Finite Group Databasebeta

← #14650985

Subgroups — #14650985

Order 2816.

774 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 115 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#13071457C211yesmaximal, characteristic, complemented
2#13069453C211yesmaximal, characteristic, complemented
3#13068560C211yesmaximal, characteristic, complemented
4#13067132C211yesmaximal, characteristic, complemented
5#13066521C211yesmaximal, characteristic, complemented
6#13066501C211yesmaximal, characteristic, complemented
7C11×#3006C211yesmaximal, characteristic
8C22×C11×#41C2211yescharacteristic
9C2×C11×AGL(1,ℤ/8)C412yescomplemented
10C2×C11×#121C2211yescharacteristic
11C2×Q8×Dic11—21no—
12C11×#449—22no—
13C11×#448—21no—
14C11×#447—21no—
15C11×#417C412yescomplemented
16C11×#407C2211yescharacteristic
17C2×#66901—22no—
18#10622834—21no—
19#10622834—22no—
20C2×#66898—22no—
21#10622825—21no—
22#10622825C2211yescharacteristic
23C4×C22⋊Dic11—21no—
24C4×C22⋊Dic11C2211yescharacteristic
25C4×C22⋊Dic11C2211yescharacteristic
26#10622820C2211yescharacteristic
27#10622175—21no—
28#10622175—21no—
29C2×C11×#41—21no—
30C2×C11×#41—21no—
31C2×C11×#41—44no—
32C2×C11×#41C2×C412yes—
33C2×C11×#41D412yes—
34C22×Q8×C11D411yescharacteristic
35C22×D4×C11—21no—
36C22×D4×C11—21no—
37C22×D4×C11C2×C411yescharacteristic
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C11×AGL(1,ℤ/8)—44no—
42C2×C11×SD16—22no—
43C2×C11×D8—22no—
44C2×C11×M16C2×C412yes—
45C11×#121—21no—
46C11×#121—21no—
47C11×#121—21no—
48C11×#121—21no—
49C2×C11×C4⋊C4C2×C411yescharacteristic
50C2×C11×C22⋊C4—21no—
51C2×C22⋊Dic11—21no—
52C2×C22⋊Dic11—22no—
53C2×C22⋊Dic11—21no—
54C2×C22⋊Dic11—22no—
55C2×C22⋊Dic11D412yes—
56Q8×Dic11—44no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—21no—
59C2×C4×Dic11—22no—
60C2×C4×Dic11—21no—
61C2×C4×Dic11—21no—
62C2×#4318—21no—
63C11×#103—22no—
64C11×#102—22no—
65C11×C22⋊C8—21no—
66C11×C22⋊C8—21no—
67#66901—44no—
68#66898—44no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95D411yescharacteristic
72C11⋊#95D411yescharacteristic
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75#9368—111nomaximal, Sylow
76C24×C11—21no—
77C24×C11—21no—
78C24×C11C2×D411yescharacteristic
79C11×#41—24no—
80C11×#41—24no—
81C11×#41—42no—
82C11×#41—42no—
83C11×#41—44no—
84C11×#41—44no—
85C2×Q8×C11—24no—
86C2×Q8×C11—21no—
87C2×Q8×C11C22⋊C412yes—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—42no—
94C2×D4×C11—44no—
95C2×D4×C11—42no—
96C2×D4×C11—42no—
97C2×D4×C11—42no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11C22⋊C412yes—
101C22×C4×C11—21no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—42no—
106C22×C4×C11—44no—
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—22no—
115C22×Dic11—21no—
116C22×Dic11—41no—
117C11×SD16—44no—
118C11×D8—44no—
119C11×M16—42no—
120C2×C8×C11—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C22⋊C4—41no—
124C11×C22⋊C4—41no—
125C22⋊Dic11—22no—
126C22⋊Dic11—42no—
127C22⋊Dic11—41no—
128C22⋊Dic11—42no—
129C22⋊Dic11—44no—
130C22⋊Dic11—82no—
131C4⋊Dic11—44no—
132C4⋊Dic11—42no—
133C4×Dic11—44no—
134C4×Dic11—42no—
135C4×Dic11—42no—
136#4318—42no—
137C2×C11⋊C8—41no—
138#3006D1111yescharacteristic
139#2341—111no—
140#1964—111no—
