Finite Group Databasebeta

← #14736708

Subgroups — #14736708

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#13079012C211yesmaximal, characteristic
2#13078647C211yesmaximal, characteristic
3Q8×#4318C211yesmaximal, characteristic, complemented
4#13068186C212yesmaximal, complemented
5#13068172C212yesmaximal, complemented
6#13068062C212yesmaximal, complemented
7#13068048C212yesmaximal, complemented
8#13067366C211yesmaximal, characteristic, complemented
9#13067301C211yesmaximal, characteristic, complemented
10#13067291C211yesmaximal, characteristic
11C2×C11×#462C211yesmaximal, characteristic, complemented
12C22×C11×Q16—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15#10623008C2211yescharacteristic
16C11×#462—21no—
17C11×#462—21no—
18C11×#462C2212yes—
19C11×#462C2212yes—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×#103—21no—
22#10622840—21no—
23#10622706C2212yes—
24#10622702—22no—
25#10622701C2212yes—
26#10622640C2211yescharacteristic
27#10622640C2211yescharacteristic
28C4×#4325—21no—
29C4×#4325—21no—
30#10622637—22no—
31#10622637C2212yes—
32Q8×C11⋊C8C2212yes—
33#10622633C2211yescharacteristic
34#10622633C2211yescharacteristic
35#10622581—21no—
36#10622579—21no—
37#10622579—21no—
38#10622538C2211yescharacteristic
39#10622537—21no—
40#10622537C2211yescharacteristic
41C4×#4318—21no—
42C4×#4318C2211yescharacteristic
43#10622185C2212yes—
44#10622185C2212yes—
45#10622124C2212yes—
46#10622123C2212yes—
47#10622118C2212yes—
48#10622117C2212yes—
49C22×Q8×C11—21no—
50C22×Q8×C11D411yescharacteristic
51C2×#4339—21no—
52C2×C11×Q16—22no—
53C2×C11×Q16—22no—
54C2×C11×Q16—44no—
55C22×C8×C11—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8—21no—
59C11×C4⋊Q8C2312yes—
60C4×Q8×C11—21no—
61C4×Q8×C11—21no—
62C4×Q8×C11D411yescharacteristic
63C4×Q8×C11D411yescharacteristic
64C4×Q8×C11C2311yescharacteristic
65C4×Q8×C11C2311yescharacteristic
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4325—21no—
73C2×#4325—21no—
74#66983—21no—
75#66983—21no—
76C2×#4318—21no—
77C2×#4318D411yescharacteristic
78C2×#4318D411yescharacteristic
79#66928—21no—
80#66927C2311yescharacteristic
81C4×D44—21no—
82C4×D44—21no—
83#66922C2311yescharacteristic
84C11×C4⋊C8—21no—
85C11×C4⋊C8C2312yes—
86C11×#103—22no—
87C11×#103—22no—
88#66899—21no—
89#66899—21no—
90C22⋊(C11⋊C8)—21no—
91#66874—22no—
92#66874—22no—
93#66873—21no—
94#66873—21no—
95#66873—22no—
96#66873—22no—
97#66872—21no—
98#66872—21no—
99C4⋊(C11⋊C8)—21no—
100C4⋊(C11⋊C8)—22no—
101C4⋊(C11⋊C8)—22no—
102C4⋊(C11⋊C8)C2312yes—
103C4⋊(C11⋊C8)C2311yescharacteristic
104C4⋊(C11⋊C8)C2311yescharacteristic
105#66867—22no—
106#66867D412yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—22no—
109C4×C11⋊C8C2312yes—
110#19177—111nomaximal, Sylow
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—42no—
116C2×Q8×C11—42no—
117C2×Q8×C11—41no—
118C2×Q8×C11C2×D411yescharacteristic
119C2×Q8×C11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—41no—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C2×C22⋊D11—41no—
127#4339—42no—
128#4339—42no—
129C2×D44—21no—
130C2×D44—21no—
131C2×D44—21no—
132C2×C4×D11—41no—
133C2×Dic22—21no—
134C11×Q16—44no—
135C11×Q16—44no—
136C2×C8×C11—22no—
137C2×C8×C11—42no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4C2×D411yescharacteristic
148C11×C4⋊C4C2×D411yescharacteristic
149C42×C11—21no—
150C42×C11—21no—
151C42×C11—21no—
152C42×C11—21no—
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11#4111yescharacteristic
156C42×C11C2411yescharacteristic
157#4325—42no—
158#4325—42no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163#4318—22no—
164#4318—22no—
165#4318—42no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—21no—
168C2×C11⋊C8—21no—
169C2×C11⋊C8C2×D412yes—
170C2×C11⋊C8C2×D412yes—
171#3141—111no—
172#3103—111no—
173C2×#462D1111yescharacteristic, complemented
174Q8×M16—111no—
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×C11—42no—
189Q8×C11—42no—
190Q8×C11—82no—
191Q8×C11AGL(1,ℤ/8)12yes—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—41no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—81no—
202C2×C4×C11—82no—
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12111yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#13512yes—
207C2×C4×C11#13712yes—
208C2×C4×C11C22×D411yescharacteristic
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C2×#4111yescharacteristic
211C22⋊D11—82no—
212C2×Dic11—41no—
213D44—41no—
214D44—41no—
215D44—41no—
216D44—41no—
217D44—81no—
218C4×D11—82no—
219Dic22—41no—
220Dic22—41no—
221C8×C11—42no—
222C11⋊C8—22no—
223C11⋊C8—22no—
224C11⋊C8—42no—
225C11⋊C8—41no—
226C11⋊C8—41no—
227C22×Q16—21no—
228#532—111no—
229C2×C4⋊Q8C2×D1111yescharacteristic
230C2×C4×Q8C2×D1111yescharacteristic
