Finite Group Databasebeta

← #14736704

Subgroups — #14736704

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079010C211yesmaximal, characteristic
2#13078647C211yesmaximal, characteristic
3C2×#10622644C211yesmaximal, characteristic, complemented
4#13068184C212yesmaximal, complemented
5#13068170C212yesmaximal, complemented
6#13068060C212yesmaximal, complemented
7#13068046C212yesmaximal, complemented
8#13067368C211yesmaximal, characteristic, complemented
9#13067302C211yesmaximal, characteristic, complemented
10#13067294C211yesmaximal, characteristic
11Q8×C11×M16C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C22×#4326—21no—
14#10623008C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C11×#446—22no—
17C11×#446C2212yes—
18C8×Q8×C11C2212yes—
19C11×#423—21no—
20C11×#423C2211yescharacteristic
21C4×C11×M16—21no—
22C4×C11×M16C2211yescharacteristic
23#10622840—21no—
24#10622746—21no—
25#10622746—21no—
26#10622644—21no—
27#10622644—21no—
28#10622644C2212yes—
29#10622644C2212yes—
30#10622640C2211yescharacteristic
31#10622640C2211yescharacteristic
32C4×#4325—21no—
33C4×#4325—21no—
34#10622633C2211yescharacteristic
35#10622633C2211yescharacteristic
36C2×#66874—21no—
37#10622581—21no—
38#10622538C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622327—22no—
41#10622307C2212yes—
42#10622294C2212yes—
43#10622124C2212yes—
44#10622124C2212yes—
45#10622123C2212yes—
46#10622120C2212yes—
47#10622096C2212yes—
48#10622095C2212yes—
49C22×Q8×C11D411yescharacteristic
50C2×#4339—21no—
51C22×Dic22—21no—
52C2×C11×M16—21no—
53C2×C11×M16D411yescharacteristic
54C2×C11×M16D411yescharacteristic
55C4×Q8×C11—21no—
56C4×Q8×C11—21no—
57C4×Q8×C11D411yescharacteristic
58C4×Q8×C11D411yescharacteristic
59C4×Q8×C11C2311yescharacteristic
60C4×Q8×C11C2311yescharacteristic
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×#4326—22no—
66C2×#4326—22no—
67C2×#4326—44no—
68C2×#4325—21no—
69C2×#4325—21no—
70#66983—21no—
71#66983—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C22×C11⋊C8—21no—
75#66928—21no—
76#66927C2311yescharacteristic
77C4×D44—21no—
78C4×D44—21no—
79#66922—21no—
80#66922—21no—
81#66922—21no—
82#66922C2312yes—
83#66922C2311yescharacteristic
84C11×C4⋊C8—22no—
85C11×C4⋊C8—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2312yes—
88C11×#97—22no—
89C11×#97D412yes—
90C4×C8×C11—22no—
91C4×C8×C11C2312yes—
92#66899—21no—
93#66899—21no—
94C22⋊(C11⋊C8)—21no—
95#66885—22no—
96#66885—22no—
97#66880—22no—
98#66880—22no—
99#66874—22no—
100#66874—22no—
101#66873—21no—
102#66873—21no—
103#66872—21no—
104#66872—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2311yescharacteristic
108C4⋊(C11⋊C8)C2311yescharacteristic
109C4×C11⋊C8—21no—
110#19177—111nomaximal, Sylow
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—41no—
114C2×Q8×C11C2×D411yescharacteristic
115C2×Q8×C11C2×D411yescharacteristic
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11#4111yescharacteristic
121C2×C22⋊D11—41no—
122C22×Dic11—41no—
123#4339—42no—
124#4339—42no—
125C2×D44—21no—
126C2×D44—21no—
127C2×D44—21no—
128C2×C4×D11—41no—
129C2×Dic22—22no—
130C2×Dic22—21no—
131C2×Dic22—42no—
132C2×Dic22—42no—
133C2×Dic22—41no—
134C11×M16—22no—
135C11×M16—22no—
136C11×M16—42no—
137C2×C8×C11—22no—
138C2×C8×C11C2×D412yes—
139C2×C8×C11C2×D412yes—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4C2×D411yescharacteristic
146C11×C4⋊C4C2×D411yescharacteristic
147C42×C11—21no—
