Finite Group Databasebeta

← #16790393

Subgroups — #16790393

Order 3328.

494 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
1C22×#88106C211yesmaximal, characteristic, complemented
2C2×#11718270C212yesmaximal, complemented
3C2×C22⋊#6092C211yesmaximal, characteristic, complemented
4#13129891C212yesmaximal, complemented
5#13123526C211yesmaximal, characteristic
6#11719496C411yescharacteristic
7C23×#1055C2211yescharacteristic
8C2×#88161C2211yescharacteristic
9C2×#88106—21no—
10C2×#88106—24no—
11C2×#88106C2212yes—
12C22×#6092—21no—
13C22×#6092C2212yes—
14C13×#407C411yescharacteristic
15#11718790C411yescharacteristic
16#11718783C2211yescharacteristic
17#11718780C411yescharacteristic
18#11718391—21no—
19#11718391—21no—
20#11718386—21no—
21#11718386—21no—
22C22⋊#6092—21no—
23C22⋊#6092—21no—
24#11718270—24no—
25C23×C4×C13C2×C411yescharacteristic
26C2×#6127C2×C411yescharacteristic
27C2×C13×M16C2×C411yescharacteristic
28C2×C13×M16C2×C411yescharacteristic
29#88207—21no—
30#88184C811yescharacteristic
31#88184C811yescharacteristic
32#88183—21no—
33C4×C22⋊D13—21no—
34C4×C22⋊D13—21no—
35#88180C2×C411yescharacteristic
36#88178C811yescharacteristic
37#88178C811yescharacteristic
38C22×#1055—22no—
39C22×#1055—22no—
40C22×#1055C2×C411yescharacteristic
41C22×#1055D411yescharacteristic
42C22×#1055D411yescharacteristic
43C22×#1055D411yescharacteristic
44C22×#1055D411yescharacteristic
45C22×#1055C2311yescharacteristic
46#88161—22no—
47#88161—22no—
48C2×#6094—21no—
49C2×C8×D13—21no—
50#88106—24no—
51#88106—22no—
52#88106D414yescomplemented
53C2×#6092—24no—
54C2×#6092—22no—
55C2×#6092—22no—
56C2×#6092—22no—
57C2×#6092—22no—
58C13×C22⋊C8—21no—
59C13×C22⋊C8—21no—
60#88060—21no—
61#88060—21no—
62#88055—21no—
63#88054—21no—
64#88054—21no—
65C8×Dic13—21no—
66#12978—131nomaximal, Sylow
67C24×C13M1611yescharacteristic
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C2×C811yescharacteristic
73C22×C4×C13C2×C811yescharacteristic
74C22×C4×C13M1611yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C2×C22⋊D13—21no—
77C2×C22⋊D13—21no—
78C2×C22⋊D13—21no—
79#6127—22no—
80#6127—22no—
81C2×D52C2×C811yescharacteristic
82C2×C4×D13—21no—
83C2×Dic26C2×C811yescharacteristic
84C13×M16—22no—
85C13×M16—22no—
86C2×C8×C13—21no—
87C2×C8×C13—21no—
88C22⋊Dic13—21no—
89C22⋊Dic13—21no—
90C22⋊Dic13—21no—
91#6103—21no—
92#6103—21no—
93C4⋊Dic13C2×C811yescharacteristic
94C4⋊Dic13C2×C811yescharacteristic
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C2×#1055—22no—
99C2×#1055—21no—
100C2×#1055—21no—
101C2×#1055—22no—
102C2×#1055—22no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055C22⋊C411yescharacteristic
106C2×#1055C22⋊C411yescharacteristic
107C2×#1055C2×D412yes—
108C2×#1055C2×D411yescharacteristic
109C2×#1055C2×D411yescharacteristic
110C2×#1055#4112yes—
111#6094—42no—
112C8×D13—41no—
113C8×D13—41no—
114#6092—24no—
115#6092—42no—
116C22×M32—131no—
117#2929—131no—
118C2×#350—132no—
119C2×C22⋊C16—131no—
120#1379—132no—
121C23×C13—22no—
122C23×C13—22no—
123C23×C13—41no—
124C23×C13C22⋊C811yescharacteristic
125C23×C13C22⋊C811yescharacteristic
126C23×C13C2×M1611yescharacteristic
127C22×D13—21no—
128C2×C4×C13—22no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13C22⋊C811yescharacteristic
136C2×C4×C13C22⋊C811yescharacteristic
137C2×C4×C13C2×C22⋊C411yescharacteristic
138C2×C4×C13C4×D412yes—
139C2×C4×C13C22×C811yescharacteristic
140C2×C4×C13#13112yes—
141C22⋊D13—42no—
142C22⋊D13—42no—
143C22⋊D13—42no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147D52—22no—
148C4×D13—41no—
149C4×D13—41no—
150Dic26—22no—
151C8×C13—41no—
152C8×C13—41no—
153#1055—21no—
154#1055—21no—
155#1055#12011yescharacteristic
156#1055#12112yes—
157#1055#12311yescharacteristic
158C2×#131—131no—
159C23×C8—131no—
160#525—131no—
161C2×M32—132no—
162C2×M32—264no—
163C2×M32—261no—
164C22×C16—132no—
165C22×C16—261no—
166#435—261no—
167#435—261no—
168C8×D4—261no—
169C8×D4—261no—
170#424—131no—
171#408—131no—
