Finite Group Databasebeta

← #14664229

Subgroups — #14664229

Order 2816.

778 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 95 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×#10622164C211yesmaximal, characteristic, complemented
2#13066943C211yesmaximal, characteristic, complemented
3#13066637C212yesmaximal, complemented
4#13066613C212yesmaximal, complemented
5C11×#2404C211yesmaximal, characteristic
6C22×C11×#41C411yescharacteristic, complemented
7C2×C11×#120—21no—
8C22×C11×C22⋊C4C2211yescharacteristic
9C22×C22⋊Dic11—21no—
10C11×#393C411yescharacteristic, complemented
11C11×#393C2211yescharacteristic
12C11×#392C411yescharacteristic, complemented
13C11×#392C2211yescharacteristic
14C11×#386—21no—
15C11×#386—21no—
16C11×#386—21no—
17C11×#381C411yescharacteristic, complemented
18#10622820—21no—
19#10622164—21no—
20#10622164C2212yes—
21#10622163—21no—
22#10622163C2212yes—
23C25×C11D411yescharacteristic
24C2×C11×#41—41no—
25C2×C11×#41—41no—
26C2×C11×#41—44no—
27C22×Q8×C11C2×C411yescharacteristic, complemented
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11C2×C411yescharacteristic, complemented
32C23×C4×C11—21no—
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×Dic11—41no—
36C11×#120—44no—
37C2×C11×C22⋊C4—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C11×C22⋊C4—41no—
43C2×C11×C22⋊C4—41no—
44C2×C11×C22⋊C4C2×C411yescharacteristic
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C11×C22⋊C4D411yescharacteristic
47C2×C11×C22⋊C4C2311yescharacteristic
48C2×C22⋊Dic11—24no—
49C2×C22⋊Dic11—22no—
50C2×C22⋊Dic11—41no—
51C2×C22⋊Dic11—42no—
52C2×#4318—41no—
53C11×#95—21no—
54C11×#95—21no—
55C11×#95—21no—
56C11×#95C2×C411yescharacteristic, complemented
57C11×#95C2×C411yescharacteristic, complemented
58C22⋊(C11⋊C8)—22no—
59C22⋊(C11⋊C8)—41no—
60#11753—111nomaximal, Sylow
61C24×C11—21no—
62C24×C11—21no—
63C24×C11—22no—
64C24×C11—21no—
65C24×C11—21no—
66C24×C11—21no—
67C24×C11—42no—
68C24×C11—81no—
69C24×C11C22⋊C411yescharacteristic
70C24×C11C22⋊C411yescharacteristic
71C24×C11C2×D411yescharacteristic
72C11×#41—44no—
73C11×#41—44no—
74C11×#41—44no—
75C11×#41—44no—
76C2×Q8×C11—42no—
77C2×Q8×C11—41no—
78C2×D4×C11—24no—
79C2×D4×C11—41no—
80C2×D4×C11—42no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—42no—
85C2×D4×C11—42no—
86C2×D4×C11—42no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—81no—
90C2×D4×C11—81no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—42no—
99C22×C4×C11—42no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11—81no—
103C22×C4×C11C22⋊C411yescharacteristic
104C22×C4×C11C22⋊C411yescharacteristic
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×Dic11—44no—
108C22×Dic11—42no—
109C22×Dic11—82no—
110C22×Dic11—82no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—42no—
116C11×C22⋊C4—42no—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—81no—
119C11×C22⋊C4—81no—
120C22⋊Dic11—24no—
121C22⋊Dic11—44no—
122C22⋊Dic11—42no—
123#4318—82no—
124C2×C11⋊C8—42no—
125#2404D1111yescharacteristic
126C2×#342—111no—
127#1462—111no—
128#1351—112no—
129#1343—112no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11—21no—
138C23×C11—21no—
139C23×C11—21no—
140C23×C11—21no—
141C23×C11—22no—
142C23×C11—41no—
143C23×C11—42no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—41no—
151C23×C11—42no—
152C23×C11—41no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—81no—
