Finite Group Databasebeta

← #15767197

Subgroups — #15767197

Order 3328.

364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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#13125358C211yesmaximal, characteristic
2#13115557C211yesmaximal, characteristic
3#13113494C211yesmaximal, characteristic
4#13113336C211yesmaximal, characteristic
5#13113335C211yesmaximal, characteristic
6#13112666C211yesmaximal, characteristic
7C13×#1542C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88054—21no—
13#11718741—21no—
14#11718741—21no—
15#11718726—21no—
16#11718726—21no—
17#11718659—21no—
18#11718659—21no—
19C4×C4⋊Dic13C2211yescharacteristic
20#11718586C2211yescharacteristic
21C2×#88043C2211yescharacteristic
22C13×#333—21no—
23C13×#332—21no—
24#11718142—21no—
25#11718130—21no—
26#11718130—21no—
27#11718078—21no—
28#11718073—21no—
29#11718059—21no—
30#11718059—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8D411yescharacteristic
33C13×C4⋊Q8D411yescharacteristic
34C13×#125—21no—
35C13×C22⋊Q8—21no—
36C13×C22⋊Q8—21no—
37C4×Q8×C13—21no—
38C4×Q8×C13—21no—
39C13×#117—21no—
40C2×C42×C13C2311yescharacteristic
41#88180—21no—
42C2×C4⋊Dic13—21no—
43#88178—21no—
44#88178—21no—
45C2×C4×Dic13—21no—
46C22×#1055D411yescharacteristic
47C22×#1055D411yescharacteristic
48#88124—21no—
49#88123D411yescharacteristic
50#88123D411yescharacteristic
51C4×Dic26—21no—
52C4×Dic26—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55C13×C4⋊C8—21no—
56C13×C22⋊C8—21no—
57C4×C8×C13—21no—
58#88071D411yescharacteristic
59#88071D411yescharacteristic
60C22⋊#1055—21no—
61#88054—42no—
62#88048—21no—
63#88048—21no—
64#88048—21no—
65#88048—21no—
66#88047—21no—
67#88047—21no—
68#88047—21no—
69#88047—21no—
70C4⋊#1055—21no—
71#88043—21no—
72#88043—21no—
73C4×#1055—21no—
74#10548—131nomaximal, Sylow
75C2×Q8×C13—21no—
76C2×Q8×C13—21no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×Dic13—21no—
81C22×Dic13—21no—
82C2×Dic26—21no—
83C2×Dic26—21no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C22⋊C4—41no—
95C42×C13—41no—
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13#4111yescharacteristic
99C42×C13#4111yescharacteristic
100C22⋊Dic13—41no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13—21no—
104C4⋊Dic13—21no—
105C4⋊Dic13—42no—
106#6101—41no—
107#6101—41no—
108C4×Dic13—41no—
109C4×Dic13—41no—
110C4×Dic13—41no—
111C2×#1055—21no—
112C2×#1055—21no—
113C2×#1055—21no—
114C2×#1055—21no—
115C2×#1055—41no—
116C2×#1055SD1612yes—
117C2×#1055Q1612yes—
118#3162—131no—
119#1940—131no—
120#1542—131no—
121#1542D1311yescharacteristic
122#1503—131no—
123#1503—131no—
124#1275—131no—
125C23×C13#12111yescharacteristic
126Q8×C13—81no—
127Q8×C13—81no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12311yescharacteristic
136C2×C4×C13#12311yescharacteristic
137C2×C4×C13#12411yescharacteristic
138C2×C4×C13C2×SD1611yescharacteristic
139C2×C4×C13C2×Q1611yescharacteristic
140C2×C4×C13#13711yescharacteristic
141C2×C4×C13#13711yescharacteristic
142C2×Dic13—22no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150Dic26—81no—
151Dic26—81no—
152C8×C13—81no—
153C8×C13—81no—
154#1055—22no—
155#1055—22no—
156#1055—81no—
157#533—131no—
158#533C2×D1311yescharacteristic
159#501—261no—
160#501—261no—
161#501—261no—
162#501—261no—
163#431—131no—
164#431C2×D1311yescharacteristic
165#427—261no—
166#427—261no—
167C2×C4⋊C8—261no—
168C2×C4⋊C8C2×D1311yescharacteristic
169C2×#97—131no—
170C4×C4⋊C4—131no—
171#336—261no—
172#333—21no—
173#333—261no—
174#332—21no—
175#332—261no—
176#328—261no—
177#328—261no—
178#328—261no—
179#328—261no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13#39411yescharacteristic
