Finite Group Databasebeta

← #15779723

Subgroups — #15779723

Order 3328.

580 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#11718137C211yesmaximal, characteristic
2#13115235C211yesmaximal, characteristic
3#13115116C212yesmaximal, complemented
4#13112954C212yesmaximal, complemented
5C13×#2380C211yesmaximal, characteristic
6C2×C13×#127C2211yescharacteristic
7#11719503C2211yescharacteristic
8C13×#386—21no—
9C13×#386—22no—
10C13×#386—22no—
11C13×#386C2212yes—
12C13×#383—21no—
13C2×#88074C2212yes—
14C2×#88073C2211yescharacteristic
15#11718876—21no—
16#11718871—22no—
17#11718137C414yescomplemented
18#11718119—22no—
19#11718115—21no—
20C22×D4×C13—22no—
21C22×D4×C13D411yescharacteristic
22C22×D4×C13C2311yescharacteristic
23C23×C4×C13—21no—
24C23×C4×C13D412yes—
25C13×#127—22no—
26C13×#127C2×C412yes—
27C13×#127Q812yes—
28C2×C13×C22⋊C4—21no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4D412yes—
32C2×C42×C13D411yescharacteristic
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13—22no—
35D4×Dic13—42no—
36#88180—21no—
37C2×#6101—42no—
38C2×#6099—21no—
39C13×#95—21no—
40C13×#95—22no—
41C13×#95—21no—
42C13×#95—22no—
43#88074—22no—
44#88074C2×C414yescomplemented
45#88073—22no—
46#88072—42no—
47#88071—42no—
48#12966—131nomaximal, Sylow
49C24×C13—21no—
50C24×C13C2×D412yes—
51C2×D4×C13—24no—
52C2×D4×C13—24no—
53C2×D4×C13—21no—
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13—82no—
59C2×D4×C13—82no—
60C2×D4×C13C4⋊C412yescomplemented
61C2×D4×C13C22×C411yescharacteristic
62C2×D4×C13C2×Q811yescharacteristic
63C2×D4×C13#4112yes—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—42no—
68C22×C4×C13—82no—
69C22×C4×C13—82no—
70C22×C4×C13—81no—
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—22no—
73C22×Dic13—22no—
74C22×Dic13—42no—
75C13×C22⋊C4—42no—
76C13×C22⋊C4—82no—
77C13×C22⋊C4—82no—
78C13×C22⋊C4—81no—
79C42×C13—21no—
80C42×C13C4⋊C412yescomplemented
81C22⋊Dic13—24no—
82C22⋊Dic13—42no—
83C22⋊Dic13—42no—
84C22⋊Dic13—41no—
85C4⋊Dic13—22no—
86#6101—84no—
87C4×Dic13—41no—
88#6099—41no—
89#6099—41no—
90C2×#1055—41no—
91#2380D1311yescharacteristic
92C2×#353—131no—
93#1887—131no—
94#1867—132no—
95#1390—132no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13C4×D412yes—
106C23×C13#12011yescharacteristic
107C23×C13C22⋊Q812yes—
108D4×C13—41no—
109D4×C13—41no—
110D4×C13—42no—
111D4×C13—42no—
112D4×C13—81no—
113D4×C13—84no—
114D4×C13—84no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—44no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—84no—
127C2×C4×C13—82no—
128C2×C4×C13C2×C4⋊C411yescharacteristic
129C2×C4×C13#12311yescharacteristic
130C2×Dic13—44no—
131C2×Dic13—42no—
132C2×Dic13—82no—
133C2×Dic13—82no—
134C2×Dic13—82no—
135C2×Dic13—82no—
136#1055—81no—
137C2×#127C2×D1311yescharacteristic
138#518—131no—
139#418—261no—
140C2×#100—131no—
141C2×#99—132no—
142#386—21no—
143#386—22no—
144#386—22no—
145#386C2×D1312yes—
146#385—262no—
147#383—21no—
148#353—134no—
149#342—262no—
150#339—261no—
151C22×C13—22no—
152C22×C13—22no—
153C22×C13—22no—
154C22×C13—42no—
155C22×C13—42no—
156C22×C13—44no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—82no—
161C22×C13—81no—
162C22×C13—81no—
163C22×C13—82no—
164C22×C13#38511yescharacteristic
165C22×C13B(4,𝔽2)11yescharacteristic
166C22×C13#45811yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—42no—
