Finite Group Databasebeta

← #14644677

Subgroups — #14644677

Order 2816.

724 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊(C11⋊C8)C211yesmaximal, 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#10622175C418yescomplemented
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—22no—
32C11×#121C2×C414yes—
33C4×D4×C11—42no—
34C4×D4×C11—42no—
35C4×D4×C11—42no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4C2×C411yescharacteristic
38C2×C11×C4⋊C4C2×C411yescharacteristic
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C42×C11—21no—
46C2×C42×C11—42no—
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C22×C11⋊C8—22no—
52C11×#95—21no—
53C11×#95—21no—
54C11×#95—21no—
55C11⋊#95—22no—
56C11⋊#95—42no—
57C11⋊#95—42no—
58C11⋊#95C2×C414yescomplemented
59C22⋊(C11⋊C8)—22no—
60C22⋊(C11⋊C8)C2×C414yescomplemented
61C4×C11⋊C8—42no—
62#8220—111nomaximal, Sylow
63C24×C11—21no—
64C24×C11C2×D411yescharacteristic
65C2×D4×C11—24no—
66C2×D4×C11—21no—
67C2×D4×C11—41no—
68C2×D4×C11—41no—
69C2×D4×C11—41no—
70C2×D4×C11—41no—
71C2×D4×C11—42no—
72C2×D4×C11C4212yes—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—22no—
76C22×C4×C11—21no—
77C22×C4×C11—21no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—42no—
84C22×C4×C11—42no—
85C22×C4×C11—42no—
86C22×C4×C11C22⋊C411yescharacteristic
87C22×C4×C11C22⋊C411yescharacteristic
88C22×C4×C11C22⋊C411yescharacteristic
89C22×C4×C11C22⋊C411yescharacteristic
90C22×C4×C11D812yes—
91C22×C4×C11SD1612yes—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4112yes—
96C22×Dic11—24no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C22×Dic11—42no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—41no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—42no—
107C11×C4⋊C4C4212yes—
108C11×C22⋊C4—24no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—42no—
113C11×C22⋊C4—42no—
114C42×C11—22no—
115C42×C11—22no—
116C42×C11—41no—
117C42×C11—41no—
118C42×C11—42no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—42no—
122C4×#121D1111yescharacteristic
123C4×C22⋊C8—111no—
124C2×#327—112no—
125#1434—111no—
126#1294—112no—
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—22no—
132C23×C11—41no—
133C23×C11—41no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11—41no—
137C23×C11—41no—
138C23×C11C2×C22⋊C411yescharacteristic
139C23×C11C4×D412yes—
140C23×C11C2×D811yescharacteristic
141C23×C11C2×SD1611yescharacteristic
142C23×C11#13512yes—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—44no—
146D4×C11—44no—
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—22no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—21no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—44no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—84no—
175C2×C4×C11#9912yes—
176C2×C4×C11#10212yes—
177C2×C4×C11#10212yes—
178C2×C4×C11C2×C4211yescharacteristic
179C2×C4×C11#11711yescharacteristic
180C2×C4×C11C4×D412yes—
181C2×Dic11—44no—
182C2×Dic11—44no—
183C2×Dic11—44no—
184C2×Dic11—82no—
185C2×Dic11—82no—
186C2×Dic11—82no—
187C2×Dic11—82no—
188C11⋊C8—44no—
189C2×#121C2×D1111yescharacteristic
190C2×C4×D4—21no—
191C2×C4×D4Dic1111yescharacteristic, complemented
192C22×C42C2×D1111yescharacteristic
193C2×C22⋊C8—112no—
194C2×C4×C8—221no—
195#390Dic1111yescharacteristic, complemented
196#389Dic1111yescharacteristic, complemented
197#388—21no—
198#386—21no—
199#380C2×D1111yescharacteristic
200C4×C4⋊C4Dic1111yescharacteristic, complemented
201C4×C22⋊C4—21no—
202C2×#95—112no—
203C2×#95—221no—
204C2×#95—221no—
205#336—221no—
206#327—118no—
207C22×C11—22no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—22no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—42no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11—81no—
222C22×C11C4×C22⋊C411yescharacteristic
223C22×C11C2×#9911yescharacteristic
224C22×C11#41011yescharacteristic
225C22×C11C2×#10211yescharacteristic
226C22×C11#41611yescharacteristic
227C22×C11#42111yescharacteristic
228C22×C11#42111yescharacteristic
229C22×C11C4×D812yes—
230C22×C11C4×SD1612yes—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—22no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—42no—
238C4×C11—41no—
239C4×C11—81no—
240C4×C11—81no—
241Dic11—84no—
242C22×D4—21no—
243C22×D4C2×Dic1111yescharacteristic
244C23×C4—21no—
245C23×C4—222no—
246C23×C4C22⋊D1111yescharacteristic
247C23×C4C22⋊D1111yescharacteristic
