Finite Group Databasebeta

← #16782149

Subgroups — #16782149

Order 3328.

496 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 116 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#13130690C211yesmaximal, characteristic
2C4×C22⋊#1057C211yesmaximal, characteristic
3#13129672C212yesmaximal, complemented
4#13129672C212yesmaximal, complemented
5#13117231C211yesmaximal, characteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—21no—
8C2×C22⋊#1057—21no—
9C2×C4⋊#1057C2212yes—
10C2×C4×#1057C2212yes—
11C13×#380C411yescharacteristic
12#11718873C411yescharacteristic
13#11718638C411yescharacteristic
14#11718638C411yescharacteristic
15C4⋊C4×Dic13C2211yescharacteristic
16C4⋊C4×Dic13C2211yescharacteristic
17#11718604—21no—
18C22⋊C4×Dic13—21no—
19#11718312—21no—
20#11718309—21no—
21#11718290—21no—
22#11718290—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×#1057—22no—
27C22×#1057—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4—21no—
31C2×C22⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4×Dic13—24no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13C2311yescharacteristic
41C22⋊#1057—24no—
42C22⋊#1057—42no—
43C4⋊#1057—24no—
44C4×#1057—24no—
45C13×#95—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#8711—131nomaximal, Sylow
54C24×C13C22⋊C411yescharacteristic
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—41no—
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C22×Dic13C2×D411yescharacteristic
75C2×#1057—24no—
76C2×#1057—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C22⋊C4—42no—
84C22⋊Dic13—42no—
85C4⋊Dic13—22no—
86C4⋊Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—22no—
89C4×Dic13—22no—
90C4×Dic13—42no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93C4×Dic13#4114yes—
94#2283—131no—
95#1797—131no—
96C4×C22⋊C8—131no—
97#1279—132no—
98#1279—132no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13#10412yes—
106C23×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—44no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13#11712yes—
118C2×C4×C13#13112yes—
119C2×C4×C13#13112yes—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—44no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13#12312yes—
138C2×Dic13#12312yes—
139C2×Dic13#13512yes—
140C2×Dic13AGL(1,ℤ/8)11yescharacteristic
141C2×Dic13#13711yescharacteristic
142#1057—44no—
143#1057—82no—
144C22×C42—131no—
145C2×C4⋊C8—132no—
146C2×C22⋊C8—261no—
147C2×C22⋊C8—261no—
148C2×C4×C8—132no—
149#383—261no—
150#382—131no—
151#382—131no—
152#381—261no—
153#380—131no—
154#380#26111yescharacteristic
155C4×C4⋊C4—131no—
156C4×C4⋊C4—131no—
157C4×C22⋊C4—261no—
158#376—261no—
159#336—261no—
160#336—261no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13#38111yescharacteristic
169C22×C13#40811yescharacteristic
170C22×C13#40811yescharacteristic
171C22×C13#41611yescharacteristic
172C22×C13#41711yescharacteristic
173C22×C13C2×#10411yescharacteristic
174C22×C13#42111yescharacteristic
175C4×C13—41no—
176C4×C13—81no—
177C4×C13—81no—
178C4×C13#43314yes—
179Dic13—22no—
180Dic13—41no—
181Dic13—41no—
182Dic13—81no—
183Dic13—81no—
184Dic13#48212yes—
185Dic13#48512yes—
186C23×C4—131no—
187C23×C4—131no—
188C23×C4C2×#26111yescharacteristic
189C22×C8—262no—
190C22×C8—262no—
191C2×C4⋊C4—131no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4C2×#26111yescharacteristic
194C2×C4⋊C4C2×#26111yescharacteristic
195C2×C22⋊C4—21no—
196C2×C22⋊C4—261no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—264no—
202C2×C42—261no—
203C2×C42—261no—
204C4⋊C8—264no—
205C22⋊C8—264no—
206C22⋊C8—522no—
207C4×C8—264no—
208#95—21no—
209#95—261no—
210#95—261no—
211#95—261no—
212#95—261no—
213#95—261no—
214#95—261no—
215#95—261no—
216C2×C13—42no—
217C2×C13#148211yescharacteristic
218C2×C13#148311yescharacteristic
219C2×C13#149411yescharacteristic
220C2×C13#149511yescharacteristic
221C2×C13#181811yescharacteristic
222C2×C13#182511yescharacteristic
223C2×C13#182611yescharacteristic
224C24C22⋊#26111yescharacteristic
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—131no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—261no—
235C22×C4—262no—
236C22×C4—262no—
237C22×C4—261no—
238C22×C4—262no—
239C22×C4—262no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—521no—
243C22×C4C22⋊#26111yescharacteristic
244C22×C4C22×#26111yescharacteristic
245C2×C8—264no—
246C2×C8—522no—
247C2×C8—522no—
248C2×C8—522no—
249C2×C8—522no—
250C2×C8—522no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—262no—
254C4⋊C4—262no—
255C22⋊C4—42no—
256C22⋊C4—522no—
257C42—134no—
258C42—262no—
259C42—262no—
260C42—262no—
261C42—521no—
262C42—521no—
263C42—522no—
264C13#871111yescharacteristic, complemented, Sylow
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23#8811812yes—
272C23C2×C22⋊#26111yescharacteristic
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—44no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—132no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—132no—
287C2×C4—132no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4—524no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4#8823712yes—
306C2×C4#8823812yes—
307C2×C4#8823812yes—
308C8—524no—
309C8—1042no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1171913511yescharacteristic
318C22#1171914011yescharacteristic
319C22#1171914611yescharacteristic
320C22#1171914611yescharacteristic
321C22C2×#8811811yescharacteristic
322C22#1171916411yescharacteristic
323C22#1171916511yescharacteristic
324C4—41no—
325C4—81no—
326C4—81no—
327C4—132no—
328C4—132no—
329C4—262no—
330C4—521no—
331C4—521no—
332C4—1041no—
333C4—1041no—
334C4#1171906814yes—
335C2—42no—
336C2#1313014711yescharacteristic
337C2#1313015311yescharacteristic
338C2#1313018911yescharacteristic
339C2#1313019111yescharacteristic
340C2#1313072911yescharacteristic
341C2#1313074111yescharacteristic
342C2#1313074311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#380C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#380#261
hypocenterC13#8711
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13129672C2semidirect
4. #13129672C2semidirect
264. C13#8711semidirect

Maximal subgroups

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

subgroupindex
#131306902
C4×C22⋊#10572
#131296722
#131172312
#871113