231#489—222no—
232#487—112no—
233#486—112no—
234#481—221no—
235#475—111no—
236#475—111no—
237#462—21no—
238#462—21no—
239#462C2×D1112yes—
240#462C2×D1112yes—
241#460—111no—
242#460—111no—
243#448—221no—
244#446—112no—
245#446—222no—
246C8×Q8—112no—
247C4×SD16—221no—
248C4×SD16—221no—
249#431—111no—
250#423—111no—
251#423—221no—
252C2×C4⋊C8C2×D1111yescharacteristic
253#417—221no—
254#417—221no—
255C2×#103—21no—
256C4×M16—111no—
257C4×M16—221no—
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—82no—
279C4×C11#46412yes—
280C4×C11C2×#13511yescharacteristic
281C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
282C4×C11C2×#13711yescharacteristic
283C4×C11#57511yescharacteristic
284Dic11—81no—
285C2×#41—221no—
286C22×Q8—21no—
287C22×Q8C22⋊D1111yescharacteristic
288C2×Q16—22no—
289C2×Q16—22no—
290C2×Q16—44no—
291C2×SD16—221no—
292C2×SD16—221no—
293C2×M16—111no—
294C2×M16—111no—
295C2×M16—221no—
296C22×C8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8—111no—
301C4⋊Q8C22×D1112yes—
302#127—111no—
303#124—221no—
304#121—221no—
305#121—221no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8C22⋊D1111yescharacteristic
309C4×Q8C22⋊D1111yescharacteristic
310C4×Q8C22×D1111yescharacteristic
311C4×Q8C22×D1111yescharacteristic
312C4×D4—221no—
313C4×D4—221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4C22⋊D1111yescharacteristic
318C2×C42—21no—
319C2×C42C22×D1111yescharacteristic
320#106—221no—
321#106—221no—
322C4⋊C8—21no—
323C4⋊C8—112no—
324C4⋊C8—111no—
325C4⋊C8—111no—
326C4⋊C8—222no—
327C4⋊C8—222no—
328C4⋊C8—221no—
329C4⋊C8C22×D1112yes—
330#103—22no—
331#103—22no—
332#103—222no—
333#103—222no—
334#103—221no—
335#103—221no—
336#102—222no—
337#102—222no—
338#102—221no—
339#102—221no—
340C22⋊C8—221no—
341#97—112no—
342#97—222no—
343C4×C8—112no—
344C4×C8—222no—
345C4×C8—221no—
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—22no—
356C2×Q8—41no—
357C2×Q8—42no—
358C2×Q8—42no—
359C2×Q8—41no—
360C2×Q8—221no—
361C2×Q8C2×C22⋊D1111yescharacteristic
362C2×Q8C2×C22⋊D1111yescharacteristic
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—441no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—41no—
370C22×C4—441no—
371C22×C4D4×D1111yescharacteristic
372C22×C4#434111yescharacteristic
373C22×C4C2×C22⋊D1111yescharacteristic
374Q16—44no—
375Q16—44no—
376SD16—442no—
377SD16—442no—
378M16—222no—
379M16—222no—
380M16—442no—
381C2×C8—22no—
382C2×C8—42no—
383C2×C8—112no—
384C2×C8—112no—
385C2×C8—222no—
386C2×C8—221no—
387C2×C8—221no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—221no—
398C4⋊C4—221no—
399C4⋊C4C2×C22⋊D1111yescharacteristic
400C4⋊C4C2×C22⋊D1111yescharacteristic
401C22⋊C4—441no—
402C22⋊C4—441no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42D4×D1111yescharacteristic
408C42#434111yescharacteristic
409C42C2×C22⋊D1111yescharacteristic
410C42C23×D1111yescharacteristic
411C11#1917711yescharacteristic, complemented, Sylow
412C23—441no—
413C23#6699211yescharacteristic
414Q8—21no—
415Q8—21no—
416Q8—21no—
417Q8—42no—
418Q8—42no—
419Q8—42no—
420Q8—82no—
421Q8—441no—
422Q8—441no—
423Q8#6698512yes—
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—42no—
439C2×C4—81no—
440C2×C4—82no—
441C2×C4—441no—
442C2×C4—882no—
443C2×C4#6697112yes—
444C2×C4#6697212yes—
445C2×C4#6699211yescharacteristic
446C2×C4#6699211yescharacteristic
447C2×C4#6699211yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4C2×#434111yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—42no—
452C8—222no—
453C8—222no—
454C8—442no—
455C8—441no—
456C8—441no—
457C22—21no—
458C22—21no—
459C22—881no—
460C22—881no—
461C22—881no—
462C22#1062279812yes—
463C22C2×#6699211yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—22no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—82no—
472C4—881no—
473C4#1062279812yes—
474C4C2×#6697111yescharacteristic
475C4C2×#6697211yescharacteristic
476C4C2×#6698511yescharacteristic
477C4#1062335311yescharacteristic
478C2—22no—
479C2—1761no—
480C2C2×#1062279811yescharacteristic
481C2#1307823111yescharacteristic
482C2#1307835011yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#462C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#462D11
hypocenterC11#19177
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. Q8×#4318C2semidirect
4. #13068186C2semidirect
5. #13068172C2semidirect
6. #13068062C2semidirect
7. #13068048C2semidirect
8. #13067366C2semidirect
9. #13067301C2semidirect
11. C2×C11×#462C2semidirect
173. C2×#462D11semidirect
411. C11#19177semidirect

Maximal subgroups

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

subgroupindex
#130790122
#130786472
Q8×#43182
#130681862
#130681722
#130680622
#130680482
#130673662
#130673012
#130672912
C2×C11×#4622
#1917711