253C22×C4#610311yescharacteristic
254C22×C4C2×C4×D1311yescharacteristic
255C22×C4C2×D5211yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257M16—264no—
258M16—522no—
259C2×C8—24no—
260C2×C8—522no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—22no—
264C4⋊C4—262no—
265C22⋊C4—522no—
266C22⋊C4—522no—
267C22⋊C4—522no—
268C22⋊C4—522no—
269C22⋊C4—522no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—522no—
275C42#612712yes—
276C42C2×C22⋊D1312yes—
277C13#903211yescharacteristic, complemented, Sylow
278C23—262no—
279C23—521no—
280C23—521no—
281C23—521no—
282C23—521no—
283C23—521no—
284C23—521no—
285C23C2×#610311yescharacteristic
286Q8—44no—
287D4—264no—
288D4—522no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—1042no—
312C2×C4—1042no—
313C2×C4#8806512yes—
314C2×C4C4×C22⋊D1312yes—
315C2×C4#8818311yescharacteristic
316C2×C4#8818412yes—
317C2×C4#8820711yescharacteristic
318C8—44no—
319C8—524no—
320C22—21no—
321C22—21no—
322C22—522no—
323C22—522no—
324C22—522no—
325C22—1041no—
326C22—1041no—
327C22—1041no—
328C22—1041no—
329C22C2×#8806511yescharacteristic
330C22#1171880011yescharacteristic
331C22#1171887411yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—1041no—
340C4—1041no—
341C4—1041no—
342C4#1171890612yes—
343C2—21no—
344C2—21no—
345C2—1042no—
346C2#1311513811yescharacteristic
347C2#1311523911yescharacteristic
348C2#1311525411yescharacteristic
subgroupG/H
centerC2×C4#88207
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#386
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#9032
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. C4×#88076C2semidirect
4. #13112728C2semidirect
5. C13×#2983C2semidirect
104. #2983D13semidirect
277. C13#9032semidirect

Maximal subgroups

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

subgroupindex
#131181192
C4×#880762
#131132782
#131127282
C13×#29832
#903213