Finite Group Databasebeta

← #14651434

Subgroups — #14651434

Order 2816.

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

normal subgroups only

This group has 486 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#13077700C211yesmaximal, characteristic, complemented
2#13073597C211yesmaximal, characteristic
3#13067240C211yesmaximal, characteristic
4#13066959C211yesmaximal, characteristic, complemented
5#13066473C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1533C211yesmaximal, characteristic
8C2×C11×#124C2211yescharacteristic
9C2×#66997C411yescharacteristic
10C2×#66989C411yescharacteristic
11C2×C4×Dic22C2211yescharacteristic
12C11×#432C2211yescharacteristic
13C11×#432C2211yescharacteristic
14#10622843C411yescharacteristic
15#10622834C411yescharacteristic
16#10622561—21no—
17#10622561—21no—
18#10622557—21no—
19#10622557—21no—
20C4×C4⋊Dic11C2211yescharacteristic
21#10622539C2211yescharacteristic
22#10622539C2211yescharacteristic
23#10622441—22no—
24#10622332—21no—
25#10622331—21no—
26#10622314—22no—
27C11×#329—22no—
28#10622178—22no—
29#10622107—21no—
30#10622107—21no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×D4×C11C2×C411yescharacteristic
33C22×Dic22C2×C411yescharacteristic
34C11×#124—21no—
35C11×#124—21no—
36C11×#124—21no—
37C11×#124—21no—
38C2×C11×C22⋊C4—21no—
39C2×C11×C22⋊C4—21no—
40C2×C42×C11C2311yescharacteristic
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11—21no—
43C2×C22⋊Dic11—21no—
44C2×C22⋊Dic11—21no—
45#66997—42no—
46#66989—42no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11C2×C411yescharacteristic
49C2×Dic11⋊C4—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4D411yescharacteristic
52C2×Dic11⋊C4D411yescharacteristic
53C2×C4×Dic11C2×C411yescharacteristic
54C2×C4×Dic11C2×C411yescharacteristic
55C2×C4×Dic11D411yescharacteristic
56C2×C4×Dic11D411yescharacteristic
57C4×Dic22—21no—
58C4×Dic22—21no—
59C4×Dic22—21no—
60C4×Dic22—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8—21no—
63C11×C22⋊C8—21no—
64C11×C22⋊C8—21no—
65C11×#97—21no—
66C11×#97D412yes—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—21no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#66879—22no—
73Dic11⋊C8—22no—
74Dic11⋊C8—22no—
75C8×Dic11—22no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)—21no—
78#66867—21no—
79#66867D412yes—
80#9448—111nomaximal, Sylow
81C24×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C22×C4×C11—21no—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×Dic11—21no—
95C22×Dic11—21no—
96C22×Dic11C22⋊C411yescharacteristic
97C22×Dic11C22⋊C411yescharacteristic
98C22×Dic11C22⋊C411yescharacteristic
99C22×Dic11C22⋊C411yescharacteristic
100C2×Dic22—22no—
101C2×Dic22—21no—
102C2×Dic22—21no—
103C2×Dic22—41no—
104C2×C8×C11—22no—
105C2×C8×C11—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C42×C11C2×D411yescharacteristic
111C42×C11C2×D411yescharacteristic
112C42×C11#4111yescharacteristic
113C42×C11#4111yescharacteristic
114C22⋊Dic11—42no—
115C22⋊Dic11—42no—
116C22⋊Dic11—42no—
117C22⋊Dic11—42no—
118C4⋊Dic11—21no—
119C4⋊Dic11—21no—
120C4⋊Dic11—42no—
121Dic11⋊C4—21no—
122Dic11⋊C4—21no—
123Dic11⋊C4—21no—
124Dic11⋊C4—21no—
125Dic11⋊C4—42no—
126Dic11⋊C4—42no—
127C4×Dic11—21no—
128C4×Dic11—21no—
129C4×Dic11—21no—
130C4×Dic11—21no—
131C4×Dic11—41no—
132C4×Dic11—41no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—41no—
135#2983—111no—
136#2545—111no—
137#1533—111no—
138#1533D1111yescharacteristic
139#1467—111no—
140#1285—111no—
141#1285—111no—
142C23×C11—41no—
143C23×C11—41no—
144C23×C11—41no—
145C23×C11—41no—
146C23×C11—41no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11C2×C22⋊C411yescharacteristic
150Q8×C11—81no—
151Q8×C11—81no—
152D4×C11—81no—
153D4×C11—81no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11C4×D411yescharacteristic
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12311yescharacteristic
167C2×Dic11—21no—
168C2×Dic11—21no—
169C2×Dic11—22no—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—21no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11#10012yes—
183Dic22—42no—
184Dic22—42no—
185C8×C11—42no—
186C8×C11—81no—
187C11⋊C8—42no—
188C11⋊C8—81no—
189C2×C4⋊Q8—111no—
190C2×#124—111no—
191C2×#124C2×D1111yescharacteristic
192C2×C4×Q8—111no—
193#446—222no—
194#446—222no—
195#432—111no—
196#432—111no—
197#432—221no—
198#432C2×D1111yescharacteristic
199#432C2×D1111yescharacteristic
200#431—221no—
