Finite Group Databasebeta

← #14647713

Subgroups — #14647713

Order 2816.

516 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622451C211yesmaximal, characteristic
2#13069335C211yesmaximal, characteristic, complemented
3C4×#66873C211yesmaximal, characteristic
4C2×#10622117C211yesmaximal, characteristic, complemented
5C2×#10622097C211yesmaximal, characteristic
6C11⋊#1273C211yesmaximal, characteristic, complemented
7C11×#1279C211yesmaximal, characteristic, complemented
8C22×#4313—21no—
9C2×C4×D44C2211yescharacteristic
10C2×C11×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C11C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×#66873C411yescharacteristic
15C2×#66873C411yescharacteristic
16C2×C4⋊(C11⋊C8)—21no—
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20#10622451—22no—
21#10622451—22no—
22#10622167C411yescharacteristic
23#10622167C411yescharacteristic
24#10622162—21no—
25#10622117—22no—
26#10622097—22no—
27C22×D44C2×C411yescharacteristic
28C22×C4×D11—21no—
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4C2×C411yescharacteristic
33C2×C42×C11—21no—
34C2×C42×C11C2311yescharacteristic
35C2×(C2×D11)⋊C4—21no—
36C2×C4⋊Dic11C2×C411yescharacteristic
37C22×C11⋊C8—21no—
38C22×C11⋊C8C2×C411yescharacteristic
39C22×C11⋊C8C2×C411yescharacteristic
40C22×C11⋊C8D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42C2×#4313—24no—
43C2×#4313—42no—
44C2×#4313—42no—
45C4×D44—21no—
46C4×D44—21no—
47C4×D44D412yes—
48C4×D44Q812yes—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D412yes—
51C4×C8×C11—21no—
52C4×C8×C11—21no—
53C11×#95—21no—
54(C2×D11)⋊C8—24no—
55#66873—22no—
56#66873—22no—
57C4⋊(C11⋊C8)—21no—
58C4⋊(C11⋊C8)—21no—
59C4⋊(C11⋊C8)—42no—
60C4×C11⋊C8—21no—
61C4×C11⋊C8—21no—
62C4×C11⋊C8—21no—
63C4×C11⋊C8—21no—
64#8847—111nomaximal, Sylow
65C23×D11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C22×C411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11#4111yescharacteristic
71C22×Dic11—21no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44C4⋊C412yes—
78C2×C4×D11—22no—
79C2×C4×D11—22no—
80C2×C4×D11—41no—
81C2×C4×D11—41no—
82C2×C4×D11—41no—
83C2×C4×D11—41no—
84C2×C8×C11—22no—
85C2×C8×C11—22no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C2×C8×C11—41no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C11×C4⋊C4M1612yescomplemented
94C42×C11—41no—
95C42×C11—41no—
96C42×C11C2×D411yescharacteristic
97C42×C11C2×D411yescharacteristic
98C42×C11C2×Q811yescharacteristic
99C42×C11#4111yescharacteristic
100(C2×D11)⋊C4—22no—
101(C2×D11)⋊C4—22no—
102C4⋊Dic11—21no—
103C4⋊Dic11C4⋊C412yes—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—21no—
114C2×C11⋊C8—41no—
115C2×C11⋊C8—41no—
116C2×C11⋊C8—41no—
117C2×C11⋊C8M1612yescomplemented
118C2×C11⋊C8D812yes—
119#4313—48no—
120C2×#436—111no—
121#1939—111no—
122C4×#102—111no—
123C2×#335—111no—
124C2×D4⋊C8—111no—
125#1279D1111yescharacteristic, complemented
126#1273—111no—
127C23×C11C4×D411yescharacteristic
128C22×D11—22no—
129C22×D11—41no—
130C22×D11—41no—
131C22×D11—41no—
132C22×D11—41no—
133C22×D11—41no—
134C22×D11—41no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—22no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11C2×C4⋊C411yescharacteristic
