Finite Group Databasebeta

← #14650293

Subgroups — #14650293

Order 2816.

480 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079744C211yesmaximal, characteristic
2#13077362C211yesmaximal, characteristic
3#13067294C211yesmaximal, characteristic
4C2×#10622185C211yesmaximal, characteristic, complemented
5#13066511C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#1997C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×#66960—21no—
10#10623008C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622742—21no—
14#10622701—21no—
15#10622697—22no—
16#10622692—21no—
17#10622581C414yes—
18#10622538C2211yescharacteristic
19C2×C4⋊(C11⋊C8)C2211yescharacteristic
20C2×C4⋊(C11⋊C8)C2211yescharacteristic
21#10622319—22no—
22#10622301—21no—
23C8×D44—21no—
24C11×#343—21no—
25C11×#343—21no—
26#10622185—21no—
27#10622185—21no—
28#10622123—21no—
29#10622120—21no—
30C22×Q8×C11—21no—
31C2×#4339—21no—
32C2×C11×M16—21no—
33C2×C11×M16D411yescharacteristic
34C2×C11×M16D411yescharacteristic
35C11×C4⋊Q8—21no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4C2×C412yes—
41C2×C42×C11C2311yescharacteristic
42#66983—21no—
43#66983C2×C412yes—
44C22×C11⋊C8—21no—
45C22×C11⋊C8—21no—
46#66960—42no—
47#66960—42no—
48C2×#4313—22no—
49C2×C8×D11—22no—
50#66928—21no—
51#66927D411yescharacteristic
52C4×D44—21no—
53C4×D44D412yes—
54#66922D411yescharacteristic
55C11×C4⋊C8—21no—
56C11×C4⋊C8—21no—
57C11×#97—21no—
58C4×C8×C11—21no—
59C22⋊(C11⋊C8)C2×C412yes—
60(C2×D11)⋊C8—22no—
61(C2×D11)⋊C8—22no—
62#66873—24no—
63#66872—24no—
64C4⋊(C11⋊C8)—21no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)D411yescharacteristic
69C4⋊(C11⋊C8)D411yescharacteristic
70C4×C11⋊C8—21no—
71#9269—111nomaximal, Sylow
72C2×Q8×C11—41no—
73C2×Q8×C11—41no—
74C2×Q8×C11—81no—
75C2×Q8×C11—81no—
76C22×C4×C11—22no—
77C22×C4×C11C22×C411yescharacteristic
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C2×C22⋊D11—22no—
81#4339—41no—
82#4339—41no—
83#4339—41no—
84#4339—41no—
85C2×D44—21no—
86C2×D44—21no—
87C2×D44C22⋊C412yes—
88C2×C4×D11—22no—
89C2×Dic22—21no—
90C11×M16—21no—
91C11×M16—21no—
92C11×M16—21no—
93C11×M16—41no—
94C11×M16—41no—
95C11×M16SD1612yes—
96C2×C8×C11—21no—
97C2×C8×C11—21no—
98C2×C8×C11—41no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4—22no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D411yescharacteristic
106C42×C11#4111yescharacteristic
107(C2×D11)⋊C4—22no—
108(C2×D11)⋊C4—22no—
109C4⋊Dic11—21no—
110C4⋊Dic11C22⋊C412yes—
111C2×C11⋊C8—22no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8—81no—
118#4313—44no—
119C8×D11—44no—
120#3227—111no—
121#2935—111no—
122#1997D1111yescharacteristic, complemented
123#1547—111no—
124C2×#332—111no—
125#1301—111no—
126#1283—111no—
127C23×C11C4×D411yescharacteristic
128C22×D11—22no—
129Q8×C11—82no—
130Q8×C11—81no—
131Q8×C11—81no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—42no—
136C2×C4×C11—82no—
137C2×C4×C11C2×C22⋊C411yescharacteristic
138C2×C4×C11C4×D411yescharacteristic
139C2×C4×C11#12011yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12311yescharacteristic
143C2×C4×C11C2×SD1611yescharacteristic
144C2×C4×C11#13511yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C22⋊D11—42no—
148C22⋊D11—42no—
149C2×Dic11—22no—
150D44—42no—
151D44—41no—
152D44—41no—
153D44—41no—
154D44—41no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—41no—
158Dic22—41no—
159C8×C11—22no—
160C8×C11—41no—
161C8×C11—81no—
162C11⋊C8—42no—
163C11⋊C8—41no—
164C11⋊C8—41no—
165C11⋊C8—81no—
166C2×#131—221no—
167#532—111no—
168C2×C4⋊Q8C2×D1111yescharacteristic
169#498—221no—
170#486—221no—
171#481—114no—
172#476—222no—
173#436—221no—
174#435—222no—
175C8×D4—221no—
176#431—111no—
177#423C2×D1111yescharacteristic
178C2×C4⋊C8—111no—
179C2×C4⋊C8—111no—
180#408—221no—
181C4×M16C2×D1111yescharacteristic
182#343—21no—
183#343—21no—
184#332—221no—
185#332—221no—
186#332—221no—
187#331—221no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11#38611yescharacteristic
191C22×C11C4×SD1611yescharacteristic
192C22×C11#44011yescharacteristic
