Finite Group Databasebeta

← #15758122

Subgroups — #15758122

Order 3328.

476 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 109 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#13124844C211yesmaximal, characteristic
2#13123776C211yesmaximal, characteristic, complemented
3#13113494C211yesmaximal, characteristic, complemented
4#13113261C211yesmaximal, characteristic
5#13112733C211yesmaximal, characteristic, complemented
6#13112681C211yesmaximal, characteristic, complemented
7C13×#1955C211yesmaximal, characteristic
8C2×C4×D4×C13C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×C22⋊C8—21no—
12C2×C13×C22⋊C8—21no—
13C2×C13×#97C2211yescharacteristic
14#11718879C412yes—
15#11718763—21no—
16#11718762—21no—
17#11718680—21no—
18C4×#6105—22no—
19#11718669—21no—
20#11718632C412yes—
21#11718586C2211yescharacteristic
22#11718586C2211yescharacteristic
23#11718585C2211yescharacteristic
24#11718362—22no—
25#11718362—22no—
26D4⋊#1055—22no—
27#11718078—21no—
28#11718073—21no—
29C22×D4×C13C2×C411yescharacteristic
30C23×C4×C13—21no—
31C22×C8×C13—21no—
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C4×D4×C13—21no—
35C4×D4×C13—21no—
36C4×D4×C13—21no—
37C4×D4×C13—21no—
38C2×C13×C4⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4—21no—
40C2×C42×C13C2311yescharacteristic
41C2×#6105—22no—
42#88180—21no—
43#88178—21no—
44#88178C2×C412yes—
45C2×#6099—21no—
46#88124—21no—
47#88123D411yescharacteristic
48#88123D411yescharacteristic
49C4×Dic26—21no—
50C4×Dic26D412yes—
51C13×C4⋊C8—21no—
52C13×C4⋊C8—21no—
53C13×C22⋊C8—42no—
54C13×C22⋊C8—42no—
55C13×#97—21no—
56C13×#97—21no—
57#88072—22no—
58C22⋊#1055—21no—
59C22⋊#1055C2×C412yes—
60#88055—22no—
61#88054—24no—
62C8×Dic13—22no—
63#88050—22no—
64#88048—22no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68C4⋊#1055D412yes—
69C4×#1055—21no—
70C4×#1055—21no—
71#9050—131nomaximal, Sylow
72C24×C13—21no—
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13—42no—
76C22×C4×C13—21no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—41no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13#4111yescharacteristic
86C2×Dic26—21no—
87C2×Dic26C22⋊C412yes—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—21no—
92C2×C8×C13—21no—
93C2×C8×C13—41no—
94C2×C8×C13—41no—
95C2×C8×C13—41no—
96C2×C8×C13SD1612yescomplemented
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—41no—
101C42×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13#4111yescharacteristic
105C22⋊Dic13—22no—
106#6105—44no—
107C4⋊Dic13—21no—
108C4⋊Dic13—21no—
109C4⋊Dic13—21no—
110C4⋊Dic13C22⋊C412yes—
111#6101—22no—
112#6101—22no—
113C4×Dic13—22no—
114#6099—41no—
115#6099—41no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—41no—
119#3101—131no—
120#2961—131no—
121#1955D1311yescharacteristic
122#1542—131no—
123#1486—131no—
124#1301—131no—
125#1281—131no—
126C23×C13—22no—
127C23×C13—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—41no—
132C23×C13—41no—
133C23×C13C4×D411yescharacteristic
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×C13C2×C22⋊C411yescharacteristic
148C2×C4×C13C4×D411yescharacteristic
149C2×C4×C13#12011yescharacteristic
150C2×C4×C13#12111yescharacteristic
151C2×C4×C13#12111yescharacteristic
152C2×C4×C13#12311yescharacteristic
153C2×C4×C13C2×SD1611yescharacteristic
154C2×C4×C13#13511yescharacteristic
155C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C13#13711yescharacteristic
157C2×Dic13—22no—
158C2×Dic13—22no—
159Dic26—42no—
160Dic26—81no—
161C8×C13—22no—
162C8×C13—41no—
163C8×C13—81no—
164#1055—42no—
165#1055—42no—
166#1055—81no—
167#533—131no—
168C2×C4×D4C2×D1311yescharacteristic
169#483—132no—
170#476—261no—
171#461—261no—
172#450—132no—
173#446—262no—
174#446—262no—
175C4×SD16—262no—
176#431—131no—
177#431—131no—
178#424—261no—
179#423—131no—
180C2×C4⋊C8C2×D1311yescharacteristic
181C2×C22⋊C8—21no—
182C2×C22⋊C8—21no—
183#405—261no—
184C2×#97C2×D1311yescharacteristic
185#333—261no—
186#332—261no—
187D4⋊C8—262no—
188C22×C13—21no—
