Finite Group Databasebeta

← #14649813

Subgroups — #14649813

Order 2816.

684 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 113 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#13074423C211yesmaximal, characteristic
2#13071229C211yesmaximal, characteristic
3#13067188C211yesmaximal, characteristic, complemented
4C2×#10622106C211yesmaximal, characteristic
5#13066484C211yesmaximal, characteristic, complemented
6#13066483C211yesmaximal, characteristic, complemented
7C11×#1520C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×(C2×D11)⋊C4C2211yescharacteristic
10C2×C22⋊C4×D11—21no—
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622844C412yescomplemented
14#10622825C2211yescharacteristic
15#10622825C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622607—22no—
18#10622605C412yescomplemented
19#10622602—22no—
20#10622568—21no—
21#10622559—21no—
22#10622555—21no—
23#10622281—22no—
24C11×#328—22no—
25#10622176—22no—
26#10622106—22no—
27C24×D11D411yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic, complemented
29C23×C4×C11C2311yescharacteristic
30C23×Dic11D411yescharacteristic
31C22×C4×D11—22no—
32C22×C8×C11—21no—
33C11×C22⋊Q8—21no—
34C11×C22⋊Q8—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
40C2×C11×C22⋊C4—21no—
41C2×C11×C22⋊C4—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4—22no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4C2×C412yes—
52C2×(C2×D11)⋊C4D412yes—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×Dic11⋊C4—22no—
56C2×Dic11⋊C4—22no—
57C22×C11⋊C8—21no—
58C22⋊C4×D11—42no—
59C22⋊C4×D11—42no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#95D412yes—
63C11⋊#95—22no—
64C11⋊#95—22no—
65C11⋊#95C2×C412yescomplemented
66C11⋊#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69#9199—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C23×D11—21no—
72C23×D11—21no—
73C23×D11—21no—
74C23×D11—21no—
75C23×D11—81no—
76C23×D11—81no—
77C23×D11C22⋊C412yes—
78C23×D11SD1612yes—
79C23×D11Q1612yes—
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—81no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—22no—
86C22×C4×C11—81no—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×Dic11—22no—
94C22×Dic11—21no—
95C22×Dic11—22no—
96C22×Dic11—21no—
97C22×Dic11—81no—
98C22×Dic11C22⋊C412yes—
99C2×C4×D11—44no—
100C2×C4×D11—82no—
101C2×C4×D11—82no—
102C2×C8×C11—41no—
103C2×C8×C11—81no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—21no—
106C11×C4⋊C4—41no—
107C11×C4⋊C4—41no—
108C11×C4⋊C4—81no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C11×C22⋊C4—41no—
112C11×C22⋊C4—41no—
113C22⋊Dic11—41no—
114C22⋊Dic11—41no—
115C22⋊Dic11—41no—
116C22⋊Dic11—41no—
117(C2×D11)⋊C4—22no—
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—44no—
122(C2×D11)⋊C4—82no—
123(C2×D11)⋊C4—82no—
124C4⋊Dic11—81no—
125C4⋊Dic11—81no—
126Dic11⋊C4—82no—
127Dic11⋊C4—82no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—81no—
130#2626—111no—
131#2315—111no—
132#1520—111no—
133#1520D1111yescharacteristic, complemented
134C2×#323—111no—
135#1289—111no—
136#1289—111no—
137C23×C11—41no—
138C23×C11—41no—
139C23×C11C2×C22⋊C411yescharacteristic
140C23×C11#12011yescharacteristic
141C23×C11#12311yescharacteristic
142C23×C11C2×SD1611yescharacteristic
143C23×C11C2×Q1611yescharacteristic
144C23×C11AGL(1,ℤ/8)11yescharacteristic
145C23×C11#13711yescharacteristic
146C22×D11—22no—
147C22×D11—22no—
148C22×D11—22no—
149C22×D11—22no—
150C22×D11—22no—
151C22×D11—22no—
152C22×D11—42no—
153C22×D11—42no—
154C22×D11—42no—
155C22×D11—42no—
156C22×D11—82no—
157C22×D11—82no—
158C22×D11—81no—
159C22×D11—81no—
160C22×D11—82no—
161C22×D11—82no—
162C22×D11#10314yes—
163Q8×C11—81no—
164Q8×C11—81no—
165C2×C4×C11—41no—
166C2×C4×C11—41no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11C4×D411yescharacteristic
179C2×C4×C11C4×D411yescharacteristic
180C2×C4×C11#12111yescharacteristic
181C2×C4×C11#12111yescharacteristic
182C2×Dic11—22no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—81no—
192C4×D11—88no—
193C8×C11—81no—
194C11⋊C8—81no—
195C2×C22⋊Q8C2×D1111yescharacteristic
196C22×C22⋊C4—111no—
197C22×C22⋊C4—221no—
198C2×C22⋊C8—111no—
199C2×C22⋊C8C2×D1111yescharacteristic
200#399—112no—
201#396—222no—
202#393—112no—
203#385—222no—
204#385—221no—
205#385—222no—
206#380—111no—
207#380—111no—
208#380—221no—
209#380C2×D1111yescharacteristic
210#379—221no—
211#328—22no—
212#328—222no—
213#323—222no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11—41no—
223C22×C11—41no—
224C22×C11#38611yescharacteristic
225C22×C11C2×#10311yescharacteristic
226C22×C11#41711yescharacteristic
227C22×C11#45011yescharacteristic
228C22×C11#45111yescharacteristic
229C22×C11#48311yescharacteristic
230C22×C11#48411yescharacteristic
231C2×D11—24no—
