Finite Group Databasebeta

← #15765665

Subgroups — #15765665

Order 3328.

576 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 109 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#13125977C211yesmaximal, characteristic
2#13123232C211yesmaximal, characteristic
3#13115814C211yesmaximal, characteristic
4#13113508C211yesmaximal, characteristic
5#13113507C211yesmaximal, characteristic
6#13112668C211yesmaximal, characteristic
7C13×#3229C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×#88198—22no—
11C2×#88123C2211yescharacteristic
12C13×#498—21no—
13C13×#487—21no—
14C13×#483—22no—
15C13×#475—22no—
16C13×#431C2211yescharacteristic
17#11718742—21no—
18#11718740—21no—
19#11718704—22no—
20#11718681—22no—
21#11718637—22no—
22#11718637—22no—
23C42×Dic13C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718585C2211yescharacteristic
26#11718139—22no—
27#11718124—22no—
28#11718078—22no—
29C22×Q8×C13—21no—
30C22×Dic26—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8D411yescharacteristic
36C13×C4⋊Q8D411yescharacteristic
37C13×#125—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C4×Q8×C13—21no—
41C4×Q8×C13—21no—
42C13×#117—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4D412yes—
45C2×C42×C13C2311yescharacteristic
46#88198—44no—
47#88198—44no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13D412yes—
50C2×#6101—28no—
51C2×C4×Dic13—21no—
52C2×C4×Dic13—21no—
53C2×C4×Dic13D412yes—
54C2×#6099—21no—
55#88123—21no—
56#88123—21no—
57#88123—21no—
58#88123—21no—
59C13×#106—24no—
60C13×C4⋊C8D412yes—
61C13×#103—24no—
62C13×C22⋊C8—21no—
63C4×C8×C13—21no—
64#88075—24no—
65C22⋊#1055—21no—
66#88048—24no—
67C4⋊#1055—21no—
68C4⋊#1055—21no—
69C4⋊#1055D412yes—
70C4×#1055—21no—
71#10299—131nomaximal, Sylow
72C2×Q8×C13—21no—
73C2×Q8×C13—21no—
74C2×Q8×C13—41no—
75C2×Q8×C13—41no—
76C2×Q8×C13—42no—
77C2×Q8×C13—42no—
78C22×C4×C13—22no—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×Dic13—22no—
83C22×Dic13—22no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×Dic26—42no—
87C2×Dic26—42no—
88C2×C8×C13—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—21no—
94C13×C4⋊C4—21no—
95C13×C4⋊C4—41no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C22⋊C4—41no—
100C42×C13—41no—
101C42×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13#4111yescharacteristic
105C4⋊Dic13—22no—
106C4⋊Dic13—22no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109#6101—416no—
110C4×Dic13—24no—
111C4×Dic13—24no—
112C4×Dic13—22no—
113C4×Dic13SD1614yes—
114#6099—42no—
115C2×#1055—22no—
116C2×#1055—41no—
117#3229—131no—
118#3229D1311yescharacteristic
119#2868—131no—
120#1994—131no—
121#1546—131no—
122#1546—131no—
123#1276—131no—
124C23×C13#12011yescharacteristic
125Q8×C13—42no—
126Q8×C13—42no—
127Q8×C13—82no—
128Q8×C13—81no—
129Q8×C13—81no—
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—44no—
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12111yescharacteristic
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12711yescharacteristic
142C2×C4×C13C2×SD1612yes—
143C2×C4×C13AGL(1,ℤ/8)12yes—
144C2×Dic13—24no—
145C2×Dic13—24no—
146C2×Dic13—24no—
147C2×Dic13—42no—
148C2×Dic13—44no—
149Dic26—82no—
150Dic26—81no—
151Dic26—81no—
152C8×C13—42no—
153#1055—42no—
154#1055—81no—
155#533C2×D1311yescharacteristic
156C2×C4⋊Q8—131no—
157C2×C4⋊Q8—262no—
158C2×C4⋊Q8C2×D1311yescharacteristic
159#498—21no—
160#498—261no—
161#487—21no—
162#487—261no—
163#483—22no—
164#483—262no—
165#475—22no—
166#475—262no—
167#431—131no—
168#431C2×D1311yescharacteristic
169#423—131no—
170#384—262no—
171#384—262no—
172C43—131no—
173#339—262no—
174#332—262no—
