Finite Group Databasebeta

← #14651084

Subgroups — #14651084

Order 2816.

462 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079802C211yesmaximal, characteristic
2#13071420C211yesmaximal, characteristic, complemented
3#13067217C211yesmaximal, characteristic, complemented
4#13067163C211yesmaximal, characteristic
5#13066481C211yesmaximal, characteristic, complemented
6#13066472C211yesmaximal, characteristic, complemented
7C11×#1980C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×#66923C2211yescharacteristic
10C2×C11×#104—21no—
11C2×C11×#104—21no—
12C4×C11×M16C2211yescharacteristic
13C4×C11×C4⋊C4C2211yescharacteristic
14#10622693C412yescomplemented
15#10622684C412yescomplemented
16#10622647—21no—
17#10622646—21no—
18#10622622—22no—
19#10622591—21no—
20#10622585—21no—
21#10622550C2211yescharacteristic
22#10622546—21no—
23C4×Dic11⋊C4—21no—
24#10622539C2211yescharacteristic
25#10622539C2211yescharacteristic
26#10622267—21no—
27#10622266—21no—
28#10622175—21no—
29#10622175—21no—
30#10622103—22no—
31C2×C11×#41—21no—
32C2×C11×M16—21no—
33C11×C4⋊Q8C2×C411yescharacteristic
34C11×#127C2×C411yescharacteristic
35C11×#124—21no—
36C11×#121—21no—
37C11×#121—21no—
38C4×D4×C11—21no—
39C4×D4×C11—21no—
40C2×C11×C4⋊C4—21no—
41C2×C42×C11D411yescharacteristic
42C2×C42×C11D411yescharacteristic
43C2×C42×C11C2311yescharacteristic
44C2×C4⋊Dic11D411yescharacteristic
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—21no—
52#66923—21no—
53#66923—21no—
54#66923C2×C412yes—
55#66923D412yes—
56C11×#104—42no—
57C11×#104—42no—
58C11×#97—21no—
59C4×C8×C11—21no—
60C11×#95—21no—
61#66896—22no—
62#66896—22no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95D411yescharacteristic
70C11⋊#95D411yescharacteristic
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73#66872—22no—
74#66871—22no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)—21no—
77#66867—21no—
78#66867C2×C412yes—
79#9382—111nomaximal, Sylow
80C11×#41—41no—
81C11×#41—41no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C11×M16—22no—
100C11×M16—41no—
101C2×C8×C11—41no—
102C11×C4⋊C4—21no—
103C11×C4⋊C4—21no—
104C11×C4⋊C4—42no—
105C11×C22⋊C4—41no—
106C11×C22⋊C4—41no—
107C42×C11—41no—
108C42×C11—41no—
109C42×C11C22×C411yescharacteristic
110C42×C11C2×D411yescharacteristic
111C42×C11#4111yescharacteristic
112C42×C11#4111yescharacteristic
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11C22⋊C412yes—
116C4⋊Dic11C22⋊C412yes—
117Dic11⋊C4—22no—
118Dic11⋊C4—22no—
119Dic11⋊C4—22no—
120Dic11⋊C4—22no—
121Dic11⋊C4—42no—
122Dic11⋊C4—81no—
123C4×Dic11—42no—
124C4×Dic11—81no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127#3234—111no—
128#2336—111no—
129#1980D1111yescharacteristic
130#1528—111no—
131#1514—111no—
132#1288—111no—
133#1285—111no—
134C23×C11—41no—
135C23×C11#12011yescharacteristic
136Q8×C11—41no—
137Q8×C11—41no—
138D4×C11—42no—
139D4×C11—41no—
140D4×C11—41no—
141D4×C11—81no—
142D4×C11—81no—
143D4×C11—81no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—22no—
147C2×C4×C11—41no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—81no—
156C2×C4×C11—81no—
157C2×C4×C11C2×C22⋊C411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11C4×D411yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12311yescharacteristic
163C2×Dic11—22no—
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C8×C11—42no—
176C11⋊C8—42no—
177C11⋊C8—81no—
178#532C2×D1111yescharacteristic
179C2×#125—111no—
180#501—112no—
181#490—112no—
182#481—221no—
183#480—221no—
184#478—222no—
185#432—111no—
186#432—111no—
187C2×#104—21no—
188C2×#104—21no—
189C4×M16C2×D1111yescharacteristic
190#389—221no—
191#387—221no—
192#387—221no—
193#387—221no—
194#387—221no—
195#383—111no—
196C4×C4⋊C4—221no—
197C4×C4⋊C4C2×D1111yescharacteristic
198#330—222no—
199#327—221no—
200#327—221no—