141#1789—111no—
142#1507—111no—
143#1305—111no—
144#1297—111no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—22no—
148C23×C11—41no—
149C23×C11—41no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—42no—
153C23×C11—41no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—81no—
157C23×C11—81no—
158C23×C11C4×D411yescharacteristic
159C23×C11#12011yescharacteristic
160C23×C11#12111yescharacteristic
161Q8×C11—24no—
162Q8×C11—22no—
163Q8×C11#9914yescomplemented
164D4×C11—22no—
165D4×C11—22no—
166D4×C11—44no—
167D4×C11—44no—
168D4×C11—42no—
169D4×C11—42no—
170D4×C11—81no—
171D4×C11—82no—
172D4×C11—81no—
173D4×C11—81no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—44no—
183C2×C4×C11—44no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11C2×C22⋊C411yescharacteristic
187C2×C4×C11C4×D411yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12311yescharacteristic
190C2×Dic11—22no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—42no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—81no—
201C2×Dic11—81no—
202C8×C11—42no—
203C11⋊C8—81no—
204C22×#41C2×D1111yescharacteristic
205C2×AGL(1,ℤ/8)Dic1112yescomplemented
206C2×#121C2×D1111yescharacteristic
207C2×C4×Q8—221no—
208#449—22no—
209#448—21no—
210#447—21no—
211C2×#104—222no—
212#417Dic1112yescomplemented
213C2×#99—222no—
214#407—111no—
215#407C2×D1111yescharacteristic
216#390—222no—
217#390—221no—
218#380—111no—
219#380—221no—
220C4×C22⋊C4—111no—
221C4×C22⋊C4—111no—
222C4×C22⋊C4—221no—
223#327—221no—
224#327—221no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—42no—
236C22×C11—81no—
237C22×C11—81no—
238C22×C11—82no—
239C22×C11—82no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—162no—
244C22×C11#38611yescharacteristic
245C22×C11#45311yescharacteristic
246C22×C11#45411yescharacteristic
247C4×C11—24no—
248C4×C11—21no—
249C4×C11—21no—
250C4×C11—21no—
251C4×C11—81no—
252C4×C11C2×#9912yes—
253Dic11—42no—
254Dic11—82no—
255Dic11—81no—
256Dic11—82no—
257C2×#41—21no—
258C2×#41—21no—
259C2×#41—44no—
260C2×#41C2×Dic1112yes—
261C2×#41C22⋊D1112yes—
262C22×Q8C22⋊D1111yescharacteristic
263C22×D4—21no—
264C22×D4—21no—
265C22×D4C2×Dic1111yescharacteristic
266C22×D4C22⋊D1111yescharacteristic
267C23×C4—21no—
268C23×C4C22×D1111yescharacteristic
269AGL(1,ℤ/8)—44no—
270C2×SD16—22no—
271C2×D8—22no—
272C2×M16—221no—
273C2×M16C2×Dic1112yes—
274#121—21no—
275#121—21no—
276#121—21no—
277#121—21no—
278C4×Q8—444no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4C2×Dic1111yescharacteristic
282C2×C22⋊C4—21no—
283C2×C22⋊C4—112no—
284C2×C22⋊C4—221no—
285C2×C22⋊C4—222no—
286C2×C22⋊C4—221no—
287C2×C22⋊C4—222no—
288C2×C42—222no—
289C2×C42—221no—
290C2×C42—221no—
291#104—444no—
292#103—22no—
293#102—22no—
294#99—444no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—221no—
298C22⋊C8—221no—
299#95—111no—
300#95—111no—
301#95—221no—
302#95—221no—
303C2×C11—21no—
304C2×C11—21no—
305C2×C11—41no—
306C2×C11—41no—
307C2×C11—82no—
308C2×C11—161no—
309C2×C11#188311yescharacteristic
310C2×C11#189811yescharacteristic
311C2×C11#190611yescharacteristic
312C24—21no—
313C24—21no—
314C24D4×D1111yescharacteristic
315#41—24no—
316#41—24no—
317#41—42no—
318#41—42no—
319#41—44no—
320#41—44no—
