Finite Group Databasebeta

← #14651649

Subgroups — #14651649

Order 2816.

544 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 93 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#13077033C211yesmaximal, characteristic
2#13074187C211yesmaximal, characteristic
3#13067063C211yesmaximal, characteristic, complemented
4#13066948C211yesmaximal, characteristic
5#13066482C211yesmaximal, characteristic, complemented
6#13066481C211yesmaximal, characteristic, complemented
7C11×#1491C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C11C2211yescharacteristic
9C2×M16×D11—21no—
10C2×#66925C2211yescharacteristic
11C11×#432C2211yescharacteristic
12C4×C11×M16C2211yescharacteristic
13#10622844C411yescharacteristic
14#10622842C411yescharacteristic
15M16×Dic11—21no—
16#10622606C411yescharacteristic
17#10622602—21no—
18#10622593C411yescharacteristic
19#10622591—21no—
20#10622553—21no—
21#10622550C2211yescharacteristic
22#10622546—21no—
23#10622539C2211yescharacteristic
24C4×#4318C2211yescharacteristic
25#10622321—22no—
26#10622302—22no—
27C11×Q8⋊C8—22no—
28Q8⋊(C11⋊C8)—22no—
29#10622107—21no—
30#10622106—21no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×C4×D11D411yescharacteristic
33C2×C11×M16—21no—
34C4×Q8×C11—21no—
35C4×Q8×C11—21no—
36C4×Q8×C11—21no—
37C4×Q8×C11—21no—
38C2×C11×C4⋊C4—21no—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C42×C11—21no—
41C2×C42×C11C2311yescharacteristic
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4C2×C411yescharacteristic
45C2×(C2×D11)⋊C4D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4C2×C411yescharacteristic
49C2×Dic11⋊C4D411yescharacteristic
50C2×C4×Dic11D411yescharacteristic
51C2×#4318—21no—
52M16×D11—24no—
53M16×D11—24no—
54C2×#4313—22no—
55C2×C8×D11—22no—
56#66925—21no—
57#66925—21no—
58#66925—21no—
59#66925—21no—
60C11×C4⋊C8—21no—
61C11×C22⋊C8—21no—
62C11×#97—21no—
63C11×#97—21no—
64C4×C8×C11D412yes—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95C2×C411yescharacteristic
72C11⋊#95C2×C411yescharacteristic
73C22⋊(C11⋊C8)—21no—
74#66879—22no—
75C8×Dic11—22no—
76C4⋊(C11⋊C8)—21no—
77#66867—21no—
78#66867—21no—
79C4×C11⋊C8D412yes—
80#9491—111nomaximal, Sylow
81C23×D11C22⋊C411yescharacteristic
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—42no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11C22⋊C411yescharacteristic
93C22×Dic11C22⋊C411yescharacteristic
94C22×Dic11C22⋊C411yescharacteristic
95C2×C4×D11—22no—
96C2×C4×D11—22no—
97C2×C4×D11—21no—
98C2×C4×D11—21no—
99C11×M16—22no—
100C11×M16—22no—
101C2×C8×C11—22no—
102C2×C8×C11—41no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—21no—
105C11×C4⋊C4—41no—
106C11×C4⋊C4—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C2×D411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113(C2×D11)⋊C4—21no—
114(C2×D11)⋊C4—21no—
115(C2×D11)⋊C4—21no—
116(C2×D11)⋊C4—21no—
117(C2×D11)⋊C4—42no—
118(C2×D11)⋊C4—42no—
119Dic11⋊C4—21no—
120Dic11⋊C4—21no—
121Dic11⋊C4—21no—
122Dic11⋊C4—21no—
123Dic11⋊C4—42no—
124Dic11⋊C4—42no—
125C4×Dic11—21no—
126C4×Dic11—21no—
127#4318—22no—
128#4318—22no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—41no—
131#4313—28no—
132C8×D11—28no—
133#2873—111no—
134#2599—111no—
135#1491—111no—
136#1491D1111yescharacteristic, complemented
137#1464—111no—
138#1288—111no—
139#1288—111no—
140C23×C11C2×C22⋊C411yescharacteristic
141C22×D11—21no—
142C22×D11—21no—
143C22×D11—41no—
144C22×D11—41no—
145C22×D11#10412yes—
146Q8×C11—22no—
147Q8×C11—22no—
148Q8×C11—41no—
149Q8×C11—41no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11C4×D411yescharacteristic
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12311yescharacteristic
166C2×Dic11—21no—
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—21no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11#10412yes—
179C4×D11—22no—
180C4×D11—22no—
181C4×D11—24no—
182C8×C11—24no—
183C8×C11—81no—
184C11⋊C8—24no—
185C11⋊C8—81no—
186C22×M16—221no—
187C2×C4×Q8C2×D1111yescharacteristic
188C2×#117—111no—
189#432—111no—
190#432C2×D1111yescharacteristic
191#405—222no—
192#405—222no—
193C4×M16—111no—
194C4×M16—221no—
195C4×M16C2×D1111yescharacteristic
196#398—111no—
197#397—111no—
198#395—111no—
199#393—111no—
200#388—221no—
201#387—221no—
202#387—221no—
203#385—221no—
204#383—111no—
205Q8⋊C8—22no—
