Finite Group Databasebeta

← #14810476

Subgroups — #14810476

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic
2C2×#10622695C211yesmaximal, characteristic, complemented
3C2×#10622694C211yesmaximal, characteristic, complemented
4#13069767C212yesmaximal, complemented
5#13069757C212yesmaximal, complemented
6#13069588C211yesmaximal, characteristic, complemented
7#13069580C211yesmaximal, characteristic, complemented
8#13068929C212yesmaximal
9#13068924C212yesmaximal
10#13068382C211yesmaximal, characteristic
11C11×#2621C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8C2212yes—
14C2×C11×#117C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17#10623050—24no—
18#10623050—24no—
19C2×#66943—21no—
20C2×#66941—21no—
21C2×#66931—21no—
22C2×#66931—21no—
23C2×#66923C2211yescharacteristic
24C2×#66923C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#398—21no—
28C11×#398—21no—
29C11×#397—21no—
30C11×#397—21no—
31C11×#391C2212yes—
32C11×#382C2211yescharacteristic
33C2×#66899C2212yes—
34C2×#66899C2212yes—
35C2×#66899C2212yes—
36C2×#66899C2212yes—
37C2×C22⋊(C11⋊C8)C2212yes—
38#10622695—24no—
39#10622694—24no—
40C2×#66867C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×Dic11—21no—
50C22×Dic22—21no—
51C22×Dic22—21no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×C22⋊Q8—28no—
55C11×#117—22no—
56C11×#117—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4D411yescharacteristic
61C2×C11×C4⋊C4D411yescharacteristic
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4D411yescharacteristic
65C2×C11×C22⋊C4D411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11—21no—
69#66979—22no—
70#66979—22no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×C4×Dic11—21no—
85C22×C11⋊C8C2312yes—
86C22×C11⋊C8C2312yes—
87#66943—28no—
88#66941—28no—
89#66931—28no—
90#66931—28no—
91#66923—22no—
92#66923—22no—
93#66923—22no—
94#66923D414yes—
95#66922—22no—
96#66922—22no—
97#66922—22no—
98#66922D414yes—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—22no—
102C11×#95—22no—
103#66899—24no—
104#66899—24no—
105#66899—24no—
106#66899—24no—
107C22⋊(C11⋊C8)—24no—
108#66867—22no—
109C4×C11⋊C8—22no—
110#25914—111nomaximal, Sylow
111C24×C11C2×D411yescharacteristic
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—24no—
115C2×Q8×C11—24no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11#4114yes—
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—24no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—82no—
134C2×Dic22—24no—
135C2×Dic22—24no—
136C2×Dic22—82no—
137C2×Dic22—82no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—42no—
142C11×C4⋊C4—42no—
143C11×C4⋊C4—44no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—22no—
146C11×C22⋊C4—44no—
147C42×C11—21no—
148C42×C11—21no—
149C42×C11C2×D412yes—
150C42×C11C2×D412yes—
151C22⋊Dic11—24no—
152C4⋊Dic11—24no—
153C4⋊Dic11—24no—
154C4⋊Dic11—24no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11C2×D412yes—
160C4⋊Dic11C2×D412yes—
161C4⋊Dic11C2×D412yes—
162C4⋊Dic11C2×D412yes—
163Dic11⋊C4—24no—
164Dic11⋊C4—24no—
165Dic11⋊C4—24no—
166Dic11⋊C4—24no—
167C4×Dic11—24no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×#544—111no—
175C2×#491—111no—
176C2×#487—111no—
177#2621D1111yescharacteristic
178#2026—112no—
179#2024—112no—
180#1993—111no—
181#1991—111no—
182#1873—112no—
183#1872—112no—
184#1750—111no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11#12412yes—
190C23×C11C22×D411yescharacteristic
191Q8×C11—44no—
192Q8×C11—44no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11#12012yes—
210C2×C4×C11#12012yes—
211C2×C4×C11#12412yes—
212C2×C4×C11C22×D411yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4112yes—
215C2×C4×C112−1+412yes—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—84no—
225Dic22—84no—
226Dic22—84no—
227C11⋊C8—42no—
228C11⋊C8—42no—
229#544—224no—
230#544—224no—
231C2×C4⋊Q8—111no—
232C2×C4⋊Q8—111no—
233C2×C4⋊Q8—221no—
234C2×C4⋊Q8C2×D1111yescharacteristic
235C2×#125—111no—
236C2×#125—111no—
237C2×#125—221no—
238C2×C22⋊Q8—221no—
239C2×C22⋊Q8—221no—
240C2×C22⋊Q8C2×D1112yes—
241C2×#117—111no—
242C2×#117C2×D1111yescharacteristic
243C22×C4⋊C4—111no—
244#491—224no—
245#487—224no—
246C2×#103—112no—
247C2×#103—112no—
248C2×#103—112no—
249C2×#103—112no—
250C2×C22⋊C8—112no—
251C2×#97—111no—
252C2×C4×C8—111no—
253#398—21no—
254#398—21no—
255#397—21no—
256#397—21no—
257#391C2×D1112yes—
258#382C2×D1111yescharacteristic
259#340—112no—
260#340—112no—
261#340—112no—
262#340—112no—
263#336—112no—
264C22×C11—24no—
265C22×C11—22no—
266C22×C11—42no—
