Finite Group Databasebeta

← #16785060

Subgroups — #16785060

Order 3328.

506 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130768C211yesmaximal, characteristic
2#13130551C211yesmaximal, characteristic
3#13129672C212yesmaximal
4#13129672C212yesmaximal
5#13117407C211yesmaximal, characteristic
6C2×#88142C411yescharacteristic
7C2×#88141—21no—
8C2×C4⋊#1057—21no—
9C2×C4⋊#1057—21no—
10C2×C4⋊#1057C2212yes—
11C2×C4×#1057C2212yes—
12C13×#389C411yescharacteristic
13#11718637C411yescharacteristic
14C4⋊C4×Dic13C2211yescharacteristic
15C4⋊C4×Dic13C2211yescharacteristic
16#11718633—21no—
17C42×Dic13C2211yescharacteristic
18#11718589C411yescharacteristic
19#11718310—21no—
20#11718307—21no—
21#11718290—21no—
22#11718290—21no—
23C22×Dic26—21no—
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44#88142—22no—
45#88142—22no—
46#88141—42no—
47#88141—42no—
48C4⋊#1057—24no—
49C4⋊#1057—42no—
50C4⋊#1057—42no—
51C4×#1057—22no—
52C4×#1057Q814yescomplemented
53C13×#95—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#9874—131nomaximal, Sylow
58C22×C4×C13—21no—
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×Dic26—24no—
70C2×Dic26—42no—
71C2×Dic26—42no—
72C2×#1057—24no—
73C2×#1057—42no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78C13×C4⋊C4—21no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4M1612yes—
82C42×C13—22no—
83C4⋊Dic13—21no—
84C4⋊Dic13—22no—
85C4⋊Dic13M1612yes—
86#6101—24no—
87#6101—42no—
88#6101—42no—
89#6101—42no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C4×Dic13—41no—
93C4×Dic13—41no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96C4×Dic13—41no—
97C4×Dic13—41no—
98C4×Dic13D812yes—
99C4×Dic13SD1612yes—
100C4×Dic13SD1612yes—
101C4×Dic13Q1612yes—
102C4×Dic13C2×Q812yes—
103C4×Dic13#4112yes—
104C4×C4⋊Q8—131no—
105#1842—131no—
106#1744—131no—
107#1279—132no—
108#1279—132no—
109C23×C13C2×C22⋊C411yescharacteristic
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13#10212yes—
121C2×C4×C13#10312yes—
122C2×C4×C13C4×Q812yes—
123C2×C4×C13C2×M1611yescharacteristic
124C2×C4×C13C2×M1611yescharacteristic
125C2×C4×C13#13112yes—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13#10212yes—
139C2×Dic13#10312yes—
140C2×Dic13C22⋊Q812yes—
141C2×Dic13#12411yescharacteristic
142C2×Dic13C4⋊Q811yescharacteristic
143C2×Dic13C2×D811yescharacteristic
144C2×Dic13C2×SD1611yescharacteristic
145C2×Dic13C2×SD1611yescharacteristic
146C2×Dic13C2×Q1611yescharacteristic
147Dic26—48no—
148#1057—44no—
149#1057—82no—
150C2×C4⋊Q8—131no—
151C2×C4×Q8—261no—
152C2×C4⋊C8—132no—
153C2×C4⋊C8—261no—
154C2×C4⋊C8—261no—
155C2×C4×C8—132no—
156#391—261no—
157#389—131no—
158#389—261no—
159#389#26111yescharacteristic
160#384—131no—
161C4×C4⋊C4—131no—
162C4×C4⋊C4—131no—
163C4×C4⋊C4—261no—
164C43—131no—
165#336—261no—
166#336—261no—
167C22×C13#39111yescharacteristic
168C22×C13#40711yescharacteristic
169C22×C13#40811yescharacteristic
170C22×C13C2×#10211yescharacteristic
171C22×C13C2×#10311yescharacteristic
172C22×C13#42111yescharacteristic
173C22×C13#42111yescharacteristic
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—42no—
177C4×C13—81no—
178C4×C13#44612yes—
179C4×C13#44612yes—
180Dic13—22no—
181Dic13—22no—
182Dic13—22no—
