Finite Group Databasebeta

← #14808285

Subgroups — #14808285

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079163C211yesmaximal, characteristic, complemented
2#13079009C211yesmaximal, characteristic
3#13073821C211yesmaximal, characteristic, complemented
4#13069830C214yesmaximal, complemented
5#13069561C211yesmaximal, characteristic, complemented
6#13069536C211yesmaximal, characteristic
7#13068842C214yesmaximal, complemented
8C4×#66900C211yesmaximal, characteristic, complemented
9C11×#3507C211yesmaximal, characteristic
10C11×#559—21no—
11C11×#557—21no—
12C11×#556—21no—
13C11×#556—22no—
14C11×#554—21no—
15C11×#552—22no—
16C11×#539—22no—
17C11×#536C2212yes—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#529—22no—
21C11×#520C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#66922C2211yescharacteristic
24C2×#66901C2214yes—
25#10622845C2214yes—
26#10622843C2212yes—
27C2×#66900C2212yes—
28#10622694—21no—
29#10622692—21no—
30#10622691—21no—
31#10622683—21no—
32#10622678—22no—
33#10622668—22no—
34#10622608C2214yes—
35#10622592—22no—
36#10622589C2212yes—
37C4×C4⋊Dic11C2211yescharacteristic
38#10622541—22no—
39C4×#4318C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622170C2214yes—
42#10622168C2212yes—
43C2×C11×#41C2312yes—
44C22×Q8×C11C2311yescharacteristic
45C22×Dic22—21no—
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8D411yescharacteristic
48C11×C4⋊Q8D411yescharacteristic
49C11×C4⋊Q8D411yescharacteristic
50C11×#127D411yescharacteristic
51C11×#126—24no—
52C11×#126—24no—
53C11×#125—22no—
54C11×#125—24no—
55C11×#125D412yes—
56C11×#124—22no—
57C11×#124—22no—
58C11×#124D412yes—
59C11×#123—24no—
60C11×#123—24no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C11×#121—21no—
67C11×#121—21no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—21no—
71C4×Q8×C11—21no—
72C4×Q8×C11—21no—
73C4×Q8×C11—21no—
74C4×Q8×C11—21no—
75C4×Q8×C11—21no—
76C4×D4×C11—22no—
77C4×D4×C11—22no—
78C4×D4×C11—24no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C11×#117—24no—
82C11×#117—22no—
83C11×#117C2312yes—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4D412yes—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C42×C11D412yes—
88C2×C42×C11C2311yescharacteristic
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2312yes—
92C2×Dic11⋊C4—24no—
93C2×C4×Dic11C2312yes—
94C2×#4318C2312yes—
95C2×#4318C2312yes—
96#66922—21no—
97#66922—21no—
98#66922—21no—
99#66922—21no—
100#66901—28no—
101#66900—24no—
102#66899—24no—
103#66896—24no—
104C11⋊#95—24no—
105C11⋊#95—21no—
106#66872—24no—
107#66871—24no—
108#66867—21no—
109#66867—21no—
110C4×C11⋊C8—21no—
111C4×C11⋊C8—21no—
112#25695—111nomaximal, Sylow
113C11×#41—24no—
114C11×#41—24no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11—22no—
120C2×Q8×C11—22no—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—22no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11C2×D412yes—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—22no—
134C22×Dic11—22no—
135C2×Dic22—41no—
136C2×Dic22—41no—
137C2×Dic22—82no—
138C11×C4⋊C4—24no—
139C11×C4⋊C4—24no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
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—24no—
156C11×C22⋊C4—22no—
157C11×C22⋊C4—22no—
