Finite Group Databasebeta

← #14646707

Subgroups — #14646707

Order 2816.

454 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622625C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13067374C211yesmaximal, characteristic, complemented
4#13067371C211yesmaximal, characteristic, complemented
5#13066490C211yesmaximal, characteristic, complemented
6#13066490C211yesmaximal, characteristic, complemented
7C11×#1800C211yesmaximal, characteristic
8C2×C4×D4×C11C2211yescharacteristic
9C22×#4318C412yes—
10C11×#423C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C2×C11×#100—21no—
13C2×#66897—21no—
14C2×C22⋊(C11⋊C8)C412yes—
15#10622625—21no—
16#10622625—21no—
17#10622625—21no—
18#10622625—21no—
19#10622537C2211yescharacteristic
20#10622537C2211yescharacteristic
21C2×C4⋊(C11⋊C8)C2211yescharacteristic
22C2×C4×C11⋊C8C2211yescharacteristic
23C11×#343—21no—
24#10622168—21no—
25#10622118—21no—
26#10622118—21no—
27#10622117—21no—
28#10622117—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11C2×C412yes—
31C2×C11×M16—21no—
32C2×C11×M16—21no—
33C4×D4×C11—21no—
34C4×D4×C11—21no—
35C4×D4×C11—21no—
36C4×D4×C11—21no—
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4Q812yes—
39C2×C42×C11C2311yescharacteristic
40C2×#4318—22no—
41C2×#4318—22no—
42C2×#4318—21no—
43C2×#4318—21no—
44C2×#4318—44no—
45C22×C11⋊C8C2×C411yescharacteristic
46C22×C11⋊C8C2×C412yes—
47C22×C11⋊C8C2×C411yescharacteristic
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8—21no—
51C11×C4⋊C8—21no—
52C11×#100—42no—
53#66897—42no—
54C22⋊(C11⋊C8)—22no—
55C22⋊(C11⋊C8)—22no—
56C4⋊(C11⋊C8)—21no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—21no—
60C4⋊(C11⋊C8)—21no—
61C4⋊(C11⋊C8)—21no—
62C4×C11⋊C8D411yescharacteristic
63C4×C11⋊C8D411yescharacteristic
64C4×C11⋊C8D411yescharacteristic
65C4×C11⋊C8D411yescharacteristic
66#8618—111nomaximal, Sylow
67C24×C11C4⋊C412yes—
68C2×D4×C11—21no—
69C2×D4×C11—21no—
70C2×D4×C11—21no—
71C2×D4×C11—21no—
72C2×D4×C11—21no—
73C2×D4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—42no—
77C22×C4×C11—42no—
78C22×C4×C11C4⋊C412yes—
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×Q811yescharacteristic
82C11×M16—41no—
83C11×M16—41no—
84C11×M16—41no—
85C11×M16—41no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C11×C4⋊C4—21no—
89C11×C4⋊C4—21no—
90C11×C22⋊C4—22no—
91C11×C22⋊C4—22no—
92C42×C11C2×D411yescharacteristic
93C42×C11C2×D411yescharacteristic
94C42×C11#4111yescharacteristic
95C42×C11#4111yescharacteristic
96#4318—44no—
97#4318—44no—
98#4318—41no—
99#4318—41no—
100#4318—41no—
101#4318—41no—
102C2×C11⋊C8—22no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—41no—
105C2×C11⋊C8—42no—
106C2×C11⋊C8—41no—
107C2×C11⋊C8—41no—
108C2×C11⋊C8C22⋊C411yescharacteristic
109C2×C11⋊C8C22⋊C411yescharacteristic
110C2×C11⋊C8C22⋊C411yescharacteristic
111C2×C11⋊C8C22⋊C411yescharacteristic
112C2×#436—111no—
113#1800—111no—
114#1800D1111yescharacteristic
115#1567—111no—
116#1566—111no—
117#1292—111no—
118#1292—111no—
119C23×C11—22no—
120C23×C11—22no—
121C23×C11—22no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11C2×C4⋊C411yescharacteristic
125D4×C11—41no—
126D4×C11—41no—
127D4×C11—41no—
128D4×C11—41no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—41no—
133C2×C4×C11—44no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11#11711yescharacteristic
139C2×C4×C11#12111yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11C22⋊Q811yescharacteristic
142C2×C4×C11C22⋊Q811yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C11#13711yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C8×C11—81no—
148C8×C11—81no—
149C11⋊C8—21no—
150C11⋊C8—21no—
151C11⋊C8—21no—
152C11⋊C8—42no—
153C11⋊C8—81no—
154C11⋊C8—81no—
155C11⋊C8#10012yescomplemented
156C22×M16—112no—
157C2×C4×D4C2×D1111yescharacteristic
158#436—221no—
159#436—221no—
160#436—221no—
161#436—221no—
162#423—111no—
163#423—111no—
164#423C2×D1111yescharacteristic
165#423C2×D1111yescharacteristic
166C2×C4⋊C8—111no—
167C2×#100—21no—
168C2×#100—221no—
169C2×C22⋊C8—112no—
170C2×C4×C8—111no—
