Finite Group Databasebeta

← #14645232

Subgroups — #14645232

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068684C211yesmaximal, characteristic, complemented
2C2×#10622175C214yesmaximal, complemented
3#13066843C211yesmaximal, characteristic, complemented
4C2×C11×#532C211yesmaximal, characteristic
5C22×C11×#41—21no—
6C11×#532—28no—
7C2×C11×C4⋊Q8C411yescharacteristic, complemented
8C2×C11×#127C411yescharacteristic, complemented
9C2×C11×#124—21no—
10C2×C11×#121—21no—
11C2×C11×#121C2212yes—
12C2×C4×D4×C11—21no—
13C2×C4×D4×C11C412yescomplemented
14C22×C42×C11C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95—21no—
17C2×C11⋊#95C2212yes—
18C2×C22⋊(C11⋊C8)C2212yes—
19#10622175—28no—
20#10622162—21no—
21#10622162—21no—
22C2×C11×#41—28no—
23C2×C11×#41—44no—
24C2×C11×#41—42no—
25C2×C11×#41—42no—
26C22×Q8×C11—21no—
27C22×D4×C11—22no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11C2×C412yes—
31C23×C4×C11—22no—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—22no—
36C11×C4⋊Q8—24no—
37C11×#127—24no—
38C11×#124—28no—
39C11×#121—28no—
40C11×#121—24no—
41C11×#121D418yes—
42C4×D4×C11—28no—
43C4×D4×C11—24no—
44C4×D4×C11—24no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4C2×C412yes—
47C2×C11×C22⋊C4—22no—
48C2×C11×C22⋊C4—22no—
49C2×C42×C11—24no—
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2×C411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11D411yescharacteristic
54C22×C11⋊C8—22no—
55C11⋊#95—24no—
56C11⋊#95—24no—
57C11⋊#95—42no—
58C22⋊(C11⋊C8)—24no—
59#8332—111nomaximal, Sylow
60C24×C11—22no—
61C24×C11C2×D411yescharacteristic
62C11×#41—416no—
63C11×#41—416no—
64C2×Q8×C11—24no—
65C2×Q8×C11—42no—
66C2×Q8×C11—42no—
67C2×D4×C11—24no—
68C2×D4×C11—24no—
69C2×D4×C11—28no—
70C2×D4×C11—22no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11—42no—
74C2×D4×C11—42no—
75C2×D4×C11—42no—
76C2×D4×C11—42no—
77C2×D4×C11—44no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11C22⋊C414yes—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—28no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—44no—
91C22×C4×C11—44no—
92C22×C4×C11C22⋊C411yescharacteristic
93C22×C4×C11C22⋊C411yescharacteristic
94C22×C4×C11C22⋊C411yescharacteristic
95C22×C4×C11C22⋊C411yescharacteristic
96C22×C4×C11D812yes—
97C22×C4×C11SD1612yes—
98C22×C4×C11C22×C411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D414yes—
101C22×Dic11—24no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11—42no—
105C22×Dic11—42no—
106C22×Dic11—42no—
107C22×Dic11—42no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4C22⋊C414yes—
111C11×C22⋊C4—28no—
112C11×C22⋊C4—28no—
113C42×C11—22no—
114C42×C11—22no—
115C42×C11—22no—
116C42×C11—22no—
117C2×C11⋊C8—42no—
118C2×C11⋊C8—42no—
119C2×C11⋊C8—42no—
120C2×#532D1111yescharacteristic
121#1817—111no—
122C2×#327—114no—
123#1434—111no—
124C23×C11—21no—
125C23×C11—21no—
126C23×C11—21no—
127C23×C11—21no—
128C23×C11—24no—
129C23×C11—42no—
130C23×C11—42no—
131C23×C11—42no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11C2×C22⋊C411yescharacteristic
136C23×C11#12012yes—
137C23×C11C2×D811yescharacteristic
