Finite Group Databasebeta

← #14651781

Subgroups — #14651781

Order 2816.

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

normal subgroups only

This group has 520 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#13077643C211yesmaximal, characteristic
2#13073965C211yesmaximal, characteristic
3#13066952C211yesmaximal, characteristic
4#13066945C211yesmaximal, characteristic, complemented
5#13066945C211yesmaximal, characteristic, complemented
6#13066522C211yesmaximal, characteristic, complemented
7C11×#1305C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊D11C2211yescharacteristic
9C22×Dic11⋊C4C2211yescharacteristic
10C11×#407C2211yescharacteristic
11C11×#407C2211yescharacteristic
12C11×#380C2211yescharacteristic
13#10622820C2211yescharacteristic
14#10622820C2211yescharacteristic
15#10622740—22no—
16#10622607—21no—
17#10622596—21no—
18#10622571C411yescharacteristic
19#10622571C411yescharacteristic
20#10622563C411yescharacteristic
21#10622563C411yescharacteristic
22#10622341—22no—
23D11×C22⋊C8—21no—
24#10622332—21no—
25#10622281—21no—
26#10622266—21no—
27#10622107—21no—
28#10622107—22no—
29#10622107—22no—
30#10622106—21no—
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11C2×C411yescharacteristic
33C23×Dic11C2×C411yescharacteristic
34C23×Dic11C2×C411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C2×C11×M16—21no—
37C2×C11×M16—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C22⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4C2×C411yescharacteristic
41C2×C22⋊Dic11C2×C411yescharacteristic
42C4×C22⋊D11—21no—
43C4×C22⋊D11—21no—
44C4×C22⋊D11—21no—
45C4×C22⋊D11—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×(C2×D11)⋊C4—21no—
48C2×(C2×D11)⋊C4D411yescharacteristic
49C2×C4⋊Dic11—21no—
50C2×C4⋊Dic11—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4D411yescharacteristic
58C2×C4×Dic11D411yescharacteristic
59C2×#4318—21no—
60C2×#4318—21no—
61C2×C8×D11—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—
76#66879—22no—
77Dic11⋊C8—22no—
78#9517—111nomaximal, Sylow
79C24×C11C22×C411yescharacteristic
80C23×D11C22⋊C411yescharacteristic
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—81no—
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C22×C4×C11#4111yescharacteristic
90C2×C22⋊D11—21no—
91C2×C22⋊D11—21no—
92C2×C22⋊D11—22no—
93C2×C22⋊D11—41no—
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—42no—
101C22×Dic11—81no—
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—81no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C22⋊Dic11—21no—
116C22⋊Dic11—21no—
117(C2×D11)⋊C4—21no—
118(C2×D11)⋊C4—21no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—81no—
121C4⋊Dic11—42no—
122C4⋊Dic11—81no—
123Dic11⋊C4—21no—
124Dic11⋊C4—21no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131#4318—81no—
132#4318—81no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—41no—
135C8×D11—82no—
136#2973—111no—
137#2579—111no—
138#1465—111no—
139#1463—111no—
140#1463—111no—
141#1305—111no—
142#1305D1111yescharacteristic, complemented
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—41no—
153C22×D11—41no—
154C22×D11#10112yes—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
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#12011yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12311yescharacteristic
171C22⋊D11—42no—
172C22⋊D11—42no—
173C2×Dic11—22no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—21no—
177C2×Dic11—21no—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187C2×Dic11—41no—
188C2×Dic11—41no—
189C2×Dic11—41no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192C4×D11—42no—
193C4×D11—81no—
194C8×C11—42no—
195C8×C11—81no—
196C11⋊C8—42no—
197C11⋊C8—81no—
198C2×C4×D4—111no—
199C22×C4⋊C4—111no—
200#435—222no—
201#435—222no—
202#432—221no—
203#407—111no—
204#407—111no—
205#407C2×D1111yescharacteristic
206#407C2×D1111yescharacteristic
207C2×C22⋊C8—221no—
