Finite Group Databasebeta

← #14654314

Subgroups — #14654314

Order 2816.

944 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 944 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#10622840C211yesmaximal, characteristic, complemented
2#13074720C211yesmaximal, characteristic
3C2×#10622108C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic, complemented
5#13066887C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C2×C11×#448C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C22×C11×SD16—21no—
10C2×C11×#121C2211yescharacteristic
11C22×#4325—21no—
12C2×#66992—22no—
13C2×#66983C2211yescharacteristic
14C11×#448—22no—
15C11×#448—22no—
16C2×C11×#103—21no—
17C2×C11×C22⋊C8C2211yescharacteristic
18#10622840—22no—
19#10622840—22no—
20C2×#66899—21no—
21#10622836—21no—
22C2×C11⋊#95—22no—
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26#10622605—21no—
27#10622573—21no—
28#10622562—21no—
29#10622175—22no—
30#10622108—22no—
31C22×Q8×C11—21no—
32C22×Q8×C11—21no—
33C22×Q8×C11—21no—
34C22×Q8×C11—21no—
35C22×Q8×C11—21no—
36C22×Q8×C11—44no—
37C22×Q8×C11D412yescomplemented
38C22×D4×C11—21no—
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—21no—
43C22×C22⋊D11—22no—
44C23×Dic11—21no—
45C23×Dic11D412yes—
46C22×D44D411yescharacteristic
47C2×C11×SD16—24no—
48C2×C11×SD16—44no—
49C22×C8×C11—21no—
50C11×#121—21no—
51C11×#121—21no—
52C11×#121—21no—
53C11×#121—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C22⋊Dic11—22no—
57C2×#4325—24no—
58C2×#4325—44no—
59#66992—44no—
60#66992—44no—
61#66983—21no—
62#66983—21no—
63#66983—21no—
64#66983—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×Dic11⋊C4—22no—
69C22×C11⋊C8—21no—
70C11×#103—24no—
71C11×C22⋊C8—21no—
72C11×C22⋊C8D412yescomplemented
73#66899—24no—
74C11⋊#95—21no—
75C11⋊#95—21no—
76C11⋊#95—21no—
77C11⋊#95—21no—
78C11⋊#95—44no—
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)D412yescomplemented
81#9964—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11C2×D411yescharacteristic
84C23×D11—21no—
85C2×Q8×C11—24no—
86C2×Q8×C11—24no—
87C2×Q8×C11—22no—
88C2×Q8×C11—22no—
89C2×Q8×C11—44no—
90C2×Q8×C11—42no—
91C2×Q8×C11—42no—
92C2×Q8×C11—44no—
93C2×Q8×C11—44no—
94C2×Q8×C11—44no—
95C2×Q8×C11—41no—
96C2×Q8×C11—41no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—42no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—42no—
103C2×D4×C11—42no—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—41no—
110C22×C4×C11—41no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C2×C22⋊D11—44no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—42no—
122C2×C22⋊D11—82no—
123C2×C22⋊D11—82no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—42no—
129C22×Dic11—42no—
130C22×Dic11—42no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—42no—
134C22×Dic11SD1614yescomplemented
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—42no—
138C11×SD16—48no—
139C2×C8×C11—22no—
140C2×C8×C11—42no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C22⋊C4—41no—
144C11×C22⋊C4—41no—
145C22⋊Dic11—44no—
146#4325—48no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—41no—
149(C2×D11)⋊C4—41no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152Dic11⋊C4—44no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—42no—
155C2×#448—111no—
156C2×#448D1111yescharacteristic, complemented
157#2656—111no—
158C2×#327—111no—
159C2×#327—111no—
160#1446—111no—
161#1280—111no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—22no—
165C23×C11—41no—
166C23×C11—42no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—42no—
170C23×C11#12011yescharacteristic
171C23×C11#12111yescharacteristic
172C23×C11#12711yescharacteristic
173C23×C11C2×SD1612yes—
174C23×C11AGL(1,ℤ/8)12yes—
175C22×D11—41no—
176C22×D11—42no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—42no—
180Q8×C11—24no—
181Q8×C11—24no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—44no—
185Q8×C11—44no—
186D4×C11—42no—
187D4×C11—81no—
188D4×C11—82no—
189D4×C11—81no—
190D4×C11—81no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—44no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C22⋊D11—88no—
209C22⋊D11—82no—
210C22⋊D11—81no—
211C22⋊D11—81no—
212C2×Dic11—24no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—44no—
216C2×Dic11—44no—
217C2×Dic11—42no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—82no—
221C2×Dic11—82no—
222C2×Dic11—81no—
223C2×Dic11—81no—
224D44—42no—
225D44—81no—
226C8×C11—42no—
227C11⋊C8—42no—
228C23×Q8C2×D1111yescharacteristic
229C22×SD16—21no—
230C22×SD16—221no—
231C2×#121—111no—
232C2×#121—222no—
233C2×#121C2×D1111yescharacteristic
234#448—22no—
235#448—22no—
236#448—222no—
237#448—222no—
238C2×#103—21no—
239C2×#103—221no—
240C2×C22⋊C8—111no—
241C2×C22⋊C8C2×D1111yescharacteristic
242#399—221no—
243#399—221no—
244#392—221no—
245#392—221no—
246C2×#95—111no—
247C2×#95—111no—
248C2×#95—222no—
249#327—222no—
250#327—222no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—22no—
254C22×C11—22no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—82no—
260C22×C11—82no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11#39211yescharacteristic
265C22×C11#45012yes—
266C22×C11#45511yescharacteristic
267C22×C11#45611yescharacteristic