156C23×C11—81no—
157C23×C11—84no—
158C23×C11—82no—
159C23×C11—82no—
160C23×C11#9911yescharacteristic
161C23×C11#9911yescharacteristic
162C23×C11#10412yes—
163C23×C11C2×C22⋊C411yescharacteristic
164C23×C11AGL(1,ℤ/8)11yescharacteristic
165C23×C11#13711yescharacteristic
166Q8×C11—42no—
167Q8×C11—42no—
168D4×C11—44no—
169D4×C11—42no—
170D4×C11—42no—
171D4×C11—44no—
172D4×C11—84no—
173D4×C11—82no—
174D4×C11—82no—
175C2×C4×C11—22no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—48no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—81no—
197C2×Dic11—44no—
198C2×Dic11—88no—
199C2×Dic11—82no—
200C2×Dic11—82no—
201C11⋊C8—82no—
202C22×#41Dic1111yescharacteristic, complemented
203C2×#120—21no—
204C22×C22⋊C4—221no—
205C22×C22⋊C4C2×D1111yescharacteristic
206#407—221no—
207#393Dic1111yescharacteristic, complemented
208#393C2×D1111yescharacteristic
209#392Dic1111yescharacteristic, complemented
210#392C2×D1111yescharacteristic
211#386—21no—
212#386—21no—
213#386—21no—
214#381Dic1111yescharacteristic, complemented
215#342—112no—
216#342—221no—
217#323—112no—
218#323—221no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—22no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11—42no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11—44no—
235C22×C11—44no—
236C22×C11—42no—
237C22×C11—42no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11—41no—
241C22×C11—41no—
242C22×C11—42no—
243C22×C11—81no—
244C22×C11—81no—
245C22×C11—81no—
246C22×C11—81no—
247C22×C11—82no—
248C22×C11—82no—
249C22×C11—81no—
250C22×C11—81no—
251C22×C11AΣL(1,𝔽16)12yes—
252C22×C11C2×#9911yescharacteristic
253C22×C11#41711yescharacteristic
254C22×C11C2×#10411yescharacteristic
255C4×C11—41no—
256C4×C11—42no—
257C4×C11—41no—
258C4×C11—41no—
259C4×C11—41no—
260C4×C11—81no—
261C4×C11—81no—
262Dic11—84no—
263C25C22⋊D1111yescharacteristic
264C2×#41—41no—
265C2×#41—41no—
266C2×#41—44no—
267C22×Q8C2×Dic1111yescharacteristic, complemented
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—21no—
271C22×D4C2×Dic1111yescharacteristic, complemented
272C23×C4—21no—
273C23×C4—441no—
274C23×C4C2×Dic1111yescharacteristic
275C23×C4C22⋊D1111yescharacteristic
276C2×M16—441no—
277#120—44no—
278C2×C22⋊C4—21no—
279C2×C22⋊C4—21no—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282C2×C22⋊C4—21no—
283C2×C22⋊C4—41no—
284C2×C22⋊C4—41no—
285C2×C22⋊C4—224no—
286C2×C22⋊C4—222no—
287C2×C22⋊C4—441no—
288C2×C22⋊C4—442no—
289C2×C22⋊C4C2×Dic1111yescharacteristic
290C2×C22⋊C4C22⋊D1111yescharacteristic
291C2×C22⋊C4C22⋊D1111yescharacteristic
292C2×C22⋊C4C22×D1111yescharacteristic
293C22⋊C8—222no—
294C22⋊C8—441no—
295#95—21no—
296#95—21no—
297#95—21no—
298#95C2×Dic1111yescharacteristic, complemented
299#95C2×Dic1111yescharacteristic, complemented
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—22no—
303C2×C11—41no—
304C2×C11—41no—
305C2×C11—42no—
306C2×C11—41no—
307C2×C11—82no—
308C2×C11#150411yescharacteristic
309C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
310C2×C11#212711yescharacteristic
311C24—21no—
312C24—21no—
313C24—22no—
314C24—21no—
315C24—21no—
316C24—21no—
317C24—42no—
318C24—81no—
319C24C22⋊Dic1111yescharacteristic
320C24C22⋊Dic1111yescharacteristic
321C24C2×C22⋊D1111yescharacteristic
322#41—44no—
323#41—44no—
324#41—44no—
325#41—44no—
326C2×Q8—42no—
327C2×Q8—41no—
328C2×D4—24no—
329C2×D4—41no—
330C2×D4—42no—
