Finite Group Databasebeta

← #16782122

Subgroups — #16782122

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130727C212yesmaximal
2#13129674C212yesmaximal
3#13129674C212yesmaximal
4C2×C4×#6101C211yesmaximal, characteristic
5C22×C42×C13C411yescharacteristic
6C22×#6101C411yescharacteristic
7C22×#6101C411yescharacteristic
8C22×C4×Dic13C411yescharacteristic
9C22×C4×Dic13C2211yescharacteristic
10C2×C22⋊#1057C2214yes—
11C2×#88071C2211yescharacteristic
12C2×#88071C2211yescharacteristic
13C4×#6101—22no—
14C4×#6101—22no—
15#11718290—22no—
16#11718290—22no—
17C23×C4×C13C2×C411yescharacteristic
18C23×C4×C13C2×C411yescharacteristic
19C23×C4×C13C2×C411yescharacteristic
20C23×Dic13C2×C411yescharacteristic
21C23×Dic13C2×C411yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2311yescharacteristic
24C22×#1057—24no—
25C2×C42×C13—21no—
26C2×C42×C13—21no—
27C2×C42×C13—42no—
28C2×#6101—22no—
29C2×#6101—22no—
30C2×#6101—22no—
31C2×#6101—22no—
32C2×#6101—22no—
33C2×#6101C814yescomplemented
34C2×C4×Dic13—22no—
35C2×C4×Dic13—22no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—42no—
39C2×C4×Dic13D412yes—
40C2×C4×Dic13D412yes—
41C22⋊#1057—24no—
42C22⋊#1057—24no—
43#88071—22no—
44#88071—22no—
45#8701—131nomaximal, Sylow
46C24×C13C22×C411yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13—41no—
58C22×C4×C13—41no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C2×C812yes—
62C22×C4×C13M1612yes—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—41no—
72C22×Dic13—41no—
73C22×Dic13—41no—
74C22×Dic13—41no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C22×Dic13C22⋊C412yes—
78C22×Dic13C2×C812yes—
79C22×Dic13C2×C812yes—
80C22×Dic13M1612yes—
81C22×Dic13M1612yes—
82C22×Dic13C2×D412yes—
83C22×Dic13#4112yes—
84C22×Dic13#4112yes—
85C2×#1057—44no—
86C2×#1057—44no—
87C2×#1057—44no—
88C42×C13—42no—
89C42×C13—42no—
90#6101—28no—
91#6101—28no—
92C4×Dic13—24no—
93C4×Dic13—24no—
94C4×Dic13—42no—
95C4×Dic13—42no—
96C2×C4×C4⋊C4—131no—
97#1817—132no—
98#1280—132no—
99#1280—132no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13#11711yescharacteristic
106C23×C13#11711yescharacteristic
107C23×C13C22×C811yescharacteristic
108C23×C13C2×M1611yescharacteristic
109C23×C13C2×M1611yescharacteristic
110C23×C13C2×M1611yescharacteristic
111C2×C4×C13—24no—
112C2×C4×C13—24no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13#10012yes—
128C2×C4×C13#10112yes—
129C2×Dic13—22no—
130C2×Dic13—22no—
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—22no—
134C2×Dic13—22no—
135C2×Dic13—22no—
136C2×Dic13—22no—
137C2×Dic13—22no—
138C2×Dic13—22no—
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13C22⋊C814yes—
150C2×Dic13#12314yes—
151#1057—84no—
152C22×C4⋊C4—131no—
153C22×C4⋊C4—131no—
154C22×C42—131no—
155C22×C42—131no—
156C22×C42#26111yescharacteristic
157C2×C22⋊C8—134no—
158C4×C4⋊C4—262no—
159C4×C4⋊C4—262no—
160C2×#95—131no—
161C2×#95—131no—
162#336—262no—
163#336—262no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13#38111yescharacteristic
177C22×C13C2×C22⋊C811yescharacteristic
178C22×C13#40711yescharacteristic
179C22×C13#41011yescharacteristic
180C22×C13#41011yescharacteristic
181C22×C13C2×#10011yescharacteristic
182C22×C13C2×#10111yescharacteristic
183C22×C13#43111yescharacteristic
184C22×C13#43111yescharacteristic
185C22×C13#43211yescharacteristic
186C22×C13#43211yescharacteristic
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—42no—
190C4×C13—42no—
191Dic13—24no—
192Dic13—24no—
193Dic13—42no—
194Dic13—42no—
195C23×C4—131no—
196C23×C4—131no—
