Finite Group Databasebeta

← #14808198

Subgroups — #14808198

Order 2816.

968 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622678C211yesmaximal, characteristic, complemented
2C2×#10622694C211yesmaximal, characteristic, complemented
3#13074437C211yesmaximal, characteristic
4#13069816C212yesmaximal
5#13069809C212yesmaximal
6#13069582C211yesmaximal, characteristic, complemented
7#13069437C211yesmaximal, characteristic, complemented
8#13068884C212yesmaximal, complemented
9#13068870C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic
11C2×C11×#541C211yesmaximal, characteristic
12C11×#541—24no—
13C11×#541—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#126—21no—
16C2×C11×#126—21no—
17C2×C11×#125—21no—
18C2×C11×#125—21no—
19C2×C11×#125C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C2×#66899C2212yes—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30#10622825C2212yes—
31C2×C22⋊(C11⋊C8)C2212yes—
32#10622694—24no—
33#10622678—24no—
34#10622599—21no—
35#10622592—21no—
36C2×#66872C2212yes—
37C2×#66871C2212yes—
38#10622562—21no—
39#10622560—21no—
40#10622549C2211yescharacteristic
41#10622541C2212yes—
42C2×#66867C2211yescharacteristic
43C2×C4×C11⋊C8C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C22×Dic22—21no—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8D414yes—
53C11×#126—28no—
54C11×#126—28no—
55C11×#125—28no—
56C11×#125—28no—
57C11×#125—22no—
58C11×#125D414yes—
59C11×C22⋊Q8—22no—
60C11×C22⋊Q8—22no—
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C11×#117—22no—
68C11×#117—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2312yes—
92C2×C4⋊Dic11C2312yes—
93C2×Dic11⋊C4—22no—
94C22×C11⋊C8C2312yes—
95C22×C11⋊C8C2312yes—
96#66922—22no—
97#66922—22no—
98#66899—24no—
99#66899—24no—
100#66899—24no—
101#66899—24no—
102C11⋊#95—22no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—22no—
106C22⋊(C11⋊C8)—24no—
107#66872—24no—
108#66871—24no—
109#66867—22no—
110C4×C11⋊C8—22no—
111#25686—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C2×Q8×C11—21no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11C2×D412yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—22no—
136C22×Dic11—22no—
137C2×Dic22—42no—
138C2×Dic22—82no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142C11×C4⋊C4—24no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4C2×D412yes—
152C11×C4⋊C4C2×D412yes—
153C11×C22⋊C4—24no—
154C11×C22⋊C4—24no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C42×C11—24no—
158C42×C11—24no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11C2×D412yes—
162C42×C11C2×D412yes—
163C22⋊Dic11—82no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—42no—
169Dic11⋊C4—82no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8#4114yes—
176C2×#541D1111yescharacteristic
177C2×#501—111no—
178C2×#487—111no—
179#2628—111no—
180#2036—112no—
181#2035—112no—
182#1991—111no—
183#1960—111no—
184#1865—112no—
185#1863—112no—
186#1750—111no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—22no—
191C23×C11—22no—
192C23×C11C22×D411yescharacteristic
193Q8×C11—24no—
194Q8×C11—24no—
195Q8×C11—42no—
196Q8×C11—42no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11#12012yes—
219C2×C4×C11#12012yes—
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4112yes—
223C2×C4×C112−1+412yes—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—42no—
230Dic22—84no—
231C11⋊C8—24no—
232C11⋊C8—42no—
233#541—24no—
234#541—24no—
235C2×C4⋊Q8—111no—
236C2×C4⋊Q8C2×D1111yescharacteristic
237C2×#126—21no—
238C2×#126—21no—
239C2×#125—21no—
240C2×#125—21no—
241C2×#125C2×D1111yescharacteristic
242C2×C22⋊Q8C2×D1111yescharacteristic
243C2×C22⋊Q8C2×D1111yescharacteristic
244C2×C4×Q8C2×D1111yescharacteristic
245C2×C4×Q8C2×D1111yescharacteristic
246C2×#117C2×D1111yescharacteristic
247#501—224no—
248#487—224no—
249C2×#107—112no—
250C2×#106—112no—
251C2×#103—112no—
252C2×#103—112no—
253C2×#103—112no—
254C2×#103—112no—
255C2×C22⋊C8—112no—
256C2×#97—111no—
257C2×C4×C8—111no—
258#400—221no—
259#399—221no—
260#395—221no—
261#393—221no—
262#389—112no—
263#382—111no—
264#380—112no—
265#340—112no—
266#340—112no—
267#336—112no—
268C22×C11—42no—
269C22×C11—41no—
