Finite Group Databasebeta

← #14656920

Subgroups — #14656920

Order 2816.

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

normal subgroups only

This group has 508 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#13073628C211yesmaximal, characteristic, complemented
2#13069451C211yesmaximal, characteristic
3#13067183C211yesmaximal, characteristic
4C2×#10622108C211yesmaximal, characteristic
5#13066494C211yesmaximal, characteristic, complemented
6#13066462C211yesmaximal, characteristic, complemented
7C11×#1289C211yesmaximal, characteristic, complemented
8C2×#66983C2211yescharacteristic
9C2×#66931—21no—
10C2×C11×C22⋊C8C2211yescharacteristic
11C11×#380C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C4×C22⋊Dic11C2211yescharacteristic
14C2×C11⋊#95C2211yescharacteristic
15C2×C22⋊(C11⋊C8)C2211yescharacteristic
16#10622597—21no—
17#10622592—21no—
18C2×#66870—21no—
19C2×#66870—21no—
20#10622559—21no—
21#10622260—21no—
22#10622259—21no—
23#10622108—21no—
24#10622108—21no—
25#10622089—21no—
26#10622089—21no—
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11—21no—
30C22×D44Q811yescharacteristic, complemented
31C22×Dic22—21no—
32C22×C8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4—21no—
37C2×C22⋊Dic11D411yescharacteristic
38C2×C22⋊Dic11D411yescharacteristic
39#66983—21no—
40#66983—21no—
41#66983—21no—
42#66983—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11Q811yescharacteristic, complemented
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C2×Dic11⋊C4—21no—
50C2×C4×Dic11—21no—
51C22×C11⋊C8—21no—
52#66931—42no—
53#66931—42no—
54C11×C22⋊C8—21no—
55C11×C22⋊C8—21no—
56C11×#95—21no—
57C11×#95D411yescharacteristic
58C11×#95D411yescharacteristic
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95D411yescharacteristic
64C11⋊#95D411yescharacteristic
65C22⋊(C11⋊C8)—21no—
66C22⋊(C11⋊C8)—21no—
67#66870—42no—
68#66870—42no—
69#10374—111nomaximal, Sylow
70C24×C11C2×D411yescharacteristic
71C23×D11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—41no—
75C22×C4×C11—81no—
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C22×C4×C11C2×Q811yescharacteristic
79C22×C4×C11#4111yescharacteristic
80C22×C4×C11#4111yescharacteristic
81C22×C4×C11#4111yescharacteristic
82C2×C22⋊D11—41no—
83C2×C22⋊D11—41no—
84C2×C22⋊D11—41no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C2×C22⋊D11—41no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—42no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C22×Dic11—81no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—81no—
100C2×Dic22—42no—
101C2×Dic22—42no—
102C2×Dic22—81no—
103C2×C8×C11—41no—
104C2×C8×C11—81no—
105C11×C4⋊C4—81no—
106C11×C4⋊C4—81no—
107C11×C22⋊C4—41no—
108C11×C22⋊C4—41no—
109C11×C22⋊C4—41no—
110C11×C22⋊C4—41no—
111C22⋊Dic11—21no—
112C22⋊Dic11—21no—
113C22⋊Dic11D812yes—
114C22⋊Dic11SD1612yes—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117C4⋊Dic11—21no—
118C4⋊Dic11—21no—
119C4⋊Dic11—42no—
120Dic11⋊C4—42no—
121Dic11⋊C4—42no—
122Dic11⋊C4—42no—
123Dic11⋊C4—81no—
124C4×Dic11—81no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—81no—
127#2549—111no—
128#1964—111no—
129#1519—111no—
130C2×#327—111no—
131#1294—111no—
132#1289D1111yescharacteristic, complemented
133#1282—111no—
134C23×C11—41no—
135C23×C11—41no—
136C23×C11#12011yescharacteristic
137C23×C11C22⋊Q811yescharacteristic
138C23×C11#12411yescharacteristic
139C23×C11C2×D811yescharacteristic
140C23×C11C2×SD1611yescharacteristic
141C23×C11AGL(1,ℤ/8)11yescharacteristic
142C23×C11#13711yescharacteristic
143C22×D11—41no—
144C22×D11—41no—
145C22×D11—41no—
146C22×D11—81no—
147C22×D11—81no—
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—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—81no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11C22⋊Q811yescharacteristic
164C2×C4×C11C22⋊Q811yescharacteristic
165C2×C4×C11#12411yescharacteristic
166C2×C4×C11#12411yescharacteristic
167C22⋊D11—81no—
168C22⋊D11—81no—
169C22⋊D11—81no—
170C22⋊D11—81no—
171C2×Dic11—22no—
172C2×Dic11—22no—
173C2×Dic11—22no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—82no—
187C2×Dic11—82no—
188D44—81no—
189D44—81no—
190Dic22—84no—
191C8×C11—81no—
192C11⋊C8—81no—
193C2×C22⋊Q8—221no—
194C2×#121—111no—
195C2×#99—221no—
196C2×#99—221no—
197C2×C22⋊C8—111no—
198C2×C22⋊C8C2×D1111yescharacteristic
199#398—221no—
200#395—221no—
201#391—221no—
202#389—221no—
203#385—221no—
204#380C2×D1111yescharacteristic
205#380C2×D1111yescharacteristic
206C4×C22⋊C4—111no—
207C2×#95—111no—
208#327—221no—
209#327—221no—
210#327—221no—