268C22×C11B(4,𝔽2)12yes—
269C22×C11#46012yes—
270C22×C11#49211yescharacteristic
271C22×C11#49611yescharacteristic
272C2×D11—82no—
273C2×D11—82no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—44no—
282C4×C11—81no—
283Dic11—44no—
284Dic11—82no—
285Dic11—81no—
286C22×Q8—21no—
287C22×Q8—21no—
288C22×Q8—21no—
289C22×Q8—21no—
290C22×Q8—21no—
291C22×Q8—44no—
292C22×Q8C22⋊D1112yescomplemented
293C22×D4—21no—
294C22×D4—111no—
295C22×D4—221no—
296C22×D4—222no—
297C22×D4C22⋊D1111yescharacteristic
298C23×C4—21no—
299C23×C4—112no—
300C23×C4—221no—
301C23×C4C22×D1111yescharacteristic
302C2×SD16—24no—
303C2×SD16—44no—
304C2×SD16—224no—
305C2×SD16—444no—
306C22×C8—21no—
307C22×C8—221no—
308#121—21no—
309#121—21no—
310#121—21no—
311#121—21no—
312#121—221no—
313#121—221no—
314#121—221no—
315#121—221no—
316#121—444no—
317#121—444no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4C22⋊D1111yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—222no—
323C2×C22⋊C4—222no—
324C2×C22⋊C4—221no—
325#103—24no—
326#103—224no—
327C22⋊C8—21no—
328C22⋊C8—112no—
329C22⋊C8—221no—
330C22⋊C8C22⋊D1112yescomplemented
331#95—221no—
332#95—221no—
333#95—221no—
334#95—221no—
335#95—444no—
336C2×C11—21no—
337C2×C11—22no—
338C2×C11—21no—
339C2×C11—161no—
340C2×C11#160112yes—
341C2×C11#160412yes—
342C2×C11#200711yescharacteristic
343C2×C11#201411yescharacteristic
344C2×C11#202111yescharacteristic
345D11—161no—
346C24—21no—
347C24—221no—
348C24D4×D1111yescharacteristic
349C2×Q8—24no—
350C2×Q8—24no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—44no—
354C2×Q8—42no—
355C2×Q8—42no—
356C2×Q8—44no—
357C2×Q8—44no—
358C2×Q8—44no—
359C2×Q8—41no—
360C2×Q8—41no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—442no—
371C2×D4—444no—
372C2×D4—442no—
373C2×D4—442no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—882no—
377C2×D4—882no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—114no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—221no—
390C22×C4—442no—
391C22×C4—442no—
392C22×C4—442no—
393C22×C4—441no—
394C22×C4—442no—
395C22×C4—441no—
396C22×C4D4×D1111yescharacteristic
397C22×C4D4×D1111yescharacteristic
398C22×C4#434111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402SD16—48no—
403SD16—448no—
404C2×C8—22no—
405C2×C8—42no—
406C2×C8—222no—
407C2×C8—442no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—444no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—444no—
416C22⋊C4—444no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C11#996411yescharacteristic, complemented, Sylow
420C23—21no—
421C23—21no—
422C23—22no—
423C23—42no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—42no—
428C23—442no—
429C23—441no—
430C23—441no—
431C23—441no—
432C23—442no—
433C23SD16×D1112yes—
434C23#6696712yes—
435C23#6699011yescharacteristic
436C23#6699211yescharacteristic
437C23#6699311yescharacteristic
438Q8—24no—
439Q8—24no—
440Q8—42no—
441Q8—42no—
442Q8—44no—
443Q8—44no—
444D4—42no—
445D4—81no—
446D4—82no—
447D4—81no—
448D4—81no—
449D4—442no—
450D4—881no—
451D4—888no—
452D4—882no—
453D4—881no—
454D4—881no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—24no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—42no—
465C2×C4—44no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—224no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—444no—
472C2×C4—444no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—441no—
476C2×C4—882no—
477C2×C4—882no—
478C2×C4—881no—
479C2×C4—881no—
480C2×C4#6699011yescharacteristic
481C2×C4#6699111yescharacteristic
482C2×C4#6699211yescharacteristic
483C2×C4#6700611yescharacteristic
484C8—42no—
485C8—442no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—82no—
495C22—82no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—882no—
500C22—882no—
501C22—881no—
502C22—881no—
503C22—881no—
504C22#1062264512yes—
505C22#1062277612yes—
506C22#1062278212yes—
507C22#1062278811yescharacteristic
508C22#1062278911yescharacteristic
509C22#1062281511yescharacteristic
510C22#1062281811yescharacteristic
511C22#1062283611yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—44no—
517C4—81no—
518C4—444no—
519C4—882no—
520C4—881no—
521C2—21no—
522C2—22no—
523C2—21no—
524C2—161no—
525C2—1761no—
526C2#1306756612yes—
527C2#1306758312yes—
528C2#1306966111yescharacteristic
529C2#1306970211yescharacteristic
530C2#1306973911yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC2×C11×#448C2
socleC23×C11#120
prime radical#13074720C2
hypercenterC2×#448D11
hypocenterC11#9964
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#448

Complements

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

NH ≅ G/Ntype
1. C2×#10622840C2semidirect
3. C2×#10622108C2semidirect
4. C2×#10622175C2semidirect
5. #13066887C2semidirect
6. #13066458C2semidirect
7. C2×C11×#448C2semidirect
37. C22×Q8×C11D4semidirect
72. C11×C22⋊C8D4semidirect
80. C22⋊(C11⋊C8)D4semidirect
134. C22×Dic11SD16semidirect
156. C2×#448D11semidirect
292. C22×Q8C22⋊D11semidirect
330. C22⋊C8C22⋊D11semidirect
419. C11#9964semidirect

Maximal subgroups

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

subgroupindex
C2×#106228402
#130747202
C2×#106221082
C2×#106221752
#130668872
#130664582
C2×C11×#4482
#996411