Finite Group Databasebeta

← #15751928

Subgroups — #15751928

Order 3328.

436 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 85 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#13122800C211yesmaximal, characteristic
2#13116161C211yesmaximal, characteristic
3#13115936C211yesmaximal, characteristic
4#13112662C211yesmaximal, characteristic
5#13112661C211yesmaximal, characteristic
6#13112658C211yesmaximal, characteristic
7C13×#2024C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C22×#6107—21no—
10C2×C13×#103—21no—
11C13×#391C2211yescharacteristic
12#11718891—21no—
13C2×#88075—21no—
14#11718645—21no—
15C2×#88047—21no—
16#11718590C2211yescharacteristic
17#11718589C2211yescharacteristic
18#11718322—21no—
19#11718317—21no—
20#11718315—21no—
21#11718308—21no—
22C13×#340—21no—
23C13×#336C2211yescharacteristic
24#11718121—21no—
25#11718116C2211yescharacteristic
26#11718116C2211yescharacteristic
27C22×Q8×C13—21no—
28C22×Q8×C13D411yescharacteristic
29C22×Dic26D411yescharacteristic
30C22×C8×C13—21no—
31C13×C4⋊Q8—42no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C42×C13C2311yescharacteristic
36C2×#6107—42no—
37C2×#6107—42no—
38C2×#6107—42no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C2×C4⋊Dic13D411yescharacteristic
43C2×C4⋊Dic13D411yescharacteristic
44C2×#6101—21no—
45C2×#6101—21no—
46C2×#6101—21no—
47C2×C4×Dic13—21no—
48C22×#1055—21no—
49C22×#1055—21no—
50C13×#103—42no—
51C13×#95—21no—
52C13×#95—21no—
53#88075—42no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88047—42no—
61#7784—131nomaximal, Sylow
62C2×Q8×C13—21no—
63C2×Q8×C13—22no—
64C2×Q8×C13—41no—
65C2×Q8×C13—41no—
66C2×Q8×C13—41no—
67C2×Q8×C13—41no—
68C2×Q8×C13—41no—
69C2×Q8×C13—41no—
70C2×Q8×C13—41no—
71C2×Q8×C13Q1612yescomplemented
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—41no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×Dic13—21no—
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C2×Dic26—21no—
83C2×Dic26—21no—
84C2×Dic26—41no—
85C2×Dic26—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C2×C8×C13—41no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C42×C13—41no—
95#6107—48no—
96C4⋊Dic13—21no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99C4⋊Dic13—81no—
100C4⋊Dic13—81no—
101C4⋊Dic13Q1612yescomplemented
102#6101—41no—
103#6101—41no—
104#6101—81no—
105#6101—81no—
106C4×Dic13—81no—
107C2×#1055—22no—
108C2×#1055—22no—
109C2×#1055—41no—
110C2×#1055—41no—
111C2×#1055—41no—
112C2×#1055—41no—
113#2806—131no—
114#2057—131no—
115#2024D1311yescharacteristic
116#2016—131no—
117#1272—131no—
118#1272—131no—
119#1271—131no—
120C23×C13#12011yescharacteristic
121Q8×C13—42no—
122Q8×C13—42no—
123Q8×C13—42no—
124Q8×C13—81no—
125Q8×C13—81no—
126Q8×C13—81no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—22no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13C2×Q1611yescharacteristic
143C2×C4×C13C2×Q1611yescharacteristic
144C2×C4×C13#13511yescharacteristic
145C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C13#13711yescharacteristic
147C2×C4×C13#13711yescharacteristic
148C2×Dic13—22no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160Dic26—42no—
161Dic26—81no—
162C8×C13—81no—
163#1055—42no—
164#1055—42no—
165C22×Q16—261no—
166C2×C4⋊Q8C2×D1311yescharacteristic
167C2×#107—261no—
168C2×#103—21no—
169C2×#103—261no—
170#398—261no—
171#398—261no—
172#395—261no—
173#391—131no—
174#391—261no—
175#391C2×D1311yescharacteristic
176#389—131no—
177#389—261no—
178#387—261no—
179#340—21no—
180#340—261no—
181#336—131no—
182#336—131no—
183#336C2×D1311yescharacteristic