211#327—221no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—41no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11—41no—
222C22×C11#39311yescharacteristic
223C22×C11#44711yescharacteristic
224C22×C11#44811yescharacteristic
225C22×C11#47411yescharacteristic
226C22×C11#47611yescharacteristic
227C22×C11#48611yescharacteristic
228C22×C11#48911yescharacteristic
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—161no—
233C2×D11—161no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—81no—
239C4×C11—81no—
240C4×C11—161no—
241Dic11—42no—
242Dic11—42no—
243Dic11—42no—
244Dic11—81no—
245Dic11—81no—
246C22×Q8—221no—
247C22×D4—111no—
248C22×D4—221no—
249C23×C4—221no—
250C23×C4C22×D1111yescharacteristic
251C22×C8—21no—
252C22×C8—221no—
253C22⋊Q8—442no—
254C22⋊Q8—442no—
255#121—221no—
256#121—221no—
257#121—221no—
258#121—221no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—221no—
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—221no—
272C2×C42—221no—
273#99—442no—
274#99—442no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8—221no—
278C22⋊C8—221no—
279#95—21no—
280#95—111no—
281#95—111no—
282#95—221no—
283#95—221no—
284#95—221no—
285#95—221no—
286#95D4411yescharacteristic
287#95D4411yescharacteristic
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11—21no—
292C2×C11—21no—
293C2×C11—21no—
294C2×C11#202311yescharacteristic
295C2×C11#203111yescharacteristic
296C2×C11#203211yescharacteristic
297D11—161no—
298C24—221no—
299C24D4×D1111yescharacteristic
300C2×Q8—442no—
301C2×Q8—442no—
302C2×Q8—881no—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—441no—
306C2×D4—441no—
307C2×D4—441no—
308C2×D4—441no—
309C2×D4—441no—
310C2×D4—441no—
311C2×D4—881no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—41no—
315C22×C4—81no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—442no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4—881no—
325C22×C4C2×D4411yescharacteristic
326C22×C4#433911yescharacteristic
327C22×C4#433911yescharacteristic
328C22×C4D4×D1111yescharacteristic
329C22×C4#434111yescharacteristic
330C22×C4Q8×D1111yescharacteristic
331C2×C8—41no—
332C2×C8—81no—
333C2×C8—441no—
334C2×C8—881no—
335C4⋊C4—81no—
336C4⋊C4—81no—
337C4⋊C4—221no—
338C4⋊C4—221no—
339C4⋊C4—442no—
340C4⋊C4—442no—
341C4⋊C4—442no—
342C4⋊C4—442no—
343C4⋊C4—881no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4—112no—
349C22⋊C4—112no—
350C22⋊C4—221no—
351C22⋊C4—221no—
352C22⋊C4—441no—
353C22⋊C4—441no—
354C42—881no—
355C11#1037411yescharacteristic, complemented, Sylow
356C23—41no—
357C23—41no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—881no—
362C23—881no—
363C23#6693511yescharacteristic
364C23#6693811yescharacteristic
365C23#6694911yescharacteristic
366C23D8×D1111yescharacteristic
367C23SD16×D1111yescharacteristic
368C23#6696711yescharacteristic
369C23#6697111yescharacteristic
370Q8—884no—
371D4—881no—
372D4—881no—
373D4—881no—
374D4—881no—
375D4—881no—
376D4—881no—
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—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
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—882no—
408C2×C4—882no—
409C2×C4#6692811yescharacteristic
410C2×C4#6693811yescharacteristic
411C2×C4#6694911yescharacteristic
412C2×C4#6695011yescharacteristic
413C8—81no—
414C8—881no—
415C22—21no—
416C22—21no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22—1761no—
429C22—1761no—
430C22#1062228611yescharacteristic
431C22#1062237311yescharacteristic
432C22#1062238611yescharacteristic
433C22#1062240811yescharacteristic
434C22#1062241911yescharacteristic
435C22#1062248311yescharacteristic
436C22#1062250311yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—21no—
441C4—81no—
442C4—81no—
443C4—161no—
444C4—442no—
445C4—442no—
446C4—442no—
447C4—881no—
448C4—881no—
449C2—21no—
450C2—21no—
451C2—21no—
452C2—21no—
453C2—21no—
454C2—21no—
455C2—1761no—
456C2#1306975111yescharacteristic
457C2#1306978711yescharacteristic
458C2#1306979411yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1289C2
socleC22×C11#393
prime radicalC2×#66983C22
hypercenter#1289D11
hypocenterC11#10374
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1289

Complements

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

NH ≅ G/Ntype
1. #13073628C2semidirect
5. #13066494C2semidirect
6. #13066462C2semidirect
7. C11×#1289C2semidirect
30. C22×D44Q8semidirect
45. C2×C4⋊Dic11Q8semidirect
132. #1289D11semidirect
355. C11#10374semidirect

Maximal subgroups

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

subgroupindex
#130736282
#130694512
#130671832
C2×#106221082
#130664942
#130664622
C11×#12892
#1037411