193C2×D11—42no—
194C2×D11—42no—
195C2×D11—42no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—82no—
200C4×C11#45011yescharacteristic
201C4×C11#45211yescharacteristic
202C4×C11#46111yescharacteristic
203C4×C11#46311yescharacteristic
204C4×C11#47111yescharacteristic
205C4×C11#47211yescharacteristic
206Dic11—42no—
207C2×#41—221no—
208C22×Q8—21no—
209#131—442no—
210#131—442no—
211C2×M16—21no—
212C2×M16—222no—
213C2×M16C22⋊D1111yescharacteristic
214C2×M16C22⋊D1111yescharacteristic
215C22×C8—222no—
216C22×C8—221no—
217C22×C8—221no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—111no—
223#127—111no—
224#124—221no—
225#121—112no—
226#121—221no—
227C4×D4—112no—
228C4×D4—221no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C4×D1112yes—
231C2×C42C22×D1111yescharacteristic
232#106—224no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C4⋊C8—111no—
236C4⋊C8—111no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239C4⋊C8—221no—
240C4⋊C8—221no—
241#102—224no—
242C22⋊C8—112no—
243C22⋊C8—222no—
244C22⋊C8—222no—
245#97—21no—
246C4×C8—21no—
247C4×C8—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11#187711yescharacteristic
251C2×C11#190711yescharacteristic
252C2×C11#191511yescharacteristic
253D11—82no—
254#41—441no—
255#41—441no—
256#41—441no—
257#41—441no—
258C2×Q8—41no—
259C2×Q8—41no—
260C2×Q8—81no—
261C2×Q8—81no—
262C2×Q8—221no—
263C2×D4—112no—
264C2×D4—222no—
265C2×D4—221no—
266C2×D4—221no—
267C22×C4—22no—
268C22×C4—222no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4#433911yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272M16—21no—
273M16—21no—
274M16—21no—
275M16—41no—
276M16—41no—
277M16—444no—
278M16#432512yes—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—41no—
282C2×C8—222no—
283C2×C8—221no—
284C2×C8—221no—
285C2×C8—444no—
286C2×C8—441no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8—881no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—112no—
295C4⋊C4—221no—
296C22⋊C4—222no—
297C22⋊C4—222no—
298C42D4×D1111yescharacteristic
299C42D4×D1111yescharacteristic
300C42D4×D1111yescharacteristic
301C42#434111yescharacteristic
302C11#926911yescharacteristic, complemented, Sylow
303C23—222no—
304C23C4×C22⋊D1111yescharacteristic
305Q8—82no—
306Q8—81no—
307Q8—81no—
308Q8—441no—
309Q8—441no—
310D4—442no—
311D4—442no—
312D4—442no—
313D4—441no—
314D4—441no—
315D4—441no—
316D4—441no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—82no—
322C2×C4—222no—
323C2×C4—442no—
324C2×C4—442no—
325C2×C4C22⋊C4×D1111yescharacteristic
326C2×C4(C22⋊D11)⋊C411yescharacteristic
327C2×C4#6693611yescharacteristic
328C2×C4#6693711yescharacteristic
329C2×C4#6699011yescharacteristic
330C2×C4#6699111yescharacteristic
331C2×C4C2×#432511yescharacteristic
332C2×C4#6699511yescharacteristic
333C2×C4#6700211yescharacteristic
334C2×C4#6700311yescharacteristic
335C8—22no—
336C8—41no—
337C8—81no—
338C8—442no—
339C8—441no—
340C8—441no—
341C8—881no—
342C22—21no—
343C22—21no—
344C22—442no—
345C22—442no—
346C22—442no—
347C22#1062256911yescharacteristic
348C22C4×#432511yescharacteristic
349C22#1062263911yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—82no—
354C4—442no—
355C4#1062236111yescharacteristic
356C4#1062236211yescharacteristic
357C4#1062265911yescharacteristic
358C4#1062266011yescharacteristic
359C4#1062267011yescharacteristic
360C4#1062269611yescharacteristic
361C2—21no—
362C2—21no—
363C2—882no—
364C2#1306895311yescharacteristic
365C2#1306912111yescharacteristic
366C2#1306916511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1997C2
socleC22×C11#386
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1997D11
hypocenterC11#9269
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
4. C2×#10622185C2semidirect
5. #13066511C2semidirect
6. #13066467C2semidirect
7. C11×#1997C2semidirect
122. #1997D11semidirect
302. C11#9269semidirect

Maximal subgroups

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

subgroupindex
#130797442
#130773622
#130672942
C2×#106221852
#130665112
#130664672
C11×#19972
#926911