Finite Group Databasebeta

← #14673116

Subgroups — #14673116

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622764C211yesmaximal, characteristic
2C2×#10622147C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic, complemented
5#13069350C211yesmaximal, characteristic, complemented
6#13066693C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×#66993—21no—
10C22×#4323—21no—
11C22×D88C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14#10622764—22no—
15#10622764—22no—
16C2×#66882C2211yescharacteristic
17C2×C8×Dic11C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19#10622598—21no—
20C11×#357—22no—
21#10622200—22no—
22#10622167—21no—
23#10622147—22no—
24#10622129—22no—
25C22×D4×C11—21no—
26C22×C22⋊D11—41no—
27C22×C22⋊D11—41no—
28C22×D44—21no—
29C2×C11×D8—21no—
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8—21no—
34C2×C11×D8D412yes—
35C22×C8×C11C2311yescharacteristic
36C2×C11×C4⋊C4—21no—
37#66993—24no—
38#66993—42no—
39C2×#4323—24no—
40C2×#4323—42no—
41C2×#4323—42no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—41no—
44C2×C4×Dic11D411yescharacteristic
45C22×C11⋊C8D411yescharacteristic
46C2×D88—21no—
47C2×D88—21no—
48C2×D88—21no—
49C2×D88—21no—
50C2×D88—21no—
51C2×D88D412yes—
52C2×C11×C16—21no—
53C2×C11×C16—21no—
54C2×C11×C16—21no—
55C11×#107—21no—
56C11×#107D412yescomplemented
57C11⋊#95—41no—
58#66882—21no—
59#66882—21no—
60C8×Dic11—21no—
61C8×Dic11—21no—
62C2×C11⋊C16—21no—
63C2×C11⋊C16—21no—
64C2×C11⋊C16—21no—
65#13407—111nomaximal, Sylow
66C24×C11—41no—
67C23×D11—41no—
68C2×D4×C11—22no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C2×D4×C11—41no—
73C2×D4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—44no—
77C2×C22⋊D11—44no—
78C2×C22⋊D11—82no—
79C2×C22⋊D11—82no—
80C2×C22⋊D11—82no—
81C2×C22⋊D11—82no—
82C22×Dic11—41no—
83C22×Dic11D811yescharacteristic
84C22×Dic11D811yescharacteristic
85C2×D44—22no—
86C2×D44—41no—
87C2×D44—41no—
88C2×D44—41no—
89C2×D44—41no—
90C2×D44—41no—
91C11×D8—22no—
92C11×D8—22no—
93C11×D8—41no—
94C11×D8—41no—
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11#4111yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C11×C4⋊C4—22no—
102C11×C4⋊C4—41no—
103#4323—48no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—82no—
107C4×Dic11—21no—
108C4×Dic11—21no—
109C2×C11⋊C8—21no—
110C2×C11⋊C8—21no—
111C2×C11⋊C8SD1612yes—
112D88—22no—
113D88—22no—
114D88—41no—
115D88—41no—
116C11×C16—41no—
117C11⋊C16—41no—
118C2×#493—111no—
119C2×#357—111no—
120C2×#357—111no—
121C2×#357—111no—
122C2×#357D1111yescharacteristic, complemented
123#1942—111no—
124#1374—111no—
125C23×C11—42no—
126C23×C11—81no—
127C23×C11—81no—
128C23×C11—81no—
129C23×C11—81no—
130C23×C11—81no—
131C23×C11—81no—
132C23×C11C2×D811yescharacteristic
133C22×D11—42no—
134C22×D11—81no—
135C22×D11—81no—
136C22×D11—81no—
137C22×D11—81no—
138C22×D11—81no—
139C22×D11—81no—
140D4×C11—42no—
141D4×C11—42no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—42no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11#12011yescharacteristic
148C2×C4×C11#12111yescharacteristic
149C2×C4×C11#12411yescharacteristic
150C2×C4×C11C2×SD1611yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C22⋊D11—88no—
154C22⋊D11—88no—
155C2×Dic11—21no—
156C2×Dic11—21no—
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—81no—
160C2×Dic11—81no—
161C2×Dic11—81no—
162C2×Dic11D1612yes—
163C2×Dic11SD3212yes—
164D44—42no—
165D44—42no—
166D44—81no—
167D44—81no—
168C8×C11#12111yescharacteristic
169C8×C11#12111yescharacteristic
170C8×C11#12311yescharacteristic
171C8×C11#12311yescharacteristic
172C11⋊C8—22no—
173C22×D8—111no—
174C22×D8—221no—
175C22×D8C2×D1111yescharacteristic
176C2×#127—221no—
177C22×C16—111no—
178C22×C16C2×D1111yescharacteristic
179#493—222no—
180#493—222no—
181C2×#107—111no—
182C2×#107C2×D1111yescharacteristic
183C2×C4×C8—111no—
184#389—221no—
185#357—22no—
186#357—222no—
187#357—222no—
188#357—222no—
189#340—221no—
190C22×C11—82no—
191C22×C11—82no—
192C22×C11—82no—
193C22×C11—161no—
194C22×C11—161no—
195C22×C11—161no—
196C22×C11—161no—
197C22×C11#44711yescharacteristic
198C22×C11#45911yescharacteristic
199C22×C11#48611yescharacteristic
200C22×C11C2×D1611yescharacteristic
201C22×C11C2×SD3211yescharacteristic
202C22×C11#50911yescharacteristic
203C22×C11#50911yescharacteristic
204C2×D11—82no—
205C2×D11—82no—
206C2×D11—82no—
207C2×D11—161no—
208C2×D11—161no—
209C2×D11—161no—
210C2×D11—161no—
211C4×C11—82no—
212C4×C11#39411yescharacteristic
