Finite Group Databasebeta

← #14770987

Subgroups — #14770987

Order 2816.

978 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
1C2×#10622846C211yesmaximal, characteristic
2#13071507C211yesmaximal, characteristic, complemented
3#13069302C212yesmaximal, complemented
4#13069240C212yesmaximal, complemented
5#13068884C212yesmaximal, complemented
6#13068708C211yesmaximal, characteristic, complemented
7#13068639C211yesmaximal, characteristic, complemented
8#13068556C211yesmaximal, characteristic
9C4×#66899C212yesmaximal, complemented
10C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#2341C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C2×C4×Q8×C11C2212yes—
14C2×#66979C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C11×#390—22no—
17C11×#390C2212yes—
18C11×#380—21no—
19C11×#380C2211yescharacteristic
20C4×C11×C22⋊C4—21no—
21C4×C11×C22⋊C4C2211yescharacteristic
22#10622846C418yescomplemented
23C2×#66899C2212yes—
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66896C2212yes—
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66872C2212yes—
32#10622558—22no—
33C4×C4⋊Dic11C2212yes—
34#10622541C2212yes—
35C2×C4×C11⋊C8C2212yes—
36#10622264—21no—
37#10622262—21no—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622162C2212yes—
42C2×C11×#41—22no—
43C2×C11×#41—24no—
44C2×C11×#41—42no—
45C2×C11×#41C2×C414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C4×Q8×C11—24no—
52C4×Q8×C11—42no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4D412yes—
59C2×C42×C11—22no—
60C2×C42×C11C2312yes—
61C2×C22⋊Dic11—21no—
62C2×C22⋊Dic11—21no—
63#66979—22no—
64#66979C2×C414yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11—21no—
70C2×C4×Dic11—22no—
71C22×C11⋊C8—42no—
72C22×C11⋊C8C2×C414yes—
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C22×C11⋊C8C2311yescharacteristic
76C11×#95—21no—
77C11×#95D411yescharacteristic
78C11×#95D411yescharacteristic
79#66899—24no—
80#66899C2×C414yes—
81#66899C2×C414yes—
82#66896—42no—
83#66896C2×C414yes—
84#66896C2×C414yes—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C22⋊(C11⋊C8)—22no—
89#66872—42no—
90C4×C11⋊C8—42no—
91#22577—111nomaximal, Sylow
92C24×C11—21no—
93C24×C11C2×D411yescharacteristic
94C11×#41—28no—
95C11×#41—44no—
96C11×#41—48no—
97C2×Q8×C11—21no—
98C2×Q8×C11—22no—
99C2×Q8×C11C22×C412yes—
100C2×Q8×C11#4114yes—
101C2×D4×C11—24no—
102C2×D4×C11—22no—
103C2×D4×C11—21no—
104C2×D4×C11—22no—
105C2×D4×C11—44no—
106C2×D4×C11C22×C412yes—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11#4112yes—
118C22×C4×C11C2411yescharacteristic
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—44no—
125C11×C22⋊C4—24no—
126C11×C22⋊C4—44no—
127C11×C22⋊C4—82no—
128C11×C22⋊C4—81no—
129C42×C11—22no—
130C42×C11—22no—
131C42×C11—44no—
132C22⋊Dic11—24no—
133C22⋊Dic11—81no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11C22×C412yes—
139C4⋊Dic11C22×C412yes—
140Dic11⋊C4—44no—
141C4×Dic11—24no—
142C4×Dic11—82no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—44no—
149C2×C11⋊C8C22×C412yes—
150C2×C11⋊C8C22×C412yes—
151C2×#416—111no—
152#2347—111no—
153#2341D1111yescharacteristic
154#1934—112no—
155#1926—112no—
156#1865—112no—
157#1825—111no—
158#1807—111no—
159#1788—111no—
160C4×#103—112no—
161C8×C22⋊C4—111no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—21no—
165C23×C11—21no—
166C23×C11—22no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11C4×D412yes—
172C23×C11C22×D411yescharacteristic
173Q8×C11—22no—
174Q8×C11—24no—
175Q8×C11#11714yes—
176D4×C11—22no—
177D4×C11—22no—
178D4×C11—48no—
179D4×C11—42no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—48no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11C4×D412yes—
196C2×C4×C11#13514yes—
197C2×C4×C11C23×C411yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4112yes—
200C2×C4×C11H(5,𝔽2)12yes—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C11⋊C8—22no—
210C11⋊C8—22no—
211C11⋊C8—42no—
212C22×#41C2×D1111yescharacteristic
213C23×C8—111no—
214C2×C4×Q8C2×D1112yes—
215C2×#117—111no—
216C2×#106—112no—
217#416—118no—
218C2×#103—111no—
219C2×#103—111no—
220C2×#103—112no—
221C2×#102—111no—
222C2×#102—111no—
223C2×#102—112no—
224C2×C22⋊C8—111no—
225C2×C4×C8—112no—
226#390—22no—
227#390C2×D1112yes—
228#389—112no—
229#388—222no—
230#383—221no—
231#380—21no—
232#380—111no—
233#380C2×D1111yescharacteristic
234C4×C4⋊C4—112no—
235C4×C4⋊C4—221no—
236C4×C22⋊C4—21no—
237C4×C22⋊C4C2×D1111yescharacteristic
238#340—112no—
239#340—112no—
240#340—112no—
241#336—112no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—42no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11C2×C4×D411yescharacteristic
