Finite Group Databasebeta

← #15766524

Subgroups — #15766524

Order 3328.

408 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 101 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#13114832C211yesmaximal, characteristic
2#13113610C211yesmaximal, characteristic
3#13113508C211yesmaximal, characteristic
4#13113508C211yesmaximal, characteristic
5#13113231C211yesmaximal, characteristic
6#13112733C211yesmaximal, characteristic
7C2×C13×#462C211yesmaximal, characteristic
8C22×C13×Q16—21no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8×C13C2211yescharacteristic
11C13×#462—22no—
12C13×#462—22no—
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×#103—21no—
15C2×#88076—21no—
16#11718586C2211yescharacteristic
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718585C2211yescharacteristic
20#11718139—22no—
21#11718139—22no—
22Q8⋊#1055—22no—
23#11718122—21no—
24#11718071—22no—
25C22×Q8×C13—21no—
26C22×Q8×C13D411yescharacteristic
27C2×C13×Q16—24no—
28C2×C13×Q16—42no—
29C2×C13×Q16—42no—
30C22×C8×C13—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8D412yes—
35C4×Q8×C13—21no—
36C4×Q8×C13—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C2×C13×C4⋊C4—21no—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4D411yescharacteristic
43C2×C42×C13—21no—
44C2×C42×C13C2311yescharacteristic
45C2×#6099—21no—
46C2×#6099—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8D412yes—
49C13×#103—24no—
50#88076—42no—
51C22⋊#1055—21no—
52C22⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055—21no—
58C4⋊#1055D412yes—
59C4×#1055—21no—
60C4×#1055—21no—
61#10446—131nomaximal, Sylow
62C2×Q8×C13—21no—
63C2×Q8×C13—21no—
64C2×Q8×C13—22no—
65C2×Q8×C13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13D812yes—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—41no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C13×Q16—48no—
81C2×C8×C13—22no—
82C2×C8×C13—41no—
83C2×C8×C13—41no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C42×C13—41no—
93C42×C13—41no—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13#4111yescharacteristic
98#6099—41no—
99#6099—41no—
100#6099—41no—
101#6099—41no—
102C2×#1055—22no—
103C2×#1055—41no—
104C2×#1055—41no—
105C2×#1055—41no—
106C2×#462D1311yescharacteristic
107#1801—131no—
108#1571—131no—
109#1546—131no—
110#1546—131no—
111#1479—131no—
112#1301—131no—
113C23×C13#12311yescharacteristic
114Q8×C13—22no—
115Q8×C13—22no—
116Q8×C13—41no—
117Q8×C13—41no—
118Q8×C13—42no—
119Q8×C13—42no—
120Q8×C13—81no—
121Q8×C13—81no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—81no—
130C2×C4×C13—81no—
131C2×C4×C13—81no—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12311yescharacteristic
137C2×C4×C13#12411yescharacteristic
138C2×C4×C13C2×D811yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C8×C13—42no—
143#1055—42no—
144#1055—81no—
145#1055—81no—
146#1055—81no—
147C22×Q16—21no—
148C2×C4⋊Q8C2×D1311yescharacteristic
149C2×C4×Q8C2×D1311yescharacteristic
150#462—22no—
151#462—22no—
152#431—131no—
153#431—131no—
154#423—131no—
155#423—131no—
156C2×C4⋊C8C2×D1311yescharacteristic
157C2×#103—21no—
158C2×#101—261no—
159#343—261no—
160#335—262no—
161#332—262no—
162#332—262no—
163Q8⋊C8—262no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13#39411yescharacteristic
167C22×C13#48011yescharacteristic
168C22×C13#48211yescharacteristic
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—42no—
173C4×C13—81no—
174C4×C13—82no—
175C4×C13#44711yescharacteristic
176C4×C13#45211yescharacteristic
177C4×C13#46611yescharacteristic
178C4×C13#46811yescharacteristic
179C4×C13#47312yes—
180C22×Q8—21no—
181C22×Q8C22⋊D1311yescharacteristic
182C2×Q16—24no—
183C2×Q16—42no—
184C2×Q16—42no—
185C2×M16—261no—
186C2×M16—261no—
187C22×C8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8C22⋊D1312yes—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4C22⋊D1311yescharacteristic
200C2×C42—21no—
201C2×C42C22×D1311yescharacteristic
202C4⋊C8—21no—
203C4⋊C8—132no—
204C4⋊C8—261no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209C4⋊C8C22⋊D1312yes—
210#103—24no—
211#101—522no—
212C22⋊C8—261no—
213C22⋊C8—261no—
214C4×C8—261no—
215C4×C8—261no—
216C2×C13—21no—
217C2×C13—21no—
218C2×C13#203311yescharacteristic
219C2×C13#204711yescharacteristic
220C2×C13#204911yescharacteristic
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8#610412yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—41no—
236C22×C4#612911yescharacteristic
237C22×C4#612911yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239Q16—48no—
240M16—521no—
241M16—521no—
242M16—521no—
243M16—521no—
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—262no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C42—41no—
260C42—41no—
261C42D4×D1311yescharacteristic
262C42#612911yescharacteristic
263C42C2×C22⋊D1311yescharacteristic
264C42C2×C22⋊D1311yescharacteristic
265C13#1044611yescharacteristic, complemented, Sylow
266C23#8818911yescharacteristic
267Q8—22no—
268Q8—22no—
269Q8—41no—
270Q8—41no—
271Q8—42no—
272Q8—42no—
273Q8—81no—
274Q8—81no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4C2×#610411yescharacteristic
286C2×C4#8818611yescharacteristic
287C2×C4#8818911yescharacteristic
288C2×C4#8819011yescharacteristic
289C2×C4#8819211yescharacteristic
290C2×C4#8819311yescharacteristic
291C2×C4#8819311yescharacteristic
292C2×C4#8820411yescharacteristic
293C2×C4#8820511yescharacteristic
294C2×C4#8820711yescharacteristic
295C8—42no—
296C8—522no—
297C8—1041no—
298C8—1041no—
299C8—1041no—
300C22—21no—
301C22—21no—
302C22#1171869411yescharacteristic
303C22#1171869611yescharacteristic
304C22#1171888311yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—42no—
309C4—82no—
310C4—81no—
311C4#1171869911yescharacteristic
312C4#1171870311yescharacteristic
313C4#1171885312yes—
314C4#1171887811yescharacteristic
315C4#1171890011yescharacteristic
316C2—21no—
317C2—21no—
318C2#1311601511yescharacteristic
319C2#1311610111yescharacteristic
320C2#1311611311yescharacteristic
subgroupG/H
centerC22#11718883
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#462C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenterC2×#462D13
hypocenterC13#10446
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
265. C13#10446semidirect

Maximal subgroups

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

subgroupindex
#131148322
#131136102
#131135082
#131132312
#131127332
C2×C13×#4622
#1044613