Finite Group Databasebeta

← #14646516

Subgroups — #14646516

Order 2816.

698 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068596C211yesmaximal, characteristic, complemented
2C2×#10622175C212yesmaximal
3#13066843C211yesmaximal, characteristic, complemented
4#13066494C212yesmaximal, complemented
5C4×C11×#121C211yesmaximal, characteristic
6C2×C11×#121C2211yescharacteristic
7C2×C4×D4×C11—21no—
8C2×C4×D4×C11C411yescharacteristic, complemented
9C22×C42×C11C2211yescharacteristic
10C11×#390C411yescharacteristic, complemented
11C11×#389C411yescharacteristic, complemented
12C11×#388—21no—
13C11×#386—21no—
14C11×#380C2211yescharacteristic
15C4×C11×C4⋊C4C411yescharacteristic, complemented
16C4×C11×C22⋊C4—21no—
17C2×C11⋊#95—21no—
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×C4⋊(C11⋊C8)—21no—
22#10622175—24no—
23#10622162—21no—
24C22×D4×C11—21no—
25C22×D4×C11C2×C411yescharacteristic
26C23×C4×C11—21no—
27C23×C4×C11D411yescharacteristic
28C23×C4×C11D411yescharacteristic
29C23×C4×C11C2311yescharacteristic
30C23×Dic11—22no—
31C11×#121—21no—
32C11×#121—21no—
33C11×#121D412yes—
34C11×#121Q812yes—
35C4×D4×C11—42no—
36C4×D4×C11—44no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C4⋊C4C2×C411yescharacteristic
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C42×C11—21no—
47C2×C42×C11—42no—
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C22×C11⋊C8—22no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11⋊#95—24no—
57C11⋊#95—22no—
58C11⋊#95—22no—
59C11⋊#95—42no—
60C22⋊(C11⋊C8)—22no—
61C22⋊(C11⋊C8)—22no—
62C4⋊(C11⋊C8)—42no—
63#8575—111nomaximal, Sylow
64C24×C11—21no—
65C24×C11C2×D411yescharacteristic
66C2×D4×C11—22no—
67C2×D4×C11—22no—
68C2×D4×C11—21no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—42no—
72C2×D4×C11—42no—
73C2×D4×C11C4⋊C412yes—
74C22×C4×C11—21no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11C22⋊C411yescharacteristic
91C22×C4×C11C22⋊C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×Q811yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—24no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C22×Dic11—42no—
104C22×Dic11—42no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—41no—
109C11×C4⋊C4C4⋊C412yes—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C11×C22⋊C4—42no—
115C11×C22⋊C4—42no—
116C42×C11—22no—
117C42×C11—22no—
118C42×C11—41no—
119C42×C11—41no—
120C42×C11—42no—
121C2×C11⋊C8—42no—
122C2×C11⋊C8—42no—
123C2×C11⋊C8—42no—
124C4×#121D1111yescharacteristic
125#1797—111no—
126C2×#327—112no—
127#1434—111no—
128#1294—112no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11—22no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11—41no—
140C23×C11C2×C22⋊C411yescharacteristic
141C23×C11#12111yescharacteristic
142C23×C11C22⋊Q811yescharacteristic
143C23×C11#13512yes—
144C23×C11AGL(1,ℤ/8)12yes—
145D4×C11—42no—
146D4×C11—42no—
147D4×C11—44no—
148D4×C11—44no—
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—22no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—21no—
164C2×C4×C11—41no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—44no—
169C2×C4×C11—44no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—84no—
179C2×C4×C11#9912yes—
180C2×C4×C11#10412yes—
181C2×C4×C11C2×C4⋊C411yescharacteristic
182C2×C4×C11#11711yescharacteristic
183C2×C4×C11#12111yescharacteristic
184C2×C4×C11C22⋊Q811yescharacteristic
185C2×Dic11—44no—
186C2×Dic11—44no—
187C2×Dic11—44no—
188C2×Dic11—82no—
189C2×Dic11—82no—
190C2×Dic11—82no—
191C2×Dic11—82no—
192C11⋊C8—82no—
193C2×#121C2×D1111yescharacteristic
194C2×C4×D4—21no—
195C2×C4×D4Dic1111yescharacteristic, complemented
196C22×C42C2×D1111yescharacteristic
197C2×C4⋊C8—221no—
198C2×C22⋊C8—112no—
199#390Dic1111yescharacteristic, complemented
200#389Dic1111yescharacteristic, complemented
201#388—21no—
202#386—21no—
203#380C2×D1111yescharacteristic
204C4×C4⋊C4Dic1111yescharacteristic, complemented
205C4×C22⋊C4—21no—
206C2×#95—112no—
207C2×#95—221no—
208C2×#95—221no—
209#336—221no—
210#327—224no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—22no—
216C22×C11—22no—
217C22×C11—22no—
218C22×C11—22no—
219C22×C11—42no—
220C22×C11—42no—
221C22×C11—42no—
222C22×C11—81no—
223C22×C11—81no—
224C22×C11—81no—
225C22×C11—81no—
226C22×C11#38011yescharacteristic
227C22×C11C2×#9911yescharacteristic
228C22×C11#41011yescharacteristic
229C22×C11#41611yescharacteristic
230C22×C11#41811yescharacteristic
231C22×C11C2×#10411yescharacteristic
232C22×C11#42111yescharacteristic
233C22×C11#46312yes—
234C22×C11#47812yes—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—22no—
