Finite Group Databasebeta

← #14810779

Subgroups — #14810779

Order 2816.

1072 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622682C211yesmaximal, characteristic, complemented
2C2×#10622632C211yesmaximal, characteristic
3#13073828C211yesmaximal, characteristic, complemented
4#13069764C212yesmaximal, complemented
5#13069754C212yesmaximal, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068950C212yesmaximal
9#13068950C212yesmaximal
10#13068441C211yesmaximal, characteristic
11C2×C11×#554C211yesmaximal, characteristic
12C11×#554—24no—
13C11×#554—24no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×C11×#125C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C22×C11×C4⋊C4—21no—
25C22×#4324C2212yes—
26C2×#66922C2211yescharacteristic
27#10622843—21no—
28C2×#66896C2212yes—
29#10622682—24no—
30#10622632—24no—
31#10622599—21no—
32#10622599—21no—
33#10622590—21no—
34C2×#66874C2212yes—
35C2×#66874C2212yes—
36C2×#66874C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38#10622542C2212yes—
39#10622542C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622162C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11D411yescharacteristic
49C22×D4×C11C2311yescharacteristic
50C23×C4×C11—21no—
51C23×C4×C11—21no—
52C23×C4×C11—21no—
53C22×Dic22C2312yes—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×#125—22no—
57C11×#125—22no—
58C11×#125—22no—
59C11×#125D414yes—
60C11×C22⋊Q8—28no—
61C11×C22⋊Q8—28no—
62C11×C22⋊Q8—28no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11D414yes—
71C2×C11×C4⋊C4—28no—
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⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×#4324—24no—
90C2×#4324—28no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2312yes—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2312yes—
96C22×C11⋊C8C2312yes—
97#66922—22no—
98#66922—22no—
99#66896—24no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—21no—
105#66874—24no—
106#66874—24no—
107#66874—24no—
108C4⋊(C11⋊C8)—22no—
109#66867—22no—
110#25945—111nomaximal, Sylow
111C24×C11—21no—
112C2×Q8×C11—24no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—41no—
116C2×Q8×C11—82no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11C2×D412yes—
120C2×D4×C11#4114yes—
121C22×C4×C11—24no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—82no—
130C22×C4×C11—82no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—22no—
139C22×Dic11—22no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—24no—
143C2×Dic22—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4C2×D412yes—
156C11×C4⋊C4C2×D412yes—
157C11×C4⋊C4C2×D412yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—24no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11C2×D412yes—
166C42×C11C2×D412yes—
167#4324—48no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—42no—
171C4⋊Dic11—42no—
172C4×Dic11—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—24no—
177C2×C11⋊C8—22no—
178C2×#554D1111yescharacteristic
179C2×#491—111no—
180C2×#461—111no—
181#2568—111no—
182#2026—112no—
183#2024—112no—
184#1989—111no—
185#1985—111no—
186#1877—112no—
187#1877—112no—
188#1762—111no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—42no—
194C23×C11C22×D411yescharacteristic
195Q8×C11—44no—
196Q8×C11—84no—
197D4×C11—22no—
198D4×C11—24no—
199D4×C11#12414yes—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
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—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—48no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—84no—
221C2×C4×C11—84no—
222C2×C4×C11#12012yes—
223C2×C4×C11#12012yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4112yes—
228C2×C4×C112−1+412yes—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—44no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234Dic22—42no—
235Dic22—42no—
236Dic22—44no—
237C11⋊C8—42no—
238C11⋊C8—42no—
239C22×SD16—112no—
240#554—24no—
241#554—24no—
242C2×C4⋊Q8—111no—
243C2×C4⋊Q8C2×D1111yescharacteristic
244C2×#125C2×D1111yescharacteristic
245C2×#125C2×D1111yescharacteristic
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8—21no—
248C2×C22⋊Q8—21no—
249C2×C4×Q8C2×D1111yescharacteristic
250C2×C4×D4C2×D1111yescharacteristic
251C2×C4×D4C2×D1111yescharacteristic
252C2×C4×D4C2×D1111yescharacteristic
253C22×C4⋊C4—21no—
254#491—224no—
255#461—224no—
256C2×C4⋊C8—111no—
257C2×#103—112no—
258C2×#103—112no—
259C2×#103—112no—
260C2×#102—112no—
261C2×#97—111no—
262#400—221no—
263#400—221no—
264#391—112no—
265#391—112no—
266#391—221no—
267#382—221no—
268C4×C4⋊C4—111no—
269#340—112no—
270#340—112no—
271#340—112no—
272#336—112no—
273#336—112no—
274C22×C11—24no—
275C22×C11—44no—
276C22×C11—44no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11C2×#12011yescharacteristic