148C42×C11—21no—
149C42×C11—21no—
150C42×C11—21no—
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11#4111yescharacteristic
154C42×C11C2411yescharacteristic
155#4326—44no—
156#4326—44no—
157#4325—42no—
158#4325—42no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161C4⋊Dic11—21no—
162C4⋊Dic11—22no—
163C4⋊Dic11—22no—
164C4⋊Dic11—21no—
165C4⋊Dic11—41no—
166C4⋊Dic11—41no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—42no—
171#3141—111no—
172#3103—111no—
173C2×#462—111no—
174Q8×M16D1111yescharacteristic, complemented
175#1702—112no—
176#1700—112no—
177#1682—112no—
178#1680—112no—
179#1565—111no—
180#1549—111no—
181#1547—111no—
182C23×C11#12111yescharacteristic
183C22×D11—41no—
184Q8×C11—21no—
185Q8×C11—21no—
186Q8×C11—21no—
187Q8×C11—42no—
188Q8×C11AGL(1,ℤ/8)12yes—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—81no—
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#13512yes—
202C2×C4×C11#13712yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C22⋊D11—82no—
207C2×Dic11—42no—
208C2×Dic11—41no—
209C2×Dic11—82no—
210D44—41no—
211D44—41no—
212D44—41no—
213D44—41no—
214D44—81no—
215C4×D11—82no—
216Dic22—41no—
217Dic22—42no—
218Dic22—41no—
219Dic22—42no—
220Dic22—82no—
221C8×C11—22no—
222C8×C11—22no—
223C8×C11—42no—
224C11⋊C8—42no—
225C11⋊C8—41no—
226C11⋊C8—41no—
227C22×Q16—221no—
228#532—111no—
229C2×C4⋊Q8—111no—
230C2×C4×Q8C2×D1111yescharacteristic
231#489—222no—
232#487—112no—
233#486—112no—
234#481—221no—
235#475—111no—
236#475—111no—
237#462—112no—
238#462—112no—
239#462—221no—
240#462—221no—
241#460—111no—
242#460—111no—
243#448—221no—
244#446—22no—
245#446C2×D1112yes—
246C8×Q8C2×D1112yes—
247C4×SD16—221no—
248C4×SD16—221no—
249#431—111no—
250#423—21no—
251#423C2×D1111yescharacteristic
252C2×C4⋊C8—111no—
253#417—221no—
254#417—221no—
255C2×#103—221no—
256C4×M16—21no—
257C4×M16C2×D1111yescharacteristic
258#335—112no—
259#334—112no—
260#332—112no—
261#332—112no—
262#332—112no—
263#331—112no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11#46412yes—
267C22×C11C2×#12111yescharacteristic
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C4×C11—21no—
272C4×C11—22no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—41no—
276C4×C11—41no—
277C4×C11—41no—
278C4×C11#46412yes—
279C4×C11C2×#13511yescharacteristic
280C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C11C2×#13711yescharacteristic
282C4×C11#57511yescharacteristic
283Dic11—81no—
284Dic11—82no—
285C2×#41—221no—
286C22×Q8—221no—
287C22×Q8D4411yescharacteristic
288C2×Q16—222no—
289C2×Q16—222no—
290C2×Q16—444no—
291C2×SD16—221no—
292C2×SD16—221no—
293C2×M16—21no—
294C2×M16C22⋊D1111yescharacteristic
295C2×M16C22⋊D1111yescharacteristic
296C22×C8—221no—
297C4⋊Q8—112no—
298C4⋊Q8—111no—
299C4⋊Q8—221no—
300C4⋊Q8—221no—
301C4⋊Q8—221no—
302#127—111no—
303#124—221no—
304#121—221no—
305#121—221no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8D4411yescharacteristic
309C4×Q8D4411yescharacteristic
310C4×Q8C22×D1111yescharacteristic
311C4×Q8C22×D1111yescharacteristic
312C4×D4—221no—
313C4×D4—221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4D4411yescharacteristic
318C2×C42—21no—
319C2×C42C22×D1111yescharacteristic
320#106—221no—
321#106—221no—
322C4⋊C8—22no—
323C4⋊C8—22no—
324C4⋊C8—21no—
325C4⋊C8—112no—
326C4⋊C8—111no—
327C4⋊C8—111no—
328C4⋊C8—221no—
329C4⋊C8C22×D1112yes—
330#103—221no—
331#103—221no—
332#103—222no—
333#103—222no—
