Finite Group Databasebeta

← #14672933

Subgroups — #14672933

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×#10622770C211yesmaximal, characteristic
2C2×#10622128C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic, complemented
4C2×(C2×D11)⋊C16C211yesmaximal, characteristic, complemented
5#13068642C211yesmaximal, characteristic, complemented
6#13066708C211yesmaximal, characteristic, complemented
7C2×C11×#357C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C2×#66991—21no—
10C22×C8×D11C2211yescharacteristic
11C22×C11×C16C2211yescharacteristic
12C2×C11×#107C2211yescharacteristic
13C2×#66896—21no—
14#10622770—22no—
15#10622770—22no—
16C2×#66882C2211yescharacteristic
17C2×#66882C2211yescharacteristic
18C22×C11⋊C16C2211yescharacteristic
19#10622600—21no—
20C11×#357—22no—
21#10622200—22no—
22#10622167—21no—
23(C2×D11)⋊C16—22no—
24#10622128—22no—
25C22×D4×C11—21no—
26C22×C22⋊D11—41no—
27C22×C4×D11D411yescharacteristic
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C2×C11×D8—21no—
31C2×C11×D8—21no—
32C2×C11×D8—21no—
33C2×C11×D8D412yes—
34C22×C8×C11C2311yescharacteristic
35C2×C11×C4⋊C4—21no—
36C2×C22⋊Dic11—41no—
37#66991—24no—
38#66991—42no—
39C2×(C2×D11)⋊C4—41no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C22×C11⋊C8D411yescharacteristic
43C2×C8×D11—21no—
44C2×C8×D11—21no—
45C2×C8×D11—21no—
46C2×C8×D11—21no—
47C2×C8×D11—21no—
48C2×C8×D11—21no—
49C2×C11×C16—21no—
50C2×C11×C16—21no—
51C2×C11×C16—21no—
52C11×#107—21no—
53C11×#107—21no—
54#66896—24no—
55C11⋊#95—41no—
56#66882—21no—
57#66882—21no—
58#66882—21no—
59#66882D412yes—
60C2×C11⋊C16—21no—
61C2×C11⋊C16—21no—
62C2×C11⋊C16D412yescomplemented
63#13381—111nomaximal, Sylow
64C24×C11—41no—
65C23×D11D811yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11C2×D411yescharacteristic
74C2×C22⋊D11—44no—
75C2×C22⋊D11—82no—
76C2×C22⋊D11—82no—
77C22×Dic11—41no—
78C22×Dic11—41no—
79C22×Dic11D811yescharacteristic
80C2×C4×D11—21no—
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C11×D8—22no—
87C11×D8—22no—
88C11×D8—41no—
89C11×D8—41no—
90C2×C8×C11C2×D411yescharacteristic
91C2×C8×C11C2×D411yescharacteristic
92C2×C8×C11C2×D411yescharacteristic
93C2×C8×C11#4111yescharacteristic
94C2×C8×C11#4111yescharacteristic
95C2×C8×C11#4111yescharacteristic
96C11×C4⋊C4—41no—
97C11×C4⋊C4—41no—
98C22⋊Dic11—44no—
99(C2×D11)⋊C4—82no—
100C4⋊Dic11—22no—
101C4⋊Dic11—41no—
102C4⋊Dic11—41no—
103C4⋊Dic11—41no—
104C2×C11⋊C8—21no—
105C2×C11⋊C8—21no—
106C2×C11⋊C8—21no—
107C8×D11—41no—
108C8×D11—41no—
109C8×D11—41no—
110C8×D11—41no—
111C11×C16—41no—
112C11⋊C16—22no—
113C2×#466—111no—
114C2×#367—111no—
115C2×#357—111no—
116C2×#357D1111yescharacteristic, complemented
117C2×C22⋊C16—111no—
118#1808—111no—
119#1380—111no—
120C23×C11—42no—
121C23×C11—81no—
122C23×C11—81no—
123C23×C11—81no—
124C23×C11—81no—
125C23×C11—81no—
126C23×C11—81no—
127C23×C11C2×D811yescharacteristic
128C22×D11—21no—
129C22×D11—21no—
130C22×D11—21no—
131C22×D11—21no—
132C22×D11—21no—
133C22×D11—21no—
134C22×D11SD3212yes—
135D4×C11—42no—
136D4×C11—42no—
137D4×C11—81no—
138D4×C11—81no—
139C2×C4×C11—81no—
140C2×C4×C11—81no—
141C2×C4×C11—81no—
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—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—42no—
153C2×Dic11—81no—
154C2×Dic11—81no—
155C2×Dic11—81no—
156C2×Dic11—81no—
157C2×Dic11—81no—
158C4×D11—41no—
159C4×D11—41no—
160C4×D11—41no—
161C4×D11—41no—
162C8×C11#12111yescharacteristic
163C8×C11#12111yescharacteristic
164C8×C11#12311yescharacteristic
165C8×C11#12411yescharacteristic
166C11⋊C8—41no—
167C22×D8C2×D1111yescharacteristic
168C23×C8—111no—
169C2×#121—221no—
170C22×C16—111no—
171C22×C16C2×D1111yescharacteristic
172#466—222no—
173#466—222no—
174C2×#107—111no—
175C2×#107—111no—
176C2×#107C2×D1111yescharacteristic
177C2×#102—221no—
178#380—221no—
179#367—222no—
180#357—22no—
181#357—222no—
182C22⋊C16—222no—
183#340—221no—
184C22×C11—82no—
185C22×C11—82no—
186C22×C11—82no—
187C22×C11—161no—
188C22×C11—161no—
189C22×C11—161no—
190C22×C11—161no—
191C22×C11#44711yescharacteristic
192C22×C11#46611yescharacteristic
193C22×C11#48011yescharacteristic
194C22×C11C2×SD3211yescharacteristic
195C22×C11#50811yescharacteristic
196C22×C11#50911yescharacteristic
197C22×C11#50911yescharacteristic
198C2×D11—22no—
199C2×D11—22no—
200C2×D11—22no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C4×C11—161no—
