Finite Group Databasebeta

← #14648261

Subgroups — #14648261

Order 2816.

426 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#13077360C211yesmaximal, characteristic
2#13069389C211yesmaximal, characteristic, complemented
3#13067388C211yesmaximal, characteristic, complemented
4#13067265C211yesmaximal, characteristic
5#13066453C211yesmaximal, characteristic, complemented
6#13066451C211yesmaximal, characteristic, complemented
7C11×#1492C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#67001—21no—
10C11×#423C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12#10622847—21no—
13C2×#66886—21no—
14#10622625—21no—
15#10622624—22no—
16D4×C11⋊C8—21no—
17#10622538C2211yescharacteristic
18C2×C4⋊(C11⋊C8)C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C4×#4318C2211yescharacteristic
21C11×D4⋊C8—22no—
22#10622196—21no—
23#10622185C411yescharacteristic
24#10622185C411yescharacteristic
25#10622182C411yescharacteristic
26#10622182C411yescharacteristic
27#10622118—21no—
28#10622118—21no—
29C2×C11×#41—21no—
30C2×C11×M16—21no—
31C22×C8×C11—21no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#127C2×C411yescharacteristic
34C11×#124—21no—
35C11×#121—21no—
36C11×#121Q812yes—
37C4×D4×C11—21no—
38C4×D4×C11D412yes—
39C2×C42×C11C2311yescharacteristic
40#67001—42no—
41#67001—42no—
42C2×#4318—22no—
43C2×#4318D411yescharacteristic
44C2×#4318D411yescharacteristic
45C22×C11⋊C8—22no—
46C22×C11⋊C8—21no—
47C22×C11⋊C8—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C4×C8×C11—21no—
51C4×C8×C11—21no—
52C22⋊(C11⋊C8)—22no—
53C22⋊(C11⋊C8)—22no—
54C22⋊(C11⋊C8)—21no—
55#66886—42no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)C2×C411yescharacteristic
59C4⋊(C11⋊C8)C2×C411yescharacteristic
60C4⋊(C11⋊C8)C2×C411yescharacteristic
61C4⋊(C11⋊C8)C2×C411yescharacteristic
62C4⋊(C11⋊C8)D411yescharacteristic
63C4⋊(C11⋊C8)D411yescharacteristic
64#66867—21no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8—21no—
67#8932—111nomaximal, Sylow
68C11×#41—41no—
69C11×#41—41no—
70C11×#41—41no—
71C11×#41—41no—
72C2×Q8×C11—21no—
73C2×D4×C11—22no—
74C2×D4×C11—21no—
75C2×D4×C11—21no—
76C2×D4×C11C4⋊C412yes—
77C22×C4×C11—22no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×Q811yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C11×M16—41no—
82C11×M16—41no—
83C2×C8×C11—22no—
84C2×C8×C11—41no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4C4⋊C412yes—
89C11×C22⋊C4—22no—
90C11×C22⋊C4—22no—
91C42×C11C22×C411yescharacteristic
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11#4111yescharacteristic
95#4318—21no—
96#4318—21no—
97#4318—21no—
98#4318—44no—
99#4318SD1612yes—
100C2×C11⋊C8—21no—
101C2×C11⋊C8—21no—
102C2×C11⋊C8—21no—
103C2×C11⋊C8—21no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—44no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113#2935—111no—
114#1950—111no—
115#1570—111no—
116#1540—111no—
117#1492D1111yescharacteristic
118#1278—111no—
119#1277—111no—
120C23×C11—22no—
121C23×C11C22⋊Q811yescharacteristic
122Q8×C11—41no—
123Q8×C11—41no—
124D4×C11—42no—
125D4×C11—42no—
126D4×C11—42no—
127D4×C11—41no—
128D4×C11—41no—
129D4×C11—41no—
130D4×C11—41no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—22no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11C2×C4⋊C411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C8×C11—42no—
148C8×C11—81no—
149C11⋊C8—22no—
150C11⋊C8—41no—
151C11⋊C8—41no—
152C11⋊C8—41no—
153C11⋊C8—41no—
154C11⋊C8—41no—
155C11⋊C8—41no—
156C11⋊C8—41no—
157C2×#131—221no—
158#532C2×D1111yescharacteristic
159#436—221no—
160#435—222no—
161C8×D4—221no—
162#431—111no—
163C2×#108—221no—
164#423C2×D1111yescharacteristic
165C2×C4⋊C8—111no—
166C2×C4⋊C8—111no—
167#408—221no—
168C4×M16—111no—
169C2×C4×C8C2×D1111yescharacteristic
170#341—221no—
171#334—221no—
172#334—221no—
173#332—111no—
174#332—111no—
175#331—111no—
176#331—111no—
177D4⋊C8—22no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11—42no—
183C22×C11#38511yescharacteristic
