Finite Group Databasebeta

← #14788995

Subgroups — #14788995

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082387C211yesmaximal, characteristic
2#13078088C212yesmaximal, complemented
3C2×#10622708C212yesmaximal, complemented
4#13069840C212yesmaximal, complemented
5#13069662C212yesmaximal, complemented
6#13069444C212yesmaximal, complemented
7#13068612C211yesmaximal, characteristic, complemented
8#13068574C212yesmaximal, complemented
9C4×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
10C2×#67040C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×C4×Q8×C11C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66995C2214yes—
15#10623108—22no—
16#10623107—24no—
17Q8×D44—22no—
18#10623041—22no—
19#10623041C2212yes—
20#10623008—22no—
21#10623008C2212yes—
22C11×#391C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#389—22no—
25C11×#384C2211yescharacteristic
26C4×C11×C4⋊C4—22no—
27C43×C11C2211yescharacteristic
28C2×#66900C2212yes—
29#10622708—28no—
30#10622644—22no—
31#10622641—24no—
32#10622640—22no—
33#10622579C2214yes—
34C2×#66869C2214yes—
35C2×#66869C2214yes—
36#10622537C2212yes—
37#10622168C2212yes—
38C22×Q8×C11C2311yescharacteristic
39C22×Q8×C11C2311yescharacteristic
40#67040—24no—
41#67040—24no—
42#67040—44no—
43C2×#4343—24no—
44C2×Q8×D11—24no—
45C2×#4339—24no—
46C2×#4339C2314yes—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8D414yescomplemented
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C4×Q8×C11—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11—21no—
60C2×C42×C11—21no—
61C2×C42×C11—21no—
62C2×C42×C11D412yes—
63C2×C42×C11C2311yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×#4326—24no—
67#66995—28no—
68#66995—44no—
69C2×#4325—24no—
70#66983—22no—
71#66983—24no—
72#66983—22no—
73C2×#4318C2314yes—
74#66950—28no—
75#66950—24no—
76#66948—28no—
77#66948—24no—
78#66928—24no—
79#66928D414yes—
80#66927—22no—
81#66927D412yes—
82C4×D44—24no—
83C4×D44—24no—
84C4×D44—22no—
85C4×D44—22no—
86#66922—22no—
87#66922D412yes—
88C11×#95—22no—
89C11×#95—22no—
90#66900—24no—
91#66874—24no—
92#66873—24no—
93#66869—28no—
94#66869—44no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)—22no—
97#24225—111nomaximal, Sylow
98C2×Q8×C11—22no—
99C2×Q8×C11—21no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11C2×D412yes—
104C2×Q8×C11C2×D412yes—
105C2×Q8×C11#4112yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—24no—
116#4343—48no—
117#4343—48no—
118Q8×D11—48no—
119Q8×D11—48no—
120#4339—24no—
121#4339—24no—
122#4339—24no—
123#4339—24no—
124#4339—48no—
125#4339—48no—
126C2×D44—24no—
127C2×D44—24no—
128C2×D44—22no—
129C2×D44—22no—
130C2×D44C2×D414yes—
131C2×C4×D11—28no—
132C2×C4×D11—24no—
133C2×Dic22—24no—
134C2×Dic22C2×D414yes—
135C11×C4⋊C4—24no—
136C11×C4⋊C4—28no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—44no—
140C11×C4⋊C4—42no—
141C42×C11—24no—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11—21no—
145C42×C11—22no—
146C42×C11—42no—
147C42×C11—41no—
148C42×C11—41no—
149C42×C11C2×D412yes—
150C42×C11C2×D412yes—
151C42×C11C2×D412yes—
152#4326—48no—
