Finite Group Databasebeta

← #15760283

Subgroups — #15760283

Order 3328.

558 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 117 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#13123859C211yesmaximal, characteristic
2#13119831C211yesmaximal, characteristic
3#13114825C211yesmaximal, characteristic
4#13113509C211yesmaximal, characteristic, complemented
5#13113507C211yesmaximal, characteristic, complemented
6#13112739C211yesmaximal, characteristic, complemented
7C13×#1303C211yesmaximal, characteristic, complemented
8C2×#88129—21no—
9C2×C4×D52C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#423C2211yescharacteristic
13C4×C13×C4⋊C4C2211yescharacteristic
14C2×#88063—21no—
15#11718648—22no—
16#11718590—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718495—22no—
20D13×C22⋊C8—22no—
21C8×D52—22no—
22#11718335C414yes—
23#11718146—21no—
24#11718078—22no—
25#11718074—22no—
26C22×D52D411yescharacteristic
27C22×C4×D13D412yes—
28C22×Dic26—21no—
29C2×C13×M16—21no—
30C2×C13×C4⋊C4—21no—
31C2×C42×C13—21no—
32C2×C42×C13C2311yescharacteristic
33C2×#6103—24no—
34C2×#6103C2×C412yes—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13C2×C412yes—
37C2×C4⋊Dic13D411yescharacteristic
38C2×#6099—21no—
39C2×C8×D13—24no—
40#88129—42no—
41#88129—42no—
42C4×D52—21no—
43C4×D52—21no—
44C4×D52—21no—
45C4×D52—21no—
46#88123—21no—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8D412yes—
53C13×C22⋊C8—21no—
54C4×C8×C13—21no—
55C13×#95C2×C412yes—
56#88071—24no—
57C22⋊#1055—21no—
58#88063—42no—
59#88060—24no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055D412yes—
63C4×#1055—21no—
64#9393—131nomaximal, Sylow
65C23×D13C22⋊C412yes—
66C22×C4×C13—22no—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×Dic13—22no—
71C22×Dic13C22⋊C412yes—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52—21no—
75C2×D52—21no—
76C2×D52D812yes—
77C2×D52SD1612yes—
78C2×C4×D13—22no—
79C2×C4×D13—22no—
80C2×C4×D13—44no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26—41no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×Dic26—41no—
87C13×M16—41no—
88C13×M16—41no—
89C2×C8×C13—22no—
90C2×C8×C13—41no—
91C13×C4⋊C4—42no—
92C42×C13—41no—
93C42×C13—41no—
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13#4111yescharacteristic
97C42×C13#4111yescharacteristic
98#6103—22no—
99#6103—22no—
100#6103—48no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107#6099—41no—
108#6099—41no—
109C2×#1055—22no—
110C2×#1055—41no—
111C8×D13—84no—
112#2972—131no—
113#2547—131no—
114#1800—131no—
115#1546—131no—
116#1546—131no—
117#1303—131no—
118#1303D1311yescharacteristic, complemented
119C23×C13C2×C22⋊C411yescharacteristic
120C22×D13—22no—
121C22×D13—22no—
122C22×D13—42no—
123C22×D13—42no—
124C22×D13#10214yes—
125C2×C4×C13—22no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13C4×D411yescharacteristic
131C2×C4×C13C4×D411yescharacteristic
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12311yescharacteristic
136C2×C4×C13C2×D811yescharacteristic
137C2×C4×C13C2×SD1611yescharacteristic
138C2×C4×C13#13511yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145D52—22no—
146D52—22no—
147D52—22no—
148D52—22no—
149C4×D13—44no—
150C4×D13—82no—
151Dic26—81no—
152Dic26—81no—
153Dic26—81no—
154Dic26—81no—
155C8×C13—42no—
156C8×C13—81no—
157#1055—42no—
158#1055—81no—
159C2×C4⋊Q8—131no—
160C2×#124—261no—
161C2×C4×D4—131no—
162C8×D4—262no—
163C8×D4—262no—
164#431—131no—
165#431C2×D1311yescharacteristic
166#423—131no—
167#423C2×D1311yescharacteristic
168C2×#100—261no—
169C2×C22⋊C8—262no—
170#397—134no—
171#391—261no—
172#380—262no—
173C4×C4⋊C4C2×D1311yescharacteristic
174#343—261no—
175#332—262no—
176#332—262no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13#38611yescharacteristic
180C22×C13C2×#10211yescharacteristic
181C22×C13#41611yescharacteristic
182C2×D13—24no—
183C2×D13—42no—
184C2×D13—42no—
185C2×D13—44no—
186C2×D13—82no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—21no—