183Dic13—42no—
184Dic13—81no—
185Dic13#48611yescharacteristic
186Dic13#48711yescharacteristic
187Dic13#49811yescharacteristic
188Dic13#50011yescharacteristic
189C22×Q8—261no—
190C22×C8—262no—
191C22×C8—262no—
192C4⋊Q8—262no—
193C4⋊Q8—262no—
194C4×Q8—522no—
195C4×Q8—522no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4C2×#26111yescharacteristic
204C2×C4⋊C4C2×#26111yescharacteristic
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—131no—
209C2×C42—131no—
210C2×C42—131no—
211C2×C42—261no—
212C2×C42—261no—
213C2×C42C2×#26111yescharacteristic
214C4⋊C8—264no—
215C4⋊C8—522no—
216C4⋊C8—522no—
217C4×C8—134no—
218C4×C8—262no—
219#95—21no—
220#95—261no—
221#95—261no—
222#95—261no—
223C2×C13#148011yescharacteristic
224C2×C13#148111yescharacteristic
225C2×C13#148611yescharacteristic
226C2×C13#148711yescharacteristic
227C2×C13#198511yescharacteristic
228C2×C13#199011yescharacteristic
229C2×C13#199511yescharacteristic
230C2×Q8—264no—
231C2×Q8—522no—
232C2×Q8—522no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—261no—
240C22×C4—261no—
241C22×C4C22⋊#26111yescharacteristic
242C22×C4C22⋊#26111yescharacteristic
243C22×C4C22×#26111yescharacteristic
244C2×C8—264no—
245C2×C8—522no—
246C2×C8—522no—
247C2×C8—522no—
248C2×C8—522no—
249C2×C8—522no—
250C4⋊C4—21no—
251C4⋊C4—22no—
252C4⋊C4—42no—
253C4⋊C4—132no—
254C4⋊C4—264no—
255C4⋊C4—261no—
256C4⋊C4—262no—
257C4⋊C4—522no—
258C4⋊C4—522no—
259C4⋊C4—522no—
260C4⋊C4#611812yes—
261C42—22no—
262C42—132no—
263C42—132no—
264C42—132no—
265C42—132no—
266C42—132no—
267C42—132no—
268C42—261no—
269C42—261no—
270C42—521no—
271C42—521no—
272C42—521no—
273C42—521no—
274C42—521no—
275C42—521no—
276C13#987411yescharacteristic, complemented, Sylow
277C23C2×C22⋊#26111yescharacteristic
278Q8—528no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—131no—
290C2×C4—131no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—132no—
296C2×C4—132no—
297C2×C4—132no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—262no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4#8811512yes—
311C2×C4#8811712yes—
312C2×C4C2×#611811yescharacteristic
313C2×C4D13⋊M1611yescharacteristic
314C2×C4#8823812yes—
315C2×C4Q8×#26112yes—
316C8—524no—
317C8—1042no—
318C22#1171912711yescharacteristic
319C22C2×#8811511yescharacteristic
320C22#1171914611yescharacteristic
321C22C2×#8811711yescharacteristic
322C22(C2×#261)⋊Q811yescharacteristic
323C22#1171916611yescharacteristic
324C22#1171916611yescharacteristic
325C4—22no—
326C4—22no—
327C4—42no—
328C4—81no—
329C4—131no—
330C4—131no—
331C4—131no—
332C4—131no—
333C4—262no—
334C4—262no—
335C4—262no—
336C4—522no—
337C4—1041no—
338C4#1171907812yes—
339C4#1171908012yes—
340C2#1313014111yescharacteristic
341C2#1313014411yescharacteristic
342C2#1313016211yescharacteristic
343C2#1313016511yescharacteristic
344C2#1313100911yescharacteristic
345C2#1313101711yescharacteristic
346C2#1313102311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#9874
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
52. C4×#1057Q8semidirect
276. C13#9874semidirect

Maximal subgroups

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

subgroupindex
#131307682
#131305512
#131296722
#131174072
#987413