Finite Group Databasebeta

← #16778239

Subgroups — #16778239

Order 3328.

538 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊#1057C211yesmaximal, characteristic, complemented
2#13130550C211yesmaximal, characteristic, complemented
3#13129655C212yesmaximal, complemented
4#13129653C212yesmaximal
5#13117297C211yesmaximal, characteristic
6C2×C4×D52C411yescharacteristic
7C2×#88126—21no—
8C2×C4⋊#1057—21no—
9C2×C4×#1057—21no—
10C2×C4×#1057—21no—
11C4×C13×C4⋊C4C411yescharacteristic
12#11718649C411yescharacteristic
13#11718649C2211yescharacteristic
14#11718634C411yescharacteristic
15#11718634C2211yescharacteristic
16C4×#6103—21no—
17C42×Dic13C2211yescharacteristic
18#11718330—21no—
19#11718330—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×D52C2×C411yescharacteristic
24C22×C4×D13—21no—
25C22×#1057—22no—
26C22×#1057—22no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C42×C13—21no—
30C2×C42×C13C2×C411yescharacteristic
31C2×#6103—21no—
32C2×#6103—21no—
33C2×#6103—21no—
34C2×#6103—21no—
35C2×#6103—21no—
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
45C4×D52—22no—
46C4×D52C814yescomplemented
47#88126—42no—
48#88126—42no—
49C4⋊#1057—24no—
50C4×#1057—24no—
51C4×#1057—42no—
52C13×#95—21no—
53#88071—21no—
54#88071—21no—
55#7560—131nomaximal, Sylow
56C23×D13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C2×D52—21no—
68C2×D52—41no—
69C2×D52—41no—
70C2×D52C2×C812yes—
71C2×C4×D13—24no—
72C2×C4×D13—42no—
73C2×C4×D13—42no—
74C2×#1057—24no—
75C2×#1057—24no—
76C2×#1057—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C42×C13—42no—
83C42×C13C2×C812yes—
84C42×C13M1612yes—
85#6103—24no—
86#6103—42no—
87#6103—42no—
88#6103—41no—
89#6103—41no—
90#6103—42no—
91C4⋊Dic13—21no—
92C4⋊Dic13C2×C812yes—
93#6101—42no—
94#6101—41no—
95#6101—41no—
96C4×Dic13—22no—
97C4×Dic13—22no—
98C4×Dic13—22no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101C4×Dic13D812yes—
102C4×Dic13SD1612yes—
103#2293—131no—
104C4×C4⋊C8—131no—
105#1744—131no—
106#1271—132no—
107#1270—132no—
108C23×C13C2×C22⋊C411yescharacteristic
109C22×D13—22no—
110C22×D13—41no—
111C22×D13—41no—
112C22×D13—41no—
113C22×D13—41no—
114C22×D13—41no—
115C22×D13—41no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13C22⋊C812yes—
127C2×C4×C13C22⋊C812yes—
128C2×C4×C13#10212yes—
129C2×C4×C13#10412yes—
130C2×C4×C13C22×C811yescharacteristic
131C2×C4×C13C2×M1611yescharacteristic
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—22no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13#10212yes—
144C2×Dic13#10412yes—
145C2×Dic13C2×D811yescharacteristic
146C2×Dic13C2×SD1611yescharacteristic
147C2×Dic13#13512yes—
148D52—42no—
149D52—42no—
150C4×D13—48no—
151#1057—44no—
152#1057—44no—
153C2×C4×D4—131no—
154C2×#117—261no—
155C2×C4⋊C8—261no—
156C2×C4×C8—261no—
157C2×C4×C8—261no—
158#390—131no—
159#390—131no—
160#389—131no—
161#389—131no—
162#388—261no—
163#388—261no—
164C4×C4⋊C4#26111yescharacteristic
165C4×C22⋊C4—261no—
166C43—131no—
167#336—132no—
168#336—132no—
169#336—261no—
170C22×C13C2×C22⋊C811yescharacteristic
171C22×C13#41011yescharacteristic
172C22×C13#41311yescharacteristic
173C22×C13C2×#10211yescharacteristic
174C22×C13#41611yescharacteristic
175C22×C13C2×#10411yescharacteristic
176C22×C13C2×#10411yescharacteristic
177C2×D13—42no—
178C2×D13—42no—
179C2×D13—42no—
180C2×D13—81no—
181C2×D13—81no—
182C2×D13—81no—
183C2×D13—81no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—22no—
187C4×C13—81no—
188C4×C13—81no—
189C4×C13D4⋊C814yes—
190Dic13—22no—
191Dic13—22no—
192Dic13—21no—
193Dic13—21no—
194Dic13—22no—
195Dic13—42no—
196C22×D4—131no—
197C23×C4—261no—
198C22×C8—262no—
