Finite Group Databasebeta

← #14654375

Subgroups — #14654375

Order 2816.

742 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 85 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#13079369C211yesmaximal, characteristic, complemented
2#13077868C211yesmaximal, characteristic
3#13068528C211yesmaximal, characteristic, complemented
4#13066980C211yesmaximal, characteristic, complemented
5#13066977C211yesmaximal, characteristic, complemented
6#13066492C211yesmaximal, characteristic, complemented
7C11×#3007C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C2×C11×#137—21no—
10C2×C11×C22⋊Q8C2211yescharacteristic
11C2×#67002—21no—
12C2×#66983C2211yescharacteristic
13C11×#452—22no—
14C11×#451—21no—
15C11×#450—21no—
16C11×#417—21no—
17C11×#407C2211yescharacteristic
18#10622851—22no—
19#10622845—21no—
20#10622840—21no—
21#10622840—21no—
22#10622830—21no—
23#10622820C2211yescharacteristic
24C2×C22⋊(C11⋊C8)—22no—
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×C22⋊(C11⋊C8)C2211yescharacteristic
27#10622661—22no—
28#10622659—21no—
29#10622656—21no—
30#10622581—21no—
31#10622166—22no—
32#10622106—22no—
33C2×C11×#41—21no—
34C2×C11×#41—21no—
35C2×C11×#41—21no—
36C2×C11×#41—21no—
37C2×C11×#41—44no—
38C22×Q8×C11D411yescharacteristic
39C22×Q8×C11D411yescharacteristic
40C22×D4×C11—21no—
41C22×D4×C11D411yescharacteristic
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C22×D44D411yescharacteristic
46C11×#137—44no—
47C2×C11×Q16—22no—
48C2×C11×SD16—22no—
49C2×C11×M16—21no—
50C11×C22⋊Q8—21no—
51C11×C22⋊Q8—21no—
52C11×C22⋊Q8—21no—
53C11×C22⋊Q8—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4—21no—
57#67002—44no—
58C2×#4325—22no—
59C2×#4325—22no—
60C2×#4323—22no—
61#66983—21no—
62#66983—21no—
63#66983—21no—
64#66983—21no—
65C2×(C2×D11)⋊C4—21no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×#4318—21no—
68C22×C11⋊C8—21no—
69C22×C11⋊C8D412yes—
70C11×#103—22no—
71C11×#102—22no—
72C11×C22⋊C8—21no—
73C11×C22⋊C8D412yes—
74#66899—22no—
75#66899—22no—
76#66896—22no—
77C22⋊(C11⋊C8)—21no—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)—21no—
80C22⋊(C11⋊C8)—21no—
81C22⋊(C11⋊C8)—21no—
82C22⋊(C11⋊C8)—44no—
83C22⋊(C11⋊C8)D412yes—
84#66873—22no—
85#66872—22no—
86#9975—111nomaximal, Sylow
87C24×C11—21no—
88C24×C11#4111yescharacteristic
89C23×D11—21no—
90C11×#41—24no—
91C11×#41—24no—
92C11×#41—42no—
93C11×#41—42no—
94C11×#41—42no—
95C11×#41—42no—
96C11×#41—42no—
97C11×#41—42no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—42no—
103C2×Q8×C11—42no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—42no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C22×C4×C11—24no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—42no—
116C22×C4×C11—42no—
117C22×C4×C11—41no—
118C22×C4×C11—41no—
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C2×C22⋊D11—82no—
128C22×Dic11—21no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—42no—
132C11×Q16—44no—
133C11×SD16—44no—
134C11×M16—42no—
135C2×C8×C11—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C22⋊C4—41no—
141C11×C22⋊C4—41no—
142#4325—44no—
143#4325—82no—
144#4323—44no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149#4318—42no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—42no—
153C2×C11⋊C8—42no—
154C2×C11⋊C8—41no—
155#3187—111no—
156#3007D1111yescharacteristic, complemented
157#3006—111no—
158#1780—111no—
159#1472—111no—
160#1471—111no—
161#1293—111no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—42no—
168C23×C11—41no—
169C23×C11—42no—
170C23×C11#12111yescharacteristic
171C23×C11#12111yescharacteristic
172C23×C11#12111yescharacteristic
173C22×D11—41no—
174C22×D11—42no—
175C22×D11—81no—
176C22×D11—81no—
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—41no—
180Q8×C11—41no—
181Q8×C11—42no—
182Q8×C11—42no—
183D4×C11—22no—
184D4×C11—22no—
185D4×C11—41no—
186D4×C11—41no—
187D4×C11—44no—
188D4×C11—44no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—44no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—44no—
200C2×C4×C11—42no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—81no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#12711yescharacteristic
208C22⋊D11—82no—
209C22⋊D11—82no—
210C2×Dic11—41no—
211C2×Dic11—81no—
212D44—42no—
213D44—42no—
214C8×C11—42no—
215C11⋊C8—42no—
216C11⋊C8—42no—
217C11⋊C8—81no—
218C22×#41C2×D1111yescharacteristic
219C2×#137—21no—
220C2×AGL(1,ℤ/8)—221no—
221C2×C22⋊Q8C2×D1111yescharacteristic
222C2×#121—111no—
223#483—221no—
224#481—221no—
225#465—222no—
226#452—22no—
227#451—21no—
228#450—21no—
229#450—221no—
230#449—222no—
231#448—221no—
232#448—221no—
