Finite Group Databasebeta

← #15760790

Subgroups — #15760790

Order 3328.

522 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 105 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#13123919C211yesmaximal, characteristic, complemented
2#13119745C211yesmaximal, characteristic
3#13114829C211yesmaximal, characteristic, complemented
4#13113261C211yesmaximal, characteristic
5#13112696C211yesmaximal, characteristic, complemented
6#13112695C211yesmaximal, characteristic, complemented
7C13×#1486C211yesmaximal, characteristic
8C2×C4×D4×C13C2211yescharacteristic
9C2×#88178—21no—
10C2×C4×Dic26C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#423C2211yescharacteristic
13#11718883C412yes—
14#11718873—21no—
15C2×#88064—21no—
16#11718641C412yes—
17#11718605—22no—
18#11718597C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718585C2211yescharacteristic
21#11718492—22no—
22#11718380—22no—
23#11718340—22no—
24C13×D4⋊C8—22no—
25#11718146—21no—
26D4⋊#1055—22no—
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13—21no—
29C22×Dic26D411yescharacteristic
30C2×C13×M16—21no—
31C4×D4×C13—21no—
32C4×D4×C13—21no—
33C4×D4×C13—21no—
34C4×D4×C13—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—22no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42#88178—42no—
43#88178—42no—
44C2×#6101—22no—
45C2×#6101C2×C412yes—
46C2×C4×Dic13D412yes—
47C2×#6099—21no—
48C4×Dic26—21no—
49C4×Dic26—21no—
50C4×Dic26—21no—
51C4×Dic26—21no—
52C13×C4⋊C8—21no—
53C13×C4⋊C8—21no—
54C13×C4⋊C8—21no—
55C13×C22⋊C8—21no—
56C4×C8×C13D412yes—
57#88071—21no—
58#88071—22no—
59#88071C2×C412yes—
60C22⋊#1055—21no—
61#88064—42no—
62#88055—24no—
63#88054—24no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4×#1055D412yes—
68#9490—131nomaximal, Sylow
69C24×C13—21no—
70C2×D4×C13—21no—
71C2×D4×C13—21no—
72C2×D4×C13—42no—
73C22×C4×C13—21no—
74C22×C4×C13—41no—
75C22×C4×C13—41no—
76C22×C4×C13—41no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×Dic13—22no—
84C22×Dic13C22⋊C412yes—
85C22×Dic13C22⋊C412yes—
86C2×Dic26—21no—
87C2×Dic26—21no—
88C2×Dic26—21no—
89C2×Dic26—21no—
90C2×Dic26—21no—
91C2×Dic26—21no—
92C13×M16—41no—
93C13×M16—41no—
94C2×C8×C13—22no—
95C2×C8×C13—41no—
96C13×C4⋊C4—21no—
97C13×C4⋊C4—21no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C42×C13C2×D411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13#4111yescharacteristic
103C42×C13#4111yescharacteristic
104C22⋊Dic13—44no—
105C22⋊Dic13—44no—
106C4⋊Dic13—21no—
107C4⋊Dic13—21no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110#6101—22no—
111#6101—22no—
112#6101—44no—
113C4×Dic13—22no—
114C4×Dic13—22no—
115#6099—41no—
116#6099—41no—
117C2×#1055—22no—
118C2×#1055—41no—
119#2983—131no—
120#2536—131no—
121#1801—131no—
122#1486—131no—
123#1486D1311yescharacteristic
124#1286—131no—
125#1286—131no—
126C23×C13—22no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13C2×C22⋊C411yescharacteristic
134D4×C13—22no—
135D4×C13—22no—
136D4×C13—41no—
137D4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13—81no—
146C2×C4×C13—81no—
147C2×C4×C13C4×D411yescharacteristic
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13#12011yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12311yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C13#13711yescharacteristic
157C2×Dic13—22no—
158C2×Dic13—22no—
159C2×Dic13—22no—
160C2×Dic13—22no—
161C2×Dic13—42no—
162C2×Dic13—42no—
163C2×Dic13—42no—
164C2×Dic13—42no—
165Dic26—41no—
166Dic26—41no—
167Dic26—41no—
168Dic26—41no—
169C8×C13—42no—
170C8×C13—81no—
171#1055—42no—
172#1055—81no—
173C2×C22⋊Q8—261no—
174C2×C4×Q8—131no—
175C2×C4×D4C2×D1311yescharacteristic
176#446—262no—
177#446—262no—
178#432—262no—
179#431—131no—
180#431C2×D1311yescharacteristic
181#423—131no—
182#423C2×D1311yescharacteristic
183C2×#101—261no—
184#398—132no—
185#394—132no—
186#388—262no—
187#382—131no—
188#380—261no—
189#343—261no—
190D4⋊C8—22no—
191D4⋊C8—262no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13—42no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13#38611yescharacteristic
