Finite Group Databasebeta

← #14650290

Subgroups — #14650290

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#13079741C211yesmaximal, characteristic
2#13069605C211yesmaximal, characteristic, complemented
3#13067293C211yesmaximal, characteristic
4C2×#10622124C211yesmaximal, characteristic, complemented
5#13066513C211yesmaximal, characteristic, complemented
6#13066467C211yesmaximal, characteristic, complemented
7C11×#2935C211yesmaximal, characteristic
8C2×C11×#131—21no—
9C11×#532C2211yescharacteristic
10C2×#66922C2211yescharacteristic
11C11×#436—21no—
12C11×#435—22no—
13C8×D4×C11—21no—
14C2×C11×C4⋊C8C2211yescharacteristic
15C11×#408—21no—
16C4×C11×M16C2211yescharacteristic
17#10622692—21no—
18#10622683—21no—
19#10622647C414yes—
20#10622621—22no—
21#10622538C2211yescharacteristic
22#10622537C2211yescharacteristic
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24#10622192—21no—
25#10622192—21no—
26#10622185—21no—
27#10622182—21no—
28#10622124—21no—
29#10622124—21no—
30C2×C11×#41—21no—
31C22×Dic22—21no—
32C11×#131—42no—
33C11×#131—42no—
34C2×C11×M16—22no—
35C2×C11×M16D411yescharacteristic
36C2×C11×M16D411yescharacteristic
37C22×C8×C11—22no—
38C22×C8×C11—21no—
39C11×C4⋊Q8D411yescharacteristic
40C11×#127D411yescharacteristic
41C11×#124—21no—
42C11×#121—21no—
43C11×#121C2×C412yes—
44C4×D4×C11—21no—
45C4×D4×C11D412yes—
46C2×C42×C11C2311yescharacteristic
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11C2×C412yes—
49C2×#4318—21no—
50C22×C11⋊C8—21no—
51#66922—21no—
52#66922—21no—
53#66922—21no—
54#66922—21no—
55C11×C4⋊C8—21no—
56C11×C4⋊C8D411yescharacteristic
57C11×C4⋊C8D411yescharacteristic
58C11×C22⋊C8—22no—
59C11×C22⋊C8—22no—
60C11×#97—21no—
61C4×C8×C11—21no—
62#66896—24no—
63C22⋊(C11⋊C8)C2×C412yes—
64#66872—24no—
65C4⋊(C11⋊C8)—21no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4×C11⋊C8—21no—
71#9269—111nomaximal, Sylow
72C11×#41—41no—
73C11×#41—41no—
74C11×#41—41no—
75C11×#41—41no—
76C2×Q8×C11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—21no—
79C2×D4×C11—21no—
80C2×D4×C11C22⋊C412yes—
81C22×C4×C11—22no—
82C22×C4×C11C22×C411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—22no—
86C2×Dic22—41no—
87C2×Dic22—41no—
88C2×Dic22—81no—
89C2×Dic22—81no—
90C11×M16—21no—
91C11×M16—21no—
92C11×M16—21no—
93C11×M16—44no—
94C11×M16SD1612yes—
95C2×C8×C11—21no—
96C2×C8×C11—21no—
97C2×C8×C11—21no—
98C2×C8×C11—21no—
99C2×C8×C11—44no—
100C2×C8×C11—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4C22⋊C412yes—
104C11×C22⋊C4—22no—
105C11×C22⋊C4—22no—
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C42×C11#4111yescharacteristic
110C4⋊Dic11—22no—
111C4⋊Dic11—22no—
112C4⋊Dic11—41no—
113C4⋊Dic11—41no—
114#4318—41no—
115#4318—41no—
116C2×C11⋊C8—22no—
117C2×C11⋊C8—41no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8—81no—
120#3227—111no—
121#2935D1111yescharacteristic
122#1997—111no—
123#1547—111no—
124C2×#332—111no—
125#1301—111no—
126#1283—111no—
127C23×C11—22no—
128C23×C11C4×D411yescharacteristic
129Q8×C11—41no—
130Q8×C11—41no—
131D4×C11—42no—
132D4×C11—42no—
133D4×C11—42no—
134D4×C11—41no—
135D4×C11—41no—
136D4×C11—41no—
137D4×C11—41no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—22no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11—42no—
144C2×C4×C11C2×C22⋊C411yescharacteristic
145C2×C4×C11C4×D411yescharacteristic
146C2×C4×C11#12011yescharacteristic
147C2×C4×C11#12111yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12311yescharacteristic
150C2×C4×C11C2×SD1611yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C2×Dic11—42no—
155C2×Dic11—82no—
156Dic22—82no—
157Dic22—81no—
158Dic22—81no—
159C8×C11—22no—
160C8×C11—41no—
161C8×C11—41no—
162C8×C11—41no—
163C11⋊C8—42no—
164C11⋊C8—81no—
165C11⋊C8—81no—
166C2×#131—21no—
167#532C2×D1111yescharacteristic
168C2×C4⋊Q8—111no—
169#498—221no—
170#486—221no—
171#481—114no—
172#476—222no—
173#436—21no—
174#435—22no—
175C8×D4—21no—
176#431—111no—
177#423—111no—
178C2×C4⋊C8—111no—
179C2×C4⋊C8C2×D1111yescharacteristic
180#408—21no—
181C4×M16C2×D1111yescharacteristic
182#343—221no—
183#343—221no—
184#332—221no—
185#332—221no—
