Finite Group Databasebeta

← #15766051

Subgroups — #15766051

Order 3328.

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

normal subgroups only

This group has 416 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#13118130C211yesmaximal, characteristic
2#13115816C211yesmaximal, characteristic
3#13113336C211yesmaximal, characteristic
4#13113334C211yesmaximal, characteristic
5#13112737C211yesmaximal, characteristic
6#13112664C211yesmaximal, characteristic
7C13×#1303C211yesmaximal, characteristic
8#11719175C2211yescharacteristic
9C2×C4×Dic26—21no—
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13#11718645—21no—
14#11718640—21no—
15C4×C4⋊Dic13C2211yescharacteristic
16#11718593C2211yescharacteristic
17C4×#6101—21no—
18#11718586C2211yescharacteristic
19#11718318—21no—
20#11718317—21no—
21#11718147—21no—
22#11718147—21no—
23#11718059—21no—
24#11718059—21no—
25#11718044—21no—
26#11718044—21no—
27C22×Dic26—21no—
28C2×C13×M16—21no—
29C2×C13×C4⋊C4—21no—
30C2×C42×C13—21no—
31C2×C42×C13C2311yescharacteristic
32#88180—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35#88178—21no—
36#88178—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44#88124—21no—
45#88123Q811yescharacteristic, complemented
46#88123Q811yescharacteristic, complemented
47C4×Dic26—21no—
48C4×Dic26—21no—
49C4×Dic26—42no—
50C4×Dic26—42no—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C22⋊C8—21no—
55C4×C8×C13—21no—
56C13×#95D411yescharacteristic
57C13×#95D411yescharacteristic
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62#88071D411yescharacteristic
63#88071D411yescharacteristic
64C22⋊#1055—21no—
65C4⋊#1055—21no—
66C4×#1055—21no—
67#10371—131nomaximal, Sylow
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C2×Dic26—21no—
78C2×Dic26—21no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C13×M16—41no—
83C13×M16—41no—
84C2×C8×C13—41no—
85C2×C8×C13—41no—
86C13×C4⋊C4—42no—
87C42×C13—41no—
88C42×C13—41no—
89C42×C13C2×Q811yescharacteristic
90C42×C13#4111yescharacteristic
91C42×C13#4111yescharacteristic
92C42×C13#4111yescharacteristic
93C22⋊Dic13—41no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—42no—
99C4⋊Dic13—42no—
100#6101—42no—
101#6101—42no—
102#6101—42no—
103#6101—42no—
104#6101—41no—
105#6101—41no—
106C4×Dic13—21no—
107C4×Dic13—21no—
108C4×Dic13—41no—
109C4×Dic13—41no—
110C4×Dic13—41no—
111C4×Dic13SD1612yes—
112C4×Dic13Q1612yes—
113C2×#1055—41no—
114#2399—131no—
115#1995—131no—
116#1503—131no—
117#1503—131no—
118#1303—131no—
119#1303D1311yescharacteristic
120#1274—131no—
121C23×C13#12011yescharacteristic
122C2×C4×C13—22no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13C22⋊Q811yescharacteristic
131C2×C4×C13C22⋊Q811yescharacteristic
132C2×C4×C13C22⋊Q811yescharacteristic
133C2×C4×C13#12411yescharacteristic
134C2×C4×C13#12411yescharacteristic
135C2×C4×C13#12411yescharacteristic
136C2×C4×C13C2×SD1611yescharacteristic
137C2×C4×C13C2×Q1611yescharacteristic
138C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C13#13711yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—22no—
142C2×Dic13—22no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154Dic26—48no—
155Dic26—81no—
156Dic26—81no—
157C8×C13—81no—
158C8×C13—81no—
159#1055—81no—
160#533—131no—
161C2×C4×Q8—261no—
162#431—131no—
163#431C2×D1311yescharacteristic
164#423C2×D1311yescharacteristic
165#398—261no—
166#398—261no—
167#395—261no—
168#395—261no—
169C4×C4⋊C4—131no—
170C4×C4⋊C4—261no—
171C4×C4⋊C4C2×D1311yescharacteristic
172#376—131no—
173#339—261no—
174#339—261no—
175#328—261no—
176#328—261no—
177#328—261no—