199C22×C8—262no—
200C4×D4—134no—
201C4×D4—262no—
202#117—522no—
203#117—522no—
204C2×C4⋊C4—131no—
205C2×C4⋊C4—261no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4C2×#26111yescharacteristic
208C2×C4⋊C4C2×#26111yescharacteristic
209C2×C22⋊C4—261no—
210C2×C22⋊C4—261no—
211C2×C22⋊C4—261no—
212C2×C22⋊C4—261no—
213C2×C22⋊C4—261no—
214C2×C42—21no—
215C2×C42—131no—
216C2×C42—131no—
217C2×C42—131no—
218C2×C42—131no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42C2×#26111yescharacteristic
222C4⋊C8—264no—
223C4×C8—264no—
224C4×C8—522no—
225#95—21no—
226#95—261no—
227#95—261no—
228C2×C13#145811yescharacteristic
229C2×C13C2×D4⋊C811yescharacteristic
230C2×C13#147611yescharacteristic
231C2×C13#150011yescharacteristic
232C2×C13#150211yescharacteristic
233C2×C13#152411yescharacteristic
234C2×C13#154011yescharacteristic
235D13—82no—
236C24—261no—
237C2×D4—132no—
238C2×D4—261no—
239C2×D4—521no—
240C2×D4—521no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—131no—
244C22×C4—131no—
245C22×C4—131no—
246C22×C4—131no—
247C22×C4—261no—
248C22×C4—264no—
249C22×C4—522no—
250C22×C4—522no—
251C22×C4C22⋊#26111yescharacteristic
252C22×C4C22⋊#26111yescharacteristic
253C22×C4C22×#26111yescharacteristic
254C2×C8—264no—
255C2×C8—264no—
256C2×C8—522no—
257C2×C8—522no—
258C2×C8—522no—
259C2×C8—522no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—132no—
263C4⋊C4—261no—
264C4⋊C4—521no—
265C4⋊C4—522no—
266C4⋊C4—521no—
267C22⋊C4—264no—
268C22⋊C4—521no—
269C22⋊C4—522no—
270C22⋊C4—521no—
271C22⋊C4—522no—
272C22⋊C4—522no—
273C42—42no—
274C42—132no—
275C42—132no—
276C42—262no—
277C42—262no—
278C42—262no—
279C42—521no—
280C42—521no—
281C42D13⋊C812yes—
282C42#611812yes—
283C13#756011yescharacteristic, complemented, Sylow
284C23—262no—
285C23—521no—
286C23—521no—
287C23—521no—
288C23—521no—
289C23—521no—
290C23—521no—
291C23C2×C22⋊#26111yescharacteristic
292D4—522no—
293D4—522no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—131no—
305C2×C4—132no—
306C2×C4—131no—
307C2×C4—132no—
308C2×C4—132no—
309C2×C4—261no—
310C2×C4—261no—
311C2×C4—261no—
312C2×C4—261no—
313C2×C4—261no—
314C2×C4—261no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—262no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—528no—
321C2×C4#8811112yes—
322C2×C4#8811112yes—
323C2×C4#8811512yes—
324C2×C4#8811812yes—
325C2×C4C2×D13⋊C811yescharacteristic
326C2×C4C2×#611811yescharacteristic
327C8—524no—
328C8—524no—
329C22—522no—
330C22—522no—
331C22—522no—
332C22—1041no—
333C22—1041no—
334C22—1041no—
335C22—1041no—
336C22#1171911611yescharacteristic
337C22C2×#8811111yescharacteristic
338C22#1171913211yescharacteristic
339C22C2×#8811511yescharacteristic
340C22C2×#8811811yescharacteristic
341C22D13⋊#10411yescharacteristic
342C22#1171916511yescharacteristic
343C4—21no—
344C4—21no—
345C4—22no—
346C4—81no—
347C4—81no—
348C4—262no—
349C4—262no—
350C4—262no—
351C4—261no—
352C4—261no—
353C4—522no—
354C4#1171824314yes—
355C2—1042no—
356C2#1313006911yescharacteristic
357C2C2×#1171824311yescharacteristic
358C2#1313012911yescharacteristic
359C2#1313020911yescharacteristic
360C2#1313021511yescharacteristic
361C2#1313028811yescharacteristic
362C2#1313033311yescharacteristic
subgroupG/H
centerC22×C4C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C4×Dic13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#7560
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C4×C4⋊#1057C2semidirect
2. #13130550C2semidirect
3. #13129655C2semidirect
46. C4×D52C8semidirect
283. C13#7560semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#10572
#131305502
#131296552
#131296532
#131172972
#756013