186#332—221no—
187#331—221no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—42no—
191C22×C11—42no—
192C22×C11—42no—
193C22×C11#38611yescharacteristic
194C22×C11C4×SD1611yescharacteristic
195C22×C11#44011yescharacteristic
196C4×C11—21no—
197C4×C11—21no—
198C4×C11—21no—
199C4×C11—42no—
200C4×C11#45011yescharacteristic
201C4×C11#45211yescharacteristic
202C4×C11#46111yescharacteristic
203C4×C11#46311yescharacteristic
204C4×C11#47111yescharacteristic
205C4×C11#47211yescharacteristic
206Dic11—82no—
207C2×#41—21no—
208C22×Q8—221no—
209#131—42no—
210#131—42no—
211C2×M16—22no—
212C2×M16—221no—
213C2×M16C22⋊D1111yescharacteristic
214C2×M16C22⋊D1111yescharacteristic
215C22×C8—22no—
216C22×C8—21no—
217C22×C8—221no—
218C4⋊Q8—221no—
219C4⋊Q8—221no—
220C4⋊Q8—221no—
221C4⋊Q8—221no—
222C4⋊Q8D4411yescharacteristic
223#127D4411yescharacteristic
224#124—21no—
225#121—21no—
226#121C4×D1112yes—
227C4×D4—21no—
228C4×D4C22⋊D1112yes—
229C2×C4⋊C4—112no—
230C2×C4⋊C4—221no—
231C2×C42C22×D1111yescharacteristic
232#106—224no—
233C4⋊C8—21no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C4⋊C8—221no—
237C4⋊C8—221no—
238C4⋊C8—221no—
239C4⋊C8C22⋊D1111yescharacteristic
240C4⋊C8C22⋊D1111yescharacteristic
241#102—224no—
242C22⋊C8—22no—
243C22⋊C8—22no—
244C22⋊C8—112no—
245#97—21no—
246C4×C8—21no—
247C4×C8—221no—
248C2×C11—21no—
249C2×C11—21no—
250C2×C11—82no—
251C2×C11#187711yescharacteristic
252C2×C11#190711yescharacteristic
253C2×C11#191511yescharacteristic
254#41—41no—
255#41—41no—
256#41—41no—
257#41—41no—
258C2×Q8—21no—
259C2×Q8—441no—
260C2×Q8—441no—
261C2×Q8—881no—
262C2×Q8—881no—
263C2×D4—22no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4(C2×D11)⋊C412yes—
267C22×C4—22no—
268C22×C4—222no—
269C22×C4C2×C4×D1111yescharacteristic
270C22×C4#433911yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272M16—21no—
273M16—21no—
274M16—21no—
275M16—44no—
276M16—441no—
277M16—441no—
278M16#432412yes—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—44no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—222no—
287C2×C8—441no—
288C2×C8—441no—
289C2×C8—881no—
290C4⋊C4—21no—
291C4⋊C4—222no—
292C4⋊C4—222no—
293C4⋊C4—441no—
294C4⋊C4—441no—
295C4⋊C4(C2×D11)⋊C412yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C42C2×D4411yescharacteristic
299C42#433911yescharacteristic
300C42C2×C22⋊D1111yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C11#926911yescharacteristic, complemented, Sylow
303C23—22no—
304C23C4×C22⋊D1111yescharacteristic
305Q8—41no—
306Q8—41no—
307Q8—882no—
308Q8—881no—
309Q8—881no—
310D4—42no—
311D4—42no—
312D4—42no—
313D4—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—442no—
324C2×C4—882no—
325C2×C4C2×(C2×D11)⋊C411yescharacteristic
326C2×C4C4×C22⋊D1111yescharacteristic
327C2×C4#6698211yescharacteristic
328C2×C4#6698311yescharacteristic
329C2×C4#6698311yescharacteristic
330C2×C4#6698511yescharacteristic
331C2×C4C2×#432411yescharacteristic
332C2×C4#6700311yescharacteristic
333C2×C4#6700411yescharacteristic
334C2×C4#6700611yescharacteristic
335C8—22no—
336C8—41no—
337C8—41no—
338C8—41no—
339C8—442no—
340C8—881no—
341C8—881no—
342C22—21no—
343C22—21no—
344C22—42no—
345C22—42no—
346C22—42no—
347C22C4×#432411yescharacteristic
348C22#1062263111yescharacteristic
349C22#1062282611yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—42no—
354C4—882no—
355C4#1062262911yescharacteristic
356C4#1062263211yescharacteristic
357C4#1062275411yescharacteristic
358C4#1062275511yescharacteristic
359C4#1062283111yescharacteristic
360C4#1062285211yescharacteristic
361C2—21no—
362C2—21no—
363C2—82no—
364C2#1306895011yescharacteristic
365C2#1306912411yescharacteristic
366C2#1306916811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2935C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#2935D11
hypocenterC11#9269
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
2. #13069605C2semidirect
4. C2×#10622124C2semidirect
5. #13066513C2semidirect
6. #13066467C2semidirect
302. C11#9269semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130696052
#130672932
C2×#106221242
#130665132
#130664672
C11×#29352
#926911