Finite Group Databasebeta

← #14654172

Subgroups — #14654172

Order 2816.

798 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077876C211yesmaximal, characteristic
2#13073996C211yesmaximal, characteristic, complemented
3#13068560C211yesmaximal, characteristic
4#13067148C211yesmaximal, characteristic, complemented
5#13066946C211yesmaximal, characteristic, complemented
6#13066468C211yesmaximal, characteristic, complemented
7C11×#2406C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C2×C11×#123—21no—
10C22×C11×C4⋊C4C2211yescharacteristic
11C2×#67004—21no—
12C2×#66977C2211yescharacteristic
13C11×#395—21no—
14C11×#394—21no—
15C11×#386—21no—
16C11×#385—22no—
17C11×#381C2211yescharacteristic
18#10622852—22no—
19C2×#66901—22no—
20#10622845—21no—
21#10622841—21no—
22#10622831—21no—
23#10622823—21no—
24#10622823—21no—
25C4×C22⋊Dic11C2211yescharacteristic
26#10622820C2211yescharacteristic
27#10622820C2211yescharacteristic
28#10622596—21no—
29#10622592—21no—
30#10622585—22no—
31#10622166—22no—
32#10622090—22no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—44no—
38C22×Q8×C11D411yescharacteristic
39C22×D4×C11—21no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11D411yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C22×Dic22D411yescharacteristic
46C11×#123—44no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4—21no—
57C2×C22⋊Dic11—21no—
58C2×C22⋊Dic11—21no—
59#67004—44no—
60C2×#4326—22no—
61C2×#4324—22no—
62C2×C4⋊Dic11D411yescharacteristic
63#66977—21no—
64#66977—21no—
65#66977—21no—
66#66977—21no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11D412yes—
71C2×#4318—21no—
72C2×#4318—21no—
73C11×#95—22no—
74C11×#95—21no—
75C11×#95D412yes—
76#66901—44no—
77#66899—22no—
78#66896—22no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—21no—
82C22⋊(C11⋊C8)—21no—
83C22⋊(C11⋊C8)—21no—
84C22⋊(C11⋊C8)—21no—
85C22⋊(C11⋊C8)D412yes—
86#9943—111nomaximal, Sylow
87C24×C11—21no—
88C24×C11C2×D411yescharacteristic
89C11×#41—24no—
90C11×#41—24no—
91C11×#41—42no—
92C11×#41—42no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—42no—
100C2×D4×C11—24no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—42no—
104C2×D4×C11—42no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11—42no—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11#4111yescharacteristic
128C22×Dic11—22no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C2×Dic22—21no—
132C2×Dic22—21no—
133C2×Dic22—42no—
134C11×C4⋊C4—44no—
135C11×C4⋊C4—41no—
136C11×C4⋊C4—41no—
137C11×C4⋊C4—41no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—42no—
141C11×C22⋊C4—44no—
142C22⋊Dic11—24no—
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145#4326—44no—
146#4324—44no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149Dic11⋊C4—44no—
150Dic11⋊C4—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—82no—
153C4×Dic11—42no—
154#4318—42no—
155#4318—42no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—41no—
158#3007—111no—
159#2583—111no—
160#2406D1111yescharacteristic
161#1789—111no—
162#1511—111no—
163#1463—111no—
164#1284—111no—
165C23×C11—22no—
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—41no—
169C23×C11—42no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—42no—
173C23×C11#12011yescharacteristic
174C23×C11#12011yescharacteristic
175C23×C11#12111yescharacteristic
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—41no—
179Q8×C11—41no—
180D4×C11—22no—
181D4×C11—22no—
182D4×C11—41no—
183D4×C11—41no—
184D4×C11—44no—
185D4×C11—44no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—44no—
197C2×C4×C11—44no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—81no—
211C2×C4×C11#12011yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12111yescharacteristic
214C2×C4×C11#12711yescharacteristic
215C2×Dic11—24no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222Dic22—42no—
223Dic22—81no—
224C11⋊C8—42no—
225C11⋊C8—81no—
226C22×#41C2×D1111yescharacteristic
227C2×#137—221no—
228C2×#123—21no—
229C2×C22⋊Q8—111no—
230C22×C4⋊C4C2×D1111yescharacteristic
231#452—222no—
232#451—221no—
233#450—221no—
234C2×#104—222no—
235#417—221no—
236#407—111no—
237#407—111no—
238#398—221no—
239#395—21no—
240#395—221no—
241#394—21no—
242#389—222no—
243#386—21no—
244#385—22no—