138C23×C11C2×SD1611yescharacteristic
139C23×C11AGL(1,ℤ/8)12yes—
140Q8×C11—48no—
141D4×C11—44no—
142D4×C11—44no—
143D4×C11—48no—
144D4×C11—48no—
145D4×C11—48no—
146D4×C11—48no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—21no—
160C2×C4×C11—24no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—44no—
164C2×C4×C11—44no—
165C2×C4×C11—416no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11#10212yes—
169C2×C4×C11#10212yes—
170C2×C4×C11#10412yes—
171C2×C4×C11C2×C22⋊C412yes—
172C2×C4×C11#12012yes—
173C2×Dic11—44no—
174C2×Dic11—44no—
175C2×Dic11—44no—
176C2×Dic11—82no—
177C2×Dic11—82no—
178C2×Dic11—82no—
179C2×Dic11—82no—
180C11⋊C8—82no—
181C22×#41—21no—
182#532—28no—
183C2×C4⋊Q8Dic1111yescharacteristic, complemented
184C2×#127Dic1111yescharacteristic, complemented
185C2×#124—21no—
186C2×#121—21no—
187C2×#121C2×D1112yes—
188C2×C4×D4—21no—
189C2×C4×D4Dic1112yescomplemented
190C22×C42C2×D1111yescharacteristic
191C2×C22⋊C8—112no—
192C2×#95—112no—
193C2×#95—221no—
194C2×#95—221no—
195#336—221no—
196#336—221no—
197#327—228no—
198C22×C11—21no—
199C22×C11—21no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—44no—
207C22×C11—44no—
208C22×C11—44no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—82no—
212C22×C11—82no—
213C22×C11#37911yescharacteristic
214C22×C11#41011yescharacteristic
215C22×C11#41011yescharacteristic
216C22×C11C2×#10211yescharacteristic
217C22×C11#41811yescharacteristic
218C22×C11C2×#10411yescharacteristic
219C22×C11#42111yescharacteristic
220C22×C11#44712yes—
221C22×C11#45012yes—
222C4×C11—22no—
223C4×C11—22no—
224C4×C11—22no—
225C4×C11—22no—
226C4×C11—22no—
227C4×C11—44no—
228C4×C11—41no—
229Dic11—84no—
230C2×#41—28no—
231C2×#41—44no—
232C2×#41—42no—
233C2×#41—42no—
234C22×Q8—21no—
235C22×D4—22no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C2×Dic1112yes—
239C23×C4—22no—
240C23×C4—222no—
241C23×C4C22⋊D1111yescharacteristic
242C23×C4C22⋊D1111yescharacteristic
243C23×C4C22×D1111yescharacteristic
244C22×C8—222no—
245C4⋊Q8—24no—
246#127—24no—
247#124—28no—
248#121—28no—
249#121—24no—
250#121C22⋊D1118yes—
251C4×D4—28no—
252C4×D4—24no—
253C4×D4—24no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4C2×Dic1112yes—
256C2×C22⋊C4—22no—
257C2×C22⋊C4—22no—
258C2×C42—24no—
259C2×C42C2×Dic1111yescharacteristic
260C2×C42C2×Dic1111yescharacteristic
261C2×C42C22⋊D1111yescharacteristic
262C2×C42C22⋊D1111yescharacteristic
263C22⋊C8—224no—
264#95—224no—
265#95—224no—
266#95—442no—
267C2×C11—22no—
268C2×C11—22no—
269C2×C11—84no—
270C2×C11#150211yescharacteristic
271C2×C11#150511yescharacteristic
272C2×C11#151411yescharacteristic
273C2×C11#151711yescharacteristic
274C2×C11#178211yescharacteristic
275C2×C11#178611yescharacteristic
276C2×C11#178911yescharacteristic
277C24—22no—
278C24C2×C22⋊D1111yescharacteristic
279#41—416no—
280#41—416no—
281C2×Q8—24no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×D4—24no—
285C2×D4—24no—
286C2×D4—28no—
287C2×D4—22no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—42no—
292C2×D4—42no—
293C2×D4—44no—
