Finite Group Databasebeta

← #15781593

Subgroups — #15781593

Order 3328.

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

normal subgroups only

This group has 500 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#13120009C211yesmaximal, characteristic
2#13114824C211yesmaximal, characteristic
3#13112960C214yesmaximal
4C4×C13×#99C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C2×#88123C411yescharacteristic, complemented
7C2×C13×#99C2212yes—
8C4×C13×C22⋊C4—21no—
9#11718882C2212yes—
10C2×#88074C2212yes—
11#11718873—21no—
12#11718873—21no—
13#11718873—21no—
14#11718638C412yescomplemented
15#11718608—21no—
16#11718608—21no—
17C4×C4⋊Dic13C411yescharacteristic, complemented
18C13×#342—21no—
19#11718118—21no—
20C22×D4×C13C2311yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C22×Dic26—21no—
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4D411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C42×C13—41no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C22⋊Dic13—22no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—41no—
38C2×C4⋊Dic13C2×C412yes—
39C2×C4×Dic13C2×C412yes—
40#88123—41no—
41#88123—41no—
42C13×#99—22no—
43C13×#99Q814yescomplemented
44C13×#95—41no—
45#88074—24no—
46#88071—21no—
47#88071—22no—
48#88071—22no—
49#88071—41no—
50#13299—131nomaximal, Sylow
51C24×C13C2×D411yescharacteristic
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×C13C22×C411yescharacteristic
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—42no—
72C2×Dic26—42no—
73C2×Dic26—82no—
74C13×C4⋊C4—41no—
75C13×C22⋊C4—24no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—41no—
78C13×C22⋊C4—42no—
79C42×C13—21no—
80C42×C13—21no—
81C42×C13—82no—
82C22⋊Dic13—42no—
83C22⋊Dic13—42no—
84C22⋊Dic13—82no—
85C22⋊Dic13—82no—
86C4⋊Dic13—42no—
87C4⋊Dic13—41no—
88C4⋊Dic13—41no—
89C4⋊Dic13—42no—
90C4⋊Dic13—82no—
91C4×Dic13—42no—
92#2563—131no—
93#1799—131no—
94C4×#99D1311yescharacteristic
95#1393—134no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13C22⋊Q812yes—
106C23×C13#12411yescharacteristic
107C23×C13C4⋊Q811yescharacteristic
108D4×C13—42no—
109D4×C13—42no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—44no—
122C2×C4×C13—81no—
123C2×C4×C13—81no—
124C2×C4×C13—82no—
125C2×C4×C13—82no—
126C2×C4×C13#9911yescharacteristic
127C2×C4×C13#9911yescharacteristic
128C2×C4×C13C4×Q812yes—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—82no—
136C2×Dic13—82no—
137C2×Dic13—82no—
138Dic26—84no—
139C2×C4⋊Q8—131no—
140C2×C4×D4C2×D1311yescharacteristic
141C2×#99—132no—
142C2×#99C2×D1312yes—
143#393—261no—
144#393—261no—
145#390—132no—
146#382—132no—
147#380—261no—
148#380—261no—
149#380—261no—
150C4×C4⋊C4—131no—
151C4×C22⋊C4—21no—
152#342—21no—
153#342—261no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—22no—
158C22×C13—21no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13#39111yescharacteristic
169C22×C13C2×#9911yescharacteristic
170C22×C13#41011yescharacteristic
171C4×C13—21no—
172C4×C13—22no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—84no—
177C4×C13#35412yes—
178Dic13—82no—
179Dic13—82no—
180Dic13—162no—
181C22×Q8—261no—
182C22×D4C22×D1311yescharacteristic
183C23×C4D5211yescharacteristic
184C23×C4C22⋊D1311yescharacteristic
185C4⋊Q8—521no—
186C4⋊Q8—521no—
187C4×D4—41no—
188C4×D4—41no—
189C2×C4⋊C4—132no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—521no—
193C2×C4⋊C4C4×D1311yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—262no—
196C2×C22⋊C4—262no—
197C2×C22⋊C4—262no—
198C2×C22⋊C4D5211yescharacteristic
199C2×C22⋊C4C22⋊D1311yescharacteristic
200C2×C42—41no—
201C2×C42—132no—
202C2×C42C4×D1311yescharacteristic
203#99—22no—
204#99—264no—
205#99Dic2614yescomplemented
206#95—41no—
207#95—261no—
208#95—262no—
209#95—262no—
210#95—521no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—41no—
214C2×C13—42no—
215C2×C13—41no—
216C2×C13#199611yescharacteristic
217C2×C13C2×#35411yescharacteristic
218C2×C13#212811yescharacteristic
219C24C2×D5211yescharacteristic
220C24C2×C22⋊D1311yescharacteristic
221C2×Q8—522no—
222C2×Q8—1042no—
223C2×D4—41no—
224C2×D4—41no—
225C2×D4C2×Dic2612yes—
226C2×D4#612712yes—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—262no—
235C22×C4—262no—
236C22×C4—522no—
237C22×C4#610311yescharacteristic
238C22×C4#610311yescharacteristic
239C22×C4#610311yescharacteristic
240C22×C4#610311yescharacteristic
241C22×C4C2×C4×D1311yescharacteristic
242C4⋊C4—41no—
243C4⋊C4—522no—
244C4⋊C4—522no—
245C4⋊C4—521no—
246C4⋊C4—521no—
247C4⋊C4—1042no—
248C22⋊C4—24no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—42no—
252C22⋊C4—522no—
253C22⋊C4—522no—
254C22⋊C4—1042no—
255C22⋊C4—1042no—
256C42—21no—
257C42—21no—
258C42—82no—
259C42—522no—
260C13#1329911yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23#8812311yescharacteristic
270C23#8812911yescharacteristic
271C23#8817812yes—
272C23C2×#610311yescharacteristic
273Q8—1044no—
274D4—42no—
275D4—42no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—44no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—82no—
291C2×C4—82no—
292C2×C4—522no—
293C2×C4—522no—
294C2×C4—522no—
295C2×C4—522no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—1042no—
299C2×C4—1042no—
300C2×C4—1042no—
301C2×C4#8804611yescharacteristic
302C2×C4#8804611yescharacteristic
303C2×C4C4×Dic2612yes—
304C22—21no—
305C22—21no—
306C22—22no—
307C22—21no—
308C22—21no—
309C22—41no—
310C22—41no—
311C22—42no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—81no—
318C22#1171859011yescharacteristic
319C22C2×#8804611yescharacteristic
320C22#1171866711yescharacteristic
321C4—21no—
322C4—22no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4—84no—
327C4—1042no—
328C4—1042no—
329C4—2082no—
330C4#1171806512yes—
331C2—21no—
332C2—21no—
333C2—42no—
334C2—41no—
335C2—41no—
336C2#1311582111yescharacteristic
337C2C2×#1171806511yescharacteristic
338C2#1311650711yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC4×C13×#99C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenterC4×#99D13
hypocenterC13#13299
LCSG ▷ C22×C4×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. C2×#88123C4semidirect
14. #11718638C4semidirect
17. C4×C4⋊Dic13C4semidirect
43. C13×#99Q8semidirect
205. #99Dic26semidirect
260. C13#13299semidirect

Maximal subgroups

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

subgroupindex
#131200092
#131148242
#131129602
C4×C13×#992
#1329913