172#407#26111yescharacteristic
173#405—131no—
174#350—264no—
175C22⋊C16—261no—
176C22⋊C16—261no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—44no—
185C22×C13#35012yescomplemented
186C22×C13C2×C22⋊C811yescharacteristic
187C22×C13#43512yes—
188C2×D13—41no—
189C2×D13—41no—
190C2×D13—41no—
191C4×C13—21no—
192C4×C13—21no—
193C4×C13#38611yescharacteristic
194C4×C13#40811yescharacteristic
195C4×C13C8×D412yes—
196Dic13—41no—
197Dic13—41no—
198Dic13—41no—
199C2×#41—131no—
200C23×C4C2×#26111yescharacteristic
201#131—262no—
202#131—262no—
203C2×M16—261no—
204C2×M16C2×#26111yescharacteristic
205C2×M16C2×#26111yescharacteristic
206C22×C8—131no—
207C22×C8—131no—
208C22×C8—131no—
209C22×C8—131no—
210C22×C8—131no—
211C22×C8—131no—
212C22×C8—261no—
213C22×C8—262no—
214C22×C8—262no—
215#123—261no—
216C22⋊Q8—131no—
217C22⋊Q8—131no—
218#121—131no—
219#121—131no—
220#120—261no—
221C4×D4—261no—
222C4×D4—261no—
223#117—131no—
224M32—134no—
225M32—262no—
226M32—264no—
227C2×C16—262no—
228C2×C16—264no—
229C2×C16—262no—
230C2×C16—262no—
231C2×C16—262no—
232C4⋊C8—261no—
233C4⋊C8—261no—
234C22⋊C8—21no—
235C22⋊C8—21no—
236C22⋊C8—261no—
237C22⋊C8—261no—
238#97—261no—
239C4×C8—261no—
240C2×C13—22no—
241C2×C13—22no—
242C2×C13—41no—
243C2×C13#186911yescharacteristic
244C2×C13C2×#35011yescharacteristic
245C2×C13#211711yescharacteristic
246D13—81no—
247C24#611811yescharacteristic
248#41—262no—
249#41—262no—
250C2×Q8—131no—
251C2×D4—131no—
252C2×D4—261no—
253C2×D4—261no—
254C2×D4—261no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—261no—
258C22×C4D13⋊C811yescharacteristic
259C22×C4D13⋊C811yescharacteristic
260C22×C4#611811yescharacteristic
261C22×C4C22⋊#26111yescharacteristic
262C22×C4C22⋊#26111yescharacteristic
263C22×C4C22×#26111yescharacteristic
264M16—22no—
265M16—22no—
266M16—522no—
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—132no—
270C2×C8—132no—
271C2×C8—131no—
272C2×C8—131no—
273C2×C8—131no—
274C2×C8—131no—
275C2×C8—261no—
276C2×C8—261no—
277C2×C8—262no—
278C2×C8—262no—
279C2×C8—261no—
280C2×C8—261no—
281C2×C8—262no—
282C2×C8—521no—
283C2×C8—521no—
284C4⋊C4—131no—
285C4⋊C4—131no—
286C4⋊C4—261no—
287C4⋊C4—261no—
288C22⋊C4—261no—
289C22⋊C4—261no—
290C22⋊C4—261no—
291C22⋊C4—261no—
292C22⋊C4—261no—
293C42—261no—
294C16—264no—
295C16—522no—
296C13#1297811yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—41no—
300C23—261no—
301C23#8811111yescharacteristic
302C23#8811111yescharacteristic
303C23C2×#611811yescharacteristic
304Q8—262no—
305D4—262no—
306D4—522no—
307D4—522no—
308D4—522no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4#8811111yescharacteristic
322C2×C4#8811111yescharacteristic
323C2×C4C2×D13⋊C811yescharacteristic
324C2×C4#8823812yes—
325C2×C4D4×#26112yes—
326C2×C4C2×C22⋊#26111yescharacteristic
327C8—41no—
328C8—41no—
329C8—131no—
330C8—132no—
331C8—131no—
332C8—261no—
333C8—261no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—44no—
342C22—521no—
343C22—521no—
344C22—521no—
345C22#1171827012yescomplemented
346C22#1171906412yes—
347C22C2×#8811111yescharacteristic
348C4—21no—
349C4—21no—
350C4—521no—
351C4—521no—
352C4—521no—
353C4#1171906312yes—
354C4#1171914611yescharacteristic
355C4#1171915011yescharacteristic
356C2—22no—
357C2—22no—
358C2—41no—
359C2—1041no—
360C2#1313081111yescharacteristic
361C2C2×#1171827011yescharacteristic
362C2#1313108011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#407C4
socleC22×C13C2×C22⋊C8
prime radical#11719496C4
cosocleC22×#1055C23
hypercenter#407#261
hypocenterC13#12978
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#88106C2semidirect
2. C2×#11718270C2semidirect
3. C2×C22⋊#6092C2semidirect
4. #13129891C2semidirect
52. #88106D4semidirect
185. C22×C13#350semidirect
296. C13#12978semidirect
345. C22#11718270semidirect

Maximal subgroups

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

subgroupindex
C22×#881062
C2×#117182702
C2×C22⋊#60922
#131298912
#131235262
#1297813