Finite Group Databasebeta

← #14672929

Subgroups — #14672929

Order 2816.

498 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
1C2×#10622728C211yesmaximal, characteristic
2C2×#10622142C211yesmaximal, characteristic, complemented
3C2×#10622147C211yesmaximal, characteristic, complemented
4C2×#10622147C211yesmaximal, characteristic, complemented
5#13068645C211yesmaximal, characteristic, complemented
6#13066708C211yesmaximal, characteristic, complemented
7C2×C11×C22⋊C16C211yesmaximal, characteristic, complemented
8C23×C8×C11C2211yescharacteristic
9C2×#66983—21no—
10C22×D88C2211yescharacteristic
11C22×C11×C16C2211yescharacteristic
12C22×C11×C16C2211yescharacteristic
13#10622825—21no—
14#10622728—22no—
15#10622728—22no—
16C2×#66885—21no—
17C2×#66882C2211yescharacteristic
18C2×#66882C2211yescharacteristic
19C2×#66882C2211yescharacteristic
20C11×C22⋊C16—22no—
21#10622189—21no—
22#10622147—22no—
23#10622147—22no—
24#10622142—22no—
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—41no—
27C22×D44—21no—
28C22×C8×C11—21no—
29C22×C8×C11—21no—
30C22×C8×C11—21no—
31C22×C8×C11—21no—
32C22×C8×C11—21no—
33C22×C8×C11—21no—
34C22×C8×C11D411yescharacteristic
35C22×C8×C11C2311yescharacteristic
36C2×C22⋊Dic11—41no—
37#66983—24no—
38#66983—42no—
39C2×(C2×D11)⋊C4—41no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×D88—21no—
44C2×D88—21no—
45C2×D88—21no—
46C2×D88—21no—
47C2×D88—21no—
48C2×D88D412yes—
49C2×C11×C16—21no—
50C2×C11×C16—21no—
51C2×C11×C16—21no—
52C2×C11×C16—21no—
53C2×C11×C16—21no—
54C2×C11×C16D412yescomplemented
55C11⋊#95—41no—
56#66885—24no—
57#66882—21no—
58#66882—21no—
59#66882—21no—
60#66882—21no—
61#66882—21no—
62#66882D412yes—
63#13380—111nomaximal, Sylow
64C24×C11D811yescharacteristic
65C23×D11—41no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11D811yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—44no—
75C2×C22⋊D11—82no—
76C2×C22⋊D11—82no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C22×Dic11—41no—
80C2×D44—22no—
81C2×D44—41no—
82C2×D44—41no—
83C2×D44—41no—
84C2×D44—41no—
85C2×D44—41no—
86C2×C8×C11—21no—
87C2×C8×C11—21no—
88C2×C8×C11—21no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C2×C8×C11—41no—
92C2×C8×C11—41no—
93C2×C8×C11C2×D411yescharacteristic
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×D411yescharacteristic
96C2×C8×C11#4111yescharacteristic
97C2×C8×C11#4111yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C22⋊Dic11—82no—
100(C2×D11)⋊C4—44no—
101C4⋊Dic11—22no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C4⋊Dic11—41no—
105C4⋊Dic11—41no—
106C4⋊Dic11—41no—
107D88—22no—
108D88—22no—
109D88—41no—
110D88—41no—
111C11×C16—22no—
112C11×C16—41no—
113C2×#466—111no—
114C2×#366—111no—
115C2×#357—111no—
116C2×#357—111no—
117C2×C22⋊C16D1111yescharacteristic, complemented
118#1808—111no—
119#1380—111no—
120C23×C11—21no—
121C23×C11—21no—
122C23×C11—21no—
123C23×C11—21no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11D1612yes—
127C23×C11C2×D811yescharacteristic
128C22×D11—42no—
129C22×D11—81no—
130C22×D11—81no—
131C22×D11—81no—
132C22×D11—81no—
133C22×D11—81no—
134C22×D11—81no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11#12011yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12311yescharacteristic
145C2×C4×C11#13511yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11#13711yescharacteristic
148C22⋊D11—88no—
149C2×Dic11—42no—
150C2×Dic11—81no—
151C2×Dic11—81no—
152C2×Dic11—81no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158D44—42no—
159D44—42no—
160D44—81no—
161D44—81no—
162C8×C11—41no—
163C8×C11#12111yescharacteristic
164C8×C11#12111yescharacteristic
165C8×C11#12311yescharacteristic
166C8×C11#12411yescharacteristic
167C22×D8—111no—
168C23×C8C2×D1111yescharacteristic
169C2×#121—221no—
170C22×C16C2×D1111yescharacteristic
171C22×C16C2×D1111yescharacteristic
172#466—222no—
173#466—222no—
174C2×#107—111no—
175C2×#107—111no—
176C2×#107—111no—
177C2×#102—221no—
178#380—221no—
179#366—222no—
180#357—222no—
181#357—222no—
182C22⋊C16—22no—
183#340—221no—
184C22×C11—22no—
185C22×C11—22no—
186C22×C11—22no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11#44711yescharacteristic
192C22×C11#46611yescharacteristic
193C22×C11#48011yescharacteristic
194C22×C11C2×D1611yescharacteristic
195C22×C11#50811yescharacteristic
196C22×C11#50911yescharacteristic