331C2×D4—41no—
332C2×D4—41no—
333C2×D4—42no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—42no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—81no—
340C2×D4—81no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—81no—
353C22×C4—444no—
354C22×C4—442no—
355C22×C4—882no—
356C22×C4—882no—
357C22×C4C22⋊Dic1111yescharacteristic
358C22×C4C22⋊Dic1111yescharacteristic
359C22×C4C22×Dic1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361M16—882no—
362C2×C8—442no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—41no—
367C22⋊C4—42no—
368C22⋊C4—42no—
369C22⋊C4—42no—
370C22⋊C4—81no—
371C22⋊C4—81no—
372C22⋊C4—224no—
373C22⋊C4—444no—
374C22⋊C4—442no—
375C11#1175311yescharacteristic, complemented, Sylow
376C23—22no—
377C23—22no—
378C23—22no—
379C23—22no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—22no—
385C23—21no—
386C23—21no—
387C23—22no—
388C23—41no—
389C23—42no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—42no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23—84no—
404C23—82no—
405C23—82no—
406C23#6689811yescharacteristic
407C23#6689811yescharacteristic
408C23#6690112yes—
409C23#6700211yescharacteristic
410C23#6700411yescharacteristic
411C23C2×C22⋊Dic1111yescharacteristic
412Q8—42no—
413Q8—42no—
414D4—44no—
415D4—42no—
416D4—42no—
417D4—44no—
418D4—84no—
419D4—82no—
420D4—82no—
421C2×C4—22no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—48no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—444no—
444C2×C4—888no—
445C2×C4—882no—
446C2×C4—882no—
447C8—882no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—22no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22—41no—
462C22—41no—
463C22—44no—
464C22—44no—
465C22—42no—
466C22—42no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—42no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22—82no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22#1062217412yes—
481C22C2×#6689811yescharacteristic
482C22#1062284511yescharacteristic
483C22C2×#6690111yescharacteristic
484C4—41no—
485C4—42no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—81no—
490C4—81no—
491C4—884no—
492C2—21no—
493C2—21no—
494C2—22no—
495C2—41no—
496C2—41no—
497C2—42no—
498C2—41no—
499C2—82no—
500C2#1306712011yescharacteristic
501C2C2×#1062217411yescharacteristic
502C2#1307028511yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC22×C4×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
Fitting, prime radicalC11×#2404C2
socleC22×C11C2×#99
cosocleC2×C11×C22⋊C4C23
hypercenter#2404D11
hypocenterC11#11753
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C22⋊C4 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. C2×#10622164C2semidirect
2. #13066943C2semidirect
3. #13066637C2semidirect
4. #13066613C2semidirect
6. C22×C11×#41C4semidirect
10. C11×#393C4semidirect
12. C11×#392C4semidirect
17. C11×#381C4semidirect
27. C22×Q8×C11C2×C4semidirect
31. C22×D4×C11C2×C4semidirect
56. C11×#95C2×C4semidirect
57. C11×#95C2×C4semidirect
202. C22×#41Dic11semidirect
207. #393Dic11semidirect
209. #392Dic11semidirect
214. #381Dic11semidirect
267. C22×Q8C2×Dic11semidirect
271. C22×D4C2×Dic11semidirect
298. #95C2×Dic11semidirect
299. #95C2×Dic11semidirect
375. C11#11753semidirect

Maximal subgroups

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

subgroupindex
C2×#106221642
#130669432
#130666372
#130666132
C11×#24042
#1175311