153#4325—48no—
154(C2×D11)⋊C4—28no—
155(C2×D11)⋊C4—24no—
156(C2×D11)⋊C4—24no—
157C4⋊Dic11—24no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160#4318—24no—
161#4318—24no—
162C2×C11⋊C8—24no—
163#3497—111no—
164#3037—112no—
165C2×#456—112no—
166C4×C4⋊Q8D1111yescharacteristic, complemented
167#2039—112no—
168#2007—112no—
169#1962—112no—
170#1801—111no—
171#1793—112no—
172C23×C11C22×D411yescharacteristic
173C22×D11—24no—
174Q8×C11—24no—
175Q8×C11—24no—
176Q8×C11—24no—
177Q8×C11—42no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11#12012yes—
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12114yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D412yes—
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11H(5,𝔽2)12yes—
203C22⋊D11—44no—
204C22⋊D11—44no—
205C2×Dic11—24no—
206D44—24no—
207D44—24no—
208D44—48no—
209D44—44no—
210D44—82no—
211D44—84no—
212C4×D11—416no—
213C4×D11—44no—
214C4×D11—44no—
215Dic22—24no—
216Dic22—24no—
217Dic22—48no—
218C11⋊C8—44no—
219C2×2−1+4—112no—
220C2×#137—114no—
221#550—222no—
222D4×Q8—222no—
223#548—224no—
224#537—112no—
225#537—222no—
226#532—112no—
227#532—222no—
228C2×C4⋊Q8C2×D1111yescharacteristic
229C2×C4×Q8C2×D1111yescharacteristic
230C2×C4×Q8C2×D1111yescharacteristic
231#464—224no—
232#462—222no—
233#460—222no—
234#456—228no—
235#423—112no—
236C2×#104—114no—
237C2×#104—114no—
238#417—114no—
239C2×#101—112no—
240#391C2×D1111yescharacteristic
241#391C2×D1111yescharacteristic
242#389—22no—
243#384C2×D1111yescharacteristic
244C4×C4⋊C4—22no—
245C43C2×D1111yescharacteristic
246#343—112no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11C2×#12011yescharacteristic
250C22×C11C2×#12111yescharacteristic
251C22×C11#53511yescharacteristic
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—44no—
255C4×C11—24no—
256C4×C11—24no—
257C4×C11—21no—
258C4×C11—22no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—81no—
263C4×C11#45612yescomplemented
264C4×C11D4212yes—
265C4×C11#54612yes—
266Dic11—44no—
2672−1+4—224no—
2682−1+4—224no—
2692−1+4—444no—
270C2×#41—114no—
271C2×#41—224no—
272C2×#41—224no—
273C22×Q8—224no—
274C22×Q8C22×D1111yescharacteristic
275C22×Q8C22×D1111yescharacteristic
276#137—228no—
277#137—444no—
278C2×Q16—224no—
279C2×SD16—224no—
280C2×M16—114no—
281C4⋊Q8—22no—
282C4⋊Q8—112no—
283C4⋊Q8—222no—
284C4⋊Q8D4414yescomplemented
285#127—112no—
286#127—222no—
287#124—114no—
288#124—224no—
289C22⋊Q8—224no—
290C22⋊Q8—228no—
291#121—224no—
292#121—228no—
293#121—222no—
294#121—222no—
295#121—224no—
296C4×Q8—22no—
297C4×Q8—22no—
298C4×Q8—22no—
299C4×Q8—22no—
300C4×D4—224no—
301C4×D4—224no—
302C4×D4—222no—
303C4×D4—222no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4C22⋊D1112yes—
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42C22⋊D1112yes—
314C2×C42C22×D1111yescharacteristic
315C2×C42C22×D1111yescharacteristic
316C2×C42C22×D1111yescharacteristic
317C4⋊C8—222no—
318C4⋊C8—222no—
319#104—228no—
320#104—444no—
321#103—224no—
322#102—224no—
323#101—224no—
324#95—22no—
325#95—22no—
326C2×C11—21no—
327C2×C11—21no—
328C2×C11#240811yescharacteristic
