Finite Group Databasebeta

← #15773543

Subgroups — #15773543

Order 3328.

462 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 83 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#13120012C211yesmaximal, characteristic
2#13113177C211yesmaximal, characteristic
3#13112859C212yesmaximal, complemented
4#13112856C212yesmaximal, complemented
5C4×C13×#99C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178C411yescharacteristic, complemented
8C2×C13×#99—21no—
9C4×C13×C22⋊C4—21no—
10#11718881—21no—
11#11718871—21no—
12C2×#88071C411yescharacteristic, complemented
13#11718647C411yescharacteristic, complemented
14#11718640C411yescharacteristic, complemented
15#11718610C2211yescharacteristic
16#11718608C2211yescharacteristic
17#11718603—21no—
18#11718594—21no—
19#11718587—21no—
20C13×#342C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×Dic13—21no—
27C22×Dic26C2×C411yescharacteristic
28C4×D4×C13—41no—
29C4×D4×C13—41no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4C2311yescharacteristic
34C2×C42×C13—41no—
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40#88178—41no—
41#88178—41no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C13×#99—24no—
46C13×#95—41no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071C2×C411yescharacteristic
53#88071C2×C411yescharacteristic
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56#88043—41no—
57#11789—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13—41no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—42no—
68C22×C4×C13—81no—
69C22×C4×C13—81no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—42no—
80C22×Dic13—42no—
81C22×Dic13—81no—
82C2×Dic26—41no—
83C2×Dic26—81no—
84C13×C4⋊C4—41no—
85C13×C22⋊C4—24no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—42no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—82no—
92C22⋊Dic13—42no—
93C22⋊Dic13—42no—
94C22⋊Dic13—81no—
95C4⋊Dic13—41no—
96#6101—42no—
97#6101—41no—
98#6101—41no—
99#6101—81no—
100C2×#1055—42no—
101#2564—131no—
102C4×#99D1311yescharacteristic
103#1466—131no—
104#1352—132no—
105#1351—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13#10412yes—
115C23×C13C2×C22⋊C411yescharacteristic
116C23×C13#13712yes—
117D4×C13—44no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—44no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13—82no—
134C2×C4×C13—82no—
135C2×C4×C13#9911yescharacteristic
136C2×C4×C13#9911yescharacteristic
137C2×Dic13—22no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—84no—
150Dic26—82no—
151#1055—82no—
152C2×C22⋊Q8—131no—
153C2×C4×D4C2×D1311yescharacteristic
154#432—261no—
155C2×#99—21no—
156#400—131no—
157#399—131no—
158#395—131no—
159#393—131no—
160#387—261no—
161#386—261no—
162#385—261no—
163#380—261no—
164C4×C22⋊C4—21no—
165C2×#95—131no—
166#342C2×D1312yes—
167#323—132no—
168#323—261no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—22no—
172C22×C13—22no—
173C22×C13—42no—
174C22×C13—42no—
175C22×C13—42no—
176C22×C13—41no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—81no—
181C22×C13C2×#9911yescharacteristic
182C22×C13#41911yescharacteristic
183C22×C13C2×#10411yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—41no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—84no—
191Dic13—42no—
192Dic13—81no—
193Dic13—81no—
194Dic13—81no—
195C22×Q8—131no—
196C22×D4C22⋊D1311yescharacteristic
197C23×C4—261no—
198C23×C4C4×D1311yescharacteristic
199C23×C4C22⋊D1311yescharacteristic
200C22⋊Q8—521no—
201C22⋊Q8—521no—
202C4×D4—41no—
203C4×D4—41no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C4×D1311yescharacteristic
209C2×C22⋊C4—22no—
210C2×C22⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C22⋊C4D5211yescharacteristic
214C2×C22⋊C4C22×D1311yescharacteristic
215C2×C42—41no—
216C2×C42D5211yescharacteristic
217C4⋊C8—521no—
218#99—24no—
219C22⋊C8—262no—
220#97—521no—
221#95—41no—
222#95—131no—
223#95—131no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228#95—261no—
229C2×C13—21no—
230C2×C13—21no—
231C2×C13—42no—
232C2×C13—42no—
233C2×C13#150811yescharacteristic
234C2×C13#212111yescharacteristic
235C2×C13#212611yescharacteristic
236C24#610311yescharacteristic
237C24C2×C22⋊D1311yescharacteristic
238C2×Q8—521no—
239C2×Q8—1041no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—522no—
255C22×C4—522no—
256C22×C4—1041no—
257C22×C4#610311yescharacteristic
258C22×C4#610311yescharacteristic
259C22×C4#610311yescharacteristic
260C22×C4C2×C4×D1311yescharacteristic
261C22×C4C2×D5211yescharacteristic
262C2×C8—522no—
263C4⋊C4—41no—
264C4⋊C4—521no—
265C4⋊C4—522no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C4⋊C4—1041no—
269C22⋊C4—24no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—522no—
274C22⋊C4—522no—
275C22⋊C4—1041no—
276C42—21no—
277C42—21no—
278C42—82no—
279C13#1178911yescharacteristic, complemented, Sylow
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23#8804512yes—
289C23C2×#610311yescharacteristic
290C23#8820512yes—
291Q8—1042no—
292D4—44no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—44no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—262no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—1044no—
323C2×C4#8804611yescharacteristic
324C2×C4#8804611yescharacteristic
325C8—1042no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22C2×#8804511yescharacteristic
339C22C2×#8804611yescharacteristic
340C22#1171866511yescharacteristic
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—84no—
348C4—522no—
349C4—1041no—
350C4—1041no—
351C4—1041no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—42no—
356C2#1311335511yescharacteristic
357C2#1311648011yescharacteristic
358C2#1311649911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC4×C13×#99C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenterC4×#99D13
hypocenterC13#11789
LCSG ▷ C22×C4×C13 ▷ C23×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
3. #13112859C2semidirect
4. #13112856C2semidirect
7. C2×#88178C4semidirect
12. C2×#88071C4semidirect
13. #11718647C4semidirect
14. #11718640C4semidirect
279. C13#11789semidirect

Maximal subgroups

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

subgroupindex
#131200122
#131131772
#131128592
#131128562
C4×C13×#992
#1178913