144C2×C4×C11C4×D411yescharacteristic
145C2×C4×C11#12011yescharacteristic
146C2×C4×C11C22⋊Q811yescharacteristic
147C2×C4×C11C22⋊Q811yescharacteristic
148C2×C4×C11#12311yescharacteristic
149C2×C4×C11C2×M1611yescharacteristic
150C2×C4×C11C2×M1611yescharacteristic
151C2×C4×C11#13111yescharacteristic
152C2×C4×C11#13111yescharacteristic
153C2×C4×C11C2×D811yescharacteristic
154C2×C4×C11#13511yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11#13711yescharacteristic
157C2×Dic11—22no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160D44—22no—
161D44—22no—
162D44—41no—
163D44—41no—
164C4×D11—42no—
165C4×D11—42no—
166C4×D11—42no—
167C4×D11—42no—
168C8×C11—42no—
169C8×C11—42no—
170C11⋊C8—22no—
171C11⋊C8—22no—
172C11⋊C8—41no—
173C11⋊C8—41no—
174C11⋊C8—81no—
175C22×M16—221no—
176C2×C4×D4—111no—
177#436—222no—
178#436—222no—
179C2×C4⋊C8—111no—
180C2×C4⋊C8—221no—
181C2×C4⋊C8C2×D1111yescharacteristic
182C2×#102—111no—
183C2×#102—111no—
184C2×C22⋊C8—221no—
185C2×C4×C8—111no—
186C2×C4×C8—111no—
187C2×C4×C8C2×D1111yescharacteristic
188C4×C4⋊C4C2×D1111yescharacteristic
189#340—111no—
190#340—111no—
191#336—221no—
192#335—222no—
193D4⋊C8—222no—
194C22×C11#38511yescharacteristic
195C22×C11#43511yescharacteristic
196C22×C11#43611yescharacteristic
197C22×C11C4×D811yescharacteristic
198C22×C11#44011yescharacteristic
199C22×C11#44311yescharacteristic
200C22×C11#44411yescharacteristic
201C2×D11—42no—
202C2×D11—42no—
203C2×D11—42no—
204C2×D11—81no—
205C2×D11—81no—
206C2×D11—81no—
207C2×D11—81no—
208C4×C11—21no—
209C4×C11—21no—
210C4×C11—42no—
211C4×C11—81no—
212C4×C11#42311yescharacteristic
213C4×C11#42411yescharacteristic
214C4×C11#43511yescharacteristic
215C4×C11#43611yescharacteristic
216C4×C11#44711yescharacteristic
217C4×C11#45211yescharacteristic
218C4×C11#47411yescharacteristic
219C4×C11#47811yescharacteristic
220Dic11—42no—
221C22×D4—111no—
222C23×C4—221no—
223C2×M16—224no—
224C2×M16—442no—
225C2×M16—442no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—111no—
229C22×C8—111no—
230C22×C8—111no—
231C22×C8—111no—
232C22×C8—221no—
233C4×D4—112no—
234C4×D4—112no—
235C4×D4—221no—
236C4×D4—221no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4C4×D1111yescharacteristic
239C2×C4⋊C4C4×D1111yescharacteristic
240C2×C22⋊C4—221no—
241C2×C42—21no—
242C2×C42C22×D1111yescharacteristic
243C4⋊C8—21no—
244C4⋊C8—221no—
245C4⋊C8—221no—
246C4⋊C8—442no—
247C4⋊C8D4412yes—
248#102—222no—
249#102—222no—
250C22⋊C8—224no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—221no—
254C4×C8—221no—
255C4×C8—221no—
256C4×C8—221no—
257#95—21no—
258C2×C11#158111yescharacteristic
259C2×C11#158811yescharacteristic
260C2×C11#158911yescharacteristic
261C2×C11#159211yescharacteristic
262C2×C11#185111yescharacteristic
263C2×C11#186211yescharacteristic
264C2×C11#186611yescharacteristic
265D11—82no—
266C24—221no—
267C2×D4—112no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—221no—
276C22×C4—222no—
277C22×C4—222no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4—441no—
282C22×C4C2×C4×D1111yescharacteristic
283C22×C4D4×D1111yescharacteristic
284C22×C4#434111yescharacteristic
285M16—448no—