245#385—221no—
246#385—221no—
247#381C2×D1111yescharacteristic
248C4×C22⋊C4—111no—
249#328—222no—
250#324—222no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—44no—
259C22×C11—44no—
260C22×C11—42no—
261C22×C11—82no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11#39211yescharacteristic
265C22×C11#45612yes—
266C22×C11B(4,𝔽2)12yes—
267C4×C11—21no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—42no—
272C4×C11—42no—
273C4×C11—82no—
274C4×C11—81no—
275Dic11—44no—
276Dic11—81no—
277Dic11—81no—
278C2×#41—21no—
279C2×#41—21no—
280C2×#41—21no—
281C2×#41—21no—
282C2×#41—44no—
283C22×Q8—111no—
284C22×Q8C22⋊D1111yescharacteristic
285C22×D4—21no—
286C22×D4C22⋊D1111yescharacteristic
287C23×C4—21no—
288C23×C4C22⋊D1111yescharacteristic
289C23×C4C22⋊D1111yescharacteristic
290C23×C4C22×D1111yescharacteristic
291#137—444no—
292C2×Q16—222no—
293C2×SD16—222no—
294C2×M16—221no—
295C2×M16—221no—
296#123—44no—
297C22⋊Q8—221no—
298C22⋊Q8—221no—
299C22⋊Q8—221no—
300C22⋊Q8—221no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—222no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—221no—
316C2×C22⋊C4—221no—
317C2×C42—112no—
318#104—444no—
319#103—222no—
320#102—222no—
321C22⋊C8—112no—
322C22⋊C8—221no—
323C22⋊C8—221no—
324C22⋊C8—221no—
325#95—22no—
326#95—21no—
327#95—222no—
328#95—222no—
329#95—221no—
330#95C22⋊D1112yes—
331C2×C11—22no—
332C2×C11—22no—
333C2×C11—41no—
334C2×C11—82no—
335C2×C11#200511yescharacteristic
336C2×C11#201011yescharacteristic
337C2×C11#202111yescharacteristic
338C24—21no—
339C24C2×C22⋊D1111yescharacteristic
340#41—24no—
341#41—24no—
342#41—42no—
343#41—42no—
344#41—42no—
345#41—42no—
346#41—42no—
347#41—42no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—42no—
351C2×Q8—221no—
352C2×Q8—221no—
353C2×Q8—442no—
354C2×D4—24no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—41no—
360C2×D4—41no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—42no—
376C22×C4—222no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4D4×D1111yescharacteristic
380C22×C4D4×D1111yescharacteristic
381C22×C4D4×D1111yescharacteristic
382C22×C4#434111yescharacteristic
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1111yescharacteristic
385Q16—444no—
386SD16—444no—
387M16—442no—
388M16—442no—
389C2×C8—222no—
390C2×C8—441no—
391C4⋊C4—44no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—444no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—882no—
402C22⋊C4—44no—
403C22⋊C4—42no—
404C22⋊C4—44no—
405C22⋊C4—224no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C42—442no—
409C11#994311yescharacteristic, complemented, Sylow
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—42no—
415C23—41no—
416C23—41no—
417C23—42no—
418C23#6699011yescharacteristic
419C23#6699211yescharacteristic
420C23#6700611yescharacteristic
421Q8—22no—
422Q8—22no—
423Q8—41no—
424Q8—41no—
425Q8—442no—
426Q8—881no—
427D4—22no—
428D4—22no—
429D4—41no—
430D4—41no—
431D4—44no—
432D4—44no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—224no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—442no—
465C2×C4#6699011yescharacteristic
466C2×C4#6699111yescharacteristic
467C2×C4#6699211yescharacteristic
468C2×C4#6699311yescharacteristic
469C8—442no—
470C8—881no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—44no—
479C22—44no—
480C22—42no—
481C22—82no—
482C22—81no—
483C22—81no—
484C22#1062264512yes—
485C22#1062283611yescharacteristic
486C22#1062285912yes—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—444no—
496C4—881no—
497C4—881no—
498C2—22no—
499C2—22no—
500C2—41no—
501C2—82no—
502C2#1306965011yescharacteristic
503C2#1306968111yescharacteristic
504C2#1306973911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2406C2
socleC22×C11#392
prime radicalC22×C11×#41C22
hypercenter#2406D11
hypocenterC11#9943
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2406

Complements

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

NH ≅ G/Ntype
2. #13073996C2semidirect
4. #13067148C2semidirect
5. #13066946C2semidirect
6. #13066468C2semidirect
409. C11#9943semidirect

Maximal subgroups

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

subgroupindex
#130778762
#130739962
#130685602
#130671482
#130669462
#130664682
C11×#24062
#994311