Finite Group Databasebeta

← #14649783

Subgroups — #14649783

Order 2816.

504 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077178C211yesmaximal, characteristic
2#13074438C211yesmaximal, characteristic
3#13067301C211yesmaximal, characteristic, complemented
4#13066928C211yesmaximal, characteristic
5#13066476C211yesmaximal, characteristic, complemented
6#13066475C211yesmaximal, characteristic, complemented
7C11×#1549C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×M16×D11—21no—
10C2×#66925C2211yescharacteristic
11C11×#431C2211yescharacteristic
12C11×#423C2211yescharacteristic
13#10622844—21no—
14#10622842—21no—
15#10622731—21no—
16#10622605C412yes—
17#10622600—21no—
18#10622595C412yes—
19#10622586—21no—
20#10622549C2211yescharacteristic
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23#10622452—22no—
24#10622452—22no—
25C11×#332—22no—
26#10622185—22no—
27#10622107—21no—
28#10622106—21no—
29C22×Q8×C11—21no—
30C22×C4×D11D411yescharacteristic
31C2×C11×M16—21no—
32C11×C4⋊Q8—21no—
33C11×C4⋊Q8—21no—
34C11×C4⋊Q8—21no—
35C11×C4⋊Q8—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C412yes—
38C2×C42×C11C2311yescharacteristic
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4C2×C411yescharacteristic
41C2×(C2×D11)⋊C4D411yescharacteristic
42C2×C4⋊Dic11—21no—
43C2×Dic11⋊C4—22no—
44C2×Dic11⋊C4C2×C411yescharacteristic
45C2×Dic11⋊C4D411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×#4318—21no—
48M16×D11—42no—
49M16×D11—42no—
50C2×#4313—22no—
51C2×C8×D11—22no—
52#66925—21no—
53#66925—21no—
54#66925—21no—
55#66925—21no—
56C11×C4⋊C8—21no—
57C11×C4⋊C8—21no—
58C11×C4⋊C8D412yes—
59C11×C22⋊C8—21no—
60C4×C8×C11—21no—
61C11⋊#95—21no—
62C11⋊#95—22no—
63C11⋊#95—22no—
64C11⋊#95C2×C412yes—
65C22⋊(C11⋊C8)—21no—
66Dic11⋊C8—24no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70C4×C11⋊C8—21no—
71#9193—111nomaximal, Sylow
72C23×D11C22⋊C411yescharacteristic
73C2×Q8×C11—41no—
74C2×Q8×C11—41no—
75C2×Q8×C11—82no—
76C22×C4×C11—22no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D411yescharacteristic
80C22×Dic11—22no—
81C22×Dic11C22⋊C411yescharacteristic
82C22×Dic11C22⋊C411yescharacteristic
83C22×Dic11C22⋊C411yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11—21no—
88C2×C4×D11SD1612yes—
89C2×C4×D11Q1612yes—
90C11×M16—41no—
91C11×M16—41no—
92C2×C8×C11—22no—
93C2×C8×C11—41no—
94C11×C4⋊C4—22no—
95C11×C4⋊C4—22no—
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—82no—
107C4⋊Dic11—41no—
108C4⋊Dic11—41no—
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111Dic11⋊C4—21no—
112Dic11⋊C4—21no—
113Dic11⋊C4—82no—
114C4×Dic11—21no—
115C4×Dic11—21no—
116#4318—41no—
117#4318—41no—
118C2×C11⋊C8—22no—
119C2×C11⋊C8—41no—
120#4313—44no—
121C8×D11—44no—
122#2905—111no—
123#2628—111no—
124#1549—111no—
125#1549D1111yescharacteristic, complemented
126#1458—111no—
127#1286—111no—
128#1286—111no—
129C23×C11C2×C22⋊C411yescharacteristic
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11#10312yes—
135Q8×C11—82no—
136Q8×C11—82no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—42no—
141C2×C4×C11—42no—
142C2×C4×C11C4×D411yescharacteristic
143C2×C4×C11C4×D411yescharacteristic
144C2×C4×C11#12011yescharacteristic
145C2×C4×C11#12111yescharacteristic
146C2×C4×C11#12111yescharacteristic
147C2×C4×C11#12311yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11C2×Q1611yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11#13711yescharacteristic
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—21no—
155C2×Dic11—21no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—42no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161C2×Dic11#10312yes—
162C4×D11—22no—
163C4×D11—22no—
164C4×D11—22no—
165C4×D11—22no—
166C8×C11—42no—
167C8×C11—81no—
168C11⋊C8—42no—
169C11⋊C8—81no—
170C22×M16—221no—
171C2×C4⋊Q8C2×D1111yescharacteristic
172C2×#117—111no—
173#431—111no—
174#431C2×D1111yescharacteristic
175#424—222no—
176#424—222no—
177#423—111no—
178#423—221no—
179#423C2×D1111yescharacteristic
180#400—112no—
181#399—112no—
182#395—221no—
183#393—221no—
184#389—221no—
185#382—111no—
186#380—221no—
187#332—22no—
188#332—222no—
189#324—221no—
190#323—221no—
191C22×C11—21no—
192C22×C11—21no—