206Q8⋊C8—222no—
207#324—221no—
208#323—221no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11#38611yescharacteristic
212C22×C11C2×#10411yescharacteristic
213C22×C11C2×#10411yescharacteristic
214C2×D11—22no—
215C2×D11—41no—
216C2×D11—41no—
217C2×D11—42no—
218C2×D11—81no—
219C4×C11—21no—
220C4×C11—21no—
221C4×C11—21no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—42no—
226C4×C11—81no—
227Dic11—22no—
228Dic11—41no—
229Dic11—41no—
230Dic11—81no—
231Dic11—81no—
232C22×Q8C4×D1111yescharacteristic
233C23×C4—111no—
234C2×M16—21no—
235C2×M16—222no—
236C2×M16—224no—
237C2×M16—224no—
238C2×M16—221no—
239C22×C8—222no—
240C4×Q8—21no—
241C4×Q8—21no—
242C4×Q8—21no—
243C4×Q8—21no—
244#117—221no—
245#117—221no—
246#117—221no—
247#117—221no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—221no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4C4×D1111yescharacteristic
254C2×C22⋊C4—111no—
255C2×C22⋊C4—111no—
256C2×C22⋊C4—221no—
257C2×C22⋊C4—221no—
258C2×C42—21no—
259C2×C42—111no—
260C2×C42C22×D1111yescharacteristic
261C4⋊C8—21no—
262C4⋊C8—221no—
263C22⋊C8—21no—
264C22⋊C8—221no—
265#97—21no—
266#97—21no—
267#97—222no—
268#97—221no—
269#97—221no—
270C4×C8—112no—
271C4×C8—222no—
272C4×C8C22⋊D1112yes—
273#95—111no—
274#95—111no—
275#95—221no—
276#95—221no—
277#95—221no—
278#95—221no—
279#95—221no—
280#95—221no—
281C2×C11—21no—
282C2×C11—21no—
283C2×C11#189111yescharacteristic
284C2×C11#189611yescharacteristic
285C2×C11#190911yescharacteristic
286D11—42no—
287C24—111no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8—42no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—111no—
296C22×C4—222no—
297C22×C4—222no—
298C22×C4—221no—
299C22×C4—221no—
300C22×C4—221no—
301C22×C4—221no—
302C22×C4C2×C4×D1111yescharacteristic
303C22×C4D4×D1111yescharacteristic
304C22×C4D4×D1111yescharacteristic
305M16—22no—
306M16—22no—
307M16—228no—
308M16—222no—
309M16—222no—
310C2×C8—22no—
311C2×C8—41no—
312C2×C8—228no—
313C2×C8—222no—
314C2×C8—441no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—221no—
320C4⋊C4—221no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—442no—
324C4⋊C4—442no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C22⋊C4—221no—
328C22⋊C4—221no—
329C22⋊C4—442no—
330C22⋊C4—442no—
331C42—41no—
332C42—41no—
333C42—221no—
334C42—221no—
335C42#433911yescharacteristic
336C42D4×D1111yescharacteristic
337C42#434111yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C11#949111yescharacteristic, complemented, Sylow
340C23—112no—
341C23—221no—
342C23—221no—
343C23—441no—
344C23—441no—
345C23C22⋊C4×D1111yescharacteristic
346Q8—22no—
347Q8—22no—
348Q8—41no—
349Q8—41no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—112no—
361C2×C4—222no—
362C2×C4—222no—
363C2×C4—224no—
364C2×C4—221no—
365C2×C4—221no—
366C2×C4—221no—
367C2×C4—221no—
368C2×C4—441no—
369C2×C4—441no—
370C2×C4—441no—
371C2×C4—441no—
372C2×C4—441no—
373C2×C4—441no—
374C2×C4—441no—
375C2×C4—441no—
376C2×C4(C22⋊D11)⋊C411yescharacteristic
377C2×C4#6693611yescharacteristic
378C2×C4#6693711yescharacteristic
379C2×C4C4×C22⋊D1111yescharacteristic
380C2×C4#6699011yescharacteristic
381C2×C4#6699111yescharacteristic
382C8—24no—
383C8—81no—
384C8—224no—
385C8—881no—
386C22—21no—
387C22—21no—
388C22—222no—
389C22—442no—
390C22—441no—
391C22—441no—
392C22—881no—
393C22D11×#10411yescharacteristic
394C22D11×#10411yescharacteristic
395C22#1062256911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—42no—
403C4—81no—
404C4—222no—
405C4—441no—
406C4—441no—
407C4—881no—
408C4—881no—
409C2—21no—
410C2—21no—
411C2—442no—
412C2#1306903111yescharacteristic
413C2#1306905611yescharacteristic
414C2#1306913511yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1491C2
socleC22×C11#386
prime radicalC23×D11C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1491D11
hypocenterC11#9491
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1491

Complements

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

NH ≅ G/Ntype
3. #13067063C2semidirect
5. #13066482C2semidirect
6. #13066481C2semidirect
7. C11×#1491C2semidirect
136. #1491D11semidirect
339. C11#9491semidirect

Maximal subgroups

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

subgroupindex
#130770332
#130741872
#130670632
#130669482
#130664822
#130664812
C11×#14912
#949111