286C2×C8—22no—
287C2×C8—22no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—112no—
293C2×C8—112no—
294C2×C8—221no—
295C2×C8—221no—
296C2×C8—221no—
297C2×C8—221no—
298C2×C8—221no—
299C2×C8—221no—
300C2×C8—221no—
301C2×C8—221no—
302C2×C8—221no—
303C2×C8—221no—
304C2×C8—441no—
305C2×C8—441no—
306C2×C8—441no—
307C4⋊C4—21no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—112no—
311C4⋊C4—221no—
312C4⋊C4#431312yescomplemented
313C22⋊C4—222no—
314C22⋊C4—222no—
315C42—41no—
316C42—41no—
317C42C2×D4411yescharacteristic
318C42#433911yescharacteristic
319C42D4×D1111yescharacteristic
320C42Q8×D1111yescharacteristic
321C11#884711yescharacteristic, complemented, Sylow
322C23—222no—
323C23—441no—
324C23—441no—
325C23—441no—
326C23—441no—
327C23—441no—
328C23—441no—
329C23(C22⋊D11)⋊C411yescharacteristic
330D4—222no—
331D4—222no—
332D4—441no—
333D4—441no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—222no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—442no—
348C2×C4—442no—
349C2×C4C4×D4411yescharacteristic
350C2×C4#6693511yescharacteristic
351C2×C4#6693611yescharacteristic
352C2×C4C4⋊C4×D1111yescharacteristic
353C2×C4#6694911yescharacteristic
354C2×C4#6695011yescharacteristic
355C2×C4C2×#431311yescharacteristic
356C2×C4#6695411yescharacteristic
357C2×C4M16×D1111yescharacteristic
358C2×C4#6696011yescharacteristic
359C2×C4D8×D1111yescharacteristic
360C2×C4#6696711yescharacteristic
361C2×C4#6696911yescharacteristic
362C2×C4#6697111yescharacteristic
363C8—42no—
364C8—42no—
365C8—222no—
366C8—222no—
367C8—441no—
368C8—441no—
369C8—881no—
370C22—442no—
371C22—442no—
372C22—442no—
373C22—881no—
374C22—881no—
375C22—881no—
376C22—881no—
377C22#1062228111yescharacteristic
378C22#1062234211yescharacteristic
379C22#1062234311yescharacteristic
380C22#1062236911yescharacteristic
381C22#1062243011yescharacteristic
382C22#1062243611yescharacteristic
383C22#1062243711yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—81no—
388C4—442no—
389C4#1062230111yescharacteristic
390C4#1062231911yescharacteristic
391C4#1062238611yescharacteristic
392C4#1062242311yescharacteristic
393C4#1062245011yescharacteristic
394C4#1062245211yescharacteristic
395C4#1062248411yescharacteristic
396C4#1062250311yescharacteristic
397C2—882no—
398C2#1306744211yescharacteristic
399C2#1306749111yescharacteristic
400C2#1306749811yescharacteristic
401C2#1306752111yescharacteristic
402C2#1306880011yescharacteristic
403C2#1306886411yescharacteristic
404C2#1306889211yescharacteristic
subgroupG/H
centerC22×C4D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1279C2
socleC23×C11C4×D4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1279D11
hypocenterC11#8847
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
2. #13069335C2semidirect
4. C2×#10622117C2semidirect
6. C11⋊#1273C2semidirect
7. C11×#1279C2semidirect
93. C11×C4⋊C4M16semidirect
117. C2×C11⋊C8M16semidirect
125. #1279D11semidirect
312. C4⋊C4#4313semidirect
321. C11#8847semidirect

Maximal subgroups

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

subgroupindex
C2×#106224512
#130693352
C4×#668732
C2×#106221172
C2×#106220972
C11⋊#12732
C11×#12792
#884711