178#328—261no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13#39311yescharacteristic
182C22×C13#45011yescharacteristic
183C22×C13#45111yescharacteristic
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—42no—
189C4×C13—81no—
190C4×C13#47511yescharacteristic
191C4×C13#47711yescharacteristic
192C4×C13#48711yescharacteristic
193C4×C13#48911yescharacteristic
194Dic13—42no—
195Dic13—42no—
196Dic13—42no—
197Dic13—81no—
198Dic13—81no—
199Dic13—81no—
200C22×Q8—261no—
201C2×M16—21no—
202C4⋊Q8—131no—
203C4⋊Q8—131no—
204#125—261no—
205C22⋊Q8—261no—
206C22⋊Q8—261no—
207C4×Q8—261no—
208C4×Q8—261no—
209C4×Q8—522no—
210C4×Q8—522no—
211#117—261no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C42—21no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—261no—
223C2×C42C22×D1311yescharacteristic
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—261no—
228C22⋊C8—21no—
229C22⋊C8—261no—
230C4×C8—21no—
231C4×C8—261no—
232#95—131no—
233#95—131no—
234#95—261no—
235#95—261no—
236#95—261no—
237#95—261no—
238#95D5211yescharacteristic
239#95D5211yescharacteristic
240C2×C13—21no—
241C2×C13—21no—
242C2×C13#202411yescharacteristic
243C2×C13#203111yescharacteristic
244C2×C13#203111yescharacteristic
245C2×Q8—261no—
246C2×Q8—261no—
247C2×Q8—522no—
248C2×Q8—522no—
249C2×Q8—522no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4C2×D5211yescharacteristic
257C22×C4D4×D1311yescharacteristic
258C22×C4D4×D1311yescharacteristic
259M16—41no—
260M16—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—521no—
264C4⋊C4—42no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4—522no—
270C4⋊C4—522no—
271C4⋊C4—522no—
272C4⋊C4—522no—
273C4⋊C4—522no—
274C4⋊C4—522no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C22⋊C4—521no—
278C42—41no—
279C42—41no—
280C42—132no—
281C42—132no—
282C42—261no—
283C42—261no—
284C42—521no—
285C42—521no—
286C42—521no—
287C42#612711yescharacteristic
288C42#612711yescharacteristic
289C42#612911yescharacteristic
290C42Q8×D1311yescharacteristic
291C13#1037111yescharacteristic, complemented, Sylow
292C23#8813611yescharacteristic
293Q8—528no—
294Q8—1041no—
295Q8—1041no—
296C2×C4—22no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—262no—
305C2×C4—262no—
306C2×C4—262no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4#8812911yescharacteristic
319C2×C4#8813911yescharacteristic
320C2×C4#8813911yescharacteristic
321C2×C4#8815011yescharacteristic
322C2×C4#8815011yescharacteristic
323C2×C4#8815111yescharacteristic
324C2×C4#8816511yescharacteristic
325C2×C4SD16×D1311yescharacteristic
326C2×C4#8816911yescharacteristic
327C2×C4Q16×D1311yescharacteristic
328C8—81no—
329C8—81no—
330C8—1041no—
331C22—21no—
332C22—21no—
333C22#1171833411yescharacteristic
334C22#1171843711yescharacteristic
335C22#1171846911yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—81no—
342C4—522no—
343C4—522no—
344C4—522no—
345C4—1041no—
346C4—1041no—
347C4—1041no—
348C4#1171842611yescharacteristic
349C4#1171845311yescharacteristic
350C4#1171851511yescharacteristic
351C4#1171853611yescharacteristic
352C2—21no—
353C2—21no—
354C2#1311597611yescharacteristic
355C2#1311600911yescharacteristic
356C2#1311601111yescharacteristic
subgroupG/H
centerC2×C4#88139
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1303C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1303D13
hypocenterC13#10371
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
45. #88123Q8semidirect
46. #88123Q8semidirect
291. C13#10371semidirect

Maximal subgroups

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

subgroupindex
#131181302
#131158162
#131133362
#131133342
#131127372
#131126642
C13×#13032
#1037113