Finite Group Databasebeta

← #15760622

Subgroups — #15760622

Order 3328.

432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 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#13123920C211yesmaximal, characteristic
2#13120051C211yesmaximal, characteristic
3#13113554C211yesmaximal, characteristic
4#13113552C211yesmaximal, characteristic
5#13113179C211yesmaximal, characteristic
6#13112692C211yesmaximal, characteristic
7C13×#1285C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#432C2211yescharacteristic
11C13×#432C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13#11718635—21no—
14#11718635—21no—
15#11718597C412yes—
16#11718590C412yes—
17#11718587C2211yescharacteristic
18#11718587C2211yescharacteristic
19#11718489—22no—
20#11718380—21no—
21#11718379—21no—
22#11718362—22no—
23#11718320—21no—
24#11718320—21no—
25#11718078—22no—
26#11718074—22no—
27#11718061—21no—
28#11718061—21no—
29C22×Dic26—21no—
30C22×Dic26C2×C411yescharacteristic
31C2×C13×C4⋊C4—21no—
32C2×C42×C13C2×C412yes—
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C412yes—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101D411yescharacteristic
38C2×#6101D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41#88123—21no—
42#88123—21no—
43#88123—21no—
44#88123—21no—
45C4×Dic26—21no—
46C4×Dic26—21no—
47C4×Dic26—21no—
48C4×Dic26—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8D412yes—
51C13×C22⋊C8—21no—
52C13×C22⋊C8—21no—
53C13×#97—21no—
54C13×#97—21no—
55C13×#95—21no—
56#88071—22no—
57#88071—22no—
58#88071—22no—
59#88071—22no—
60C22⋊#1055—21no—
61C22⋊#1055—21no—
62#88055—22no—
63#88054—22no—
64#88054—22no—
65C8×Dic13—22no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68#88043—21no—
69#88043—21no—
70#9456—131nomaximal, Sylow
71C22×C4×C13—22no—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×Dic13—22no—
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C22⋊C411yescharacteristic
78C22×Dic13C22⋊C411yescharacteristic
79C22×Dic13C22⋊C411yescharacteristic
80C2×Dic26—21no—
81C2×Dic26—21no—
82C2×Dic26—22no—
83C2×Dic26—41no—
84C2×Dic26—44no—
85C2×Dic26—41no—
86C2×Dic26—41no—
87C2×C8×C13—22no—
88C2×C8×C13—41no—
89C13×C4⋊C4—42no—
90C42×C13—42no—
91C42×C13C2×D411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—22no—
98C4⋊Dic13—22no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101#6101—21no—
102#6101—21no—
103#6101—21no—
104#6101—21no—
105C4×Dic13—21no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13—21no—
109C2×#1055—22no—
110C2×#1055—41no—
111#2983—131no—
112#2568—131no—
113#1556—131no—
114#1556—131no—
115#1467—131no—
116#1285—131no—
117#1285D1311yescharacteristic
118C23×C13C2×C22⋊C411yescharacteristic
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13C4×D411yescharacteristic
127C2×C4×C13C4×D411yescharacteristic
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13#12111yescharacteristic
131C2×C4×C13#12311yescharacteristic
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—44no—
142C2×Dic13—42no—
143C2×Dic13#10112yes—
144Dic26—42no—
145Dic26—42no—
146Dic26—82no—
147Dic26—82no—
148C8×C13—42no—
149C8×C13—81no—
150#1055—42no—
151#1055—81no—
152C2×C4⋊Q8—131no—
153C2×C4×Q8—131no—
154#446—262no—
155#446—262no—
156#432—131no—
157#432—131no—
158#432—261no—
159#432C2×D1311yescharacteristic
160#432C2×D1311yescharacteristic
161#431—261no—
162#400—261no—
163#400—261no—
164#391—132no—
165#391—261no—
166#391—261no—
167#382—132no—
168C4×C4⋊C4C2×D1311yescharacteristic
169#332—262no—
170#332—262no—
171#324—261no—
172#324—261no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13#38611yescharacteristic
176C22×C13C2×#10111yescharacteristic
177C22×C13#41311yescharacteristic
178C4×C13—21no—
179C4×C13—21no—
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—82no—
184C4×C13#45412yes—
185Dic13—22no—
186Dic13—41no—
187Dic13—41no—
188Dic13—41no—
189Dic13—82no—
190C22×Q8—131no—
191C22×Q8—261no—
192C4⋊Q8—261no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C4×Q8—261no—
197C4×Q8—261no—
198C4×Q8—261no—
199C4×Q8—261no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4—131no—
204C2×C4⋊C4—132no—
205C2×C4⋊C4—261no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42C4×D1312yes—
209C2×C42C22×D1311yescharacteristic
210C4⋊C8—21no—
211C4⋊C8—132no—
212C4⋊C8—262no—
213C4⋊C8—262no—
214C4⋊C8—261no—
215C4⋊C8D5212yes—
216C22⋊C8—21no—
217C22⋊C8—21no—
218C22⋊C8—261no—
219C22⋊C8—261no—
220#97—21no—
221#97—21no—
222#97—262no—
223#97—261no—
224#97—261no—
225C4×C8—262no—
226#95—21no—
227#95—262no—
228#95—262no—
229#95—262no—
230#95—262no—
231C2×C13—21no—
232C2×C13—21no—
233C2×C13#188811yescharacteristic
234C2×C13#190111yescharacteristic
235C2×C13#190911yescharacteristic
236C2×Q8—262no—
237C2×Q8—261no—
238C2×Q8—261no—
239C2×Q8—521no—
240C2×Q8—524no—
241C2×Q8—521no—
242C2×Q8—521no—
243C22×C4—22no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—131no—
248C22×C4—262no—
249C22×C4C2×C4×D1311yescharacteristic
250C22×C4D4×D1311yescharacteristic
251C22×C4D4×D1311yescharacteristic
252C2×C8—22no—
253C2×C8—41no—
254C2×C8—262no—
255C2×C8—521no—
256C4⋊C4—42no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—262no—
264C4⋊C4—262no—
265C4⋊C4—521no—
266C4⋊C4—521no—
267C42—42no—
268C42—261no—
269C42—261no—
270C42—261no—
271C42—261no—
272C42C2×D5211yescharacteristic
273C42#612711yescharacteristic
274C42D4×D1311yescharacteristic
275C42#613111yescharacteristic
276C13#945611yescharacteristic, complemented, Sylow
277C23C22⋊C4×D1311yescharacteristic
278Q8—522no—
279Q8—522no—
280Q8—1042no—
281Q8—1042no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—132no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—524no—
300C2×C4—522no—
301C2×C4C4×D5211yescharacteristic
302C2×C4#8813611yescharacteristic
303C2×C4#8813811yescharacteristic
304C2×C4#8814711yescharacteristic
305C2×C4#8814811yescharacteristic
306C2×C4#8814911yescharacteristic
307C8—42no—
308C8—81no—
309C8—522no—
310C8—1041no—
311C22—21no—
312C22—21no—
313C22#1171832611yescharacteristic
314C22#1171840611yescharacteristic
315C22D13×#10111yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—262no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4—1042no—
327C4#1171848812yes—
328C2—21no—
329C2—21no—
330C2#1311523811yescharacteristic
331C2#1311530311yescharacteristic
332C2#1311535711yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1285C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1285D13
hypocenterC13#9456
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1285

Complements

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

NH ≅ G/Ntype
276. C13#9456semidirect

Maximal subgroups

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

subgroupindex
#131239202
#131200512
#131135542
#131135522
#131131792
#131126922
C13×#12852
#945613