321C2×Q8—24no—
322C2×Q8—21no—
323C2×Q8C22⋊Dic1112yes—
324C2×D4—22no—
325C2×D4—22no—
326C2×D4—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—42no—
330C2×D4—44no—
331C2×D4—42no—
332C2×D4—42no—
333C2×D4—42no—
334C2×D4—41no—
335C2×D4—41no—
336C2×D4C22⋊Dic1112yes—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—44no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—222no—
346C22×C4—441no—
347C22×C4D4×D1111yescharacteristic
348C22×C4#434111yescharacteristic
349C22×C4#434111yescharacteristic
350C22×C4C22×Dic1111yescharacteristic
351C22×C4C2×C22⋊D1111yescharacteristic
352C22×C4C2×C22⋊D1111yescharacteristic
353SD16—44no—
354D8—44no—
355M16—42no—
356M16—442no—
357C2×C8—22no—
358C2×C8—441no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—444no—
362C4⋊C4—442no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—222no—
366C22⋊C4—442no—
367C22⋊C4—444no—
368C22⋊C4—441no—
369C22⋊C4—442no—
370C22⋊C4—882no—
371C42—444no—
372C42—442no—
373C42—442no—
374C11#936811yescharacteristic, complemented, Sylow
375C23—21no—
376C23—21no—
377C23—22no—
378C23—41no—
379C23—41no—
380C23—42no—
381C23—42no—
382C23—42no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23—81no—
387C23—81no—
388C23D4×Dic1111yescharacteristic
389C23#6699011yescharacteristic
390C23#6699211yescharacteristic
391Q8—24no—
392Q8—22no—
393Q8#6689814yescomplemented
394D4—22no—
395D4—22no—
396D4—44no—
397D4—44no—
398D4—42no—
399D4—42no—
400D4—81no—
401D4—82no—
402D4—81no—
403D4—81no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—222no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—441no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—441no—
426C2×C4—881no—
427C2×C4—881no—
428C2×C4D4×Dic1111yescharacteristic
429C2×C4#6698811yescharacteristic
430C2×C4#6699211yescharacteristic
431C2×C4C2×C22⋊Dic1111yescharacteristic
432C8—42no—
433C8—881no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—42no—
443C22—42no—
444C22—42no—
445C22—81no—
446C22—81no—
447C22—82no—
448C22—82no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—162no—
453C22#1062281111yescharacteristic
454C22#1062281411yescharacteristic
455C22#1062283311yescharacteristic
456C4—21no—
457C4—24no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—442no—
462C4—882no—
463C4—881no—
464C4—882no—
465C4C2×#6689812yes—
466C2—21no—
467C2—21no—
468C2—41no—
469C2—41no—
470C2—82no—
471C2—161no—
472C2#1306899411yescharacteristic
473C2#1306907011yescharacteristic
474C2#1306911911yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
Fitting, prime radicalC11×#3006C2
socleC22×C11#386
cosocleC23×C4×C11C23
hypercenter#3006D11
hypocenterC11#9368
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. #13071457C2semidirect
2. #13069453C2semidirect
3. #13068560C2semidirect
4. #13067132C2semidirect
5. #13066521C2semidirect
6. #13066501C2semidirect
9. C2×C11×AGL(1,ℤ/8)C4semidirect
15. C11×#417C4semidirect
163. Q8×C11#99semidirect
205. C2×AGL(1,ℤ/8)Dic11semidirect
212. #417Dic11semidirect
374. C11#9368semidirect
393. Q8#66898semidirect

Maximal subgroups

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

subgroupindex
#130714572
#130694532
#130685602
#130671322
#130665212
#130665012
C11×#30062
#936811