Finite Group Databasebeta

← #14651784

Subgroups — #14651784

Order 2816.

518 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 91 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#13077655C211yesmaximal, characteristic
2#13073963C211yesmaximal, characteristic
3#13066952C211yesmaximal, characteristic
4#13066946C211yesmaximal, characteristic, complemented
5#13066523C211yesmaximal, characteristic, complemented
6#13066521C211yesmaximal, characteristic, complemented
7C11×#1463C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×C4×C22⋊D11C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#407C2211yescharacteristic
12#10622826C411yescharacteristic
13#10622826C411yescharacteristic
14#10622825C2211yescharacteristic
15#10622823C411yescharacteristic
16#10622823C411yescharacteristic
17#10622820C2211yescharacteristic
18#10622820C2211yescharacteristic
19#10622741—22no—
20#10622607—21no—
21#10622602—21no—
22#10622597—21no—
23#10622591—21no—
24#10622342—22no—
25#10622339—21no—
26#10622331—21no—
27C11×#324—22no—
28#10622166—22no—
29#10622107—21no—
30#10622106—21no—
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11C2×C411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C2×C11×M16—21no—
37C2×C11×M16—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C22⋊Dic11C2×C411yescharacteristic
45C2×C22⋊Dic11C2×C411yescharacteristic
46C2×C22⋊Dic11C2×C411yescharacteristic
47C4×C22⋊D11—21no—
48C4×C22⋊D11—21no—
49C4×C22⋊D11—21no—
50C4×C22⋊D11—21no—
51C2×(C2×D11)⋊C4—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×(C2×D11)⋊C4D411yescharacteristic
54C2×C4⋊Dic11—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4D411yescharacteristic
58C2×C4×Dic11D411yescharacteristic
59C2×#4318—21no—
60C2×#4318—21no—
61C2×#4313—22no—
62C11×C22⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×C22⋊C8D412yes—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)D412yes—
75(C2×D11)⋊C8—22no—
76Dic11⋊C8—22no—
77C8×Dic11—22no—
78#9518—111nomaximal, Sylow
79C24×C11C22×C411yescharacteristic
80C23×D11C22⋊C411yescharacteristic
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—42no—
88C22×C4×C11—81no—
89C22×C4×C11—81no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C2×C22⋊D11—22no—
97C2×C22⋊D11—21no—
98C2×C22⋊D11—21no—
99C2×C22⋊D11—41no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11C22⋊C411yescharacteristic
103C22×Dic11C22⋊C411yescharacteristic
104C22×Dic11C22⋊C411yescharacteristic
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×C4×D11—81no—
108C11×M16—81no—
109C11×M16—81no—
110C2×C8×C11—22no—
111C2×C8×C11—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C22⋊Dic11—21no—
117C22⋊Dic11—21no—
118C22⋊Dic11—41no—
119C22⋊Dic11—41no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122(C2×D11)⋊C4—42no—
123(C2×D11)⋊C4—81no—
124C4⋊Dic11—81no—
125Dic11⋊C4—21no—
126Dic11⋊C4—21no—
127Dic11⋊C4—42no—
128Dic11⋊C4—81no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131#4318—81no—
132#4318—81no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—41no—
135#4313—82no—
136#2975—111no—
137#2579—111no—
138#1465—111no—
139#1463—111no—
140#1463D1111yescharacteristic, complemented
141#1305—111no—
142#1305—111no—
143C23×C11—21no—
144C23×C11—21no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11C4×D411yescharacteristic
149C23×C11C4×D411yescharacteristic
150C22×D11—21no—
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—41no—
154C22×D11—41no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—41no—
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—81no—
172C2×C4×C11—81no—
173C2×C4×C11#12011yescharacteristic
174C2×C4×C11#12111yescharacteristic
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12311yescharacteristic
177C22⋊D11—42no—
178C22⋊D11—42no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—41no—
191C2×Dic11#10112yes—
192C4×D11—42no—
193C4×D11—81no—
194C8×C11—42no—
195C8×C11—81no—
196C11⋊C8—42no—
197C11⋊C8—81no—
198C2×C4×D4—111no—
199C22×C4⋊C4C2×D1111yescharacteristic
200#436—222no—
201#436—222no—
202#431—221no—
203#407—111no—
204#407—111no—
205#407—221no—
206#407C2×D1111yescharacteristic
207#407C2×D1111yescharacteristic
208#398—221no—
209#396—221no—
210#387—221no—
211#386—111no—
212#386—111no—