294C2×D4—42no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4C22⋊Dic1114yes—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—28no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—44no—
308C22×C4—44no—
309C22×C4—224no—
310C22×C4—442no—
311C22×C4—442no—
312C22×C4—442no—
313C22×C4—442no—
314C22×C4—442no—
315C22×C4—442no—
316C22×C4#432312yes—
317C22×C4#432412yes—
318C22×C4C22⋊Dic1111yescharacteristic
319C22×C4C22⋊Dic1111yescharacteristic
320C22×C4C22⋊Dic1111yescharacteristic
321C22×C4C22⋊Dic1111yescharacteristic
322C22×C4C22×Dic1111yescharacteristic
323C22×C4C2×C22⋊D1111yescharacteristic
324C22×C4C2×C22⋊D1114yes—
325C2×C8—442no—
326C2×C8—442no—
327C2×C8—442no—
328C4⋊C4—24no—
329C4⋊C4—22no—
330C4⋊C4C22⋊Dic1114yes—
331C22⋊C4—28no—
332C22⋊C4—28no—
333C42—22no—
334C42—22no—
335C42—22no—
336C42—22no—
337C11#833211yescharacteristic, complemented, Sylow
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—24no—
343C23—42no—
344C23—42no—
345C23—42no—
346C23—42no—
347C23—42no—
348C23—42no—
349C23C2×#432311yescharacteristic
350C23#6698512yes—
351C23C2×#432411yescharacteristic
352C23C2×C22⋊Dic1111yescharacteristic
353C23#6700612yes—
354Q8—48no—
355D4—44no—
356D4—48no—
357D4—44no—
358D4—48no—
359D4—48no—
360D4—48no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—24no—
364C2×C4—24no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—24no—
377C2×C4—44no—
378C2×C4—44no—
379C2×C4—416no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—444no—
383C2×C4—444no—
384C2×C4—444no—
385C2×C4—882no—
386C2×C4—882no—
387C2×C4—882no—
388C2×C4—882no—
389C2×C4#6689612yes—
390C2×C4#6689612yes—
391C2×C4#6690112yes—
392C2×C4C2×C22⋊Dic1112yes—
393C2×C4#6700612yes—
394C8—882no—
395C22—22no—
396C22—21no—
397C22—21no—
398C22—22no—
399C22—22no—
400C22—21no—
401C22—21no—
402C22—22no—
403C22—44no—
404C22—44no—
405C22—44no—
406C22—82no—
407C22—82no—
408C22—82no—
409C22—82no—
410C22C2×#6689611yescharacteristic
411C22#1062282811yescharacteristic
412C22#1062283012yes—
413C22#1062283112yes—
414C22C2×#6690111yescharacteristic
415C22#1062284911yescharacteristic
416C22#1062285311yescharacteristic
417C22#1062285311yescharacteristic
418C22#1062286011yescharacteristic
419C4—22no—
420C4—22no—
421C4—22no—
422C4—22no—
423C4—22no—
424C4—44no—
425C4—41no—
426C4—884no—
427C2—22no—
428C2—22no—
429C2—84no—
430C2#1306711111yescharacteristic
431C2#1306712411yescharacteristic
432C2#1306716311yescharacteristic
433C2#1306717611yescharacteristic
434C2#1306853411yescharacteristic
435C2#1306854711yescharacteristic
436C2#1306856011yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC2×C11×#532C2
socleC23×C11C2×C22⋊C4
cosocleC23×C4×C11C23
hypercenterC2×#532D11
hypocenterC11#8332
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #13068684C2semidirect
2. C2×#10622175C2semidirect
3. #13066843C2semidirect
7. C2×C11×C4⋊Q8C4semidirect
8. C2×C11×#127C4semidirect
13. C2×C4×D4×C11C4semidirect
183. C2×C4⋊Q8Dic11semidirect
184. C2×#127Dic11semidirect
189. C2×C4×D4Dic11semidirect
337. C11#8332semidirect

Maximal subgroups

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

subgroupindex
#130686842
C2×#106221752
#130668432
C2×C11×#5322
#833211