Finite Group Databasebeta

← #14672468

Subgroups — #14672468

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66890C211yesmaximal, characteristic, complemented
2C2×#10622728C211yesmaximal, characteristic, complemented
3C2×#10622200C211yesmaximal, characteristic, complemented
4C2×#10622129C211yesmaximal, characteristic, complemented
5C2×C22⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066707C211yesmaximal, characteristic, complemented
7C2×C11×#466C211yesmaximal, characteristic, complemented
8C22×C11×D8C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C2×C11×#121—21no—
11C2×#66983—21no—
12C22×D88C2211yescharacteristic
13C11×#466—22no—
14C11×#466—22no—
15C2×C11×#107C2211yescharacteristic
16C2×C11×#102—21no—
17C2×#66890—22no—
18C2×#66890—22no—
19C2×#66890—22no—
20#10622728—22no—
21#10622728—22no—
22C2×#66885—21no—
23C2×#66882C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622200—22no—
27C22⋊(C11⋊C16)—22no—
28#10622129—22no—
29C22×D4×C11—21no—
30C22×D4×C11—41no—
31C23×C4×C11D411yescharacteristic
32C22×C22⋊D11—41no—
33C22×D44—21no—
34C2×C11×D8—21no—
35C2×C11×D8—21no—
36C2×C11×D8—21no—
37C2×C11×D8—21no—
38C2×C11×D8—21no—
39C2×C11×D8D412yescomplemented
40C22×C8×C11—21no—
41C22×C8×C11—21no—
42C22×C8×C11—21no—
43C22×C8×C11—21no—
44C22×C8×C11—21no—
45C22×C8×C11—21no—
46C22×C8×C11D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×#121—24no—
49C11×#121—42no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C22⋊C4—41no—
52#66983—24no—
53#66983—42no—
54C2×(C2×D11)⋊C4—41no—
55C2×C4⋊Dic11—21no—
56C2×D88—21no—
57C2×D88—21no—
58C2×D88—21no—
59C2×D88—21no—
60C2×D88—21no—
61C2×D88D412yescomplemented
62C11×#107—21no—
63C11×#107D412yescomplemented
64C11×#102—24no—
65#66890—28no—
66#66885—24no—
67#66882—21no—
68#66882D412yescomplemented
69C2×C11⋊C16—21no—
70C2×C11⋊C16—21no—
71C2×C11⋊C16—21no—
72C2×C11⋊C16—21no—
73C2×C11⋊C16—21no—
74C2×C11⋊C16D412yescomplemented
75#13304—111nomaximal, Sylow
76C24×C11—41no—
77C24×C11D811yescharacteristic
78C23×D11—41no—
79C2×D4×C11—22no—
80C2×D4×C11—44no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—82no—
87C2×D4×C11—82no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11D811yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×C22⋊D11—44no—
98C2×C22⋊D11—82no—
99C2×C22⋊D11—82no—
100C22×Dic11—41no—
101C2×D44—22no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—41no—
107C11×D8—22no—
108C11×D8—22no—
109C11×D8—41no—
110C11×D8—41no—
111C2×C8×C11—21no—
112C2×C8×C11—21no—
113C2×C8×C11—21no—
114C2×C8×C11—41no—
115C2×C8×C11—41no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11C2×D411yescharacteristic
119C2×C8×C11C2×D411yescharacteristic
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11C2×D411yescharacteristic
122C2×C8×C11C2×D411yescharacteristic
123C2×C8×C11#4111yescharacteristic
124C11×C4⋊C4—22no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—44no—
127(C2×D11)⋊C4—44no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130D88—22no—
131D88—22no—
132D88—41no—
133D88—41no—
134C11⋊C16—22no—
135C11⋊C16—41no—
136C22×D16—111no—
137C2×#466—111no—
138C2×#466D1111yescharacteristic, complemented
139C2×#357—111no—
140C2×#357—111no—
141C2×C22⋊C16—111no—
142#1380—111no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—21no—
148C23×C11—21no—
149C23×C11—42no—
150C23×C11—81no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11—81no—
155C23×C11—81no—
156C23×C11D1612yescomplemented
157C23×C11C2×D811yescharacteristic
158C22×D11—42no—