213#385—111no—
214#385—111no—
215#385—221no—
216#380—111no—
217#324—22no—
218#324—221no—
219#324—222no—
220#323—221no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—42no—
230C22×C11—42no—
231C22×C11#38611yescharacteristic
232C22×C11C2×#10111yescharacteristic
233C22×C11#41311yescharacteristic
234C2×D11—42no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—41no—
238C2×D11—81no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—42no—
244C4×C11—81no—
245Dic11—22no—
246Dic11—41no—
247Dic11—41no—
248Dic11—81no—
249Dic11—81no—
250C22×D4—111no—
251C23×C4—111no—
252C23×C4C4×D1111yescharacteristic
253C23×C4C4×D1111yescharacteristic
254C23×C4C22×D1111yescharacteristic
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—222no—
258C2×M16—221no—
259C2×M16—221no—
260C4×D4—221no—
261C4×D4—221no—
262C4×D4—221no—
263C4×D4—221no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—111no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—111no—
276C2×C22⋊C4—111no—
277C2×C22⋊C4—111no—
278C2×C22⋊C4—221no—
279C2×C22⋊C4—221no—
280C2×C42—111no—
281C4⋊C8—222no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—112no—
286C22⋊C8—222no—
287C22⋊C8—221no—
288C22⋊C8—221no—
289C22⋊C8—221no—
290C22⋊C8C22⋊D1112yes—
291C4×C8—222no—
292#95—221no—
293#95—221no—
294#95—221no—
295#95—221no—
296#95—221no—
297C2×C11—21no—
298C2×C11—21no—
299C2×C11—41no—
300C2×C11—41no—
301C2×C11#189111yescharacteristic
302C2×C11#190111yescharacteristic
303C2×C11#191311yescharacteristic
304D11—81no—
305C24—111no—
306C24C2×C4×D1111yescharacteristic
307C2×D4—222no—
308C2×D4—221no—
309C2×D4—221no—
310C2×D4—441no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—42no—
318C22×C4—81no—
319C22×C4—81no—
320C22×C4—111no—
321C22×C4—111no—
322C22×C4—111no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—221no—
326C22×C4—221no—
327C22×C4—881no—
328C22×C4#433911yescharacteristic
329C22×C4D4×D1111yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4#434111yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334M16—81no—
335M16—81no—
336M16—882no—
337M16—881no—
338M16—881no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—222no—
342C2×C8—441no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—221no—
348C4⋊C4—221no—
349C4⋊C4—442no—
350C4⋊C4—881no—
351C4⋊C4—881no—
352C22⋊C4—221no—
353C22⋊C4—221no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C22⋊C4—442no—
357C22⋊C4—441no—
358C22⋊C4—441no—
359C22⋊C4—881no—
360C42—221no—
361C42—221no—
362C11#951811yescharacteristic, complemented, Sylow
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—221no—
368C23—221no—
369C23—221no—
370C23—441no—
371C23—441no—
372C23C22⋊C4×D1111yescharacteristic
373C23(C22⋊D11)⋊C411yescharacteristic
374C23C4×C22⋊D1111yescharacteristic
375D4—442no—
376D4—442no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—112no—
396C2×C4—221no—
397C2×C4—221no—
398C2×C4—221no—
399C2×C4—221no—
400C2×C4—442no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—881no—
410C2×C4#6693611yescharacteristic
411C2×C4#6693711yescharacteristic
412C2×C4#6699011yescharacteristic
413C2×C4#6699111yescharacteristic
414C8—42no—
415C8—81no—
416C8—442no—
417C8—881no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—42no—
427C22—42no—
428C22—442no—
429C22—441no—
430C22—441no—
431C22—441no—
432C22—881no—
433C22D11×#10111yescharacteristic
434C22#1062236411yescharacteristic
435C22#1062256911yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—81no—
442C4—222no—
443C4—441no—
444C4—441no—
445C4—881no—
446C4—881no—
447C2—21no—
448C2—21no—
449C2—41no—
450C2—41no—
451C2—881no—
452C2#1306903111yescharacteristic
453C2#1306908111yescharacteristic
454C2#1306915511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1463C2
socleC22×C11#386
prime radicalC22×C22⋊D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1463D11
hypocenterC11#9518
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
4. #13066946C2semidirect
5. #13066523C2semidirect
6. #13066521C2semidirect
7. C11×#1463C2semidirect
140. #1463D11semidirect
362. C11#9518semidirect

Maximal subgroups

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

subgroupindex
#130776552
#130739632
#130669522
#130669462
#130665232
#130665212
C11×#14632
#951811