240C4×C11—22no—
241C4×C11—42no—
242C4×C11—41no—
243C4×C11—41no—
244C4×C11—81no—
245C4×C11—81no—
246Dic11—84no—
247C22×D4—21no—
248C22×D4C2×Dic1111yescharacteristic
249C23×C4—21no—
250C23×C4—222no—
251C23×C4C22⋊D1111yescharacteristic
252C23×C4C22⋊D1111yescharacteristic
253C23×C4C22×D1111yescharacteristic
254C22×C8—222no—
255#121—21no—
256#121—21no—
257#121Dic2212yes—
258#121D4412yes—
259C4×D4—42no—
260C4×D4—44no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4C2×Dic1111yescharacteristic
263C2×C4⋊C4C2×Dic1111yescharacteristic
264C2×C4⋊C4C2×Dic1111yescharacteristic
265C2×C22⋊C4—21no—
266C2×C22⋊C4—21no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42—21no—
271C2×C42—42no—
272C2×C42C2×Dic1111yescharacteristic
273C2×C42C2×Dic1111yescharacteristic
274C2×C42C22⋊D1111yescharacteristic
275C2×C42C22⋊D1111yescharacteristic
276C4⋊C8—442no—
277C22⋊C8—222no—
278C22⋊C8—222no—
279#95—21no—
280#95—21no—
281#95—21no—
282#95—224no—
283#95—222no—
284#95—222no—
285#95—442no—
286C2×C11—22no—
287C2×C11—22no—
288C2×C11—82no—
289C2×C11#150111yescharacteristic
290C2×C11#150511yescharacteristic
291C2×C11#151011yescharacteristic
292C2×C11#152111yescharacteristic
293C2×C11#179911yescharacteristic
294C2×C11#180411yescharacteristic
295C2×C11#180611yescharacteristic
296C24—21no—
297C24C2×C22⋊D1111yescharacteristic
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—21no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4C4⋊Dic1112yes—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—42no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—224no—
321C22×C4—442no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4—442no—
325C22×C4—442no—
326C22×C4—442no—
327C22×C4C22⋊Dic1111yescharacteristic
328C22×C4C22⋊Dic1111yescharacteristic
329C22×C4C22⋊Dic1111yescharacteristic
330C22×C4C22⋊Dic1111yescharacteristic
331C22×C4C2×Dic2211yescharacteristic
332C22×C4C2×D4411yescharacteristic
333C22×C4#433911yescharacteristic
334C22×C4#433911yescharacteristic
335C22×C4C22×Dic1111yescharacteristic
336C22×C4C2×C22⋊D1111yescharacteristic
337C2×C8—442no—
338C2×C8—442no—
339C2×C8—442no—
340C4⋊C4—21no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—42no—
344C4⋊C4C4⋊Dic1112yes—
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C42—22no—
352C42—22no—
353C42—41no—
354C42—41no—
355C42—42no—
356C11#857511yescharacteristic, complemented, Sylow
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—22no—
362C23—41no—
363C23—41no—
364C23—41no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23#6697711yescharacteristic
369C23#6698311yescharacteristic
370C23#6698512yes—
371C23#6700312yes—
372C23C2×C22⋊Dic1111yescharacteristic
373D4—42no—
374D4—42no—
375D4—44no—
376D4—44no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—84no—
407C2×C4—444no—
408C2×C4—444no—
409C2×C4—444no—
410C2×C4—882no—
411C2×C4—882no—
412C2×C4—882no—
413C2×C4—882no—
414C2×C4#6689812yes—
415C2×C4#6690112yes—
416C2×C4#6697711yescharacteristic
417C2×C4C2×C4⋊Dic1111yescharacteristic
418C2×C4#6697911yescharacteristic
419C2×C4#6698311yescharacteristic
420C8—882no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22—81no—
436C22#1062262212yes—
437C22#1062262912yes—
438C22#1062282511yescharacteristic
439C22#1062282811yescharacteristic
440C22C2×#6689811yescharacteristic
441C22#1062284611yescharacteristic
442C22C2×#6690111yescharacteristic
443C22#1062284911yescharacteristic
444C22#1062285311yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—22no—
450C4—22no—
451C4—42no—
452C4—41no—
453C4—41no—
454C4—81no—
455C4—81no—
456C4—884no—
457C2—22no—
458C2—22no—
459C2—82no—
460C2#1306710711yescharacteristic
461C2#1306712411yescharacteristic
462C2#1306714511yescharacteristic
463C2#1306719311yescharacteristic
464C2#1306860411yescharacteristic
465C2#1306862611yescharacteristic
466C2#1306863611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC4×C11×#121C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC4×#121D11
hypocenterC11#8575
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. #13068596C2semidirect
3. #13066843C2semidirect
4. #13066494C2semidirect
8. C2×C4×D4×C11C4semidirect
10. C11×#390C4semidirect
11. C11×#389C4semidirect
15. C4×C11×C4⋊C4C4semidirect
195. C2×C4×D4Dic11semidirect
199. #390Dic11semidirect
200. #389Dic11semidirect
204. C4×C4⋊C4Dic11semidirect
356. C11#8575semidirect

Maximal subgroups

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

subgroupindex
#130685962
C2×#106221752
#130668432
#130664942
C4×C11×#1212
#857511