248C23×C4C22×D1111yescharacteristic
249C22×C8—222no—
250#121—22no—
251#121C4×D1114yes—
252C4×D4—42no—
253C4×D4—42no—
254C4×D4—42no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4C2×Dic1111yescharacteristic
257C2×C4⋊C4C2×Dic1111yescharacteristic
258C2×C4⋊C4C2×Dic1111yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—21no—
264C2×C42—21no—
265C2×C42—42no—
266C2×C42C2×Dic1111yescharacteristic
267C2×C42C2×Dic1111yescharacteristic
268C2×C42C22⋊D1111yescharacteristic
269C2×C42C22⋊D1111yescharacteristic
270C22⋊C8—114no—
271C22⋊C8—222no—
272C4×C8—442no—
273#95—21no—
274#95—21no—
275#95—21no—
276#95—114no—
277#95—222no—
278#95—442no—
279#95—442no—
280C2×C11—22no—
281C2×C11—22no—
282C2×C11—82no—
283C2×C11#151611yescharacteristic
284C2×C11#151711yescharacteristic
285C2×C11#151911yescharacteristic
286C2×C11#152111yescharacteristic
287C2×C11C4×#9911yescharacteristic
288C2×C11#175911yescharacteristic
289C2×C11C4×#10211yescharacteristic
290C24—21no—
291C24C2×C22⋊D1111yescharacteristic
292C2×D4—24no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4C4×Dic1112yes—
300C22×C4—22no—
301C22×C4—21no—
302C22×C4—22no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—42no—
311C22×C4—42no—
312C22×C4—42no—
313C22×C4—224no—
314C22×C4—442no—
315C22×C4—442no—
316C22×C4—442no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4#432312yes—
321C22×C4#432412yes—
322C22×C4C22⋊Dic1111yescharacteristic
323C22×C4C22⋊Dic1111yescharacteristic
324C22×C4C22⋊Dic1111yescharacteristic
325C22×C4C22⋊Dic1111yescharacteristic
326C22×C4C2×C4×D1112yes—
327C22×C4#433912yes—
328C22×C4C22×Dic1111yescharacteristic
329C22×C4C2×C22⋊D1111yescharacteristic
330C2×C8—224no—
331C2×C8—442no—
332C2×C8—442no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—42no—
337C4⋊C4C4×Dic1112yes—
338C22⋊C4—24no—
339C22⋊C4—42no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—42no—
343C22⋊C4—42no—
344C42—22no—
345C42—22no—
346C42—41no—
347C42—41no—
348C42—42no—
349C11#822011yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—41no—
361C23C4×C22⋊D1112yes—
362C23C2×#432311yescharacteristic
363C23C2×#432411yescharacteristic
364C23#6700312yes—
365C23C2×C22⋊Dic1111yescharacteristic
366D4—42no—
367D4—42no—
368D4—44no—
369D4—44no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—22no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—44no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—84no—
398C2×C4—444no—
399C2×C4—444no—
400C2×C4—444no—
401C2×C4—882no—
402C2×C4—882no—
403C2×C4—882no—
404C2×C4—882no—
405C2×C4#6689612yes—
406C2×C4#6689612yes—
407C2×C4#6689812yes—
408C2×C4C2×C4×Dic1111yescharacteristic
409C2×C4#6697911yescharacteristic
410C2×C4C4×C22⋊D1112yes—
411C8—444no—
412C22—22no—
413C22—22no—
414C22—22no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—22no—
420C22—42no—
421C22—42no—
422C22—42no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22C4×#432312yes—
428C22C4×#432412yes—
429C22C4×C22⋊Dic1111yescharacteristic
430C22C2×#6689611yescharacteristic
431C22C2×#6689811yescharacteristic
432C22#1062284611yescharacteristic
433C22#1062284911yescharacteristic
434C22#1062284911yescharacteristic
435C22#1062285311yescharacteristic
436C4—22no—
437C4—21no—
438C4—21no—
439C4—22no—
440C4—22no—
441C4—22no—
442C4—42no—
443C4—41no—
444C4—81no—
445C4—81no—
446C4—884no—
447C2—22no—
448C2—22no—
449C2—82no—
450C2#1306717211yescharacteristic
451C2#1306717611yescharacteristic
452C2#1306718411yescharacteristic
453C2#1306719311yescharacteristic
454C2C4×#6689811yescharacteristic
455C2#1306842611yescharacteristic
456C2C4×#6689611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic11
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC4×C11×#121C2
socleC23×C11C2×C22⋊C4
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC4×#121D11
hypocenterC11#8220
LCSG ▷ C2×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. C4×C22⋊(C11⋊C8)C2semidirect
3. #13066843C2semidirect
4. #13066494C2semidirect
8. C2×C4×D4×C11C4semidirect
10. C11×#390C4semidirect
11. C11×#389C4semidirect
15. C4×C11×C4⋊C4C4semidirect
22. #10622175C4semidirect
58. C11⋊#95C2×C4semidirect
60. C22⋊(C11⋊C8)C2×C4semidirect
191. C2×C4×D4Dic11semidirect
195. #390Dic11semidirect
196. #389Dic11semidirect
200. C4×C4⋊C4Dic11semidirect
349. C11#8220semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊(C11⋊C8)2
C2×#106221752
#130668432
#130664942
C4×C11×#1212
#822011