213C4×C11#45011yescharacteristic
214C4×C11#46011yescharacteristic
215C4×C11#49011yescharacteristic
216Dic11—22no—
217Dic11—22no—
218Dic11—161no—
219C22×D4—21no—
220C22×D4—221no—
221C22×D4—441no—
222C22×D4—441no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—112no—
229C2×D8—224no—
230C2×D8—221no—
231C2×D8—221no—
232C2×D8—221no—
233C2×D8—221no—
234C2×D8—221no—
235C2×D8—442no—
236C2×D8—442no—
237C2×D8D4412yes—
238C22×C8—111no—
239C22×C8C22×D1111yescharacteristic
240#127—224no—
241#127—442no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—221no—
244C2×C4⋊C4—441no—
245C2×C42—111no—
246C2×C16—21no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—221no—
250C2×C16—221no—
251C2×C16—221no—
252#107—21no—
253#107—221no—
254#107—221no—
255#107C22⋊D1112yescomplemented
256C4×C8—221no—
257C4×C8—221no—
258#95—441no—
259C2×C11—162no—
260C2×C11#204111yescharacteristic
261C2×C11#218411yescharacteristic
262C2×C11#218711yescharacteristic
263C2×C11#220611yescharacteristic
264C2×C11#220711yescharacteristic
265C2×C11#224011yescharacteristic
266C2×C11#224411yescharacteristic
267D11—162no—
268C24—41no—
269C24—441no—
270C2×D4—22no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—222no—
277C2×D4—444no—
278C2×D4—444no—
279C2×D4—441no—
280C2×D4—441no—
281C2×D4—441no—
282C2×D4—441no—
283C2×D4—441no—
284C2×D4—882no—
285C2×D4—882no—
286C2×D4—882no—
287C2×D4—882no—
288C22×C4—41no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—441no—
292C22×C4D4×D1111yescharacteristic
293D8—22no—
294D8—22no—
295D8—41no—
296D8—41no—
297D8—222no—
298D8—222no—
299D8—448no—
300D8—441no—
301D8—441no—
302C2×C8—112no—
303C2×C8—221no—
304C2×C8—221no—
305C2×C8C2×D4411yescharacteristic
306C2×C8#433911yescharacteristic
307C2×C8D4×D1111yescharacteristic
308C2×C8#434111yescharacteristic
309C2×C8#434111yescharacteristic
310C2×C8C2×C22⋊D1111yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—441no—
314C4⋊C4—441no—
315C4⋊C4—882no—
316C42—221no—
317C42—221no—
318C16—41no—
319C16—441no—
320C11#1340711yescharacteristic, complemented, Sylow
321C23—42no—
322C23—81no—
323C23—81no—
324C23—81no—
325C23—81no—
326C23—81no—
327C23—81no—
328C23—442no—
329C23—881no—
330C23—881no—
331C23—881no—
332C23—881no—
333C23—881no—
334C23—881no—
335C23D8×D1111yescharacteristic
336D4—42no—
337D4—42no—
338D4—81no—
339D4—81no—
340D4—442no—
341D4—442no—
342D4—888no—
343D4—888no—
344D4—881no—
345D4—881no—
346C2×C4—42no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—112no—
350C2×C4—112no—
351C2×C4—221no—
352C2×C4—221no—
353C2×C4—221no—
354C2×C4—221no—
355C2×C4—881no—
356C2×C4—881no—
357C2×C4—881no—
358C2×C4#6693511yescharacteristic
359C2×C4#6693811yescharacteristic
360C2×C4#6696411yescharacteristic
361C2×C4SD16×D1111yescharacteristic
362C2×C4#6696711yescharacteristic
363C2×C4#6699211yescharacteristic
364C8—222no—
365C8#6693611yescharacteristic
366C8#6693911yescharacteristic
367C8#6698311yescharacteristic
368C8#6699111yescharacteristic
369C22—82no—
370C22—82no—
371C22—82no—
372C22—161no—
373C22—161no—
374C22—161no—
375C22—161no—
376C22—882no—
377C22—882no—
378C22—882no—
379C22—1761no—
380C22—1761no—
381C22—1761no—
382C22—1761no—
383C22#1062237311yescharacteristic
384C22#1062238611yescharacteristic
385C22D11×D1611yescharacteristic
386C22#1062252411yescharacteristic
387C22D11×SD3211yescharacteristic
388C22#1062252711yescharacteristic
389C22#1062276311yescharacteristic
390C4—82no—
391C4—222no—
392C4—222no—
393C4—1761no—
394C4#1062237711yescharacteristic
395C4#1062238911yescharacteristic
396C4#1062257411yescharacteristic
397C4#1062277611yescharacteristic
398C2—162no—
399C2—1762no—
400C2#1306984911yescharacteristic
401C2#1307052911yescharacteristic
402C2#1307054611yescharacteristic
403C2#1307064911yescharacteristic
404C2#1307065411yescharacteristic
405C2#1307083811yescharacteristic
406C2#1307085611yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#357C2
socleC23×C11C2×D8
prime radicalC2×#10622764C2
hypercenterC2×#357D11
hypocenterC11#13407
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#10622147C2semidirect
3. C2×#10622200C2semidirect
4. C2×#10622129C2semidirect
5. #13069350C2semidirect
6. #13066693C2semidirect
7. C2×C11×#357C2semidirect
56. C11×#107D4semidirect
122. C2×#357D11semidirect
255. #107C22⋊D11semidirect
320. C11#13407semidirect

Maximal subgroups

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

subgroupindex
C2×#106227642
C2×#106221472
C2×#106222002
C2×#106221292
#130693502
#130666932
C2×C11×#3572
#1340711