Finite Group Databasebeta

← #15773700

Subgroups — #15773700

Order 3328.

464 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114824C211yesmaximal, characteristic, complemented
2#13113177C211yesmaximal, characteristic, complemented
3#13112860C212yesmaximal, complemented
4#13112833C212yesmaximal, complemented
5C13×#2635C211yesmaximal, characteristic
6C2×C13×#121C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#400C411yescharacteristic, complemented
9C13×#399C2211yescharacteristic
10C13×#394—21no—
11C13×#394C411yescharacteristic, complemented
12C13×#392—21no—
13C13×#392C2211yescharacteristic
14C13×#388—21no—
15C13×#386—21no—
16C13×#381C411yescharacteristic, complemented
17C2×#88074—21no—
18#11718873—21no—
19#11718587—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C22×D4×C13D411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C13×#121—41no—
30C13×#121—41no—
31C4×D4×C13—41no—
32C4×D4×C13—41no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C13×C22⋊C4C2311yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C4⋊Dic13—41no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88074—42no—
53#88071—41no—
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56#88043—41no—
57#11824—131nomaximal, Sylow
58C24×C13—21no—
59C24×C13C22⋊C411yescharacteristic
60C24×C13C2×D411yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—42no—
67C2×D4×C13—41no—
68C2×D4×C13—41no—
69C2×D4×C13—81no—
70C2×D4×C13—81no—
71C2×D4×C13—81no—
72C2×D4×C13—81no—
73C2×D4×C13—81no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—81no—
82C22×C4×C13—81no—
83C22×C4×C13C22⋊C411yescharacteristic
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×Dic13—42no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—81no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—41no—
96C13×C22⋊C4—41no—
97C13×C22⋊C4—81no—
98C13×C22⋊C4—81no—
99C13×C22⋊C4—81no—
100C13×C22⋊C4—81no—
101C42×C13—21no—
102C42×C13—21no—
103C22⋊Dic13—42no—
104C22⋊Dic13—42no—
105C4⋊Dic13—82no—
106C2×#1055—42no—
107#2635D1311yescharacteristic
108#1799—131no—
109#1466—131no—
110#1352—132no—
111#1343—132no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—41no—
128C23×C13C2×C22⋊C411yescharacteristic
129C23×C13AGL(1,ℤ/8)11yescharacteristic
130C23×C13#13711yescharacteristic
131D4×C13—42no—
132D4×C13—42no—
133D4×C13—82no—
134D4×C13—82no—
135D4×C13—82no—
136D4×C13—84no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—41no—
144C2×C4×C13—42no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—81no—
158C2×C4×C13—81no—
159C2×C4×C13—81no—
160C2×C4×C13#9911yescharacteristic
161C2×C4×C13#9911yescharacteristic
162C2×Dic13—82no—
163C2×Dic13—82no—
164C2×Dic13—82no—
165#1055—82no—
166C2×#121Dic1311yescharacteristic, complemented
167C2×C4×D4C2×D1311yescharacteristic
168#432—261no—
169C2×#99—261no—
170#400Dic1311yescharacteristic, complemented
171#399C2×D1311yescharacteristic
172#394—21no—
173#394Dic1311yescharacteristic, complemented
174#392—21no—
175#392C2×D1311yescharacteristic
176#388—21no—
177#386—21no—
178#381Dic1311yescharacteristic, complemented
179#380—261no—
180#342—132no—
181#323—132no—
182#323—261no—
183C22×C13—21no—
184C22×C13—21no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—41no—
193C22×C13—41no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13—81no—
203C22×C13—81no—
204C22×C13C2×#9911yescharacteristic
205C22×C13#41711yescharacteristic
206C22×C13#42111yescharacteristic
207C4×C13—21no—
208C4×C13—21no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—41no—
212C4×C13—41no—
213C4×C13—81no—
214C4×C13—81no—
215C4×C13—81no—
216Dic13—162no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4C2×Dic1311yescharacteristic
220C22×D4C22⋊D1311yescharacteristic
221C23×C4C2×Dic1311yescharacteristic
222C23×C4C22⋊D1311yescharacteristic
223#121—41no—
224#121—41no—
225C4×D4—41no—
226C4×D4—41no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—521no—
229C2×C4⋊C4C2×Dic1311yescharacteristic
230C2×C4⋊C4C2×Dic1311yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—262no—
238C2×C22⋊C4C22⋊D1311yescharacteristic
239C2×C22⋊C4C22×D1311yescharacteristic
240C2×C42C22⋊D1311yescharacteristic
241C4⋊C8—521no—
242#99—522no—
243C22⋊C8—262no—
244#97—521no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95—521no—
249#95C2×Dic1311yescharacteristic
250#95C2×Dic1311yescharacteristic
251C2×C13—21no—
252C2×C13—21no—
253C2×C13—41no—
254C2×C13—41no—
255C2×C13—81no—
256C2×C13—161no—
257C2×C13#151311yescharacteristic
258C2×C13#212111yescharacteristic
259C2×C13#212811yescharacteristic
260C24—21no—
261C24C22⋊Dic1311yescharacteristic
262C24C2×C22⋊D1311yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—81no—
272C2×D4—81no—
273C2×D4—81no—
274C2×D4—81no—
275C2×D4—81no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—81no—
284C22×C4—81no—
285C22×C4—522no—
286C22×C4C22⋊Dic1311yescharacteristic
287C22×C4C22⋊Dic1311yescharacteristic
288C22×C4C22⋊Dic1311yescharacteristic
289C22×C4C22×Dic1311yescharacteristic
290C22×C4C2×C22⋊D1311yescharacteristic
291C2×C8—522no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—81no—
295C4⋊C4—1042no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—81no—
305C22⋊C4—522no—
306C22⋊C4—522no—
307C42—21no—
308C42—21no—
309C13#1182411yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23#8820311yescharacteristic
327C23#8820511yescharacteristic
328C23C2×C22⋊Dic1311yescharacteristic
329D4—42no—
330D4—42no—
331D4—82no—
332D4—82no—
333D4—82no—
334D4—84no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—1042no—
359C2×C4—1042no—
360C2×C4—1042no—
361C2×C4#8807411yescharacteristic
362C2×C4#8807411yescharacteristic
363C8—1042no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—81no—
376C22—81no—
377C22—81no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22C2×#8807411yescharacteristic
386C22#1171889311yescharacteristic
387C22#1171889711yescharacteristic
388C4—21no—
389C4—21no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—41no—
394C4—81no—
395C4—81no—
396C4—81no—
397C4—2082no—
398C2—21no—
399C2—21no—
400C2—41no—
401C2—41no—
402C2—81no—
403C2—161no—
404C2#1311337911yescharacteristic
405C2#1311648211yescharacteristic
406C2#1311650811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
Fitting, prime radicalC13×#2635C2
socleC22×C13C2×#99
cosocleC2×C13×C22⋊C4C23
hypercenter#2635D13
hypocenterC13#11824
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2635

Complements

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

NH ≅ G/Ntype
1. #13114824C2semidirect
2. #13113177C2semidirect
3. #13112860C2semidirect
4. #13112833C2semidirect
6. C2×C13×#121C4semidirect
8. C13×#400C4semidirect
11. C13×#394C4semidirect
16. C13×#381C4semidirect
166. C2×#121Dic13semidirect
170. #400Dic13semidirect
173. #394Dic13semidirect
178. #381Dic13semidirect
309. C13#11824semidirect

Maximal subgroups

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

subgroupindex
#131148242
#131131772
#131128602
#131128332
C13×#26352
#1182413