170C4×C13—82no—
171C4×C13—82no—
172Dic13—84no—
173Dic13—82no—
174C22×D4—22no—
175C22×D4C22⋊D1311yescharacteristic
176C22×D4C22×D1311yescharacteristic
177C23×C4—21no—
178C23×C4C22⋊D1312yes—
179C2×M16—261no—
180#127—22no—
181#127Dic2612yes—
182#127C4×D1312yes—
183C4×D4—522no—
184#117—261no—
185C2×C4⋊C4—522no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—262no—
190C2×C22⋊C4—262no—
191C2×C22⋊C4C22⋊D1312yes—
192C2×C42C22⋊D1311yescharacteristic
193#102—522no—
194#100—262no—
195#99—134no—
196#99—262no—
197#95—21no—
198#95—22no—
199#95—21no—
200#95—22no—
201#95—522no—
202C2×C13—21no—
203C2×C13—21no—
204C2×C13—42no—
205C2×C13—42no—
206C2×C13—82no—
207C2×C13#186711yescharacteristic
208C2×C13#220012yes—
209C24—21no—
210C24C2×C22⋊D1312yes—
211C2×D4—24no—
212C2×D4—24no—
213C2×D4—21no—
214C2×D4—41no—
215C2×D4—41no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—82no—
219C2×D4—82no—
220C2×D4#610112yescomplemented
221C2×D4C2×Dic2611yescharacteristic
222C2×D4C2×C4×D1311yescharacteristic
223C2×D4#612712yes—
224C22×C4—21no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—42no—
228C22×C4—82no—
229C22×C4—82no—
230C22×C4—81no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—522no—
234C22×C4C2×C22⋊D1311yescharacteristic
235M16—521no—
236M16—521no—
237C2×C8—521no—
238C4⋊C4—262no—
239C4⋊C4—1044no—
240C22⋊C4—42no—
241C22⋊C4—82no—
242C22⋊C4—82no—
243C22⋊C4—81no—
244C22⋊C4—264no—
245C22⋊C4—522no—
246C22⋊C4—522no—
247C22⋊C4—521no—
248C42—21no—
249C42—521no—
250C42#610112yescomplemented
251C13#1296611yescharacteristic, complemented, Sylow
252C23—22no—
253C23—22no—
254C23—22no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—41no—
260C23—41no—
261C23#8817812yes—
262C23C4×C22⋊D1312yes—
263C23#8820711yescharacteristic
264D4—41no—
265D4—41no—
266D4—42no—
267D4—42no—
268D4—81no—
269D4—84no—
270D4—84no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—84no—
283C2×C4—82no—
284C2×C4—524no—
285C2×C4—522no—
286C2×C4—1042no—
287C2×C4—1042no—
288C2×C4—1042no—
289C2×C4—1042no—
290C2×C4C2×#610111yescharacteristic
291C2×C4#8818311yescharacteristic
292C8—1041no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—42no—
297C22—42no—
298C22—44no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—82no—
303C22—81no—
304C22—81no—
305C22—82no—
306C22#1171887111yescharacteristic
307C22#1171890411yescharacteristic
308C22#1171890511yescharacteristic
309C4—21no—
310C4—21no—
311C4—42no—
312C4—82no—
313C4—82no—
314C4—1044no—
315C4—1042no—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—42no—
320C2—82no—
321C2#1311511711yescharacteristic
322C2#1311684312yes—
subgroupG/H
centerC22#11718905
commutatorC2×D4×C13C22×C4
FrattiniC22×D4C22×D13
FittingC13×#2380C2
socleC22×C13B(4,𝔽2)
prime radicalC2×C13×#127C22
cosocleC22×D4×C13C23
hypercenter#2380D13
hypocenterC13#12966
LCSG ▷ C2×D4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #2380

Complements

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

NH ≅ G/Ntype
3. #13115116C2semidirect
4. #13112954C2semidirect
17. #11718137C4semidirect
44. #88074C2×C4semidirect
60. C2×D4×C13C4⋊C4semidirect
80. C42×C13C4⋊C4semidirect
220. C2×D4#6101semidirect
250. C42#6101semidirect
251. C13#12966semidirect

Maximal subgroups

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

subgroupindex
C2×#117181372
#131152352
#131151162
#131129542
C13×#23802
#1296613