197C23×C4—131no—
198C23×C4—131no—
199C23×C4C2×#26111yescharacteristic
200C23×C4C2×#26111yescharacteristic
201C23×C4C2×#26111yescharacteristic
202C22×C8—264no—
203C2×C4⋊C4—134no—
204C2×C4⋊C4—262no—
205C2×C4⋊C4—262no—
206C2×C4⋊C4—262no—
207C2×C4⋊C4—262no—
208C2×C4⋊C4—262no—
209C2×C42—21no—
210C2×C42—21no—
211C2×C42—42no—
212C2×C42—132no—
213C2×C42—132no—
214C2×C42—262no—
215C2×C42—262no—
216C2×C42—261no—
217C2×C42—261no—
218C2×C42—522no—
219C22⋊C8—264no—
220C22⋊C8—264no—
221#95—262no—
222#95—262no—
223C2×C13—21no—
224C2×C13—21no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13#146011yescharacteristic
228C2×C13#146111yescharacteristic
229C2×C13#146611yescharacteristic
230C2×C13#146711yescharacteristic
231C2×C13#181711yescharacteristic
232C2×C13#182011yescharacteristic
233C2×C13#182111yescharacteristic
234C24C22×#26111yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—132no—
248C22×C4—132no—
249C22×C4—132no—
250C22×C4—132no—
251C22×C4—132no—
252C22×C4—132no—
253C22×C4—132no—
254C22×C4—132no—
255C22×C4—261no—
256C22×C4—261no—
257C22×C4—261no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—521no—
264C22×C4—521no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4—521no—
268C22×C4—521no—
269C22×C4D13⋊C812yes—
270C22×C4#611812yes—
271C22×C4C22⋊#26111yescharacteristic
272C22×C4C22⋊#26111yescharacteristic
273C2×C8—524no—
274C2×C8—524no—
275C2×C8—524no—
276C4⋊C4—268no—
277C4⋊C4—268no—
278C42—42no—
279C42—42no—
280C42—264no—
281C42—264no—
282C42—522no—
283C42—522no—
284C13#870111yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23C2×D13⋊C811yescharacteristic
290C23C2×#611811yescharacteristic
291C23D13⋊M1611yescharacteristic
292C23D13⋊M1611yescharacteristic
293C23#8823711yescharacteristic
294C23#8823711yescharacteristic
295C23C2×C22⋊#26111yescharacteristic
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—42no—
305C2×C4—42no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—134no—
313C2×C4—134no—
314C2×C4—262no—
315C2×C4—262no—
316C2×C4—262no—
317C2×C4—262no—
318C2×C4—262no—
319C2×C4—262no—
320C2×C4—262no—
321C2×C4—262no—
322C2×C4—262no—
323C2×C4—262no—
324C2×C4—522no—
325C2×C4—522no—
326C2×C4—522no—
327C2×C4—522no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4#8811312yes—
335C2×C4#8812112yes—
336C8—1044no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22#1171904911yescharacteristic
350C22#1171905111yescharacteristic
351C22#1171905411yescharacteristic
352C22#1171905511yescharacteristic
353C22#1171911611yescharacteristic
354C22#1171911611yescharacteristic
355C22D13⋊(C22⋊C8)11yescharacteristic
356C22#1171912711yescharacteristic
357C22C2×#8811311yescharacteristic
358C22#1171913511yescharacteristic
359C22C2×#8812111yescharacteristic
360C4—22no—
361C4—22no—
362C4—42no—
363C4—42no—
364C4—264no—
365C4—264no—
366C4—522no—
367C4—522no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—21no—
372C2#1313007511yescharacteristic
373C2#1313007811yescharacteristic
374C2#1313009511yescharacteristic
375C2#1313009811yescharacteristic
376C2#1313072811yescharacteristic
377C2#1313073311yescharacteristic
378C2#1313073511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C22×C8
FrattiniC24C22×#261
FittingC22×C42×C13C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC22×C42#261
hypocenterC13#8701
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
33. C2×#6101C8semidirect
284. C13#8701semidirect

Maximal subgroups

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

subgroupindex
#131307272
#131296742
C2×C4×#61012
#870113