171#343—21no—
172#343—221no—
173#335—221no—
174#335—221no—
175#334—221no—
176#334—221no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—42no—
180C22×C11—42no—
181C22×C11—42no—
182C22×C11—82no—
183C22×C11—82no—
184C22×C11#38011yescharacteristic
185C22×C11#42811yescharacteristic
186C22×C11#42811yescharacteristic
187C4×C11—21no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—42no—
191C4×C11C2×#10011yescharacteristic
192C4×C11#41311yescharacteristic
193C4×C11#46811yescharacteristic
194C4×C11#46811yescharacteristic
195C4×C11#46911yescharacteristic
196C4×C11#47011yescharacteristic
197C22×D4C22⋊D1111yescharacteristic
198C23×C4C4×D1112yes—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16—222no—
202C2×M16—222no—
203C2×M16—221no—
204C2×M16—221no—
205C2×M16—444no—
206C22×C8—111no—
207C22×C8—111no—
208C22×C8—112no—
209C4×D4—21no—
210C4×D4—21no—
211C4×D4—21no—
212C4×D4—21no—
213C2×C4⋊C4C22⋊D1111yescharacteristic
214C2×C22⋊C4Dic2212yes—
215C2×C42C22×D1111yescharacteristic
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—221no—
221C4⋊C8—221no—
222C4⋊C8—221no—
223C4⋊C8—221no—
224C4⋊C8—221no—
225C4⋊C8—221no—
226#100—42no—
227#100—442no—
228C22⋊C8—222no—
229C22⋊C8—222no—
230C4×C8—111no—
231C4×C8—111no—
232C4×C8—111no—
233C4×C8—111no—
234C2×C11—21no—
235C2×C11—21no—
236C2×C11—82no—
237C2×C11#180011yescharacteristic
238C2×C11#180911yescharacteristic
239C2×C11#181311yescharacteristic
240C24Dic11⋊C412yes—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4Dic11⋊C412yes—
252C22×C4C2×Dic2211yescharacteristic
253C22×C4C2×C4×D1111yescharacteristic
254C22×C4C2×C22⋊D1111yescharacteristic
255M16—41no—
256M16—41no—
257M16—41no—
258M16—41no—
259M16—444no—
260M16—444no—
261M16—441no—
262M16—441no—
263M16—441no—
264M16—441no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—111no—
268C2×C8—111no—
269C2×C8—111no—
270C2×C8—111no—
271C2×C8—222no—
272C2×C8—222no—
273C2×C8—441no—
274C2×C8—442no—
275C2×C8—441no—
276C2×C8—441no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C22⋊C4—22no—
280C22⋊C4—22no—
281C42D4×D1111yescharacteristic
282C42D4×D1111yescharacteristic
283C42#434111yescharacteristic
284C42#434111yescharacteristic
285C11#861811yescharacteristic, complemented, Sylow
286C23—22no—
287C23—22no—
288C23—22no—
289C23—42no—
290C23—42no—
291C23C2×Dic11⋊C411yescharacteristic
292D4—41no—
293D4—41no—
294D4—41no—
295D4—41no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—44no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4#6693011yescharacteristic
305C2×C4#6693111yescharacteristic
306C2×C4#6693111yescharacteristic
307C2×C4C22⋊C4×D1111yescharacteristic
308C2×C4#6698511yescharacteristic
309C2×C4#6699211yescharacteristic
310C2×C4#6699211yescharacteristic
311C2×C4#6699511yescharacteristic
312C2×C4#6700211yescharacteristic
313C2×C4#6700411yescharacteristic
314C8—81no—
315C8—81no—
316C8—112no—
317C8—221no—
318C8—221no—
319C8—221no—
320C8—442no—
321C8—881no—
322C8—881no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—82no—
329C22—82no—
330C22#1062255511yescharacteristic
331C22#1062257711yescharacteristic
332C22#1062260811yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4D11×#10011yescharacteristic
338C4#1062235811yescharacteristic
339C4#1062265211yescharacteristic
340C4#1062265511yescharacteristic
341C4#1062266211yescharacteristic
342C4#1062266511yescharacteristic
343C2—21no—
344C2—21no—
345C2—82no—
346C2#1306860611yescharacteristic
347C2#1306864711yescharacteristic
348C2#1306866411yescharacteristic
subgroupG/H
centerC22#10622555
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#380
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1800D11
hypocenterC11#8618
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #13067374C2semidirect
4. #13067371C2semidirect
5. #13066490C2semidirect
6. #13066490C2semidirect
155. C11⋊C8#100semidirect
285. C11#8618semidirect

Maximal subgroups

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

subgroupindex
C2×#106226252
#130686082
#130673742
#130673712
#130664902
C11×#18002
#861811