175#332—262no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13#39211yescharacteristic
179C22×C13#45012yes—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—81no—
183C4×C13—81no—
184C4×C13—82no—
185C4×C13#45612yes—
186C4×C13#45612yes—
187C4×C13#46012yes—
188C4×C13#49211yescharacteristic
189C4×C13#49611yescharacteristic
190Dic13—28no—
191Dic13—82no—
192C22×Q8—21no—
193C22×Q8—261no—
194C2×M16—261no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—21no—
199C4⋊Q8—261no—
200C4⋊Q8—261no—
201C4⋊Q8—261no—
202C4⋊Q8—261no—
203C4⋊Q8—524no—
204C4⋊Q8—524no—
205C4⋊Q8C22⋊D1311yescharacteristic
206C4⋊Q8C22⋊D1311yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212#117—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—132no—
215C2×C4⋊C4—268no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4C22⋊D1312yes—
218C2×C42—132no—
219C2×C42—261no—
220C2×C42—261no—
221C2×C42C22×D1311yescharacteristic
222#106—24no—
223#106—264no—
224C4⋊C8—132no—
225C4⋊C8—261no—
226C4⋊C8—261no—
227C4⋊C8C22⋊D1312yes—
228#103—24no—
229#103—264no—
230C22⋊C8—21no—
231C22⋊C8—261no—
232C4×C8—21no—
233C4×C8—261no—
234C2×C13—22no—
235C2×C13#200511yescharacteristic
236C2×C13#200511yescharacteristic
237C2×C13#201411yescharacteristic
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—42no—
241C2×Q8—42no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—522no—
245C2×Q8—522no—
246C2×Q8—521no—
247C2×Q8—521no—
248C22×C4—22no—
249C22×C4—262no—
250C22×C4—262no—
251C22×C4D4×D1311yescharacteristic
252C22×C4D4×D1311yescharacteristic
253C22×C4C2×C22⋊D1311yescharacteristic
254M16—522no—
255C2×C8—22no—
256C2×C8—262no—
257C2×C8—521no—
258C4⋊C4—21no—
259C4⋊C4—22no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—22no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—262no—
269C4⋊C4—262no—
270C4⋊C4—5216no—
271C4⋊C4—521no—
272C4⋊C4—521no—
273C22⋊C4—41no—
274C42—41no—
275C42—134no—
276C42—264no—
277C42—264no—
278C42—262no—
279C42D4×D1311yescharacteristic
280C42#612911yescharacteristic
281C42C2×C22⋊D1311yescharacteristic
282C42C2×C22⋊D1311yescharacteristic
283C13#1029911yescharacteristic, complemented, Sylow
284C23#8819111yescharacteristic
285Q8—42no—
286Q8—42no—
287Q8—82no—
288Q8—81no—
289Q8—81no—
290Q8—1042no—
291Q8—1041no—
292Q8—1041no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—44no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—264no—
300C2×C4—264no—
301C2×C4—264no—
302C2×C4—524no—
303C2×C4—522no—
304C2×C4SD16×D1312yes—
305C2×C4#8816812yes—
306C2×C4#8819111yescharacteristic
307C2×C4#8819211yescharacteristic
308C2×C4#8819311yescharacteristic
309C2×C4#8819311yescharacteristic
310C2×C4#8819411yescharacteristic
311C2×C4#8820711yescharacteristic
312C8—42no—
313C8—522no—
314C8—1041no—
315C22—21no—
316C22—21no—
317C22#1171883012yes—
318C22#1171888411yescharacteristic
319C4—21no—
320C4—21no—
321C4—82no—
322C4—81no—
323C4—81no—
324C4—268no—
325C4—1042no—
326C4#1171882412yes—
327C4#1171883611yescharacteristic
328C4#1171883711yescharacteristic
329C4#1171886612yes—
330C4#1171890712yes—
331C2—22no—
332C2#1311586911yescharacteristic
333C2#1311587011yescharacteristic
334C2#1311592211yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3229C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#3229D13
hypocenterC13#10299
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3229

Complements

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

NH ≅ G/Ntype
283. C13#10299semidirect

Maximal subgroups

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

subgroupindex
#131259772
#131232322
#131158142
#131135082
#131135072
#131126682
C13×#32292
#1029913