159C22×D11—81no—
160C22×D11—81no—
161C22×D11—81no—
162C22×D11—81no—
163C22×D11—81no—
164C22×D11—81no—
165D4×C11—42no—
166D4×C11—42no—
167D4×C11—88no—
168D4×C11—81no—
169D4×C11—81no—
170C2×C4×C11—21no—
171C2×C4×C11—21no—
172C2×C4×C11—21no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—81no—
179C2×C4×C11—81no—
180C2×C4×C11#12011yescharacteristic
181C2×C4×C11#12011yescharacteristic
182C2×C4×C11#12111yescharacteristic
183C2×C4×C11#13511yescharacteristic
184C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
186C22⋊D11—88no—
187C2×Dic11—42no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190D44—42no—
191D44—42no—
192D44—81no—
193D44—81no—
194C8×C11—41no—
195C8×C11#12011yescharacteristic
196C8×C11#12111yescharacteristic
197C8×C11#12111yescharacteristic
198C8×C11#12711yescharacteristic
199C22×D8—111no—
200C22×D8C2×D1111yescharacteristic
201C23×C8C2×D1111yescharacteristic
202C2×#121—21no—
203C2×#121—221no—
204C2×D16—222no—
205C2×D16—222no—
206C2×D16—222no—
207C22×C16—111no—
208C22×C16—111no—
209#466—22no—
210#466—22no—
211#466—222no—
212#466—222no—
213C2×#107—111no—
214C2×#107C2×D1111yescharacteristic
215C2×#102—21no—
216C2×#102—221no—
217#357—222no—
218#357—222no—
219C22⋊C16—222no—
220C22×C11—22no—
221C22×C11—22no—
222C22×C11—22no—
223C22×C11—41no—
224C22×C11—41no—
225C22×C11—41no—
226C22×C11—41no—
227C22×C11—82no—
228C22×C11—82no—
229C22×C11—82no—
230C22×C11—161no—
231C22×C11—161no—
232C22×C11—161no—
233C22×C11—161no—
234C22×C11#44711yescharacteristic
235C22×C11#44711yescharacteristic
236C22×C11#46611yescharacteristic
237C22×C11C2×D1611yescharacteristic
238C22×C11#50811yescharacteristic
239C22×C11#50911yescharacteristic
240C22×C11#50911yescharacteristic
241C2×D11—82no—
242C2×D11—82no—
243C2×D11—82no—
244C2×D11—161no—
245C2×D11—161no—
246C2×D11—161no—
247C2×D11—161no—
248C4×C11—41no—
249C4×C11—82no—
250C4×C11#39211yescharacteristic
251C4×C11#44911yescharacteristic
252C4×C11#44911yescharacteristic
253C4×C11#46911yescharacteristic
254Dic11—82no—
255C22×D4—21no—
256C22×D4—41no—
257C22×D4—221no—
258C22×D4—441no—
259C23×C4C22⋊D1111yescharacteristic
260C2×D8—21no—
261C2×D8—21no—
262C2×D8—21no—
263C2×D8—21no—
264C2×D8—21no—
265C2×D8—112no—
266C2×D8—221no—
267C2×D8—221no—
268C2×D8—221no—
269C2×D8—221no—
270C2×D8—221no—
271C2×D8C22⋊D1112yescomplemented
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—21no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8C22⋊D1111yescharacteristic
279C22×C8C22×D1111yescharacteristic
280#121—24no—
281#121—42no—
282#121—224no—
283#121—442no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—221no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—441no—
288D16—228no—
289C2×C16—112no—
290C2×C16—221no—
291C2×C16—221no—
292C2×C16—221no—
293C2×C16—221no—
294C2×C16—221no—
295#107—21no—
296#107—112no—
297#107—221no—
298#107C22⋊D1112yescomplemented
299#102—24no—
300#102—224no—
301C2×C11—42no—
302C2×C11—162no—
303C2×C11#199911yescharacteristic
304C2×C11#218411yescharacteristic
305C2×C11#218411yescharacteristic
306C2×C11#218611yescharacteristic
307C2×C11#218611yescharacteristic
308C2×C11#221511yescharacteristic
309C2×C11#221811yescharacteristic
310D11—162no—
311C24—41no—
312C24—441no—
313C24#432311yescharacteristic
314C2×D4—22no—
315C2×D4—44no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—82no—
322C2×D4—82no—
323C2×D4—222no—
324C2×D4—444no—
325C2×D4—441no—
326C2×D4—441no—
327C2×D4—441no—
328C2×D4—441no—
329C2×D4—441no—
330C2×D4—882no—