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#380C2×D1111yescharacteristic
217#324—222no—
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—22no—
235C2×D11—41no—
236C2×D11—41no—
237C2×D11—42no—
238C2×D11—81no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—21no—
242C4×C11—21no—
243C4×C11—81no—
244C4×C11—81no—
245Dic11—42no—
246Dic11—41no—
247Dic11—41no—
248Dic11—41no—
249Dic11—81no—
250C22×D4—111no—
251C23×C4—111no—
252C23×C4—111no—
253C23×C4—111no—
254C23×C4C22×D1111yescharacteristic
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—221no—
258C2×M16—221no—
259C22×C8—222no—
260C4×D4—221no—
261C4×D4—221no—
262C4×D4—221no—
263C4×D4—221no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—111no—
266C2×C4⋊C4—221no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—221no—
269C2×C4⋊C4—221no—
270C2×C4⋊C4—221no—
271C2×C4⋊C4—221no—
272C2×C4⋊C4—221no—
273C2×C4⋊C4—221no—
274C2×C22⋊C4—111no—
275C2×C22⋊C4—111no—
276C2×C22⋊C4—221no—
277C2×C22⋊C4—221no—
278C2×C22⋊C4C4×D1111yescharacteristic
279C2×C22⋊C4C4×D1111yescharacteristic
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⋊C8D4412yes—
291#97—222no—
292#95—21no—
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—42no—
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—81no—
314C22×C4—111no—
315C22×C4—111no—
316C22×C4—111no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—221no—
322C22×C4—221no—
323C22×C4—221no—
324C22×C4—221no—
325C22×C4—442no—
326C22×C4—881no—
327C22×C4—881no—
328C22×C4C2×D4411yescharacteristic
329C22×C4#433911yescharacteristic
330C22×C4D4×D1111yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4D4×D1111yescharacteristic
333C22×C4#434311yescharacteristic
334M16—81no—
335M16—81no—
336M16—881no—
337M16—881no—
338C2×C8—22no—
339C2×C8—41no—
340C2×C8—222no—
341C2×C8—441no—
342C2×C8—882no—
343C4⋊C4—81no—
344C4⋊C4—221no—
345C4⋊C4—221no—
346C4⋊C4—442no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C4⋊C4—441no—
350C4⋊C4—441no—
351C4⋊C4—881no—
352C22⋊C4—41no—
353C22⋊C4—41no—
354C22⋊C4—221no—
355C22⋊C4—221no—
356C22⋊C4—221no—
357C22⋊C4—221no—
358C22⋊C4—442no—
359C22⋊C4—881no—
360C42—221no—
361C42—221no—
362C11#951711yescharacteristic, complemented, Sylow
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—112no—
368C23—221no—
369C23—221no—
370C23—441no—
371C23—441no—
372C23C4×D4411yescharacteristic
373C23C22⋊C4×D1111yescharacteristic
374C23#6694611yescharacteristic
375D4—442no—
376D4—442no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
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—222no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—221no—
393C2×C4—221no—
394C2×C4—221no—
395C2×C4—221no—
396C2×C4—221no—
397C2×C4—442no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—881no—
408C2×C4—881no—
409C2×C4—881no—
410C2×C4#6693511yescharacteristic
411C2×C4#6693711yescharacteristic
412C2×C4#6694711yescharacteristic
413C2×C4#6694811yescharacteristic
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—222no—
429C22—442no—
430C22—441no—
431C22—441no—
432C22—881no—
433C22#1062227811yescharacteristic
434C22#1062235811yescharacteristic
435C22D11×#10111yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—81no—
442C4—441no—
443C4—441no—
444C4—442no—
445C4—441no—
446C4—881no—
447C2—21no—
448C2—21no—
449C2—41no—
450C2—41no—
451C2—442no—
452C2#1306903311yescharacteristic
453C2#1306908311yescharacteristic
454C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1305C2
socleC22×C11#386
prime radicalC22×C22⋊D11C2×C4
cosocleC23×C4×C11C23
hypercenter#1305D11
hypocenterC11#9517
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
4. #13066945C2semidirect
5. #13066945C2semidirect
6. #13066522C2semidirect
7. C11×#1305C2semidirect
142. #1305D11semidirect
362. C11#9517semidirect

Maximal subgroups

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

subgroupindex
#130776432
#130739652
#130669522
#130669452
#130665222
C11×#13052
#951711