Finite Group Databasebeta

← #14653846

Subgroups — #14653846

Order 2816.

566 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076924C211yesmaximal, characteristic
2C22⋊C8×Dic11C211yesmaximal, characteristic
3#13066842C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C22×C4×Dic11C2211yescharacteristic
9C2×#66943C411yescharacteristic, complemented
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C2×C11×#95C2211yescharacteristic
13#10622825C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×C8×Dic11—21no—
19#10622598C411yescharacteristic, complemented
20#10622590C411yescharacteristic, complemented
21#10622586C411yescharacteristic, complemented
22#10622563—21no—
23#10622559—21no—
24#10622268—21no—
25#10622267—21no—
26#10622188—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×C8×C11—21no—
33C2×C11×C4⋊C4C2×C411yescharacteristic
34C2×C11×C4⋊C4C2×C411yescharacteristic
35C2×C11×C22⋊C4—21no—
36C2×C22⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11C2×C411yescharacteristic
40C2×C4⋊Dic11C2×C411yescharacteristic
41C2×Dic11⋊C4—21no—
42C2×Dic11⋊C4—21no—
43C2×C4×Dic11—42no—
44C2×C4×Dic11C2×C411yescharacteristic
45C2×C4×Dic11C2×C411yescharacteristic
46C2×C4×Dic11D411yescharacteristic
47C2×C4×Dic11D411yescharacteristic
48C22×C11⋊C8—21no—
49#66943—42no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8Q812yes—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11⋊#95—24no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—42no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)Q812yes—
66C8×Dic11—42no—
67#9886—111nomaximal, Sylow
68C24×C11C2×D411yescharacteristic
69C22×C4×C11—22no—
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11C22×C411yescharacteristic
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×Q811yescharacteristic
83C22×C4×C11C2×Q811yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×C4×C11#4111yescharacteristic
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11—22no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—21no—
95C22×Dic11—41no—
96C22×Dic11—41no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11C22⋊C411yescharacteristic
104C22×Dic11C22⋊C411yescharacteristic
105C22×Dic11C22⋊C411yescharacteristic
106C22×Dic11C22⋊C411yescharacteristic
107C2×C8×C11—22no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C22⋊Dic11—41no—
115C22⋊Dic11—41no—
116C4⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—42no—
119C4⋊Dic11—42no—
120Dic11⋊C4—42no—
121Dic11⋊C4—42no—
122C4×Dic11—22no—
123C4×Dic11—22no—
124C4×Dic11—41no—
125C4×Dic11—41no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129#2851—111no—
130C4×C22⋊C8—111no—
131#1434—111no—
132#1294—111no—
133#1294—111no—
134#1294—111no—
135#1294D1111yescharacteristic
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11C2×C22⋊C411yescharacteristic
141C23×C11#12411yescharacteristic
142C23×C11C4⋊Q811yescharacteristic
143C23×C11#13511yescharacteristic
144C23×C11#13511yescharacteristic
145C23×C11#13511yescharacteristic
146C23×C11#13511yescharacteristic
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—81no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11—81no—
168C2×C4×C11C4×Q811yescharacteristic
169C2×C4×C11C4×Q811yescharacteristic
170C2×C4×C11C22⋊Q811yescharacteristic
171C2×C4×C11C22⋊Q811yescharacteristic
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—21no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—81no—
196C2×Dic11—81no—
197C2×Dic11—81no—
198C2×Dic11—81no—
199C2×Dic11#9912yes—
200C2×Dic11#10412yes—
201C8×C11—42no—
202C11⋊C8—42no—
203C2×#125—111no—
204C22×C42—111no—
205C2×C22⋊C8—111no—
206C2×C22⋊C8C2×D1111yescharacteristic
207C2×C4×C8—221no—
208#389—111no—
209#389—111no—
210#387—221no—
211#387—221no—
212#385—221no—
213#385—221no—
214#382—111no—
215#380—111no—
216#380C2×D1111yescharacteristic
217C2×#95—111no—
218C2×#95—221no—
219C2×#95—221no—
220C2×#95C2×D1111yescharacteristic
221#336—221no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11#39111yescharacteristic
235C22×C11C2×#9911yescharacteristic
236C22×C11#41011yescharacteristic
237C22×C11#41611yescharacteristic
238C22×C11#41611yescharacteristic
239C22×C11C2×#10411yescharacteristic
240C22×C11#42111yescharacteristic
241C22×C11#48811yescharacteristic
242C22×C11#48811yescharacteristic
243C22×C11#49911yescharacteristic
244C22×C11#49911yescharacteristic
245C4×C11—21no—
