Finite Group Databasebeta

← #14672928

Subgroups — #14672928

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×#10622127C211yesmaximal, characteristic, complemented
3C2×#10622129C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic, complemented
5C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C11×#1808C211yesmaximal, characteristic, complemented
8C23×C8×C11C2211yescharacteristic
9C2×#66983—21no—
10C22×D88C2211yescharacteristic
11C2×C11×#107C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C11×#380—21no—
14#10622728—22no—
15#10622728—22no—
16C2×#66885—21no—
17C2×#66882C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19C22×C11⋊C16C2211yescharacteristic
20C11×#340—21no—
21C22⋊(C11⋊C16)—22no—
22#10622129—22no—
23#10622129—22no—
24#10622127—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×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C22⋊C4—41no—
39#66983—24no—
40#66983—42no—
41C2×(C2×D11)⋊C4—41no—
42C2×C4⋊Dic11—21no—
43C2×D88—21no—
44C2×D88—21no—
45C2×D88—21no—
46C2×D88—21no—
47C2×D88—21no—
48C2×D88D412yes—
49C11×#107—21no—
50C11×#107—21no—
51C11×#107—21no—
52C11×#107—21no—
53C11×#95—41no—
54#66885—24no—
55#66882—21no—
56#66882D412yes—
57C2×C11⋊C16—21no—
58C2×C11⋊C16—21no—
59C2×C11⋊C16—21no—
60C2×C11⋊C16—21no—
61C2×C11⋊C16—21no—
62C2×C11⋊C16D412yescomplemented
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×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11D811yescharacteristic
75C22×C4×C11C2×D411yescharacteristic
76C2×C22⋊D11—44no—
77C2×C22⋊D11—82no—
78C2×C22⋊D11—82no—
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
99C11×C4⋊C4—41no—
100C11×C4⋊C4—41no—
101C11×C4⋊C4—41no—
102C11×C4⋊C4—41no—
103C11×C22⋊C4—82no—
104(C2×D11)⋊C4—44no—
105C4⋊Dic11—22no—
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⋊C16—111no—
118#1808D1111yescharacteristic, complemented
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—81no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11—81no—
147C2×C4×C11—81no—
148C2×C4×C11#12011yescharacteristic
149C2×C4×C11#12111yescharacteristic
150C2×C4×C11#12311yescharacteristic
151C2×C4×C11#13511yescharacteristic
152C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C11#13711yescharacteristic
154C22⋊D11—88no—
155C2×Dic11—42no—
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×C16—111no—
171C22×C16—111no—
172#466—222no—
173#466—222no—
174C2×#107—111no—
175C2×#107C2×D1111yescharacteristic
176C2×#107C2×D1111yescharacteristic
177C2×#102—221no—
178#380—21no—
179#366—222no—
180#357—222no—
181#357—222no—
182C22⋊C16—222no—
183#340—21no—
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—161no—
207C4×C11—161no—
208C4×C11#39411yescharacteristic
209C4×C11#45211yescharacteristic
210C4×C11#46811yescharacteristic
211C4×C11#48211yescharacteristic
212Dic11—82no—
213C22×D4—221no—
214C22×D4—441no—
215C23×C4C22⋊D1111yescharacteristic
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×C8C22⋊D1111yescharacteristic
229C22×C8C22×D1111yescharacteristic
230#121—224no—
231#121—442no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—221no—
235C2×C22⋊C4—41no—
236C2×C22⋊C4—441no—
237C2×C16—112no—
238C2×C16—221no—
239C2×C16—221no—
240C2×C16—221no—
241C2×C16—221no—
242C2×C16—221no—
243#107—21no—
244#107—21no—
245#107—21no—
246#107—21no—
247#107—112no—
248#107—221no—
249#102—224no—
250#95—41no—
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—
261C24#432311yescharacteristic
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—41no—
278C22×C4—41no—
279C22×C4—441no—
280C22×C4#432311yescharacteristic
281C22×C4C2×C22⋊D1111yescharacteristic
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×C8#433911yescharacteristic
295C2×C8D4×D1111yescharacteristic
296C2×C8D4×D1111yescharacteristic
297C2×C8D4×D1111yescharacteristic
298C2×C8#434111yescharacteristic
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—222no—
304C4⋊C4—441no—
305C22⋊C4—82no—
306C22⋊C4—444no—
307C16—222no—
308C16—441no—
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—
323C23#6689012yes—
324C23C2×#432311yescharacteristic
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—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—442no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4#6698211yescharacteristic
347C2×C4#6699011yescharacteristic
348C2×C4#6699211yescharacteristic
349C2×C4#6699511yescharacteristic
350C2×C4#6700211yescharacteristic
351C2×C4#6700311yescharacteristic
352C8—41no—
353C8#6693611yescharacteristic
354C8#6693711yescharacteristic
355C8#6693711yescharacteristic
356C8#6693811yescharacteristic
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#1062258011yescharacteristic
372C22#1062264911yescharacteristic
373C22#1062265111yescharacteristic
374C22C2×#6689011yescharacteristic
375C22#1062279211yescharacteristic
376C22#1062280611yescharacteristic
377C22#1062280711yescharacteristic
378C4—41no—
379C4—161no—
380C4—161no—
381C4—882no—
382C4#1062257211yescharacteristic
383C4#1062261611yescharacteristic
384C4#1062266011yescharacteristic
385C4#1062266211yescharacteristic
386C2—42no—
387C2—1762no—
388C2#1306979811yescharacteristic
389C2#1307052711yescharacteristic
390C2#1307055411yescharacteristic
391C2#1307070011yescharacteristic
392C2#1307073111yescharacteristic
393C2#1307079611yescharacteristic
394C2#1307080711yescharacteristic
subgroupG/H
centerC23C2×#4323
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC11×#1808C2
socleC23×C11C2×D8
prime radicalC2×#10622728C2
hypercenter#1808D11
hypocenterC11#13380
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. C2×#10622127C2semidirect
3. C2×#10622129C2semidirect
4. C2×#10622129C2semidirect
5. C2×C22⋊(C11⋊C16)C2semidirect
6. #13066707C2semidirect
7. C11×#1808C2semidirect
62. C2×C11⋊C16D4semidirect
118. #1808D11semidirect
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×#106221272
C2×#106221292
C2×C22⋊(C11⋊C16)2
#130667072
C11×#18082
#1338011