331C2×D4—882no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—441no—
340C22×C4#432311yescharacteristic
341C22×C4C2×C22⋊D1111yescharacteristic
342D8—22no—
343D8—22no—
344D8—41no—
345D8—41no—
346D8—222no—
347D8—222no—
348D8—441no—
349D8—441no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8D4×D1111yescharacteristic
358C2×C8D4×D1111yescharacteristic
359C2×C8D4×D1111yescharacteristic
360C2×C8#434111yescharacteristic
361C2×C8C2×C22⋊D1111yescharacteristic
362C2×C8C2×C22⋊D1111yescharacteristic
363C4⋊C4—22no—
364C4⋊C4—41no—
365C4⋊C4—222no—
366C4⋊C4—441no—
367C22⋊C4—44no—
368C22⋊C4—444no—
369C16—222no—
370C16—441no—
371C11#1330411yescharacteristic, complemented, Sylow
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—42no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—81no—
383C23—81no—
384C23—81no—
385C23—442no—
386C23—881no—
387C23—881no—
388C23—881no—
389C23—881no—
390C23—881no—
391C23—881no—
392C23#6689012yescomplemented
393C23C2×#432311yescharacteristic
394D4—42no—
395D4—42no—
396D4—88no—
397D4—81no—
398D4—81no—
399D4—442no—
400D4—442no—
401D4—888no—
402D4—881no—
403D4—881no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—42no—
412C2×C4—81no—
413C2×C4—81no—
414C2×C4—442no—
415C2×C4—881no—
416C2×C4—881no—
417C2×C4#6698511yescharacteristic
418C2×C4#6699011yescharacteristic
419C2×C4#6699211yescharacteristic
420C2×C4#6700211yescharacteristic
421C2×C4#6700311yescharacteristic
422C2×C4#6700611yescharacteristic
423C8—41no—
424C8#6699011yescharacteristic
425C8#6699111yescharacteristic
426C8#6699211yescharacteristic
427C8#6699311yescharacteristic
428C22—22no—
429C22—22no—
430C22—22no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—82no—
436C22—82no—
437C22—82no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22—161no—
442C22—882no—
443C22—882no—
444C22—882no—
445C22—1761no—
446C22—1761no—
447C22—1761no—
448C22—1761no—
449C22#1062264911yescharacteristic
450C22#1062265111yescharacteristic
451C22C2×#6689011yescharacteristic
452C22#1062276011yescharacteristic
453C22#1062280611yescharacteristic
454C22#1062280711yescharacteristic
455C22#1062283011yescharacteristic
456C4—41no—
457C4—82no—
458C4—882no—
459C4#1062265011yescharacteristic
460C4#1062265211yescharacteristic
461C4#1062283611yescharacteristic
462C4#1062285111yescharacteristic
463C2—42no—
464C2—162no—
465C2—1762no—
466C2#1306961211yescharacteristic
467C2#1307052711yescharacteristic
468C2#1307052811yescharacteristic
469C2#1307053711yescharacteristic
470C2#1307053911yescharacteristic
471C2#1307070011yescharacteristic
472C2#1307071711yescharacteristic
subgroupG/H
centerC23C2×#4323
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#466C2
socleC23×C11C2×D8
hypercenterC2×#466D11
hypocenterC11#13304
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C22×#66890C2semidirect
2. C2×#10622728C2semidirect
3. C2×#10622200C2semidirect
4. C2×#10622129C2semidirect
5. C2×C22⋊(C11⋊C16)C2semidirect
6. #13066707C2semidirect
7. C2×C11×#466C2semidirect
39. C2×C11×D8D4semidirect
61. C2×D88D4semidirect
63. C11×#107D4semidirect
68. #66882D4semidirect
74. C2×C11⋊C16D4semidirect
138. C2×#466D11semidirect
156. C23×C11D16semidirect
271. C2×D8C22⋊D11semidirect
298. #107C22⋊D11semidirect
371. C11#13304semidirect
392. C23#66890semidirect

Maximal subgroups

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

subgroupindex
C22×#668902
C2×#106227282
C2×#106222002
C2×#106221292
C2×C22⋊(C11⋊C16)2
#130667072
C2×C11×#4662
#1330411