Finite Group Databasebeta

← #15757903

Subgroups — #15757903

Order 3328.

558 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 107 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#13118095C211yesmaximal, characteristic
2#13114933C212yesmaximal, complemented
3C4×#88074C211yesmaximal, characteristic
4#13112721C212yesmaximal, complemented
5C13×#2975C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88180C2211yescharacteristic
8C13×#436—24no—
9C13×#431—21no—
10C13×#407—21no—
11C13×#407C2212yes—
12#11718883—21no—
13C2×#88074—21no—
14C4×C22⋊Dic13—21no—
15C4×C22⋊Dic13C2212yes—
16C4×C22⋊Dic13C2211yescharacteristic
17#11718647C411yescharacteristic, complemented
18#11718644C411yescharacteristic, complemented
19#11718614C411yescharacteristic, complemented
20#11718613—21no—
21#11718610C411yescharacteristic, complemented
22C4×#6101—21no—
23#11718147—24no—
24#11718118—21no—
25C22×D4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C2×C13×M16—22no—
29C2×C13×M16D414yes—
30C4×D4×C13—22no—
31C4×D4×C13—22no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4D411yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13—21no—
40C2×C22⋊Dic13—21no—
41#88180—22no—
42#88180—22no—
43C2×C4⋊Dic13C2×C411yescharacteristic
44C2×C4⋊Dic13C2×C411yescharacteristic
45C2×#6101—21no—
46C2×#6101—21no—
47C2×C4×Dic13—21no—
48C2×C4×Dic13—21no—
49C2×C4×Dic13—22no—
50C13×C4⋊C8—22no—
51C13×C22⋊C8—22no—
52C13×C22⋊C8—22no—
53C13×C22⋊C8—22no—
54C4×C8×C13—22no—
55#88074—24no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88071—22no—
61#88071C2×C411yescharacteristic
62#88071C2×C411yescharacteristic
63#9012—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C24×C13C2×D411yescharacteristic
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—41no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D412yes—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4112yes—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—42no—
85C13×M16—44no—
86C13×M16—82no—
87C2×C8×C13—24no—
88C13×C4⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C42×C13—21no—
92C42×C13—21no—
93C22⋊Dic13—24no—
94C22⋊Dic13—42no—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C22⋊Dic13—42no—
98C22⋊Dic13—42no—
99C4⋊Dic13—22no—
100C4⋊Dic13—22no—
101#6101—42no—
102#6101—42no—
103C4×Dic13—42no—
104C4×Dic13—41no—
105C4×Dic13—41no—
106C4×Dic13—44no—
107#2975D1311yescharacteristic
108#2395—131no—
109#1826—132no—
110C4×#99—131no—
111#1297—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×C13C2×C22⋊C411yescharacteristic
122C23×C13#12112yes—
123D4×C13—44no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—24no—
127C2×C4×C13—22no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—81no—
136C2×C4×C13#10412yes—
137C2×C4×C13C4×D412yes—
138C2×C4×C13#12011yescharacteristic
139C2×C4×C13#12311yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—44no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—82no—
154C2×Dic13—82no—
155C8×C13—44no—
156C2×C4×D4C2×D1311yescharacteristic
157C2×#117—131no—
158#436—24no—
159#431—21no—
160C2×#99—261no—
161#407—21no—
162#407C2×D1312yes—
163#400—131no—
164#399—131no—
165#398—131no—
166#397—131no—
167#397—261no—
168#394—261no—
169C4×C4⋊C4—261no—
170C4×C22⋊C4—131no—
171C4×C22⋊C4—132no—
172C4×C22⋊C4—261no—
173#342—261no—
174#339—264no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—42no—
181C22×C13—41no—
182C22×C13—41no—
183C22×C13—41no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13#38611yescharacteristic
188C22×C13C2×#10411yescharacteristic
189C22×C13#42111yescharacteristic
190C4×C13—22no—
191C4×C13—21no—
192C4×C13—22no—
193C4×C13—41no—
194C4×C13—41no—
195C4×C13#45812yes—
196Dic13—42no—
197Dic13—81no—
198Dic13—84no—
199Dic13—81no—
200Dic13—81no—
201C22×D4D5211yescharacteristic
202C23×C4C22⋊D1311yescharacteristic
203C23×C4C22×D1311yescharacteristic
204C2×M16—22no—
205C2×M16C22⋊D1314yes—
206C4×D4—22no—
207C4×D4—22no—
208#117—262no—
209#117—262no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4C4×D1311yescharacteristic
215C2×C22⋊C4—262no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C22⋊C4—261no—
220C2×C22⋊C4C4×D1311yescharacteristic
221C2×C22⋊C4D5211yescharacteristic
222C2×C42—261no—
223C2×C42—261no—
224C2×C42—262no—
225C2×C42C22⋊D1311yescharacteristic
226C4⋊C8—22no—
227#99—264no—
228C22⋊C8—22no—
229C22⋊C8—22no—
230C22⋊C8—22no—
231C4×C8—22no—
232#95—131no—
233#95—131no—
234#95—261no—
235#95—261no—
236#95—261no—
237#95—261no—
238#95—262no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—42no—
242C2×C13—81no—
243C2×C13#187111yescharacteristic
244C2×C13#188411yescharacteristic
245C2×C13#189011yescharacteristic
246C24#610311yescharacteristic
247C24C2×D5211yescharacteristic
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—41no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—42no—
254C22×C4—42no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—522no—
260C22×C4#610311yescharacteristic
261C22×C4#610311yescharacteristic
262C22×C4#610311yescharacteristic
263C22×C4C2×C4×D1311yescharacteristic
264C22×C4#612712yes—
265C22×C4C2×C22⋊D1312yes—
266C22×C4C2×C22⋊D1311yescharacteristic
267M16—44no—
268M16—82no—
269C2×C8—24no—
270C4⋊C4—22no—
271C4⋊C4—262no—
272C4⋊C4—262no—
273C4⋊C4—522no—
274C4⋊C4—522no—
275C22⋊C4—22no—
276C22⋊C4—22no—
277C22⋊C4—264no—
278C22⋊C4—522no—
279C22⋊C4—522no—
280C22⋊C4—522no—
281C22⋊C4—522no—
282C22⋊C4—522no—
283C42—21no—
284C42—21no—
285C42—522no—
286C42—524no—
287C42—521no—
288C42—521no—
289C13#901211yescharacteristic, complemented, Sylow
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23C2×#610311yescharacteristic
300C23#8818412yes—
301D4—44no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—24no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—262no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—524no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—1042no—
328C2×C4—1042no—
329C2×C4#8806512yes—
330C2×C4C4×C22⋊D1312yes—
331C2×C4#8818311yescharacteristic
332C2×C4#8820711yescharacteristic
333C8—44no—
334C22—21no—
335C22—21no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22C2×#8806511yescharacteristic
347C22#1171880011yescharacteristic
348C22#1171887411yescharacteristic
349C4—22no—
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—522no—
355C4—1041no—
356C4—1044no—
357C4—1041no—
358C4—1041no—
359C4#1171890412yes—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—81no—
364C2#1311513811yescharacteristic
365C2#1311521911yescharacteristic
366C2#1311524911yescharacteristic
subgroupG/H
centerC2×C4#88207
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2975C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2975D13
hypocenterC13#9012
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #13114933C2semidirect
4. #13112721C2semidirect
17. #11718647C4semidirect
18. #11718644C4semidirect
19. #11718614C4semidirect
21. #11718610C4semidirect
289. C13#9012semidirect

Maximal subgroups

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

subgroupindex
#131180952
#131149332
C4×#880742
#131127212
C13×#29752
#901213