334#103—222no—
335#103—222no—
336#102—222no—
337#102—222no—
338#102—221no—
339#102—221no—
340C22⋊C8—221no—
341#97—22no—
342#97C22⋊D1112yes—
343C4×C8—22no—
344C4×C8—221no—
345C4×C8C22×D1112yes—
346C2×C11—22no—
347C2×C11C2×#46411yescharacteristic
348C2×C11#305511yescharacteristic
349C2×C11#306911yescharacteristic
350D11—161no—
351#41—442no—
352#41—442no—
353C2×Q8—21no—
354C2×Q8—22no—
355C2×Q8—41no—
356C2×Q8—222no—
357C2×Q8—221no—
358C2×Q8—442no—
359C2×Q8—442no—
360C2×Q8—441no—
361C2×Q8C2×D4411yescharacteristic
362C2×Q8C2×D4411yescharacteristic
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—441no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4C2×D4411yescharacteristic
372C22×C4#433911yescharacteristic
373C22×C4C2×C22⋊D1111yescharacteristic
374Q16—444no—
375Q16—444no—
376SD16—442no—
377SD16—442no—
378M16—22no—
379M16—22no—
380M16—42no—
381C2×C8—22no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—222no—
385C2×C8—442no—
386C2×C8C2×C22⋊D1112yes—
387C2×C8C2×C22⋊D1112yes—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—221no—
394C4⋊C4—222no—
395C4⋊C4—221no—
396C4⋊C4—222no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4C2×D4411yescharacteristic
400C4⋊C4C2×D4411yescharacteristic
401C22⋊C4—441no—
402C22⋊C4—441no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42C2×D4411yescharacteristic
408C42#433911yescharacteristic
409C42C2×C22⋊D1111yescharacteristic
410C42C23×D1111yescharacteristic
411C11#1917711yescharacteristic, complemented, Sylow
412C23—441no—
413C23#6698311yescharacteristic
414Q8—21no—
415Q8—21no—
416Q8—21no—
417Q8—42no—
418Q8—442no—
419Q8—442no—
420Q8—441no—
421Q8—441no—
422Q8—882no—
423Q8#6696112yes—
424D4—441no—
425D4—441no—
426D4—441no—
427D4—441no—
428D4—881no—
429D4—882no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—81no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—882no—
442C2×C4—882no—
443C2×C4#6698311yescharacteristic
444C2×C4#6698311yescharacteristic
445C2×C4#6698311yescharacteristic
446C2×C4#6699512yes—
447C2×C4#6700312yes—
448C2×C4C22×D4411yescharacteristic
449C2×C4C2×#433911yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—22no—
452C8—22no—
453C8—42no—
454C8—442no—
455C8—441no—
456C8—441no—
457C22—21no—
458C22—21no—
459C22—881no—
460C22—881no—
461C22—881no—
462C22#1062264112yes—
463C22C2×#6698311yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—22no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—881no—
472C4—882no—
473C4#1062264112yes—
474C4C2×#6696111yescharacteristic
475C4#1062327911yescharacteristic
476C4C2×#6699511yescharacteristic
477C4C2×#6700311yescharacteristic
478C2—22no—
479C2—1761no—
480C2C2×#1062264111yescharacteristic
481C2#1307823511yescharacteristic
482C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingQ8×C11×M16C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterQ8×M16D11
hypocenterC11#19177
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
3. C2×#10622644C2semidirect
4. #13068184C2semidirect
5. #13068170C2semidirect
6. #13068060C2semidirect
7. #13068046C2semidirect
8. #13067368C2semidirect
9. #13067302C2semidirect
11. Q8×C11×M16C2semidirect
174. Q8×M16D11semidirect
411. C11#19177semidirect

Maximal subgroups

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

subgroupindex
#130790102
#130786472
C2×#106226442
#130681842
#130681702
#130680602
#130680462
#130673682
#130673022
#130672942
Q8×C11×M162
#1917711