158C11×C22⋊C4—22no—
159C42×C11—24no—
160C42×C11—22no—
161C42×C11—22no—
162C42×C11—22no—
163C42×C11C2×D411yescharacteristic
164C42×C11C2×D411yescharacteristic
165C42×C11C2×D411yescharacteristic
166C42×C11C2×D411yescharacteristic
167C4⋊Dic11—24no—
168C4⋊Dic11—22no—
169C4⋊Dic11—22no—
170C4⋊Dic11—41no—
171C4⋊Dic11—41no—
172Dic11⋊C4—84no—
173C4×Dic11—24no—
174#4318—22no—
175#4318—22no—
176#4318—22no—
177#4318#4114yes—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180#3507D1111yescharacteristic
181#3165—111no—
182#3141—111no—
183#2567—111no—
184#2038—114no—
185#1986—111no—
186#1980—111no—
187#1859—114no—
188C4×#101—111no—
189C23×C11—22no—
190C23×C11C22×D411yescharacteristic
191Q8×C11—24no—
192Q8×C11—42no—
193Q8×C11—42no—
194Q8×C11—42no—
195Q8×C11—81no—
196D4×C11—24no—
197D4×C11—42no—
198D4×C11—42no—
199D4×C11—42no—
200D4×C11—81no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—41no—
210C2×C4×C11—44no—
211C2×C4×C11—42no—
212C2×C4×C11—84no—
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C2×C4×C11C22×D411yescharacteristic
219C2×C4×C11C2×#4112yes—
220C2×C4×C112−1+412yes—
221C2×Dic11—24no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—44no—
225C2×Dic11—42no—
226Dic22—82no—
227Dic22—82no—
228C11⋊C8—24no—
229C11⋊C8—42no—
230#559—21no—
231#557—21no—
232#556—21no—
233#556—22no—
234#554—21no—
235#552—22no—
236#539—22no—
237#536C2×D1112yes—
238#533C2×D1111yescharacteristic
239#532C2×D1111yescharacteristic
240C2×C4⋊Q8—111no—
241#529—22no—
242#520C2×D1112yes—
243C2×C4×Q8C2×D1111yescharacteristic
244#501—222no—
245#500—221no—
246#498—221no—
247#489—222no—
248#487—221no—
249#486—221no—
250#428—114no—
251C2×#104—114no—
252#417—114no—
253C2×#101—112no—
254C4×M16—111no—
255C4×M16—111no—
256#395—222no—
257#391—112no—
258#389—222no—
259#384—112no—
260C4×C4⋊C4—111no—
261#343—112no—
262#339—114no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—42no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11C2×#12011yescharacteristic
269C22×C11#53211yescharacteristic
270C22×C11#53611yescharacteristic
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—42no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11#45612yes—
280C4×C11#54712yes—
281C4×C11#54812yes—
282Dic11—44no—
283Dic11—82no—
284C2×#41C22×D1112yes—
285C22×Q8—221no—
286C22×Q8C22×D1111yescharacteristic
287C2×M16—112no—
288C2×M16—112no—
289C4⋊Q8—22no—
290C4⋊Q8—221no—
291C4⋊Q8—221no—
292C4⋊Q8—221no—
293C4⋊Q8—221no—
294C4⋊Q8C22⋊D1111yescharacteristic
295C4⋊Q8C22⋊D1111yescharacteristic
296C4⋊Q8C22⋊D1111yescharacteristic
297#127C22⋊D1111yescharacteristic
298#126—24no—
299#126—24no—
300#125—22no—
301#125—24no—
302#125C22⋊D1112yes—
303#124—22no—
304#124—22no—
305#124C22⋊D1112yes—
306#123—24no—
307#123—24no—
308C22⋊Q8—24no—
309C22⋊Q8—21no—
310C22⋊Q8—21no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313#121—21no—
314#121—21no—
315C4×Q8—22no—
316C4×Q8—22no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×D4—22no—
324C4×D4—22no—
325C4×D4—24no—
326C4×D4—21no—
327C4×D4—21no—
328#117—24no—
329#117—22no—
330#117C22×D1112yes—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—112no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4—221no—
335C2×C4⋊C4—224no—
336C2×C4⋊C4C22⋊D1112yes—