280C22×C11#54812yes—
281C22×C11C2×#13711yescharacteristic
282C22×C11#57511yescharacteristic
283C22×C11#57712yes—
284C4×C11—22no—
285C4×C11—22no—
286C4×C11—22no—
287C4×C11—41no—
288C4×C11—42no—
289C4×C11—41no—
290C4×C11—41no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11C2×#12411yescharacteristic
294C4×C11#53611yescharacteristic
295C4×C11#54812yes—
296Dic11—82no—
297Dic11—82no—
298C22×Q8—21no—
299C22×Q8—112no—
300C22×Q8C22⋊D1111yescharacteristic
301C22×D4C22×D1111yescharacteristic
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—21no—
305C2×SD16—228no—
306C2×SD16—224no—
307C22×C8—112no—
308C22×C8—112no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—222no—
312C4⋊Q8—222no—
313#125—22no—
314#125—22no—
315#125—22no—
316#125C22⋊D1114yes—
317C22⋊Q8—28no—
318C22⋊Q8—28no—
319C22⋊Q8—28no—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×D4—22no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—22no—
327C4×D4C22⋊D1114yes—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—112no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—221no—
337C2×C4⋊C4C22⋊D1111yescharacteristic
338C2×C4⋊C4C22⋊D1111yescharacteristic
339C2×C4⋊C4C22⋊D1111yescharacteristic
340C2×C4⋊C4C22×D1111yescharacteristic
341C2×C4⋊C4C22×D1111yescharacteristic
342C2×C4⋊C4C22×D1111yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C42—221no—
347C2×C42C22×D1111yescharacteristic
348C2×C42C22×D1111yescharacteristic
349C2×C42C22×D1111yescharacteristic
350C4⋊C8—222no—
351#103—224no—
352#103—224no—
353#103—224no—
354#102—224no—
355#97—222no—
356#95—221no—
357#95—222no—
358#95—222no—
359#95—222no—
360#95—222no—
361C2×C11—44no—
362C2×C11#243611yescharacteristic
363C2×C11#300711yescharacteristic
364C2×C11#300911yescharacteristic
365C2×C11#337212yes—
366C2×C11#337612yes—
367C24—21no—
368C2×Q8—24no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—41no—
372C2×Q8—82no—
373C2×Q8—224no—
374C2×Q8—224no—
375C2×Q8—222no—
376C2×Q8—222no—
377C2×D4—22no—
378C2×D4—21no—
379C2×D4#434314yes—
380C2×D4C2×C22⋊D1112yes—
381C22×C4—24no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—82no—
390C22×C4—82no—
391C22×C4—222no—
392C22×C4—222no—
393C22×C4C2×C22⋊D1111yescharacteristic
394C22×C4C2×C22⋊D1111yescharacteristic
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C23×D1111yescharacteristic
400SD16—448no—
401C2×C8—222no—
402C2×C8—224no—
403C2×C8—222no—
404C2×C8—222no—
405C2×C8—222no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—24no—
409C4⋊C4—22no—
410C4⋊C4—24no—
411C4⋊C4—24no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—222no—
418C4⋊C4—222no—
419C4⋊C4—442no—
420C4⋊C4—442no—
421C4⋊C4C2×C22⋊D1112yes—
422C4⋊C4C2×C22⋊D1112yes—
423C4⋊C4C2×C22⋊D1112yes—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—24no—
427C42—21no—
428C42—21no—
429C42—21no—
430C42—21no—
431C42—442no—
432C42C2×C22⋊D1112yes—
433C42C2×C22⋊D1112yes—
434C11#2594511yescharacteristic, complemented, Sylow
435C23—24no—
436C23—22no—
437C23—41no—
438C23—41no—
439C23—42no—
440C23C22×C22⋊D1111yescharacteristic
441Q8—44no—
442Q8—84no—
443Q8—442no—
444Q8—442no—
445Q8—444no—
446D4—22no—
447D4—24no—
448D4#6700014yes—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—48no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—84no—
470C2×C4—84no—
471C2×C4—442no—
472C2×C4—444no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4#6700412yes—
477C2×C4#6700612yes—
478C2×C4#6700612yes—
479C2×C4C2×#434312yes—
480C2×C4#6704012yes—
481C2×C4C22×C22⋊D1111yescharacteristic
482C2×C4C22×C22⋊D1111yescharacteristic
483C8—442no—
484C8—442no—
485C22—24no—
486C22—44no—
487C22—44no—
488C22—42no—
489C22—42no—
490C22#1062334812yes—
491C22#1062335311yescharacteristic
492C22C2×#6700411yescharacteristic
493C22#1062336712yes—
494C22C2×#6700611yescharacteristic
495C4—22no—
496C4—22no—
497C4—22no—
498C4—41no—
499C4—42no—
500C4—41no—
501C4—41no—
502C4—42no—
503C4—42no—
504C4—882no—
505C4—882no—
506C4C2×#6700011yescharacteristic
507C4#1062334711yescharacteristic
508C4#1062334812yes—
509C2—44no—
510C2#1307227011yescharacteristic
511C2#1307787611yescharacteristic
512C2#1307789311yescharacteristic
513C2#1308139712yes—
514C2#1308144312yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#554D11
hypocenterC11#25945
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#10622682C2semidirect
3. #13073828C2semidirect
4. #13069764C2semidirect
5. #13069754C2semidirect
6. #13069574C2semidirect
7. #13069557C2semidirect
434. C11#25945semidirect

Maximal subgroups

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

subgroupindex
C2×#106226822
C2×#106226322
#130738282
#130697642
#130697542
#130695742
#130695572
#130689502
#130684412
C2×C11×#5542
#2594511