Finite Group Databasebeta

← #16778262

Subgroups — #16778262

Order 3328.

596 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊#1057C211yesmaximal, characteristic
2C2×#11718290C211yesmaximal, characteristic
3#13129657C212yesmaximal, complemented
4#13129655C212yesmaximal, complemented
5#13117364C211yesmaximal, characteristic
6C23×#1057—21no—
7C2×#88178C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×#88141C411yescharacteristic
10C2×C22⋊#1057—21no—
11C2×C4×#1057—21no—
12C13×#380C411yescharacteristic
13C4⋊C4×Dic13C411yescharacteristic
14#11718635C2211yescharacteristic
15#11718634C2211yescharacteristic
16#11718607—21no—
17C22⋊C4×Dic13—21no—
18#11718313—21no—
19#11718310—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×#1057—24no—
28C22×#1057—22no—
29C22×#1057—22no—
30C22×#1057—42no—
31C22×#1057—42no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C22⋊Dic13—21no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37#88178—22no—
38#88178C814yescomplemented
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C2×C4×Dic13—21no—
44C2×C4×Dic13—42no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47C2×C4×Dic13D411yescharacteristic
48C2×C4×Dic13C2311yescharacteristic
49#88141—42no—
50C22⋊#1057—24no—
51C4×#1057—42no—
52C13×#95—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#7566—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C2×C812yes—
65C22×C4×C13M1612yes—
66C22×C4×C13C22×C411yescharacteristic
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—22no—
73C22×Dic13—41no—
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13SD1612yes—
77C22×Dic13Q1612yes—
78C22×Dic13C2×D411yescharacteristic
79C22×Dic13C2×D411yescharacteristic
80C2×Dic26—21no—
81C2×Dic26—41no—
82C2×Dic26—41no—
83C2×Dic26C2×C812yescomplemented
84C2×#1057—24no—
85C2×#1057—24no—
86C2×#1057—42no—
87C2×#1057—42no—
88C2×#1057—48no—
89C2×#1057—42no—
90C2×#1057—42no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C22⋊C4—42no—
94C22⋊Dic13—24no—
95C4⋊Dic13—21no—
96C4⋊Dic13C2×C812yescomplemented
97#6101—24no—
98#6101—42no—
99#6101—42no—
100C4×Dic13—22no—
101C4×Dic13—22no—
102C4×Dic13—41no—
103C4×Dic13—41no—
104C4×Dic13—42no—
105C4×Dic13—42no—
106C4×C22⋊Q8—131no—
107C4×C22⋊C8—131no—
108C2×#336—131no—
109#1272—132no—
110#1271—132no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13C22⋊C812yes—
116C23×C13#10312yes—
117C23×C13#10412yes—
118C23×C13C2×C22⋊C411yescharacteristic
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13C22⋊C812yes—
132C2×C4×C13C22×C811yescharacteristic
133C2×C4×C13C2×M1611yescharacteristic
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—24no—
139C2×Dic13—24no—
140C2×Dic13—22no—
141C2×Dic13—22no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—44no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13#9912yes—
151C2×Dic13#10312yes—
152C2×Dic13#10412yes—
153C2×Dic13C2×SD1611yescharacteristic
154C2×Dic13C2×Q1611yescharacteristic
155C2×Dic13#13512yes—
156Dic26—42no—
157Dic26—42no—
158#1057—44no—
159#1057—44no—
160C23×C8—261no—
161C2×C22⋊Q8—131no—
162C2×C4×Q8—131no—
163C22×C42—131no—
164C2×C22⋊C8—261no—
165C2×C4×C8—261no—
166#391—131no—
167#389—131no—
168#387—261no—
169#385—261no—
170#380#26111yescharacteristic
171C4×C4⋊C4—131no—
172C4×C4⋊C4—261no—
173C4×C22⋊C4—261no—
174#336—132no—
175#336—132no—
176#336—261no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13Q8⋊C814yes—
184C22×C13C2×C22⋊C811yescharacteristic
185C22×C13C2×#9911yescharacteristic
186C22×C13#41311yescharacteristic
187C22×C13C2×#10311yescharacteristic
188C22×C13#41611yescharacteristic
189C22×C13C2×#10411yescharacteristic
190C22×C13C2×#10411yescharacteristic
191C4×C13—21no—
192C4×C13—21no—
193C4×C13—22no—
194C4×C13—81no—
195C4×C13—81no—