201#396—221no—
202#396—221no—
203#391—111no—
204#390—111no—
205#388—221no—
206#388—221no—
207C4×C4⋊C4—111no—
208#329—22no—
209#329—222no—
210#324—221no—
211#324—221no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—81no—
217C22×C11—81no—
218C22×C11—81no—
219C22×C11—81no—
220C22×C11—81no—
221C22×C11#38611yescharacteristic
222C22×C11C2×#10011yescharacteristic
223C22×C11#41311yescharacteristic
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11—21no—
229C4×C11—21no—
230C4×C11—81no—
231Dic11—22no—
232Dic11—42no—
233Dic11—41no—
234Dic11—41no—
235Dic11—41no—
236Dic11—81no—
237C22×Q8—111no—
238C22×Q8C4×D1111yescharacteristic
239C22×D4C4×D1111yescharacteristic
240C4⋊Q8—442no—
241#124—21no—
242#124—21no—
243#124—21no—
244#124—21no—
245#124—442no—
246C4×Q8—221no—
247C4×Q8—221no—
248C4×Q8—221no—
249C4×Q8—221no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4—221no—
254C2×C4⋊C4—221no—
255C2×C4⋊C4—221no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C22⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C42—111no—
263C2×C42—111no—
264C2×C42—111no—
265C2×C42—111no—
266C2×C42C22×D1111yescharacteristic
267C4⋊C8—21no—
268C4⋊C8—21no—
269C4⋊C8—222no—
270C4⋊C8—222no—
271C4⋊C8—221no—
272C4⋊C8—221no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—221no—
276C22⋊C8—221no—
277#97—21no—
278#97—112no—
279#97—222no—
280#97—221no—
281#97C22⋊D1112yes—
282C4×C8—222no—
283#95—221no—
284#95—221no—
285#95—221no—
286C2×C11—21no—
287C2×C11—21no—
288C2×C11—161no—
289C2×C11#188411yescharacteristic
290C2×C11#190011yescharacteristic
291C2×C11#191211yescharacteristic
292C24—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8—41no—
296C2×Q8—41no—
297C2×Q8—222no—
298C2×Q8—221no—
299C2×Q8—221no—
300C2×Q8—441no—
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—41no—
304C2×D4—41no—
305C22×C4—21no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—221no—
311C22×C4—221no—
312C22×C4C2×C4×D1111yescharacteristic
313C22×C4D4×D1111yescharacteristic
314C22×C4D4×D1111yescharacteristic
315C2×C8—22no—
316C2×C8—41no—
317C2×C8—222no—
318C2×C8—441no—
319C4⋊C4—221no—
320C4⋊C4—221no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—442no—
326C4⋊C4—442no—
327C4⋊C4—442no—
328C22⋊C4—41no—
329C22⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—442no—
333C22⋊C4—442no—
334C22⋊C4—442no—
335C22⋊C4—442no—
336C42—221no—
337C42—221no—
338C42—221no—
339C42—221no—
340C42—441no—
341C42—441no—
342C42#433911yescharacteristic
343C42D4×D1111yescharacteristic
344C42#434111yescharacteristic
345C42C2×C22⋊D1111yescharacteristic
346C11#944811yescharacteristic, complemented, Sylow
347C23—41no—
348C23—41no—
349C23—41no—
350C23—41no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23C22⋊C4×D1111yescharacteristic
355Q8—81no—
356Q8—81no—
357Q8—442no—
358Q8—442no—
359D4—81no—
360D4—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—112no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—222no—
372C2×C4—221no—
373C2×C4—221no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—441no—
380C2×C4—441no—
381C2×C4—441no—
382C2×C4—441no—
383C2×C4—441no—
384C2×C4(C22⋊D11)⋊C411yescharacteristic
385C2×C4#6693611yescharacteristic
386C2×C4#6693711yescharacteristic
387C2×C4C4×C22⋊D1111yescharacteristic
388C2×C4#6699011yescharacteristic
389C2×C4#6699111yescharacteristic
390C8—42no—
391C8—81no—
392C8—442no—
393C8—881no—
394C22—21no—
395C22—21no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22D11×#10011yescharacteristic
404C22#1062235811yescharacteristic
405C22#1062256911yescharacteristic
406C4—21no—
407C4—21no—
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—81no—
413C4—222no—
414C4—442no—
415C4—441no—
416C4—441no—
417C4—441no—
418C4—881no—
419C2—21no—
420C2—21no—
421C2—161no—
422C2#1306899611yescharacteristic
423C2#1306907611yescharacteristic
424C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1533C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC2×C42×C11C23
hypercenter#1533D11
hypocenterC11#9448
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1533

Complements

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

NH ≅ G/Ntype
1. #13077700C2semidirect
4. #13066959C2semidirect
5. #13066473C2semidirect
6. #13066471C2semidirect
346. C11#9448semidirect

Maximal subgroups

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

subgroupindex
#130777002
#130735972
#130672402
#130669592
#130664732
#130664712
C11×#15332
#944811