232C2×D11—44no—
233C2×D11—44no—
234C2×D11—42no—
235C2×D11—42no—
236C2×D11—44no—
237C2×D11—82no—
238C2×D11—82no—
239C2×D11—82no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—21no—
244C4×C11—82no—
245C4×C11—81no—
246C4×C11—81no—
247Dic11—42no—
248Dic11—82no—
249Dic11—82no—
250C25—111no—
251C22×Q8C4×D1111yescharacteristic, complemented
252C23×C4—111no—
253C23×C4—222no—
254C23×C4C22×D1111yescharacteristic
255C22×C8—21no—
256C22×C8—221no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4C4×D1111yescharacteristic, complemented
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—112no—
271C2×C22⋊C4—112no—
272C2×C22⋊C4—221no—
273C2×C22⋊C4—221no—
274C2×C22⋊C4—221no—
275C2×C22⋊C4—221no—
276C2×C22⋊C4—222no—
277C2×C22⋊C4—221no—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—222no—
280C2×C22⋊C4—222no—
281C2×C22⋊C4—442no—
282C2×C22⋊C4—442no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—221no—
286C22⋊C8—221no—
287#95—112no—
288#95—112no—
289#95—222no—
290#95—222no—
291#95C22⋊D1112yes—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11—21no—
295C2×C11—21no—
296C2×C11—21no—
297C2×C11—21no—
298C2×C11#187211yescharacteristic
299C2×C11#191111yescharacteristic
300C2×C11#191311yescharacteristic
301D11—44no—
302C24—112no—
303C24—112no—
304C24—112no—
305C24—221no—
306C24—221no—
307C24—221no—
308C24—221no—
309C24—881no—
310C24—881no—
311C24D4×D1111yescharacteristic
312C2×Q8—21no—
313C2×Q8—21no—
314C2×Q8—81no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—81no—
319C22×C4—112no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—222no—
323C22×C4—222no—
324C22×C4—444no—
325C22×C4—882no—
326C22×C4—882no—
327C22×C4—881no—
328C22×C4C2×C4×D1111yescharacteristic
329C22×C4#433911yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4#434111yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334C2×C8—41no—
335C2×C8—81no—
336C2×C8—441no—
337C2×C8—881no—
338C4⋊C4—21no—
339C4⋊C4—21no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—81no—
343C4⋊C4—882no—
344C4⋊C4—882no—
345C4⋊C4—881no—
346C4⋊C4—881no—
347C22⋊C4—41no—
348C22⋊C4—41no—
349C22⋊C4—41no—
350C22⋊C4—41no—
351C22⋊C4—222no—
352C22⋊C4—222no—
353C22⋊C4—222no—
354C22⋊C4—222no—
355C22⋊C4—444no—
356C22⋊C4—441no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C22⋊C4—441no—
360C22⋊C4—882no—
361C22⋊C4—882no—
362C11#919911yescharacteristic, complemented, Sylow
363C23—41no—
364C23—41no—
365C23—114no—
366C23—222no—
367C23—222no—
368C23—222no—
369C23—222no—
370C23—222no—
371C23—222no—
372C23—442no—
373C23—442no—
374C23—442no—
375C23—442no—
376C23—881no—
377C23—881no—
378C23—882no—
379C23—882no—
380C23—882no—
381C23—882no—
382C23C22⋊C4×D1111yescharacteristic
383C23#6693611yescharacteristic
384C23SD16×D1111yescharacteristic
385C23#6696711yescharacteristic
386C23Q16×D1111yescharacteristic
387C23#6697111yescharacteristic
388C23#6699011yescharacteristic
389Q8—81no—
390Q8—81no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—222no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—888no—
414C2×C4—881no—
415C2×C4(C22⋊D11)⋊C411yescharacteristic
416C2×C4#6693711yescharacteristic
417C2×C4C4×C22⋊D1111yescharacteristic
418C2×C4#6699111yescharacteristic
419C8—81no—
420C8—881no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—224no—
432C22—444no—
433C22—444no—
434C22—444no—
435C22—442no—
436C22—442no—
437C22—882no—
438C22—882no—
439C22—882no—
440C22D11×#10311yescharacteristic
441C22#1062241611yescharacteristic
442C22#1062241811yescharacteristic
443C22#1062242211yescharacteristic
444C22#1062256911yescharacteristic
445C22#1062278211yescharacteristic
446C22#1062279911yescharacteristic
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—82no—
452C4—81no—
453C4—81no—
454C4—442no—
455C4—882no—
456C4—882no—
457C2—21no—
458C2—21no—
459C2—21no—
460C2—21no—
461C2—21no—
462C2—21no—
463C2—444no—
464C2#1306892011yescharacteristic
465C2#1306914511yescharacteristic
466C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1520C2
socleC22×C11#386
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenter#1520D11
hypocenterC11#9199
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1520

Complements

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

NH ≅ G/Ntype
3. #13067188C2semidirect
5. #13066484C2semidirect
6. #13066483C2semidirect
7. C11×#1520C2semidirect
13. #10622844C4semidirect
18. #10622605C4semidirect
28. C22×Q8×C11C2×C4semidirect
39. C2×C11×C4⋊C4C2×C4semidirect
65. C11⋊#95C2×C4semidirect
133. #1520D11semidirect
251. C22×Q8C4×D11semidirect
267. C2×C4⋊C4C4×D11semidirect
362. C11#9199semidirect

Maximal subgroups

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

subgroupindex
#130744232
#130712292
#130671882
C2×#106221062
#130664842
#130664832
C11×#15202
#919911