Finite Group Databasebeta

← #14651981

Subgroups — #14651981

Order 2816.

444 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069410C211yesmaximal, characteristic
2C4×#66873C211yesmaximal, characteristic
3C2×#10622118C211yesmaximal, characteristic, complemented
4C2×#10622121C211yesmaximal, characteristic
5#13066457C211yesmaximal, characteristic, complemented
6C11⋊#1273C211yesmaximal, characteristic, complemented
7C11×#1770C211yesmaximal, characteristic, complemented
8C2×C4×D44C2211yescharacteristic
9C2×C11×C4⋊C8C2211yescharacteristic
10C2×C11×#97—21no—
11C2×C4×C8×C11C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×(C2×D11)⋊C8—21no—
14C2×(C2×D11)⋊C8—21no—
15C2×#66873C411yescharacteristic
16C2×#66873C411yescharacteristic
17C2×C4⋊(C11⋊C8)C2211yescharacteristic
18C2×C4×C11⋊C8C2211yescharacteristic
19C2×C4×C11⋊C8C2211yescharacteristic
20C11×#336—21no—
21#10622167C411yescharacteristic
22#10622167C411yescharacteristic
23#10622121—22no—
24#10622118—22no—
25C22×D44C2×C411yescharacteristic
26C22×C4×D11—21no—
27C22×C8×C11—21no—
28C22×C8×C11D411yescharacteristic
29C22×C8×C11D411yescharacteristic
30C2×C11×C4⋊C4C2×C411yescharacteristic
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C42×C11—21no—
33C2×C42×C11C2311yescharacteristic
34C2×(C2×D11)⋊C4—21no—
35C2×C4⋊Dic11C2×C411yescharacteristic
36C22×C11⋊C8—21no—
37C22×C11⋊C8—21no—
38C22×C11⋊C8C2×C411yescharacteristic
39C22×C11⋊C8C2×C411yescharacteristic
40C4×D44—21no—
41C4×D44—21no—
42C4×D44—21no—
43C4×D44—21no—
44C11×C4⋊C8—21no—
45C11×C4⋊C8D412yes—
46C11×#97—42no—
47C4×C8×C11—21no—
48C4×C8×C11—21no—
49C11×#95—21no—
50(C2×D11)⋊C8—42no—
51(C2×D11)⋊C8—42no—
52#66873—22no—
53#66873—22no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4×C11⋊C8—21no—
57C4×C11⋊C8—21no—
58C4×C11⋊C8—21no—
59C4×C11⋊C8—21no—
60#9546—111nomaximal, Sylow
61C23×D11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11C22×C411yescharacteristic
65C22×C4×C11C2×D411yescharacteristic
66C22×C4×C11#4111yescharacteristic
67C22×Dic11—21no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44M1612yes—
74C2×C4×D11—41no—
75C2×C4×D11—41no—
76C2×C4×D11—41no—
77C2×C4×D11—41no—
78C2×C4×D11—41no—
79C2×C4×D11—41no—
80C2×C8×C11—22no—
81C2×C8×C11—21no—
82C2×C8×C11—21no—
83C2×C8×C11—21no—
84C2×C8×C11—21no—
85C2×C8×C11—21no—
86C2×C8×C11—41no—
87C2×C8×C11—41no—
88C2×C8×C11SD1612yes—
89C11×C4⋊C4—21no—
90C11×C4⋊C4—21no—
91C11×C4⋊C4—21no—
92C11×C4⋊C4—21no—
93C42×C11—41no—
94C42×C11—41no—
95C42×C11C2×D411yescharacteristic
96C42×C11#4111yescharacteristic
97C42×C11#4111yescharacteristic
98C42×C11#4111yescharacteristic
99(C2×D11)⋊C4—41no—
100(C2×D11)⋊C4—41no—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C2×C11⋊C8—22no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C2×C11⋊C8—21no—
108C2×C11⋊C8—21no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8—41no—
112C2×C11⋊C8—41no—
113C2×C11⋊C8—41no—
114C2×C11⋊C8M1612yes—
115#1954—111no—
116#1770D1111yescharacteristic, complemented
117C4×#102—111no—
118C2×#334—111no—
119C2×D4⋊C8—111no—
120#1279—111no—
121#1273—111no—
122C23×C11C4×D411yescharacteristic