206C4×C11#39411yescharacteristic
207C4×C11#45211yescharacteristic
208C4×C11#46811yescharacteristic
209C4×C11#48211yescharacteristic
210Dic11—41no—
211Dic11—82no—
212Dic11—161no—
213C22×D4—21no—
214C22×D4—441no—
215C23×C4—111no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8C22⋊D1112yes—
222C22×C8—111no—
223C22×C8—221no—
224C22×C8—221no—
225C22×C8—221no—
226C22×C8—221no—
227C22×C8—221no—
228C22×C8—221no—
229C22×C8C22×D1111yescharacteristic
230#121—224no—
231#121—442no—
232C2×C4⋊C4—21no—
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—112no—
241C2×C16—221no—
242C2×C16—221no—
243#107—21no—
244#107—21no—
245#107—112no—
246#107—221no—
247#107—221no—
248#107—221no—
249#102—224no—
250#95—441no—
251C2×C11—162no—
252C2×C11#203311yescharacteristic
253C2×C11#218611yescharacteristic
254C2×C11#218711yescharacteristic
255C2×C11#221711yescharacteristic
256C2×C11#221811yescharacteristic
257C2×C11#223311yescharacteristic
258C2×C11#223411yescharacteristic
259D11—42no—
260C24—41no—
261C24—111no—
262C2×D4—22no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—444no—
269C2×D4—882no—
270C2×D4—882no—
271C22×C4—41no—
272C22×C4—111no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4—221no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—221no—
279C22×C4—441no—
280C22×C4—441no—
281C22×C4D4×D1111yescharacteristic
282D8—22no—
283D8—22no—
284D8—41no—
285D8—41no—
286C2×C8—221no—
287C2×C8—221no—
288C2×C8—221no—
289C2×C8—441no—
290C2×C8—441no—
291C2×C8—441no—
292C2×C8—441no—
293C2×C8#433911yescharacteristic
294C2×C8#433911yescharacteristic
295C2×C8D4×D1111yescharacteristic
296C2×C8D4×D1111yescharacteristic
297C2×C8#434111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C4⋊C4—41no—
300C4⋊C4—41no—
301C4⋊C4—222no—
302C4⋊C4—441no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C22⋊C4—444no—
306C22⋊C4—882no—
307C16—41no—
308C16—222no—
309C11#1338111yescharacteristic, complemented, Sylow
310C23—42no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—81no—
315C23—81no—
316C23—81no—
317C23—112no—
318C23—221no—
319C23—221no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—221no—
324C23D8×D1111yescharacteristic
325D4—42no—
326D4—42no—
327D4—81no—
328D4—81no—
329D4—888no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—221no—
334C2×C4—221no—
335C2×C4—221no—
336C2×C4—441no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—442no—
341C2×C4—881no—
342C2×C4—881no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4#6693611yescharacteristic
347C2×C4#6693711yescharacteristic
348C2×C4#6696411yescharacteristic
349C2×C4#6696811yescharacteristic
350C2×C4#6696911yescharacteristic
351C2×C4#6699011yescharacteristic
352C8—441no—
353C8#6693711yescharacteristic
354C8#6693811yescharacteristic
355C8#6698211yescharacteristic
356C8#6699211yescharacteristic
357C22—82no—
358C22—82no—
359C22—82no—
360C22—161no—
361C22—161no—
362C22—161no—
363C22—161no—
364C22—222no—
365C22—222no—
366C22—222no—
367C22—441no—
368C22—441no—
369C22—441no—
370C22—441no—
371C22#1062238711yescharacteristic
372C22#1062238811yescharacteristic
373C22#1062252411yescharacteristic
374C22#1062252511yescharacteristic
375C22D11×SD3211yescharacteristic
376C22#1062252711yescharacteristic
377C22#1062276911yescharacteristic
378C4—161no—
379C4—441no—
380C4—882no—
381C4—1761no—
382C4#1062239211yescharacteristic
383C4#1062239311yescharacteristic
384C4#1062257211yescharacteristic
385C4#1062278611yescharacteristic
386C2—162no—
387C2—442no—
388C2#1306979611yescharacteristic
389C2#1307053611yescharacteristic
390C2#1307054311yescharacteristic
391C2#1307071111yescharacteristic
392C2#1307071811yescharacteristic
393C2#1307080011yescharacteristic
394C2#1307080511yescharacteristic
subgroupG/H
centerC23D8×D11
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#357C2
socleC23×C11C2×D8
prime radicalC2×#10622770C2
hypercenterC2×#357D11
hypocenterC11#13381
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×#10622128C2semidirect
3. C2×#10622200C2semidirect
4. C2×(C2×D11)⋊C16C2semidirect
5. #13068642C2semidirect
6. #13066708C2semidirect
7. C2×C11×#357C2semidirect
62. C2×C11⋊C16D4semidirect
116. C2×#357D11semidirect
309. C11#13381semidirect

Maximal subgroups

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

subgroupindex
C2×#106227702
C2×#106221282
C2×#106222002
C2×(C2×D11)⋊C162
#130686422
#130667082
C2×C11×#3572
#1338111