183C22×C13#46111yescharacteristic
184C22×C13#46211yescharacteristic
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—81no—
190C4×C13—81no—
191C4×C13#44811yescharacteristic
192C4×C13#45111yescharacteristic
193C4×C13#48711yescharacteristic
194C4×C13#49111yescharacteristic
195Dic13—42no—
196Dic13—81no—
197Dic13—81no—
198Dic13—81no—
199C22×C8—21no—
200C22×C8—131no—
201C22×C8—131no—
202C4⋊Q8—131no—
203C4⋊Q8—131no—
204C4⋊Q8C22⋊D1311yescharacteristic
205C4⋊Q8C22⋊D1311yescharacteristic
206#125—21no—
207#125—261no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C22⋊Q8—261no—
211C22⋊Q8—261no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—261no—
215C4×Q8—261no—
216#117—21no—
217#117—261no—
218C2×C4⋊C4—261no—
219C2×C42—261no—
220C2×C42C22×D1311yescharacteristic
221#107—261no—
222#107—261no—
223#107—261no—
224#107—261no—
225#106—261no—
226#106—261no—
227#106—261no—
228#106—261no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231C4⋊C8—21no—
232C4⋊C8—261no—
233C4⋊C8—522no—
234C22⋊C8—21no—
235C22⋊C8—261no—
236#97—261no—
237#97—261no—
238C4×C8—21no—
239C4×C8—261no—
240#95—131no—
241#95—131no—
242C2×C13—21no—
243C2×C13—21no—
244C2×C13#204311yescharacteristic
245C2×C13#205011yescharacteristic
246C2×C13#205311yescharacteristic
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—261no—
250C2×Q8—261no—
251C22×C4—261no—
252C22×C4—261no—
253C22×C4#612711yescharacteristic
254C22×C4D4×D1311yescharacteristic
255C22×C4D4×D1311yescharacteristic
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—132no—
261C2×C8—132no—
262C2×C8—261no—
263C2×C8—261no—
264C2×C8—261no—
265C2×C8—261no—
266C2×C8—521no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—261no—
274C4⋊C4—261no—
275C4⋊C4—261no—
276C4⋊C4—261no—
277C4⋊C4—522no—
278C4⋊C4—521no—
279C4⋊C4—521no—
280C22⋊C4—41no—
281C22⋊C4—521no—
282C42—41no—
283C42—521no—
284C42—521no—
285C42—521no—
286C42#612711yescharacteristic
287C42D4×D1311yescharacteristic
288C42#612911yescharacteristic
289C42C2×C22⋊D1311yescharacteristic
290C13#1054811yescharacteristic, complemented, Sylow
291C23#8813811yescharacteristic
292Q8—81no—
293Q8—81no—
294Q8—1041no—
295Q8—1041no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—262no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4#8813711yescharacteristic
309C2×C4#8813811yescharacteristic
310C2×C4#8813911yescharacteristic
311C2×C4SD16×D1311yescharacteristic
312C2×C4#8816911yescharacteristic
313C2×C4Q16×D1311yescharacteristic
314C2×C4#8817211yescharacteristic
315C2×C4#8818311yescharacteristic
316C2×C4#8819111yescharacteristic
317C2×C4#8819311yescharacteristic
318C8—81no—
319C8—81no—
320C8—262no—
321C8—262no—
322C8—1041no—
323C22—21no—
324C22—21no—
325C22#1171845411yescharacteristic
326C22#1171847911yescharacteristic
327C22#1171862011yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—81no—
333C4—81no—
334C4—522no—
335C4—1041no—
336C4—1041no—
337C4—1041no—
338C4#1171845311yescharacteristic
339C4#1171845811yescharacteristic
340C4#1171883111yescharacteristic
341C4#1171884711yescharacteristic
342C2—21no—
343C2—21no—
344C2#1311608011yescharacteristic
345C2#1311612111yescharacteristic
346C2#1311614011yescharacteristic
subgroupG/H
centerC2×C4#88139
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1542C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#1542D13
hypocenterC13#10548
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
290. C13#10548semidirect

Maximal subgroups

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

subgroupindex
#131253582
#131155572
#131134942
#131133362
#131133352
#131126662
C13×#15422
#1054813