201C22×C11—21no—
202C22×C11—21no—
203C22×C11—81no—
204C22×C11—81no—
205C22×C11—81no—
206C22×C11#38611yescharacteristic
207C22×C11#45311yescharacteristic
208C22×C11#45411yescharacteristic
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—42no—
216C4×C11—81no—
217C4×C11—81no—
218Dic11—42no—
219Dic11—42no—
220Dic11—81no—
221Dic11—81no—
222C2×#41—21no—
223C2×M16—21no—
224C4⋊Q8C4×D1111yescharacteristic
225#127C4×D1111yescharacteristic
226#125—112no—
227#125—112no—
228#125—221no—
229#125—221no—
230#124—21no—
231#121—21no—
232#121—21no—
233C4×D4—21no—
234C4×D4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—111no—
237C2×C4⋊C4—111no—
238C2×C4⋊C4—221no—
239C2×C4⋊C4—221no—
240C2×C4⋊C4—221no—
241C2×C4⋊C4—221no—
242C2×C42—221no—
243C2×C42—221no—
244C2×C42C22⋊D1111yescharacteristic
245C2×C42C22⋊D1111yescharacteristic
246C2×C42C22×D1111yescharacteristic
247#107—222no—
248#106—222no—
249C4⋊C8—221no—
250C4⋊C8—221no—
251#104—42no—
252#104—42no—
253#102—222no—
254#102—222no—
255C22⋊C8—221no—
256C22⋊C8—221no—
257#97—21no—
258#97—112no—
259#97—221no—
260C4×C8—21no—
261#95—21no—
262#95—111no—
263#95—111no—
264#95—221no—
265#95—221no—
266#95—221no—
267#95—221no—
268#95—221no—
269#95—221no—
270C2×C11—21no—
271C2×C11—21no—
272C2×C11—161no—
273C2×C11#188311yescharacteristic
274C2×C11#190611yescharacteristic
275C2×C11#191211yescharacteristic
276#41—41no—
277#41—41no—
278#41—41no—
279#41—41no—
280C2×Q8—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—221no—
289C22×C4—221no—
290C22×C4—221no—
291C22×C4—221no—
292C22×C4D4×D1111yescharacteristic
293C22×C4D4×D1111yescharacteristic
294C22×C4C2×C22⋊D1111yescharacteristic
295M16—22no—
296M16—41no—
297C2×C8—41no—
298C2×C8—222no—
299C2×C8—441no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—42no—
303C4⋊C4—112no—
304C4⋊C4—112no—
305C4⋊C4—222no—
306C4⋊C4—221no—
307C4⋊C4—221no—
308C4⋊C4—222no—
309C4⋊C4—222no—
310C4⋊C4—222no—
311C4⋊C4—442no—
312C4⋊C4—881no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C42—41no—
316C42—41no—
317C42—442no—
318C42—881no—
319C42C2×C4×D1111yescharacteristic
320C42#433911yescharacteristic
321C42D4×D1111yescharacteristic
322C42#434111yescharacteristic
323C11#938211yescharacteristic, complemented, Sylow
324C23—41no—
325C23#6699011yescharacteristic
326Q8—41no—
327Q8—41no—
328D4—42no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—222no—
348C2×C4—222no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4—441no—
352C2×C4—441no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4C22⋊C4×D1111yescharacteristic
360C2×C4(C22⋊D11)⋊C411yescharacteristic
361C2×C4#6693611yescharacteristic
362C2×C4#6693711yescharacteristic
363C2×C4C4×C22⋊D1111yescharacteristic
364C2×C4#6699111yescharacteristic
365C8—42no—
366C8—442no—
367C8—881no—
368C22—21no—
369C22—21no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22#1062256911yescharacteristic
374C22#1062267511yescharacteristic
375C22#1062269011yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—42no—
383C4—81no—
384C4—81no—
385C4—442no—
386C4—442no—
387C4—881no—
388C4—881no—
389C2—21no—
390C2—21no—
391C2—161no—
392C2#1306899511yescharacteristic
393C2#1306912011yescharacteristic
394C2#1306915011yescharacteristic
subgroupG/H
centerC22#10622569
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1980C2
socleC22×C11#386
prime radicalC11×#532C22
cosocleC2×C42×C11C23
hypercenter#1980D11
hypocenterC11#9382
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #13071420C2semidirect
3. #13067217C2semidirect
5. #13066481C2semidirect
6. #13066472C2semidirect
14. #10622693C4semidirect
15. #10622684C4semidirect
323. C11#9382semidirect

Maximal subgroups

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

subgroupindex
#130798022
#130714202
#130672172
#130671632
#130664812
#130664722
C11×#19802
#938211