Finite Group Databasebeta

← #15781576

Subgroups — #15781576

Order 3328.

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

normal subgroups only

This group has 488 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#13119153C211yesmaximal, characteristic
2#13114828C211yesmaximal, characteristic
3#13112953C214yesmaximal
4C4×C13×#99C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic, complemented
7C2×C13×#99C2212yes—
8C4×C13×C22⋊C4—21no—
9#11718881C2212yes—
10C2×#88073C2212yes—
11#11718873—21no—
12#11718873C411yescharacteristic, complemented
13#11718647—21no—
14#11718610—21no—
15#11718607C412yescomplemented
16#11718589—21no—
17#11718585—21no—
18C13×#342—21no—
19#11718122—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13C2×C412yes—
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4C2×C411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C42×C13—41no—
31C2×C42×C13D411yescharacteristic
32C2×C22⋊Dic13—22no—
33C2×C22⋊Dic13C2×C412yes—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—41no—
38C2×C4⋊Dic13—41no—
39C2×#6101—22no—
40C2×#6099—22no—
41C13×#99—22no—
42C13×#99Q814yes—
43C13×#95—41no—
44#88073—24no—
45#88071—22no—
46#88071—21no—
47#88071—22no—
48C4⋊#1055—41no—
49C4⋊#1055—41no—
50#13295—131nomaximal, Sylow
51C24×C13C22×C411yescharacteristic
52C24×C13C2×D411yescharacteristic
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13C2×Q812yes—
56C2×D4×C13#4112yes—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—42no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—42no—
72C22×Dic13—82no—
73C13×C4⋊C4—41no—
74C13×C22⋊C4—24no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—42no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—82no—
81C22⋊Dic13—42no—
82C22⋊Dic13—82no—
83C4⋊Dic13—42no—
84C4⋊Dic13—42no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87#6101—82no—
88#6099—42no—
89#6099—42no—
90C2×#1055—42no—
91#2487—131no—
92#1800—131no—
93C4×#99D1311yescharacteristic
94#1390—134no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13C4×Q812yes—
105C23×C13C22⋊Q812yes—
106D4×C13—42no—
107D4×C13—42no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—44no—
121C2×C4×C13—81no—
122C2×C4×C13—82no—
123C2×C4×C13—82no—
124C2×C4×C13#9911yescharacteristic
125C2×C4×C13#9911yescharacteristic
126C2×C4×C13#12411yescharacteristic
127C2×C4×C13C4⋊Q811yescharacteristic
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—84no—
135#1055—82no—
136C2×C4×D4C2×D1311yescharacteristic
137C22×C4⋊C4—131no—
138#423—261no—
139C2×#100—132no—
140C2×#99C2×D1312yes—
141#400—261no—
142#399—261no—
143#389—261no—
144#386—132no—
145#385—132no—
146#380—131no—
147#380—261no—
148C4×C22⋊C4—21no—
149#343—261no—
150#342—21no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—42no—
156C22×C13—42no—
157C22×C13—42no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—81no—
163C22×C13#39111yescharacteristic
164C22×C13C2×#9911yescharacteristic
165C22×C13#41011yescharacteristic
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—84no—
173C4×C13#35212yes—
174Dic13—82no—
175Dic13—82no—
176C22×D4C22×D1311yescharacteristic
177C23×C4—132no—
178C23×C4C4×D1311yescharacteristic
179C23×C4C22⋊D1311yescharacteristic
180C2×M16—262no—
181C4×D4—41no—
182C4×D4—41no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—262no—
187C2×C4⋊C4—521no—
188C2×C4⋊C4—521no—
189C2×C4⋊C4D5211yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—132no—
192C2×C22⋊C4—262no—
193C2×C22⋊C4C4×D1311yescharacteristic
194C2×C22⋊C4C22⋊D1311yescharacteristic
195C2×C42—41no—
196C2×C42D5211yescharacteristic
197C4⋊C8—521no—
198C4⋊C8—521no—
199#100—264no—
200#99—22no—
201#99Dic2614yes—
202#95—41no—
203#95—261no—
204#95—262no—
205#95—262no—
206C2×C13—21no—
207C2×C13—21no—
208C2×C13—42no—
209C2×C13—42no—
210C2×C13#199611yescharacteristic
211C2×C13C2×#35211yescharacteristic
212C2×C13#212211yescharacteristic
213C24C2×C4×D1311yescharacteristic
214C24C2×C22⋊D1311yescharacteristic
215C2×D4—41no—
216C2×D4—41no—
217C2×D4C2×Dic2612yes—
218C2×D4#612712yes—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—42no—
226C22×C4—262no—
227C22×C4—262no—
228C22×C4—522no—
229C22×C4—1042no—
230C22×C4#610311yescharacteristic
231C22×C4#610311yescharacteristic
232C22×C4#610311yescharacteristic
233C22×C4#610311yescharacteristic
234C22×C4C2×D5211yescharacteristic
235M16—522no—
236M16—522no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—522no—
240C4⋊C4—522no—
241C4⋊C4—521no—
242C4⋊C4—521no—
243C4⋊C4—1042no—
244C22⋊C4—24no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—42no—
248C22⋊C4—522no—
249C22⋊C4—1042no—
250C42—21no—
251C42—21no—
252C42—82no—
253C13#1329511yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23C4×Dic2612yes—
263C23#8817812yes—
264C23C2×#610311yescharacteristic
265D4—42no—
266D4—42no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—81no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—522no—
284C2×C4—522no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—1044no—
290C2×C4#8804611yescharacteristic
291C2×C4#8804611yescharacteristic
292C2×C4#8812311yescharacteristic
293C2×C4#8812911yescharacteristic
294C8—1042no—
295C22—21no—
296C22—21no—
297C22—22no—
298C22—22no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#1171859011yescharacteristic
308C22C2×#8804611yescharacteristic
309C22#1171866711yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—84no—
317C4—1042no—
318C4—1042no—
319C4#1171806412yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—42no—
324C2#1311582111yescharacteristic
325C2C2×#1171806411yescharacteristic
326C2#1311648511yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC24×C13C22×C4
FrattiniC22×D4C22×D13
FittingC4×C13×#99C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#99D13
hypocenterC13#13295
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
6. C22×C4⋊Dic13C4semidirect
12. #11718873C4semidirect
15. #11718607C4semidirect
253. C13#13295semidirect

Maximal subgroups

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

subgroupindex
#131191532
#131148282
#131129532
C4×C13×#992
#1329513