329C2×C11C2×#45611yescharacteristic
330C2×C11#301811yescharacteristic
331D11—84no—
332#41—224no—
333#41—224no—
334#41—224no—
335#41—224no—
336#41—448no—
337#41—448no—
338#41—448no—
339#41—448no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—114no—
346C2×Q8—224no—
347C2×Q8—448no—
348C2×Q8—448no—
349C2×Q8C2×D4412yes—
350C2×Q8C2×D4412yes—
351C2×Q8#433912yes—
352C2×D4—114no—
353C2×D4—224no—
354C2×D4—224no—
355C2×D4—224no—
356C2×D4—222no—
357C2×D4—222no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—228no—
363C22×C4—224no—
364C22×C4C2×C22⋊D1112yes—
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1112yes—
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C23×D1111yescharacteristic
369Q16—448no—
370SD16—448no—
371M16—224no—
372M16—224no—
373C2×C8—224no—
374C4⋊C4—28no—
375C4⋊C4—24no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—44no—
379C4⋊C4—42no—
380C4⋊C4—224no—
381C4⋊C4—222no—
382C4⋊C4—222no—
383C22⋊C4—228no—
384C22⋊C4—224no—
385C22⋊C4—224no—
386C42—24no—
387C42—22no—
388C42—22no—
389C42—21no—
390C42—22no—
391C42—42no—
392C42—41no—
393C42—41no—
394C42C2×D4412yes—
395C42D4×D1112yes—
396C42D4×D1112yes—
397C11#2422511yescharacteristic, complemented, Sylow
398C23—224no—
399C23C22×C22⋊D1111yescharacteristic
400Q8—24no—
401Q8—24no—
402Q8—24no—
403Q8—42no—
404Q8—224no—
405Q8—224no—
406Q8—448no—
407D4—224no—
408D4—224no—
409D4—448no—
410D4—444no—
411D4—444no—
412D4—444no—
413D4—882no—
414D4—884no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—224no—
433C2×C4—4416no—
434C2×C4—444no—
435C2×C4—444no—
436C2×C4#6698314yes—
437C2×C4#6699011yescharacteristic
438C2×C4#6699012yes—
439C2×C4#6699011yescharacteristic
440C2×C4C22×D4411yescharacteristic
441C2×C4C2×#433911yescharacteristic
442C2×C4C2×D4×D1112yes—
443C2×C4#6704212yes—
444C8—444no—
445C22—21no—
446C22—21no—
447C22—444no—
448C22—444no—
449C22—444no—
450C22C2×#6698311yescharacteristic
451C22C2×#6699011yescharacteristic
452C22#1062336111yescharacteristic
453C4—24no—
454C4—24no—
455C4—21no—
456C4—22no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—81no—
461C4—444no—
462C4#1062270812yescomplemented
463C4D4×D4412yes—
464C4#1062308112yes—
465C2—21no—
466C2—21no—
467C2—884no—
468C2#1307197211yescharacteristic
469C2C2×#1062270811yescharacteristic
470C2#1307796411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×C4⋊Q8C2
socleC22×C11C2×#120
prime radical#13082387C2
hypercenterC4×C4⋊Q8D11
hypocenterC11#24225
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #13078088C2semidirect
3. C2×#10622708C2semidirect
4. #13069840C2semidirect
5. #13069662C2semidirect
6. #13069444C2semidirect
7. #13068612C2semidirect
8. #13068574C2semidirect
9. C4×C11×C4⋊Q8C2semidirect
48. C11×C4⋊Q8D4semidirect
166. C4×C4⋊Q8D11semidirect
263. C4×C11#456semidirect
284. C4⋊Q8D44semidirect
397. C11#24225semidirect
462. C4#10622708semidirect

Maximal subgroups

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

subgroupindex
#130823872
#130780882
C2×#106227082
#130698402
#130696622
#130694442
#130686122
#130685742
C4×C11×C4⋊Q82
#2422511