Finite Group Databasebeta

← #16778682

Subgroups — #16778682

Order 3328.

464 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130621C211yesmaximal, characteristic, complemented
2C4×C4⋊#1057C211yesmaximal, characteristic, complemented
3#13129655C212yesmaximal, complemented
4#13129652C212yesmaximal
5#13123200C211yesmaximal, characteristic
6C2×#88133—21no—
7C2×#88112—21no—
8C2×#88110—21no—
9C2×C4⋊#1057—21no—
10C2×C4×#1057—21no—
11C13×#390C411yescharacteristic
12#11718882C411yescharacteristic
13#11718882C2211yescharacteristic
14#11718646C411yescharacteristic
15#11718634C2211yescharacteristic
16#11718612—21no—
17#11718606—21no—
18#11718605—21no—
19C42×Dic13C2211yescharacteristic
20#11718589C411yescharacteristic
21#11718290C2212yes—
22#11718290C2212yes—
23C22×D4×C13C2×C411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4—21no—
28C2×C13×C22⋊C4—21no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13C2311yescharacteristic
45#88133—42no—
46#88133—42no—
47#88112—24no—
48#88110—42no—
49C4⋊#1057—24no—
50C4×#1057—42no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#7686—131nomaximal, Sylow
55C24×C13—21no—
56C2×D4×C13—22no—
57C2×D4×C13—41no—
58C2×D4×C13—41no—
59C22×C4×C13—21no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C22×Dic13C2×D411yescharacteristic
69C2×#1057—24no—
70C2×#1057—24no—
71C2×#1057—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C13×C4⋊C4—41no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—42no—
78C42×C13—22no—
79C22⋊Dic13—42no—
80C22⋊Dic13—42no—
81C22⋊Dic13—41no—
82C22⋊Dic13—41no—
83C22⋊Dic13—41no—
84C22⋊Dic13—41no—
85C4⋊Dic13—22no—
86C4⋊Dic13—42no—
87C4⋊Dic13—41no—
88#6101—42no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—22no—
92C4×Dic13—22no—
93C4×Dic13—21no—
94C4×Dic13—21no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97C4×Dic13D812yes—
98C4×Dic13SD1612yes—
99#2860—131no—
100#1767—131no—
101C4×C4⋊C8—131no—
102#1271—132no—
103#1270—132no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13C2×C22⋊C411yescharacteristic
112D4×C13—82no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13#10212yes—
123C2×C4×C13#10412yes—
124C2×C4×C13#13112yes—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13#10212yes—
140C2×Dic13#10412yes—
141C2×Dic13C2×D811yescharacteristic
142C2×Dic13C2×SD1611yescharacteristic
143C2×Dic13AGL(1,ℤ/8)11yescharacteristic
144C2×Dic13#13711yescharacteristic
145#1057—44no—
146#1057—44no—
147C2×#126—261no—
148C2×C4⋊C8—261no—
149C2×C4⋊C8—261no—
150C2×#97—261no—
151C2×C4×C8—261no—
152#390—131no—
153#390—131no—
154#390#26111yescharacteristic
155#389—131no—
156#389—131no—
157#389—131no—
158#388—261no—
159#388—261no—
160#388—261no—
161C43—131no—
162#336—132no—
163#336—132no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13—81no—
169C22×C13—81no—
170C22×C13—81no—
171C22×C13#40811yescharacteristic
172C22×C13#41011yescharacteristic
173C22×C13#41311yescharacteristic
174C22×C13C2×#10211yescharacteristic
175C22×C13#41711yescharacteristic
176C22×C13C2×#10411yescharacteristic
177C22×C13C2×#10411yescharacteristic
178C4×C13—22no—
179C4×C13—22no—
180C4×C13—22no—
181C4×C13—81no—
182Dic13—22no—
183Dic13—21no—
184Dic13—21no—
185Dic13—21no—
186Dic13—21no—
187Dic13—22no—
188Dic13—81no—
189Dic13—81no—
190C22×D4C2×#26111yescharacteristic
191C22×C8—262no—
192C22×C8—262no—
193#126—522no—
194#126—522no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4C2×#26111yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—261no—
204C2×C22⋊C4—261no—
205C2×C22⋊C4—261no—
206C2×C22⋊C4—261no—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—131no—
212C2×C42—131no—
213C2×C42C2×#26111yescharacteristic
214C4⋊C8—264no—
215C4⋊C8—264no—
216#97—522no—
217C4×C8—522no—
218#95—261no—
219#95—261no—
220#95—261no—
221C2×C13—161no—
222C2×C13#147311yescharacteristic
223C2×C13#148311yescharacteristic
224C2×C13#149211yescharacteristic
225C2×C13#150211yescharacteristic
226C2×C13#150911yescharacteristic
227C2×C13#152411yescharacteristic
228C2×C13#154711yescharacteristic
229C24—21no—
230C2×D4—22no—
231C2×D4—41no—
232C2×D4—41no—
233C22×C4—21no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4C22⋊#26111yescharacteristic
241C22×C4C22⋊#26111yescharacteristic
242C22×C4C22×#26111yescharacteristic
243C2×C8—264no—
244C2×C8—264no—
245C2×C8—522no—
246C2×C8—522no—
247C2×C8—522no—
248C2×C8—522no—
249C4⋊C4—41no—
250C4⋊C4—262no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C4⋊C4—521no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—521no—
259C22⋊C4—522no—
260C22⋊C4—521no—
261C22⋊C4—522no—
262C22⋊C4—521no—
263C22⋊C4—521no—
264C42—22no—
265C42—132no—
266C42—132no—
267C42—261no—
268C42—262no—
269C42—261no—
270C42—262no—
271C42—521no—
272C42—521no—
273C13#768611yescharacteristic, complemented, Sylow
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23C2×C22⋊#26111yescharacteristic
282D4—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—131no—
293C2×C4—132no—
294C2×C4—131no—
295C2×C4—132no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4#8811512yes—
313C2×C4#8811612yes—
314C2×C4#8823812yes—
315C8—524no—
316C8—524no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22#1171913211yescharacteristic
325C22C2×#8811511yescharacteristic
326C22C2×#8811611yescharacteristic
327C22#1171914211yescharacteristic
328C22#1171914611yescharacteristic
329C22D13⋊#10411yescharacteristic
330C22#1171916411yescharacteristic
331C4—22no—
332C4—22no—
333C4—22no—
334C4—81no—
335C4—262no—
336C4—262no—
337C4—261no—
338C4—261no—
339C4—261no—
340C4—261no—
341C4—1041no—
342C4—1041no—
343C2—161no—
344C2#1313011811yescharacteristic
345C2#1313015111yescharacteristic
346C2#1313018111yescharacteristic
347C2#1313021611yescharacteristic
348C2#1313023711yescharacteristic
349C2#1313028611yescharacteristic
350C2#1313034711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#390C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenter#390#261
hypocenterC13#7686
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #13130621C2semidirect
2. C4×C4⋊#1057C2semidirect
3. #13129655C2semidirect
273. C13#7686semidirect

Maximal subgroups

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

subgroupindex
#131306212
C4×C4⋊#10572
#131296552
#131296522
#131232002
#768613