190C4×C13—82no—
191C4×C13#45512yes—
192C4×C13#46511yescharacteristic
193C4×C13#46511yescharacteristic
194C4×C13#46611yescharacteristic
195C4×C13#46611yescharacteristic
196Dic13—42no—
197Dic13—82no—
198C22×Q8—261no—
199C22×D4—131no—
200C23×C4—132no—
201C2×M16—21no—
202C2×M16—261no—
203C22×C8—264no—
204C4⋊Q8—261no—
205C4⋊Q8—261no—
206C4⋊Q8—261no—
207C4⋊Q8—261no—
208#124—522no—
209#124—522no—
210C4×D4—261no—
211C4×D4—261no—
212C4×D4—261no—
213C4×D4—261no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—132no—
217C2×C4⋊C4—261no—
218C2×C22⋊C4—132no—
219C2×C22⋊C4—264no—
220C2×C42—21no—
221C2×C42C22×D1311yescharacteristic
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—132no—
225C4⋊C8—261no—
226C4⋊C8—261no—
227C4⋊C8D5212yes—
228#100—522no—
229C22⋊C8—21no—
230C22⋊C8—264no—
231C22⋊C8—261no—
232C4×C8—21no—
233C4×C8—261no—
234#95—264no—
235#95C4×D1312yes—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13#188511yescharacteristic
239C2×C13#189311yescharacteristic
240C2×C13#191511yescharacteristic
241D13—44no—
242C24—132no—
243C2×Q8—521no—
244C2×Q8—521no—
245C2×Q8—521no—
246C2×Q8—521no—
247C2×Q8—521no—
248C2×Q8—521no—
249C2×D4—132no—
250C2×D4—132no—
251C2×D4—261no—
252C2×D4—261no—
253C2×D4—261no—
254C2×D4—261no—
255C22×C4—22no—
256C22×C4—132no—
257C22×C4—262no—
258C22×C4—262no—
259C22×C4—262no—
260C22×C4—524no—
261C22×C4C2×C4×D1311yescharacteristic
262C22×C4D4×D1311yescharacteristic
263C22×C4D4×D1311yescharacteristic
264M16—41no—
265M16—41no—
266M16—521no—
267M16—521no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—262no—
271C2×C8—521no—
272C2×C8—1044no—
273C4⋊C4—42no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—262no—
277C4⋊C4—262no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C22⋊C4—262no—
281C22⋊C4—262no—
282C22⋊C4—528no—
283C42—41no—
284C42—41no—
285C42C2×D5211yescharacteristic
286C42#612711yescharacteristic
287C42D4×D1311yescharacteristic
288C42#613111yescharacteristic
289C13#939311yescharacteristic, complemented, Sylow
290C23—134no—
291C23—262no—
292C23—262no—
293C23—522no—
294C23—522no—
295C23C22⋊C4×D1311yescharacteristic
296Q8—1041no—
297Q8—1041no—
298Q8—1041no—
299Q8—1041no—
300D4—262no—
301D4—262no—
302D4—262no—
303D4—262no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—262no—
310C2×C4—524no—
311C2×C4—522no—
312C2×C4—522no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4—1042no—
316C2×C4C4×D5211yescharacteristic
317C2×C4#8813611yescharacteristic
318C2×C4#8813811yescharacteristic
319C2×C4#8814711yescharacteristic
320C2×C4#8814811yescharacteristic
321C2×C4#8814911yescharacteristic
322C2×C4D8×D1311yescharacteristic
323C2×C4SD16×D1311yescharacteristic
324C2×C4#8817011yescharacteristic
325C2×C4#8817311yescharacteristic
326C8—42no—
327C8—81no—
328C8—522no—
329C8—1041no—
330C22—21no—
331C22—21no—
332C22—264no—
333C22—524no—
334C22—522no—
335C22—522no—
336C22—1042no—
337C22#1171832611yescharacteristic
338C22D13×#10211yescharacteristic
339C22#1171846511yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—82no—
344C4—522no—
345C4—1042no—
346C4#1171843611yescharacteristic
347C4#1171846811yescharacteristic
348C4#1171848612yes—
349C4#1171852511yescharacteristic
350C4#1171854411yescharacteristic
351C2—21no—
352C2—21no—
353C2—524no—
354C2#1311522311yescharacteristic
355C2#1311526311yescharacteristic
356C2#1311538711yescharacteristic
subgroupG/H
centerC22#11718326
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1303C2
socleC22×C13#386
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1303D13
hypocenterC13#9393
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. #13113509C2semidirect
5. #13113507C2semidirect
6. #13112739C2semidirect
7. C13×#1303C2semidirect
118. #1303D13semidirect
289. C13#9393semidirect

Maximal subgroups

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

subgroupindex
#131238592
#131198312
#131148252
#131135092
#131135072
#131127392
C13×#13032
#939313