196Dic13—21no—
197Dic13—21no—
198Dic13—22no—
199Dic13—42no—
200Dic13—42no—
201Dic13—41no—
202Dic13#32814yes—
203C22×Q8—131no—
204C23×C4—131no—
205C23×C4—131no—
206C23×C4C2×#26111yescharacteristic
207C22×C8—262no—
208C22×C8—262no—
209C22×C8—264no—
210C22×C8—522no—
211C22×C8—522no—
212C22⋊Q8—134no—
213C22⋊Q8—262no—
214C4×Q8—522no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4C2×#26111yescharacteristic
220C2×C4⋊C4C2×#26111yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—261no—
223C2×C42—131no—
224C2×C42—131no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—261no—
228C2×C42—261no—
229C2×C42—522no—
230C22⋊C8—264no—
231C4×C8—522no—
232#95—21no—
233#95—261no—
234#95—261no—
235#95—261no—
236#95—261no—
237C2×C13—24no—
238C2×C13#145911yescharacteristic
239C2×C13C2×Q8⋊C811yescharacteristic
240C2×C13#147611yescharacteristic
241C2×C13C2×#32811yescharacteristic
242C2×C13#150111yescharacteristic
243C2×C13#152411yescharacteristic
244C2×C13#154211yescharacteristic
245C24C22⋊#26111yescharacteristic
246C2×Q8—132no—
247C2×Q8—261no—
248C2×Q8—521no—
249C2×Q8—521no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—131no—
255C22×C4—132no—
256C22×C4—132no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—262no—
261C22×C4—262no—
262C22×C4—262no—
263C22×C4—262no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4—521no—
267C22×C4D13⋊C812yes—
268C22×C4#611812yes—
269C22×C4C22⋊#26111yescharacteristic
270C22×C4C22×#26111yescharacteristic
271C2×C8—264no—
272C2×C8—264no—
273C2×C8—522no—
274C2×C8—522no—
275C2×C8—522no—
276C2×C8—528no—
277C2×C8—522no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—132no—
281C4⋊C4—264no—
282C4⋊C4—261no—
283C4⋊C4—522no—
284C4⋊C4—522no—
285C22⋊C4—42no—
286C22⋊C4—264no—
287C42—262no—
288C42—262no—
289C42—521no—
290C42—521no—
291C42—522no—
292C42—522no—
293C13#756611yescharacteristic, complemented, Sylow
294C23—21no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23#8811112yes—
299C23#8811612yes—
300C23#8811712yes—
301C23C2×C22⋊#26111yescharacteristic
302Q8—522no—
303Q8—522no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—132no—
317C2×C4—132no—
318C2×C4—132no—
319C2×C4—131no—
320C2×C4—131no—
321C2×C4—132no—
322C2×C4—264no—
323C2×C4—264no—
324C2×C4—261no—
325C2×C4—261no—
326C2×C4—261no—
327C2×C4—261no—
328C2×C4—262no—
329C2×C4—262no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—524no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4#8811112yes—
339C2×C4C2×D13⋊C811yescharacteristic
340C2×C4C2×#611811yescharacteristic
341C8—524no—
342C8—524no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22#1171824414yes—
350C22C2×#8811111yescharacteristic
351C22C2×#8811611yescharacteristic
352C22D13⋊#9911yescharacteristic
353C22#1171914811yescharacteristic
354C22C2×#8811711yescharacteristic
355C22D13⋊#10411yescharacteristic
356C22#1171916511yescharacteristic
357C4—22no—
358C4—21no—
359C4—21no—
360C4—81no—
361C4—81no—
362C4—134no—
363C4—261no—
364C4—261no—
365C4—262no—
366C4—522no—
367C4—522no—
368C4—521no—
369C2—24no—
370C2#1313007411yescharacteristic
371C2C2×#1171824411yescharacteristic
372C2#1313012911yescharacteristic
373C2D13⋊#32811yescharacteristic
374C2#1313021211yescharacteristic
375C2#1313028711yescharacteristic
376C2#1313033811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#380C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#380#261
hypocenterC13#7566
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13129657C2semidirect
4. #13129655C2semidirect
38. #88178C8semidirect
83. C2×Dic26C2×C8semidirect
96. C4⋊Dic13C2×C8semidirect
293. C13#7566semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊#10572
C2×#117182902
#131296572
#131296552
#131173642
#756613