202C22×C13#41711yescharacteristic
203C22×C13#41811yescharacteristic
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13—21no—
208C4×C13—81no—
209C4×C13#46811yescharacteristic
210C4×C13#46811yescharacteristic
211C4×C13#46911yescharacteristic
212C4×C13#46911yescharacteristic
213Dic13—42no—
214Dic13—42no—
215Dic13—82no—
216C22×Q8—131no—
217C22×D4C4×D1311yescharacteristic
218C23×C4—21no—
219C2×M16—21no—
220C2×M16—261no—
221C22⋊Q8—522no—
222C22⋊Q8—522no—
223C4×Q8—261no—
224C4×Q8—261no—
225C4×Q8—261no—
226C4×Q8—261no—
227C4×D4—21no—
228C4×D4—21no—
229C4×D4—21no—
230C4×D4—21no—
231C2×C4⋊C4—132no—
232C2×C4⋊C4—131no—
233C2×C4⋊C4—262no—
234C2×C4⋊C4—261no—
235C2×C4⋊C4C4×D1311yescharacteristic
236C2×C22⋊C4—21no—
237C2×C22⋊C4—262no—
238C2×C22⋊C4—262no—
239C2×C42—132no—
240C2×C42C22×D1311yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—264no—
245C4⋊C8—261no—
246C4⋊C8—261no—
247C4⋊C8—261no—
248#101—522no—
249C22⋊C8—21no—
250C22⋊C8—261no—
251#97—264no—
252C4×C8—132no—
253C4×C8C22⋊D1312yes—
254#95—132no—
255#95—262no—
256#95—261no—
257C2×C13—21no—
258C2×C13—21no—
259C2×C13—82no—
260C2×C13#189111yescharacteristic
261C2×C13#189511yescharacteristic
262C2×C13#191211yescharacteristic
263C24—21no—
264C2×Q8—261no—
265C2×Q8—261no—
266C2×Q8—261no—
267C2×Q8—261no—
268C2×Q8—261no—
269C2×Q8—261no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—42no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—132no—
281C22×C4—132no—
282C22×C4—262no—
283C22×C4C2×C4×D1311yescharacteristic
284C22×C4D4×D1311yescharacteristic
285C22×C4D4×D1311yescharacteristic
286M16—41no—
287M16—41no—
288M16—521no—
289M16—521no—
290C2×C8—22no—
291C2×C8—41no—
292C2×C8—262no—
293C2×C8—521no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—262no—
297C4⋊C4—261no—
298C4⋊C4—262no—
299C4⋊C4—261no—
300C4⋊C4—524no—
301C4⋊C4—521no—
302C4⋊C4—521no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—524no—
306C22⋊C4—524no—
307C42—262no—
308C42—262no—
309C42#612711yescharacteristic
310C42D4×D1311yescharacteristic
311C42#612911yescharacteristic
312C42C2×C22⋊D1311yescharacteristic
313C13#949011yescharacteristic, complemented, Sylow
314C23—22no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23C22⋊C4×D1311yescharacteristic
322Q8—521no—
323Q8—521no—
324Q8—521no—
325Q8—521no—
326D4—22no—
327D4—22no—
328D4—41no—
329D4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—262no—
340C2×C4—262no—
341C2×C4—262no—
342C2×C4—262no—
343C2×C4—522no—
344C2×C4—522no—
345C2×C4—522no—
346C2×C4—522no—
347C2×C4#8813511yescharacteristic
348C2×C4#8813711yescharacteristic
349C2×C4#8813811yescharacteristic
350C2×C4#8816511yescharacteristic
351C2×C4#8816511yescharacteristic
352C2×C4#8816811yescharacteristic
353C2×C4#8816911yescharacteristic
354C2×C4C4×C22⋊D1311yescharacteristic
355C2×C4#8819111yescharacteristic
356C2×C4#8819211yescharacteristic
357C8—42no—
358C8—81no—
359C8—522no—
360C8—1041no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22#1171843111yescharacteristic
371C22#1171843211yescharacteristic
372C22#1171861711yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—21no—
377C4—81no—
378C4—522no—
379C4—522no—
380C4—1042no—
381C4#1171844111yescharacteristic
382C4#1171844311yescharacteristic
383C4#1171882011yescharacteristic
384C4#1171883511yescharacteristic
385C2—21no—
386C2—21no—
387C2—82no—
388C2#1311525111yescharacteristic
389C2#1311527111yescharacteristic
390C2#1311537011yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1486C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#1486D13
hypocenterC13#9490
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
1. #13123919C2semidirect
3. #13114829C2semidirect
5. #13112696C2semidirect
6. #13112695C2semidirect
313. C13#9490semidirect

Maximal subgroups

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

subgroupindex
#131239192
#131197452
#131148292
#131132612
#131126962
#131126952
C13×#14862
#949013