197C22×C11#51011yescharacteristic
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—82no—
201C2×D11—161no—
202C2×D11—161no—
203C2×D11—161no—
204C2×D11—161no—
205C4×C11—41no—
206C4×C11#39411yescharacteristic
207C4×C11#45211yescharacteristic
208C4×C11#46811yescharacteristic
209C4×C11#48211yescharacteristic
210Dic11—82no—
211Dic11—161no—
212Dic11—161no—
213C22×D4—221no—
214C22×D4—441no—
215C23×C4D4411yescharacteristic
216C2×D8—112no—
217C2×D8—221no—
218C2×D8—221no—
219C2×D8—221no—
220C2×D8—221no—
221C2×D8—221no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8D4411yescharacteristic
229C22×C8C22×D1111yescharacteristic
230#121—224no—
231#121—442no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C22⋊C4—441no—
236C2×C22⋊C4—441no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16—21no—
241C2×C16—21no—
242C2×C16C22⋊D1112yescomplemented
243#107—112no—
244#107—221no—
245#107—221no—
246#107—221no—
247#107—221no—
248#107—221no—
249#102—224no—
250#95—441no—
251C2×C11—42no—
252C2×C11#203311yescharacteristic
253C2×C11#218411yescharacteristic
254C2×C11#218911yescharacteristic
255C2×C11#221511yescharacteristic
256C2×C11#222011yescharacteristic
257C2×C11#223211yescharacteristic
258C2×C11#223411yescharacteristic
259D11—162no—
260C24—441no—
261C24D8811yescharacteristic
262C2×D4—222no—
263C2×D4—444no—
264C2×D4—441no—
265C2×D4—441no—
266C2×D4—441no—
267C2×D4—441no—
268C2×D4—441no—
269C2×D4—882no—
270C2×D4—882no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—441no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4D8811yescharacteristic
281C22×C4C2×D4411yescharacteristic
282D8—222no—
283D8—222no—
284D8—441no—
285D8—441no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8#433911yescharacteristic
294C2×C8D4×D1111yescharacteristic
295C2×C8D4×D1111yescharacteristic
296C2×C8#434111yescharacteristic
297C2×C8#434111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C4⋊C4—222no—
300C4⋊C4—441no—
301C4⋊C4—441no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C22⋊C4—444no—
306C22⋊C4—882no—
307C16—22no—
308C16—41no—
309C11#1338011yescharacteristic, complemented, Sylow
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—442no—
317C23—881no—
318C23—881no—
319C23—881no—
320C23—881no—
321C23—881no—
322C23—881no—
323C23D17612yes—
324C23C2×D8811yescharacteristic
325D4—442no—
326D4—442no—
327D4—888no—
328D4—881no—
329D4—881no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—442no—
338C2×C4—881no—
339C2×C4—881no—
340C2×C4—881no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4#6693511yescharacteristic
347C2×C4#6693911yescharacteristic
348C2×C4#6695711yescharacteristic
349C2×C4#6696111yescharacteristic
350C2×C4#6696211yescharacteristic
351C2×C4#6698311yescharacteristic
352C8—41no—
353C8#6693611yescharacteristic
354C8#6693811yescharacteristic
355C8#6699111yescharacteristic
356C8#6699211yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—882no—
365C22—882no—
366C22—882no—
367C22—1761no—
368C22—1761no—
369C22—1761no—
370C22—1761no—
371C22#1062234511yescharacteristic
372C22#1062234911yescharacteristic
373C22C2×D17611yescharacteristic
374C22#1062251711yescharacteristic
375C22#1062252111yescharacteristic
376C22#1062252211yescharacteristic
377C22#1062272811yescharacteristic
378C4—41no—
379C4—882no—
380C4—1761no—
381C4—1761no—
382C4#1062234611yescharacteristic
383C4#1062235011yescharacteristic
384C4#1062257411yescharacteristic
385C4#1062274711yescharacteristic
386C2—42no—
387C2—1762no—
388C2#1306979911yescharacteristic
389C2#1307053011yescharacteristic
390C2#1307055811yescharacteristic
391C2#1307070211yescharacteristic
392C2#1307072911yescharacteristic
393C2#1307079711yescharacteristic
394C2#1307080811yescharacteristic
subgroupG/H
centerC23C2×D88
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×C22⋊C16C2
socleC23×C11C2×D8
prime radicalC2×#10622728C2
hypercenterC2×C22⋊C16D11
hypocenterC11#13380
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#10622142C2semidirect
3. C2×#10622147C2semidirect
4. C2×#10622147C2semidirect
5. #13068645C2semidirect
6. #13066708C2semidirect
7. C2×C11×C22⋊C16C2semidirect
54. C2×C11×C16D4semidirect
117. C2×C22⋊C16D11semidirect
242. C2×C16C22⋊D11semidirect
309. C11#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#106227282
C2×#106221422
C2×#106221472
#130686452
#130667082
C2×C11×C22⋊C162
#1338011