337C2×C4⋊C4C22×D1111yescharacteristic
338C2×C42—112no—
339C2×C42C22⋊D1112yes—
340C2×C42C22×D1111yescharacteristic
341#107—224no—
342#106—224no—
343#104—228no—
344#103—224no—
345#102—224no—
346#101—224no—
347#97—221no—
348#97—221no—
349C4×C8—221no—
350C4×C8—221no—
351#95—221no—
352#95—224no—
353C2×C11—21no—
354C2×C11—21no—
355C2×C11—82no—
356C2×C11#243211yescharacteristic
357C2×C11C2×#45611yescharacteristic
358C2×C11#302111yescharacteristic
359#41—24no—
360#41—24no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—441no—
368C2×Q8—441no—
369C2×Q8—882no—
370C2×Q8C2×C22⋊D1112yes—
371C2×D4—22no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4C2×C22⋊D1112yes—
375C22×C4—24no—
376C22×C4—22no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4C2×C22⋊D1112yes—
380C22×C4C2×C22⋊D1111yescharacteristic
381C22×C4C2×C22⋊D1112yes—
382C22×C4C2×C22⋊D1111yescharacteristic
383C22×C4C23×D1111yescharacteristic
384M16—114no—
385M16—222no—
386M16—222no—
387M16—222no—
388C2×C8—222no—
389C2×C8—222no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—224no—
404C4⋊C4—222no—
405C4⋊C4—222no—
406C4⋊C4—441no—
407C4⋊C4—441no—
408C4⋊C4—884no—
409C4⋊C4C2×C22⋊D1112yes—
410C4⋊C4C2×C22⋊D1112yes—
411C22⋊C4—24no—
412C22⋊C4—24no—
413C22⋊C4—24no—
414C22⋊C4—22no—
415C22⋊C4—22no—
416C22⋊C4—22no—
417C42—24no—
418C42—22no—
419C42—22no—
420C42—22no—
421C42—224no—
422C42C2×C22⋊D1111yescharacteristic
423C42C2×C22⋊D1111yescharacteristic
424C42C2×C22⋊D1111yescharacteristic
425C42C2×C22⋊D1111yescharacteristic
426C11#2569511yescharacteristic, complemented, Sylow
427C23—22no—
428C23C22×C22⋊D1111yescharacteristic
429Q8—24no—
430Q8—42no—
431Q8—42no—
432Q8—42no—
433Q8—81no—
434Q8—882no—
435Q8—882no—
436D4—24no—
437D4—42no—
438D4—42no—
439D4—42no—
440D4—81no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—44no—
451C2×C4—42no—
452C2×C4—84no—
453C2×C4—224no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—444no—
457C2×C4—442no—
458C2×C4#6700611yescharacteristic
459C2×C4#6700611yescharacteristic
460C2×C4#6700611yescharacteristic
461C2×C4#6700611yescharacteristic
462C2×C4#41×D1112yes—
463C2×C4#6704312yes—
464C2×C4C22×C22⋊D1111yescharacteristic
465C2×C4C22×C22⋊D1111yescharacteristic
466C8—224no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22#1062335611yescharacteristic
474C22#1062336311yescharacteristic
475C22C2×#6700611yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—42no—
480C4—42no—
481C4—42no—
482C4—42no—
483C4—42no—
484C4—444no—
485C4—882no—
486C4#1062285912yes—
487C4#1062335512yes—
488C4#1062336212yes—
489C2—21no—
490C2—21no—
491C2—82no—
492C2#1307224011yescharacteristic
493C2C2×#1062285911yescharacteristic
494C2#1307798811yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3507C2
socleC22×C11C2×#120
prime radicalC11×#532C22
hypercenter#3507D11
hypocenterC11#25695
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #13079163C2semidirect
3. #13073821C2semidirect
4. #13069830C2semidirect
5. #13069561C2semidirect
7. #13068842C2semidirect
8. C4×#66900C2semidirect
426. C11#25695semidirect

Maximal subgroups

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

subgroupindex
#130791632
#130790092
#130738212
#130698302
#130695612
#130695362
#130688422
C4×#669002
C11×#35072
#2569511