267C22×C11—41no—
268C22×C11—41no—
269C22×C11C2×#12011yescharacteristic
270C22×C11C2×#12411yescharacteristic
271C22×C11#53611yescharacteristic
272C22×C11#57712yes—
273C22×C11#57812yes—
274C4×C11—22no—
275C4×C11—22no—
276C4×C11—22no—
277C4×C11—41no—
278C4×C11—41no—
279C4×C11—82no—
280C4×C11—82no—
281C4×C11#54812yes—
282C4×C11#54812yes—
283Dic11—42no—
284Dic11—42no—
285Dic11—42no—
286Dic11—42no—
287C22×Q8—221no—
288C22×Q8—221no—
289C22×Q8C22×D1112yes—
290C23×C4—221no—
291C23×C4C22×D1111yescharacteristic
292C22×C8—112no—
293C22×C8—112no—
294C4⋊Q8—22no—
295C4⋊Q8—22no—
296C4⋊Q8—114no—
297C4⋊Q8—222no—
298C4⋊Q8—222no—
299C4⋊Q8—228no—
300C4⋊Q8—222no—
301#125—114no—
302#125—222no—
303#125—222no—
304#125—228no—
305#125—222no—
306C22⋊Q8—28no—
307C22⋊Q8—228no—
308C22⋊Q8—228no—
309#117—22no—
310#117—22no—
311#117—222no—
312#117—222no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—221no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4C22⋊D1111yescharacteristic
330C2×C4⋊C4C22⋊D1111yescharacteristic
331C2×C4⋊C4C22×D1112yes—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4C22⋊D1111yescharacteristic
335C2×C22⋊C4C22⋊D1111yescharacteristic
336C2×C42—221no—
337C2×C42C22×D1111yescharacteristic
338C2×C42C22×D1111yescharacteristic
339#103—224no—
340#103—224no—
341#103—224no—
342#103—224no—
343C22⋊C8—224no—
344#97—222no—
345C4×C8—222no—
346#95—21no—
347#95—21no—
348#95—22no—
349#95—22no—
350C2×C11—42no—
351C2×C11#243611yescharacteristic
352C2×C11#300911yescharacteristic
353C2×C11#301111yescharacteristic
354C2×C11#313712yes—
355C2×C11#324212yes—
356C24C2×C22⋊D1111yescharacteristic
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—24no—
360C2×Q8—24no—
361C2×Q8—224no—
362C2×Q8—224no—
363C2×Q8—882no—
364C2×Q8—882no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—221no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—221no—
374C22×C4—224no—
375C22×C4—882no—
376C22×C4#434114yes—
377C22×C4C2×C22⋊D1111yescharacteristic
378C22×C4C2×C22⋊D1111yescharacteristic
379C22×C4C2×C22⋊D1111yescharacteristic
380C22×C4C2×C22⋊D1111yescharacteristic
381C22×C4C2×C22⋊D1111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383C2×C8—222no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8—222no—
388C2×C8—222no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—24no—
392C4⋊C4—44no—
393C4⋊C4—42no—
394C4⋊C4—42no—
395C4⋊C4—112no—
396C4⋊C4—112no—
397C4⋊C4—112no—
398C4⋊C4—112no—
399C4⋊C4—224no—
400C4⋊C4—224no—
401C4⋊C4—224no—
402C4⋊C4—224no—
403C4⋊C4—224no—
404C4⋊C4—224no—
405C4⋊C4—224no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—221no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—44no—
413C22⋊C4—224no—
414C42—21no—
415C42—21no—
416C42—224no—
417C42D4×D1112yes—
418C42D4×D1112yes—
419C11#2591411yescharacteristic, complemented, Sylow
420C23—21no—
421C23—21no—
422C23—22no—
423C23—22no—
424C23#6698912yes—
425C23C22×C22⋊D1111yescharacteristic
426Q8—44no—
427Q8—44no—
428Q8—884no—
429Q8—884no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—24no—
435C2×C4—24no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—884no—
455C2×C4#6698912yes—
456C2×C4#6699012yes—
457C2×C4#6699012yes—
458C2×C4C2×D4×D1111yescharacteristic
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×#434112yes—
461C2×C4#6704312yes—
462C8—442no—
463C8—442no—
464C22—22no—
465C22—24no—
466C22—42no—
467C22—41no—
468C22—41no—
469C22C2×#6698911yescharacteristic
470C22C2×#6699011yescharacteristic
471C22#1062335611yescharacteristic
472C22#1062336812yes—
473C22#1062336912yes—
474C4—22no—
475C4—22no—
476C4—22no—
477C4—41no—
478C4—41no—
479C4—82no—
480C4—82no—
481C4—442no—
482C4—442no—
483C4—442no—
484C4—442no—
485C4#1062312912yes—
486C4#1062312912yes—
487C2—42no—
488C2#1307227511yescharacteristic
489C2#1307789111yescharacteristic
490C2#1307790911yescharacteristic
491C2#1307898112yes—
492C2#1307987812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2621C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2621D11
hypocenterC11#25914
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2621

Complements

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

NH ≅ G/Ntype
2. C2×#10622695C2semidirect
3. C2×#10622694C2semidirect
4. #13069767C2semidirect
5. #13069757C2semidirect
6. #13069588C2semidirect
7. #13069580C2semidirect
419. C11#25914semidirect

Maximal subgroups

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

subgroupindex
C2×#106230502
C2×#106226952
C2×#106226942
#130697672
#130697572
#130695882
#130695802
#130689292
#130689242
#130683822
C11×#26212
#2591411