270C22×C11—42no—
271C22×C11—41no—
272C22×C11—41no—
273C22×C11C2×#12011yescharacteristic
274C22×C11#53211yescharacteristic
275C22×C11#53611yescharacteristic
276C22×C11#57712yes—
277C22×C11#57812yes—
278C4×C11—22no—
279C4×C11—22no—
280C4×C11—41no—
281C4×C11—42no—
282C4×C11—42no—
283C4×C11—41no—
284C4×C11—42no—
285C4×C11—41no—
286C4×C11—42no—
287C4×C11#54712yes—
288C4×C11#54812yes—
289Dic11—82no—
290Dic11—82no—
291C22×Q8—221no—
292C22×Q8C22×D1111yescharacteristic
293C22×Q8C22×D1111yescharacteristic
294C23×C4C22×D1111yescharacteristic
295C22×C8—112no—
296C22×C8—112no—
297C4⋊Q8—22no—
298C4⋊Q8—222no—
299C4⋊Q8—222no—
300C4⋊Q8C22⋊D1114yes—
301#126—28no—
302#126—28no—
303#125—28no—
304#125—28no—
305#125—22no—
306#125C22⋊D1114yes—
307C22⋊Q8—22no—
308C22⋊Q8—22no—
309C22⋊Q8—22no—
310C22⋊Q8—22no—
311C4×Q8—22no—
312C4×Q8—22no—
313C4×Q8—22no—
314C4×Q8—22no—
315#117—22no—
316#117—22no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—112no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4C22⋊D1111yescharacteristic
330C2×C4⋊C4C22⋊D1111yescharacteristic
331C2×C4⋊C4C22×D1111yescharacteristic
332C2×C4⋊C4C22×D1111yescharacteristic
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—222no—
336C2×C22⋊C4C22⋊D1111yescharacteristic
337C2×C22⋊C4C22⋊D1111yescharacteristic
338C2×C42—21no—
339C2×C42—21no—
340C2×C42C22×D1111yescharacteristic
341C2×C42C22×D1111yescharacteristic
342#107—224no—
343#106—224no—
344#103—224no—
345#103—224no—
346#103—224no—
347#103—224no—
348C22⋊C8—224no—
349#97—222no—
350C4×C8—222no—
351#95—222no—
352#95—221no—
353#95—221no—
354#95—222no—
355C2×C11—81no—
356C2×C11#243211yescharacteristic
357C2×C11#301011yescharacteristic
358C2×C11#301111yescharacteristic
359C2×C11#317812yes—
360C2×C11#324212yes—
361C24C2×C22⋊D1111yescharacteristic
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—442no—
369C2×Q8—882no—
370C2×Q8C2×C22⋊D1112yes—
371C2×Q8C2×C22⋊D1112yes—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4C2×C22⋊D1111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387C22×C4C23×D1111yescharacteristic
388C2×C8—114no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C4⋊C4—24no—
395C4⋊C4—24no—
396C4⋊C4—24no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—222no—
407C4⋊C4—222no—
408C4⋊C4—222no—
409C4⋊C4—222no—
410C4⋊C4—442no—
411C4⋊C4—882no—
412C4⋊C4C2×C22⋊D1112yes—
413C4⋊C4C2×C22⋊D1112yes—
414C22⋊C4—24no—
415C22⋊C4—24no—
416C22⋊C4—22no—
417C22⋊C4—22no—
418C22⋊C4—882no—
419C42—24no—
420C42—24no—
421C42—21no—
422C42—21no—
423C42C2×C22⋊D1112yes—
424C42C2×C22⋊D1112yes—
425C11#2568611yescharacteristic, complemented, Sylow
426C23—21no—
427C23—21no—
428C23—22no—
429C23—22no—
430C23—21no—
431C23C22×C22⋊D1111yescharacteristic
432Q8—24no—
433Q8—24no—
434Q8—42no—
435Q8—42no—
436Q8—884no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4#6700612yes—
465C2×C4#6700612yes—
466C2×C4#41×D1112yes—
467C2×C4#6704312yes—
468C2×C4C22×C22⋊D1111yescharacteristic
469C2×C4C22×C22⋊D1111yescharacteristic
470C8—224no—
471C8—442no—
472C22—42no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—42no—
477C22#1062335611yescharacteristic
478C22#1062336311yescharacteristic
479C22#1062336812yes—
480C22#1062336912yes—
481C22C2×#6700611yescharacteristic
482C4—22no—
483C4—22no—
484C4—41no—
485C4—42no—
486C4—42no—
487C4—41no—
488C4—42no—
489C4—41no—
490C4—42no—
491C4—882no—
492C4—882no—
493C4#1062335512yes—
494C4#1062336212yes—
495C2—81no—
496C2#1307224011yescharacteristic
497C2#1307790211yescharacteristic
498C2#1307791111yescharacteristic
499C2#1307928612yes—
500C2#1307987812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#541C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#541D11
hypocenterC11#25686
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
1. C2×#10622678C2semidirect
2. C2×#10622694C2semidirect
6. #13069582C2semidirect
7. #13069437C2semidirect
8. #13068884C2semidirect
9. #13068870C2semidirect
425. C11#25686semidirect

Maximal subgroups

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

subgroupindex
C2×#106226782
C2×#106226942
#130744372
#130698162
#130698092
#130695822
#130694372
#130688842
#130688702
#130683822
C2×C11×#5412
#2568611