193C22×C11#38611yescharacteristic
194C22×C11C2×#10311yescharacteristic
195C22×C11#41711yescharacteristic
196C2×D11—22no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—42no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—82no—
206C4×C11#45011yescharacteristic
207C4×C11#45111yescharacteristic
208C4×C11#48311yescharacteristic
209C4×C11#48411yescharacteristic
210Dic11—22no—
211Dic11—41no—
212Dic11—41no—
213Dic11—82no—
214C22×Q8—21no—
215C23×C4—111no—
216C2×M16—21no—
217C2×M16—222no—
218C2×M16—221no—
219C2×M16—442no—
220C2×M16—442no—
221C22×C8—222no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8—21no—
225C4⋊Q8—21no—
226#117—221no—
227#117—221no—
228#117—221no—
229#117—221no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—111no—
232C2×C4⋊C4—111no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—222no—
235C2×C4⋊C4C4×D1112yes—
236C2×C22⋊C4—111no—
237C2×C22⋊C4—111no—
238C2×C22⋊C4—222no—
239C2×C42—111no—
240C2×C42C22×D1111yescharacteristic
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—112no—
244C4⋊C8—224no—
245C4⋊C8—221no—
246C4⋊C8—221no—
247C4⋊C8C22⋊D1112yes—
248C22⋊C8—21no—
249C22⋊C8—221no—
250C4×C8—21no—
251C4×C8—221no—
252#95—112no—
253#95—222no—
254#95—222no—
255#95—221no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11#187211yescharacteristic
259C2×C11#191011yescharacteristic
260C2×C11#191511yescharacteristic
261D11—42no—
262C24—111no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—82no—
266C22×C4—22no—
267C22×C4—111no—
268C22×C4—112no—
269C22×C4—112no—
270C22×C4—111no—
271C22×C4—111no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—222no—
277C22×C4C2×C4×D1111yescharacteristic
278C22×C4D4×D1111yescharacteristic
279C22×C4D4×D1111yescharacteristic
280M16—41no—
281M16—41no—
282M16—444no—
283M16—441no—
284M16—441no—
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—222no—
288C2×C8—444no—
289C2×C8—441no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4—221no—
298C4⋊C4—441no—
299C4⋊C4—441no—
300C4⋊C4—882no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—882no—
306C42—221no—
307C42—221no—
308C42#433911yescharacteristic
309C42D4×D1111yescharacteristic
310C42#434111yescharacteristic
311C42C2×C22⋊D1111yescharacteristic
312C11#919311yescharacteristic, complemented, Sylow
313C23—112no—
314C23—221no—
315C23—221no—
316C23—441no—
317C23—441no—
318C23C22⋊C4×D1111yescharacteristic
319Q8—82no—
320Q8—82no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—112no—
327C2×C4—221no—
328C2×C4—221no—
329C2×C4—222no—
330C2×C4—222no—
331C2×C4—222no—
332C2×C4—222no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—441no—
336C2×C4—441no—
337C2×C4—442no—
338C2×C4—442no—
339C2×C4—442no—
340C2×C4(C22⋊D11)⋊C411yescharacteristic
341C2×C4#6693611yescharacteristic
342C2×C4#6693711yescharacteristic
343C2×C4SD16×D1111yescharacteristic
344C2×C4#6696711yescharacteristic
345C2×C4Q16×D1111yescharacteristic
346C2×C4#6697111yescharacteristic
347C2×C4C4×C22⋊D1111yescharacteristic
348C2×C4#6699011yescharacteristic
349C2×C4#6699111yescharacteristic
350C8—42no—
351C8—81no—
352C8—442no—
353C8—881no—
354C22—21no—
355C22—21no—
356C22—222no—
357C22—442no—
358C22—441no—
359C22—441no—
360C22—881no—
361C22D11×#10311yescharacteristic
362C22#1062241611yescharacteristic
363C22#1062256911yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—82no—
369C4—222no—
370C4—441no—
371C4—441no—
372C4—882no—
373C4#1062241811yescharacteristic
374C4#1062242211yescharacteristic
375C4#1062278211yescharacteristic
376C4#1062279911yescharacteristic
377C2—21no—
378C2—21no—
379C2—442no—
380C2#1306892011yescharacteristic
381C2#1306914011yescharacteristic
382C2#1306916511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1549C2
socleC22×C11#386
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1549D11
hypocenterC11#9193
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
3. #13067301C2semidirect
5. #13066476C2semidirect
6. #13066475C2semidirect
7. C11×#1549C2semidirect
125. #1549D11semidirect
312. C11#9193semidirect

Maximal subgroups

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

subgroupindex
#130771782
#130744382
#130673012
#130669282
#130664762
#130664752
C11×#15492
#919311