189C22×C13—21no—
190C22×C13—42no—
191C22×C13—42no—
192C22×C13—42no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13#38611yescharacteristic
198C22×C13C4×SD1611yescharacteristic
199C22×C13#44011yescharacteristic
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—21no—
203C4×C13—21no—
204C4×C13—81no—
205C4×C13#44811yescharacteristic
206C4×C13#44911yescharacteristic
207C4×C13#46011yescharacteristic
208C4×C13#46411yescharacteristic
209Dic13—42no—
210Dic13—42no—
211C22×D4C4×D1311yescharacteristic
212C23×C4—21no—
213C2×SD16—262no—
214C2×M16—261no—
215C22×C8—21no—
216C22×C8C22⋊D1311yescharacteristic
217C22×C8C22⋊D1311yescharacteristic
218C4⋊Q8—131no—
219C4⋊Q8—131no—
220#125—261no—
221C22⋊Q8—132no—
222C22⋊Q8—261no—
223C4×Q8—132no—
224C4×Q8—261no—
225C4×D4—21no—
226C4×D4—21no—
227C4×D4—21no—
228C4×D4—21no—
229#117—261no—
230C2×C4⋊C4C4×D1311yescharacteristic
231C2×C22⋊C4—21no—
232C2×C42C22×D1311yescharacteristic
233#106—262no—
234C4⋊C8—21no—
235C4⋊C8—21no—
236C4⋊C8—132no—
237C4⋊C8—264no—
238C4⋊C8—261no—
239C4⋊C8—261no—
240C4⋊C8—261no—
241#103—262no—
242#102—262no—
243C22⋊C8—42no—
244C22⋊C8—42no—
245C22⋊C8—132no—
246C22⋊C8—261no—
247#97—21no—
248#97—21no—
249#97—262no—
250C4×C8—262no—
251C4×C8—261no—
252C4×C8—261no—
253C2×C13—21no—
254C2×C13—21no—
255C2×C13—82no—
256C2×C13#188011yescharacteristic
257C2×C13#188111yescharacteristic
258C2×C13#189111yescharacteristic
259C24—21no—
260C2×Q8—132no—
261C2×Q8—261no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—42no—
265C22×C4—21no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4C2×C4×D1311yescharacteristic
273C22×C4#612711yescharacteristic
274C22×C4C2×C22⋊D1311yescharacteristic
275SD16—524no—
276M16—521no—
277M16—521no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—262no—
287C2×C8—262no—
288C2×C8—521no—
289C2×C8#610512yescomplemented
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—132no—
293C4⋊C4—262no—
294C4⋊C4—262no—
295C4⋊C4—261no—
296C4⋊C4—261no—
297C4⋊C4—261no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—262no—
301C42—262no—
302C42D4×D1311yescharacteristic
303C42D4×D1311yescharacteristic
304C42D4×D1311yescharacteristic
305C42#612911yescharacteristic
306C13#905011yescharacteristic, complemented, Sylow
307C23—22no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23C4×C22⋊D1311yescharacteristic
315Q8—522no—
316Q8—1041no—
317D4—22no—
318D4—22no—
319D4—41no—
320D4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—262no—
331C2×C4—262no—
332C2×C4C22⋊C4×D1311yescharacteristic
333C2×C4#8813511yescharacteristic
334C2×C4#8813711yescharacteristic
335C2×C4#8813811yescharacteristic
336C2×C4#8818611yescharacteristic
337C2×C4C2×#610511yescharacteristic
338C2×C4#8819111yescharacteristic
339C2×C4#8819211yescharacteristic
340C2×C4#8820411yescharacteristic
341C2×C4#8820511yescharacteristic
342C8—22no—
343C8—41no—
344C8—81no—
345C8—522no—
346C8—522no—
347C8—1041no—
348C22—21no—
349C22—21no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1171861711yescharacteristic
358C22C4×#610511yescharacteristic
359C22#1171867911yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—81no—
365C4—522no—
366C4—522no—
367C4#1171869811yescharacteristic
368C4#1171870111yescharacteristic
369C4#1171871511yescharacteristic
370C4#1171873611yescharacteristic
371C2—21no—
372C2—21no—
373C2—82no—
374C2#1311519411yescharacteristic
375C2#1311520111yescharacteristic
376C2#1311525111yescharacteristic
subgroupG/H
centerC2×C4#88191
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1955C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#1955D13
hypocenterC13#9050
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. #13123776C2semidirect
3. #13113494C2semidirect
5. #13112733C2semidirect
6. #13112681C2semidirect
96. C2×C8×C13SD16semidirect
289. C2×C8#6105semidirect
306. C13#9050semidirect

Maximal subgroups

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

subgroupindex
#131248442
#131237762
#131134942
#131132612
#131127332
#131126812
C13×#19552
#905013