123C22×D11—22no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127C22×D11—41no—
128C22×D11—41no—
129C22×D11—41no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11#11711yescharacteristic
139C2×C4×C11C4×D411yescharacteristic
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12311yescharacteristic
142C2×C4×C11#12411yescharacteristic
143C2×C4×C11#12611yescharacteristic
144C2×C4×C11C2×M1611yescharacteristic
145C2×C4×C11C2×M1611yescharacteristic
146C2×C4×C11#13111yescharacteristic
147C2×C4×C11#13111yescharacteristic
148C2×C4×C11C2×SD1611yescharacteristic
149C2×C4×C11#13511yescharacteristic
150C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155D44—22no—
156D44—22no—
157D44—41no—
158D44—41no—
159C4×D11—81no—
160C4×D11—81no—
161C4×D11—81no—
162C4×D11—81no—
163C8×C11—22no—
164C8×C11—42no—
165C8×C11—41no—
166C11⋊C8—22no—
167C11⋊C8—42no—
168C11⋊C8—41no—
169C11⋊C8—81no—
170C2×C4×D4—111no—
171C2×C4⋊C8—111no—
172C2×C4⋊C8C2×D1111yescharacteristic
173C2×#102—111no—
174C2×#102—111no—
175C2×C22⋊C8—221no—
176C2×C22⋊C8—221no—
177C2×#97—21no—
178C2×C4×C8—111no—
179C2×C4×C8—111no—
180C2×C4×C8C2×D1111yescharacteristic
181C4×C4⋊C4C2×D1111yescharacteristic
182#340—111no—
183#340—111no—
184#336—21no—
185#334—222no—
186D4⋊C8—222no—
187C22×C11#38811yescharacteristic
188C22×C11#43511yescharacteristic
189C22×C11#43611yescharacteristic
190C22×C11C4×SD1611yescharacteristic
191C22×C11#44211yescharacteristic
192C22×C11#44311yescharacteristic
193C22×C11#44411yescharacteristic
194C2×D11—42no—
195C2×D11—42no—
196C2×D11—42no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—81no—
204C4×C11—81no—
205C4×C11#43211yescharacteristic
206C4×C11#43311yescharacteristic
207C4×C11#43511yescharacteristic
208C4×C11#43511yescharacteristic
209C4×C11#46011yescharacteristic
210C4×C11#46311yescharacteristic
211C4×C11#48111yescharacteristic
212C4×C11#48211yescharacteristic
213Dic11—81no—
214C22×D4—111no—
215C23×C4—221no—
216C22×C8—21no—
217C22×C8—111no—
218C22×C8—111no—
219C22×C8—221no—
220C22×C8—221no—
221C22×C8C22⋊D1111yescharacteristic
222C22×C8C22⋊D1111yescharacteristic
223C4×D4—221no—
224C4×D4—221no—
225C4×D4—221no—
226C4×D4—221no—
227C2×C4⋊C4—111no—
228C2×C4⋊C4C4×D1111yescharacteristic
229C2×C4⋊C4C4×D1111yescharacteristic
230C2×C22⋊C4—221no—
231C2×C42—21no—
232C2×C42C22×D1111yescharacteristic
233C4⋊C8—21no—
234C4⋊C8—221no—
235C4⋊C8—221no—
236C4⋊C8D4412yes—
237#102—222no—
238#102—222no—
239C22⋊C8—442no—
240C22⋊C8—442no—
241#97—42no—
242C4×C8—21no—
243C4×C8—21no—
244C4×C8—221no—
245C4×C8—221no—
246C4×C8—221no—
247C4×C8—221no—
248#95—21no—
249C2×C11#158211yescharacteristic
250C2×C11#158611yescharacteristic
251C2×C11#159011yescharacteristic
252C2×C11#159411yescharacteristic
253C2×C11#192411yescharacteristic
254C2×C11#192611yescharacteristic
255C2×C11#192911yescharacteristic
256D11—82no—
257C24—221no—
258C2×D4—112no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—221no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—221no—
267C22×C4—441no—
268C22×C4—441no—
269C22×C4—441no—
270C22×C4—441no—
271C22×C4—441no—
272C22×C4—441no—
273C22×C4C2×C4×D1111yescharacteristic