184C22×C13#44911yescharacteristic
185C22×C13#45111yescharacteristic
186C22×C13#45111yescharacteristic
187C22×C13#45311yescharacteristic
188C22×C13#45511yescharacteristic
189C22×C13#45611yescharacteristic
190C22×C13B(4,𝔽2)11yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—42no—
198C4×C13—82no—
199C4×C13—81no—
200Dic13—42no—
201Dic13—81no—
202Dic13—81no—
203Dic13—81no—
204C22×Q8—21no—
205C22×Q8—131no—
206C22×Q8C22⋊D1311yescharacteristic
207C2×Q16—522no—
208C2×Q16—522no—
209C2×Q16—522no—
210C22×C8—21no—
211C22×C8—261no—
212C22×C8—261no—
213C4⋊Q8—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—131no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4C22⋊D1311yescharacteristic
225C2×C42—261no—
226C2×C42C22×D1311yescharacteristic
227#107—522no—
228#103—42no—
229#103—522no—
230#95—21no—
231#95—21no—
232#95—261no—
233#95—261no—
234#95—261no—
235#95—261no—
236#95—261no—
237#95—261no—
238C2×C13#160011yescharacteristic
239C2×C13#160211yescharacteristic
240C2×C13#160511yescharacteristic
241C2×C13#163311yescharacteristic
242C2×C13#164411yescharacteristic
243C2×C13#164811yescharacteristic
244C2×C13#166111yescharacteristic
245C2×Q8—21no—
246C2×Q8—22no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×Q8—41no—
254C2×Q8—261no—
255C2×Q8—261no—
256C2×Q8—521no—
257C2×Q8—521no—
258C2×Q8#610712yescomplemented
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—41no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4D4×D1311yescharacteristic
267C22×C4D4×D1311yescharacteristic
268C22×C4C2×C22⋊D1311yescharacteristic
269Q16—528no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—262no—
274C2×C8—262no—
275C2×C8—521no—
276C2×C8—521no—
277C2×C8—521no—
278C2×C8—521no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—132no—
285C4⋊C4—261no—
286C4⋊C4—521no—
287C4⋊C4—521no—
288C4⋊C4—521no—
289C4⋊C4—521no—
290C4⋊C4—1041no—
291C4⋊C4—1041no—
292C4⋊C4—1041no—
293C4⋊C4—1041no—
294C42—41no—
295C42—1041no—
296C13#778411yescharacteristic, complemented, Sylow
297C23#8819111yescharacteristic
298Q8—42no—
299Q8—42no—
300Q8—42no—
301Q8—81no—
302Q8—81no—
303Q8—81no—
304Q8—522no—
305Q8—1041no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—262no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4#8816811yescharacteristic
334C2×C4#8817011yescharacteristic
335C2×C4Q16×D1311yescharacteristic
336C2×C4#8817211yescharacteristic
337C2×C4C2×#610711yescharacteristic
338C2×C4#8820511yescharacteristic
339C8—81no—
340C8—522no—
341C8—522no—
342C22#1171869311yescharacteristic
343C22#1171871111yescharacteristic
344C22#1171872211yescharacteristic
345C22#1171883311yescharacteristic
346C22#1171884711yescharacteristic
347C22#1171885911yescharacteristic
348C22#1171886611yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—42no—
356C4—81no—
357C4—82no—
358C4—522no—
359C4—1041no—
360C4—1041no—
361C4—1041no—
362C2#1311378111yescharacteristic
363C2#1311379211yescharacteristic
364C2#1311380811yescharacteristic
365C2#1311397511yescharacteristic
366C2#1311404711yescharacteristic
367C2#1311407711yescharacteristic
368C2#1311415211yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2024C2
socle, prime radicalC23×C13#120
hypercenter#2024D13
hypocenterC13#7784
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
71. C2×Q8×C13Q16semidirect
101. C4⋊Dic13Q16semidirect
258. C2×Q8#6107semidirect
296. C13#7784semidirect

Maximal subgroups

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

subgroupindex
#131228002
#131161612
#131159362
#131126622
#131126612
#131126582
C13×#20242
#778413