184C22×C11#47611yescharacteristic
185C22×C11#47811yescharacteristic
186C4×C11—21no—
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—42no—
190C4×C11C4×SD1611yescharacteristic
191C4×C11#44211yescharacteristic
192C4×C11#44311yescharacteristic
193C4×C11#44411yescharacteristic
194C4×C11#44911yescharacteristic
195C4×C11#45011yescharacteristic
196C2×#41—21no—
197#131—442no—
198#131—442no—
199C2×M16—21no—
200C2×M16—111no—
201C2×M16—111no—
202C2×M16—222no—
203C22×C8—21no—
204C22×C8—222no—
205C22×C8—221no—
206C22×C8—221no—
207C4⋊Q8C4×D1111yescharacteristic
208#127C4×D1111yescharacteristic
209#124—21no—
210#121—21no—
211#121Dic2212yes—
212C4×D4—21no—
213C4×D4C22⋊D1112yes—
214C2×C42C22×D1111yescharacteristic
215#108—442no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—111no—
219C4⋊C8—111no—
220C4⋊C8—111no—
221C4⋊C8—111no—
222C4⋊C8—111no—
223C4⋊C8—111no—
224C4⋊C8—221no—
225C4⋊C8—221no—
226C22⋊C8—222no—
227C22⋊C8—222no—
228C22⋊C8—221no—
229#97—221no—
230C4×C8—21no—
231C4×C8—21no—
232C4×C8—221no—
233C4×C8—221no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—82no—
237C2×C11#185811yescharacteristic
238C2×C11#186411yescharacteristic
239C2×C11#186611yescharacteristic
240#41—41no—
241#41—41no—
242#41—41no—
243#41—41no—
244C2×Q8—21no—
245C2×D4—22no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4Dic11⋊C412yes—
249C22×C4—22no—
250C22×C4C2×Dic2211yescharacteristic
251C22×C4D4×D1111yescharacteristic
252C22×C4#434111yescharacteristic
253M16—41no—
254M16—41no—
255M16—112no—
256M16—221no—
257M16—221no—
258M16—221no—
259M16—444no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—221no—
265C2×C8—221no—
266C2×C8—221no—
267C2×C8—221no—
268C2×C8—221no—
269C2×C8—221no—
270C2×C8—221no—
271C2×C8—221no—
272C2×C8—444no—
273C2×C8—441no—
274C2×C8—441no—
275C2×C8—441no—
276C2×C8—441no—
277C4⋊C4—21no—
278C4⋊C4Dic11⋊C412yes—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42C2×C4×D1111yescharacteristic
282C42D4×D1111yescharacteristic
283C42#434111yescharacteristic
284C42C2×C22⋊D1111yescharacteristic
285C11#893211yescharacteristic, complemented, Sylow
286C23—22no—
287C23#6693111yescharacteristic
288Q8—41no—
289Q8—41no—
290D4—42no—
291D4—42no—
292D4—42no—
293D4—41no—
294D4—41no—
295D4—41no—
296D4—41no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4#6693111yescharacteristic
304C2×C4(C22⋊D11)⋊C411yescharacteristic
305C2×C4(C22⋊D11)⋊C411yescharacteristic
306C2×C4#6696411yescharacteristic
307C2×C4#6696511yescharacteristic
308C2×C4SD16×D1111yescharacteristic
309C2×C4#6696711yescharacteristic
310C2×C4C2×Dic11⋊C411yescharacteristic
311C2×C4#6698811yescharacteristic
312C2×C4#6699011yescharacteristic
313C8—42no—
314C8—81no—
315C8—222no—
316C8—441no—
317C8—441no—
318C8—441no—
319C8—441no—
320C8—441no—
321C8—441no—
322C8—441no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22#1062237411yescharacteristic
329C22#1062237911yescharacteristic
330C22#1062255911yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4#1062237111yescharacteristic
336C4#1062239811yescharacteristic
337C4#1062243611yescharacteristic
338C4#1062243711yescharacteristic
339C4#1062277111yescharacteristic
340C4#1062278211yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1306883511yescharacteristic
345C2#1306887511yescharacteristic
346C2#1306888911yescharacteristic
subgroupG/H
centerC2×C4#66990
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1492C2
socleC22×C11#385
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1492D11
hypocenterC11#8932
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1492

Complements

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

NH ≅ G/Ntype
2. #13069389C2semidirect
3. #13067388C2semidirect
5. #13066453C2semidirect
6. #13066451C2semidirect
285. C11#8932semidirect

Maximal subgroups

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

subgroupindex
#130773602
#130693892
#130673882
#130672652
#130664532
#130664512
C11×#14922
#893211