274C22×C4#433911yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—22no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—112no—
285C2×C8—221no—
286C2×C8—221no—
287C2×C8—222no—
288C2×C8—221no—
289C2×C8—221no—
290C2×C8—221no—
291C2×C8—441no—
292C2×C8—441no—
293C2×C8—441no—
294C2×C8—441no—
295C2×C8—441no—
296C2×C8#432512yes—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C22⋊C4—441no—
304C22⋊C4—441no—
305C42—41no—
306C42—41no—
307C42C2×D4411yescharacteristic
308C42#433911yescharacteristic
309C42#433911yescharacteristic
310C42#433911yescharacteristic
311C11#954611yescharacteristic, complemented, Sylow
312C23—222no—
313C23—441no—
314C23—441no—
315C23—441no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23C4×C22⋊D1111yescharacteristic
320D4—222no—
321D4—222no—
322D4—441no—
323D4—441no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—441no—
333C2×C4—441no—
334C2×C4—441no—
335C2×C4—881no—
336C2×C4—881no—
337C2×C4—881no—
338C2×C4—881no—
339C2×C4#6692511yescharacteristic
340C2×C4C4×D4411yescharacteristic
341C2×C4#6692811yescharacteristic
342C2×C4#6692911yescharacteristic
343C2×C4M16×D1111yescharacteristic
344C2×C4M16×D1111yescharacteristic
345C2×C4#6696011yescharacteristic
346C2×C4#6696011yescharacteristic
347C2×C4#6698211yescharacteristic
348C2×C4#6698311yescharacteristic
349C2×C4#6698511yescharacteristic
350C2×C4C2×#432511yescharacteristic
351C2×C4#6700211yescharacteristic
352C2×C4#6700311yescharacteristic
353C8—22no—
354C8—41no—
355C8—42no—
356C8—222no—
357C8—442no—
358C8—441no—
359C8—881no—
360C22—442no—
361C22—442no—
362C22—442no—
363C22—881no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22#1062255311yescharacteristic
368C22#1062262711yescharacteristic
369C22C4×#432511yescharacteristic
370C22#1062274011yescharacteristic
371C22#1062274111yescharacteristic
372C22#1062275711yescharacteristic
373C22#1062275811yescharacteristic
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—881no—
379C4#1062231811yescharacteristic
380C4#1062231911yescharacteristic
381C4#1062231911yescharacteristic
382C4#1062232211yescharacteristic
383C4#1062258111yescharacteristic
384C4#1062261611yescharacteristic
385C4#1062262911yescharacteristic
386C4#1062264011yescharacteristic
387C2—882no—
388C2#1306745011yescharacteristic
389C2#1306747811yescharacteristic
390C2#1306750611yescharacteristic
391C2#1306752811yescharacteristic
392C2#1306922911yescharacteristic
393C2#1306924311yescharacteristic
394C2#1306926411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1770C2
socleC23×C11C4×D4
prime radicalC22×D44C2×C4
cosocleC2×C42×C11C23
hypercenter#1770D11
hypocenterC11#9546
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1770

Complements

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

NH ≅ G/Ntype
3. C2×#10622118C2semidirect
5. #13066457C2semidirect
6. C11⋊#1273C2semidirect
7. C11×#1770C2semidirect
116. #1770D11semidirect
311. C11#9546semidirect

Maximal subgroups

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

subgroupindex
#130694102
C4×#668732
C2×#106221182
C2×#106221212
#130664572
C11⋊#12732
C11×#17702
#954611