233#447—221no—
234#417—21no—
235#417—221no—
236#407—111no—
237#407C2×D1111yescharacteristic
238C2×C22⋊C8—111no—
239C2×C22⋊C8—111no—
240C2×C22⋊C8—222no—
241#324—222no—
242#323—222no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—44no—
252C22×C11—42no—
253C22×C11—82no—
254C22×C11—82no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11#39211yescharacteristic
258C22×C11#47112yes—
259C2×D11—81no—
260C2×D11—81no—
261C2×D11—81no—
262C2×D11—162no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—42no—
267C4×C11—81no—
268C4×C11—81no—
269C4×C11B(4,𝔽2)12yes—
270Dic11—81no—
271C2×#41—21no—
272C2×#41—21no—
273C2×#41—21no—
274C2×#41—21no—
275C2×#41—44no—
276C22×Q8C22⋊D1111yescharacteristic
277C22×Q8C22⋊D1111yescharacteristic
278C22×D4—21no—
279C22×D4—111no—
280C22×D4—221no—
281C22×D4C22⋊D1111yescharacteristic
282C23×C4—21no—
283C23×C4C22×D1111yescharacteristic
284#137—44no—
285AGL(1,ℤ/8)—444no—
286C2×Q16—22no—
287C2×SD16—22no—
288C2×SD16—222no—
289C2×SD16—222no—
290C2×D8—222no—
291C2×M16—21no—
292C2×M16—221no—
293C22×C8—112no—
294C22×C8—221no—
295C22⋊Q8—21no—
296C22⋊Q8—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299#121—221no—
300#121—221no—
301#121—221no—
302#121—221no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4C22⋊D1111yescharacteristic
306C2×C22⋊C4—21no—
307C2×C22⋊C4—221no—
308#106—222no—
309#103—22no—
310#103—222no—
311#103—222no—
312#102—22no—
313#102—222no—
314#102—222no—
315C22⋊C8—21no—
316C22⋊C8—112no—
317C22⋊C8—221no—
318C22⋊C8—221no—
319C22⋊C8—221no—
320C22⋊C8—221no—
321C22⋊C8—221no—
322C22⋊C8—444no—
323C22⋊C8C22⋊D1112yes—
324C2×C11—22no—
325C2×C11—41no—
326C2×C11—41no—
327C2×C11—82no—
328C2×C11#201711yescharacteristic
329C2×C11#201911yescharacteristic
330C2×C11#202111yescharacteristic
331D11—161no—
332C24—21no—
333C24—221no—
334C24#434111yescharacteristic
335#41—24no—
336#41—24no—
337#41—42no—
338#41—42no—
339#41—42no—
340#41—42no—
341#41—42no—
342#41—42no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—42no—
352C2×D4—42no—
353C2×D4—42no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—442no—
359C2×D4—441no—
360C2×D4—441no—
361C2×D4—882no—
362C22×C4—24no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—221no—
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C22×C4D4×D1111yescharacteristic
374C22×C4C2×C22⋊D1111yescharacteristic
375C22×C4C2×C22⋊D1111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377Q16—44no—
378SD16—44no—
379SD16—444no—
380SD16—882no—
381D8—444no—
382M16—42no—
383M16—442no—
384C2×C8—22no—
385C2×C8—222no—
386C2×C8—222no—
387C2×C8—442no—
388C2×C8—442no—
389C2×C8—441no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—441no—
399C22⋊C4—441no—
400C11#997511yescharacteristic, complemented, Sylow
401C23—22no—
402C23—22no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—42no—
407C23—42no—
408C23—41no—
409C23—442no—
410C23—441no—
411C23—881no—
412C23—881no—
413C23#6699111yescharacteristic
414C23#6699211yescharacteristic
415C23#6699211yescharacteristic
416Q8—22no—
417Q8—22no—
418Q8—41no—
419Q8—41no—
420Q8—42no—
421Q8—42no—
422D4—22no—
423D4—22no—
424D4—41no—
425D4—41no—
426D4—44no—
427D4—44no—
428D4—442no—
429D4—442no—
430D4—882no—
431D4—882no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—44no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—81no—
447C2×C4—441no—
448C2×C4—881no—
449C2×C4#6699011yescharacteristic
450C2×C4#6699011yescharacteristic
451C2×C4#6699311yescharacteristic
452C2×C4#6700611yescharacteristic
453C8—42no—
454C8—442no—
455C8—442no—
456C8—881no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—44no—
466C22—42no—
467C22—82no—
468C22—82no—
469C22—81no—
470C22—81no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—1762no—
475C22#1062281612yes—
476C22#1062283611yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—42no—
481C4—81no—
482C4—81no—
483C4—881no—
484C4#1062264512yes—
485C2—22no—
486C2—41no—
487C2—41no—
488C2—82no—
489C2—1761no—
490C2#1306971911yescharacteristic
491C2#1306972711yescharacteristic
492C2#1306973911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#3007C2
socleC22×C11#392
prime radical#13077868C2
hypercenter#3007D11
hypocenterC11#9975
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. #13079369C2semidirect
3. #13068528C2semidirect
4. #13066980C2semidirect
5. #13066977C2semidirect
6. #13066492C2semidirect
7. C11×#3007C2semidirect
156. #3007D11semidirect
400. C11#9975semidirect

Maximal subgroups

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

subgroupindex
#130793692
#130778682
#130685282
#130669802
#130669772
#130664922
C11×#30072
#997511