246C4×C11—21no—
247C4×C11—21no—
248C4×C11—21no—
249C4×C11—82no—
250C4×C11—81no—
251C4×C11—81no—
252Dic11—22no—
253Dic11—22no—
254Dic11—41no—
255Dic11—41no—
256Dic11—82no—
257Dic11—81no—
258Dic11—81no—
259C23×C4—21no—
260C23×C4—111no—
261C23×C4—111no—
262C23×C4—221no—
263C23×C4C22×D1111yescharacteristic
264C22×C8—21no—
265C22×C8—221no—
266#125—442no—
267C2×C4⋊C4—111no—
268C2×C4⋊C4—111no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4C4×D1111yescharacteristic
274C2×C4⋊C4C4×D1111yescharacteristic
275C2×C22⋊C4—21no—
276C2×C22⋊C4—221no—
277C2×C42—111no—
278C2×C42—111no—
279C2×C42—111no—
280C2×C42—111no—
281C2×C42—442no—
282C22⋊C8—21no—
283C22⋊C8—112no—
284C22⋊C8—221no—
285C22⋊C8Dic2212yes—
286C4×C8—442no—
287#95—21no—
288#95—21no—
289#95—21no—
290#95—221no—
291#95—221no—
292#95—221no—
293#95—221no—
294#95—224no—
295#95—221no—
296#95—221no—
297#95—221no—
298#95—442no—
299C2×C11—21no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—21no—
303C2×C11#150011yescharacteristic
304C2×C11#150111yescharacteristic
305C2×C11#151611yescharacteristic
306C2×C11#152111yescharacteristic
307C2×C11#198611yescharacteristic
308C2×C11#199111yescharacteristic
309C2×C11#199611yescharacteristic
310C24D4×D1111yescharacteristic
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—111no—
323C22×C4—111no—
324C22×C4—111no—
325C22×C4—111no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4—221no—
329C22×C4—221no—
330C22×C4—221no—
331C22×C4—221no—
332C22×C4—222no—
333C22×C4—221no—
334C22×C4—221no—
335C22×C4—441no—
336C22×C4—441no—
337C22×C4—441no—
338C22×C4—441no—
339C22×C4—441no—
340C22×C4—441no—
341C22×C4—441no—
342C22×C4—441no—
343C22×C4C2×Dic2211yescharacteristic
344C22×C4C2×C4×D1111yescharacteristic
345C22×C4#433911yescharacteristic
346C22×C4D4×D1111yescharacteristic
347C22×C4#434111yescharacteristic
348C22×C4Q8×D1111yescharacteristic
349C2×C8—22no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—222no—
353C2×C8—441no—
354C2×C8—441no—
355C4⋊C4—41no—
356C4⋊C4—41no—
357C4⋊C4—441no—
358C4⋊C4—441no—
359C4⋊C4—442no—
360C4⋊C4—442no—
361C4⋊C4—442no—
362C4⋊C4—442no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—441no—
366C22⋊C4—441no—
367C42—222no—
368C42—222no—
369C42—441no—
370C42—441no—
371C11#988611yescharacteristic, complemented, Sylow
372C23—21no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23C22⋊C4×D1111yescharacteristic
377C23#6693811yescharacteristic
378C23#6694111yescharacteristic
379C23#6696511yescharacteristic
380C23#6696911yescharacteristic
381C23#6696911yescharacteristic
382C23#6697211yescharacteristic
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—112no—
405C2×C4—112no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—221no—
415C2×C4—221no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—881no—
430C2×C4—881no—
431C2×C4—881no—
432C2×C4—881no—
433C2×C4C4×Dic2211yescharacteristic
434C2×C4#6693111yescharacteristic
435C2×C4#6694011yescharacteristic
436C2×C4#6694911yescharacteristic
437C8—42no—
438C8—442no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22#1062225911yescharacteristic
452C22#1062235311yescharacteristic
453C22D11×#9911yescharacteristic
454C22#1062238111yescharacteristic
455C22#1062238511yescharacteristic
456C22#1062241311yescharacteristic
457C22#1062241711yescharacteristic
458C22D11×#10411yescharacteristic
459C22#1062243411yescharacteristic
460C22#1062247111yescharacteristic
461C22#1062249111yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—82no—
467C4—81no—
468C4—81no—
469C4—222no—
470C4—222no—
471C4—441no—
472C4—441no—
473C4—882no—
474C4—881no—
475C4—881no—
476C2—21no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2#1306709911yescharacteristic
481C2#1306710611yescharacteristic
482C2#1306716911yescharacteristic
483C2#1306719211yescharacteristic
484C2#1306955811yescharacteristic
485C2#1306957911yescharacteristic
486C2#1306959911yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11C2×C22⋊C4
prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9886
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
9. C2×#66943C4semidirect
19. #10622598C4semidirect
20. #10622590C4semidirect
21. #10622586C4semidirect
371. C11#9886semidirect

Maximal subgroups

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

subgroupindex
#130769242
C22⋊C8×Dic112
#130668422
#130664962
#130664952
#130664942
C11×#12942
#988611