253C22×C11#54612yes—
254C22×C11C2×#13512yes—
255C22×C11#57711yescharacteristic
256C22×C11#57711yescharacteristic
257C4×C11—22no—
258C4×C11—24no—
259C4×C11—24no—
260C4×C11—42no—
261C4×C11—82no—
262C4×C11C2×#11711yescharacteristic
263C4×C11#51811yescharacteristic
264C4×C11#55112yes—
265Dic11—42no—
266Dic11—42no—
267Dic11—82no—
268C2×#41—22no—
269C2×#41—24no—
270C2×#41—42no—
271C2×#41C4×D1114yes—
272C22×Q8C22×D1111yescharacteristic
273C22×D4—21no—
274C22×D4C22×D1111yescharacteristic
275C23×C4—21no—
276C23×C4C22×D1111yescharacteristic
277C22×C8—111no—
278C22×C8—111no—
279C22×C8—114no—
280C22×C8—112no—
281C22×C8—442no—
282C4×Q8—24no—
283C4×Q8—42no—
284#117—114no—
285#117—222no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4C22×D1112yes—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—21no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—221no—
297C2×C22⋊C4C22⋊D1112yes—
298C2×C42—22no—
299C2×C42—221no—
300C2×C42—222no—
301C2×C42C22×D1112yes—
302#106—442no—
303#103—114no—
304#103—114no—
305#103—224no—
306#102—114no—
307#102—114no—
308#102—442no—
309C22⋊C8—222no—
310C4×C8—442no—
311#95—21no—
312#95—222no—
313#95—221no—
314#95—222no—
315#95C22⋊D1111yescharacteristic
316#95C22⋊D1111yescharacteristic
317C2×C11—42no—
318C2×C11—82no—
319C2×C11#234211yescharacteristic
320C2×C11C4×#13511yescharacteristic
321C2×C11#295211yescharacteristic
322C2×C11#330112yes—
323C2×C11#330412yes—
324C24—21no—
325C24C2×C22⋊D1111yescharacteristic
326#41—28no—
327#41—44no—
328#41—48no—
329C2×Q8—21no—
330C2×Q8—22no—
331C2×Q8C2×C4×D1112yes—
332C2×Q8#434114yes—
333C2×D4—24no—
334C2×D4—21no—
335C2×D4—22no—
336C2×D4—22no—
337C2×D4—44no—
338C2×D4C2×C4×D1112yes—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—24no—
343C22×C4—22no—
344C22×C4—44no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—222no—
348C22×C4C2×C4×D1112yes—
349C22×C4#433912yes—
350C22×C4C2×C22⋊D1112yes—
351C22×C4C2×C22⋊D1111yescharacteristic
352C22×C4C2×C22⋊D1112yes—
353C22×C4C23×D1111yescharacteristic
354C2×C8—112no—
355C2×C8—112no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—444no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—44no—
365C4⋊C4—112no—
366C4⋊C4—112no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—444no—
372C22⋊C4—24no—
373C22⋊C4—44no—
374C22⋊C4—82no—
375C22⋊C4—81no—
376C22⋊C4—224no—
377C22⋊C4—881no—
378C42—22no—
379C42—22no—
380C42—44no—
381C42—224no—
382C42—882no—
383C11#2257711yescharacteristic, complemented, Sylow
384C23—22no—
385C23—22no—
386C23—21no—
387C23—21no—
388C23—22no—
389C23—42no—
390C23—42no—
391C23—41no—
392C23—41no—
393C23C4×C22⋊D1112yes—
394C23C22×C22⋊D1111yescharacteristic
395Q8—22no—
396Q8—24no—
397Q8#6693014yes—
398D4—22no—
399D4—22no—
400D4—48no—
401D4—42no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—48no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—222no—
418C2×C4—222no—
419C2×C4—442no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4C4×C22⋊D1112yes—
426C2×C4#6700314yes—
427C2×C4C22×C4×D1111yescharacteristic
428C2×C4C2×#433911yescharacteristic
429C2×C4C2×#434112yes—
430C2×C4#6703712yes—
431C8—222no—
432C8—222no—
433C8—442no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—42no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—42no—
442C22—82no—
443C22—82no—
444C22C2×C4×C22⋊D1111yescharacteristic
445C22#1062333712yes—
446C22C2×#6700312yes—
447C22#1062336711yescharacteristic
448C22#1062336811yescharacteristic
449C4—22no—
450C4—24no—
451C4—24no—
452C4—42no—
453C4—82no—
454C4—442no—
455C4—442no—
456C4—882no—
457C4C2×#6693011yescharacteristic
458C4#1062301711yescharacteristic
459C4#1062302612yes—
460C2—42no—
461C2—82no—
462C2#1307146111yescharacteristic
463C2C4×#6700311yescharacteristic
464C2#1307749711yescharacteristic
465C2#1308051812yes—
466C2#1308055512yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2341C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#2341D11
hypocenterC11#22577
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2341

Complements

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

NH ≅ G/Ntype
2. #13071507C2semidirect
3. #13069302C2semidirect
4. #13069240C2semidirect
5. #13068884C2semidirect
6. #13068708C2semidirect
7. #13068639C2semidirect
9. C4×#66899C2semidirect
10. C22⋊C4×C11⋊C8C2semidirect
22. #10622846C4semidirect
383. C11#22577semidirect

Maximal subgroups

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

subgroupindex
C2×#106228462
#130715072
#130693022
#130692402
#130688842
#130687082
#130686392
#130685562
C4×#668992
C22⋊C4×C11⋊C82
C11×#23412
#2257711