Finite Group Databasebeta

← #14732380

Subgroups — #14732380

Order 2816.

932 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic
2#13078647C211yesmaximal, characteristic
3#13078088C211yesmaximal, characteristic
4#13067858C214yesmaximal, complemented
5#13067712C214yesmaximal, complemented
6#13067288C211yesmaximal, characteristic, complemented
7#13067045C211yesmaximal, characteristic, complemented
8#13067011C211yesmaximal, characteristic, complemented
9C2×C11×#557C211yesmaximal, characteristic, complemented
10C11×#557—22no—
11C11×#557—22no—
12C11×#557—22no—
13C11×#557C2214yes—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—22no—
17C2×C11×#125—21no—
18C2×C4×Q8×C11—21no—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×#66995—21no—
23#10623008C2211yescharacteristic
24#10622840—21no—
25#10622701C2212yes—
26#10622700—22no—
27#10622691C2212yes—
28#10622644C2212yes—
29#10622641—22no—
30#10622640C2212yes—
31#10622640C2212yes—
32C4×#4325—22no—
33#10622633C2212yes—
34#10622581—21no—
35#10622580—22no—
36#10622579—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622185C2214yes—
41Q8⋊(C11⋊C8)C2214yes—
42Q8⋊(C11⋊C8)C2214yes—
43C22×Q8×C11—21no—
44C22×Q8×C11D411yescharacteristic
45C22×Q8×C11D411yescharacteristic
46C2×#4339—21no—
47C11×C4⋊Q8—24no—
48C11×C4⋊Q8—24no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8D412yes—
52C11×C4⋊Q8C2312yes—
53C11×#125—28no—
54C11×#125—24no—
55C11×#125—28no—
56C11×#125—24no—
57C4×Q8×C11—24no—
58C4×Q8×C11—24no—
59C4×Q8×C11—24no—
60C4×Q8×C11—24no—
61C4×Q8×C11—21no—
62C4×Q8×C11—21no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11D412yes—
66C4×Q8×C11D412yes—
67C4×Q8×C11C2312yes—
68C4×Q8×C11C2312yes—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D412yes—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C42×C11—22no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83#66995—44no—
84C2×#4325—22no—
85C2×#4325—22no—
86#66983—21no—
87#66983—21no—
88C2×#4318—21no—
89#66928—21no—
90#66927C2311yescharacteristic
91C4×D44—21no—
92C4×D44—21no—
93#66922C2311yescharacteristic
94#66899—22no—
95C22⋊(C11⋊C8)—21no—
96C22⋊(C11⋊C8)—21no—
97#66874—22no—
98#66873—22no—
99#66873—24no—
100#66873—22no—
101#66872—22no—
102#66871—24no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)C2312yes—
106C4⋊(C11⋊C8)C2312yes—
107C4×C11⋊C8—21no—
108C4×C11⋊C8C2312yes—
109#18760—111nomaximal, Sylow
110C2×Q8×C11—24no—
111C2×Q8×C11—21no—
112C2×Q8×C11—21no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11C2×D412yes—
120C2×Q8×C11C2×D412yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C2×C22⋊D11—41no—
130#4339—42no—
131#4339—42no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×C4×D11—41no—
136C2×Dic22—21no—
137C11×C4⋊C4—28no—
138C11×C4⋊C4—28no—
139C11×C4⋊C4—28no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4C2×D414yes—
150C11×C4⋊C4C2×D412yes—
151C11×C4⋊C4C2×D412yes—
152C42×C11—28no—
153C42×C11—22no—
154C42×C11—22no—
155C42×C11—22no—
156C42×C11—22no—
157C42×C11C2×D411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C42×C11C2411yescharacteristic
161#4326—44no—
162#4325—44no—
163#4325—44no—
164(C2×D11)⋊C4—41no—
165(C2×D11)⋊C4—41no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168#4318—42no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×#557D1111yescharacteristic, complemented
173#3226—111no—
174#3103—111no—
175#3037—111no—
176#1648—114no—
177#1626—114no—
178#1546—111no—
179#1487—111no—
180#1479—111no—
181C23×C11#12011yescharacteristic
182C22×D11—41no—
183Q8×C11—24no—
184Q8×C11—22no—
185Q8×C11—22no—
186Q8×C11—22no—
187Q8×C11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—44no—
191Q8×C11#13714yescomplemented
192C2×C4×C11—24no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—44no—
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12011yescharacteristic
206C2×C4×C11#12011yescharacteristic
207C2×C4×C11#13512yes—
208C2×C4×C11AGL(1,ℤ/8)12yes—
209C2×C4×C11C22×D411yescharacteristic
210C2×C4×C11C22×D411yescharacteristic
211C2×C4×C11C22×D411yescharacteristic
212C22⋊D11—82no—
213C2×Dic11—41no—
214D44—42no—
215D44—41no—
216D44—41no—
217D44—42no—
218C4×D11—82no—
219Dic22—41no—
220Dic22—41no—
221C11⋊C8—42no—
222C11⋊C8—42no—
223C11⋊C8—42no—
224C2×#137—221no—
225#557—22no—
226#557—22no—
227#557—22no—
228#557C2×D1114yes—
229#532—111no—
230C2×C4⋊Q8—21no—
231C2×C4⋊Q8C2×D1111yescharacteristic
232C2×#125—22no—
233C2×#125—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8—21no—
236C2×C4×Q8C2×D1111yescharacteristic
237C2×C4×Q8C2×D1111yescharacteristic
238#500—112no—
239#486—112no—
240#481—221no—
241#480—222no—
242#475—112no—
243#474—222no—
244#464—222no—
245#462—112no—
246#460—112no—
247#460—112no—
248#448—221no—
249C4×SD16—222no—
250#431—111no—
251#431—111no—
252#423—111no—
253#417—221no—
254#332—114no—
255Q8⋊C8—114no—
256Q8⋊C8—114no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11#44912yes—
260C22×C11C2×#12011yescharacteristic
261C2×D11—81no—
262C2×D11—81no—
263C2×D11—81no—
264C4×C11—24no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—42no—
269C4×C11—44no—
270C4×C11—42no—
271C4×C11—42no—
272C4×C11#44912yes—
273C4×C11C2×#13511yescharacteristic
274C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
275C4×C11C2×#13712yes—
276Dic11—81no—
277C2×#41—221no—
278C22×Q8—21no—
279C22×Q8C22⋊D1111yescharacteristic
280C22×Q8C22⋊D1111yescharacteristic
281#137—444no—
282C2×Q16—222no—
283C2×SD16—222no—
284C2×SD16—222no—
285C2×M16—221no—
286C4⋊Q8—24no—
287C4⋊Q8—24no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—111no—
291C4⋊Q8C22⋊D1112yes—
292C4⋊Q8C22×D1112yes—
293#127—111no—
294#125—28no—
295#125—24no—
296#125—28no—
297#125—24no—
298#124—221no—
299#121—221no—
300#121—221no—
301C4×Q8—24no—
302C4×Q8—24no—
303C4×Q8—24no—
304C4×Q8—24no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8C22⋊D1112yes—
310C4×Q8C22⋊D1112yes—
311C4×Q8C22×D1112yes—
312C4×Q8C22×D1112yes—
313C4×D4—221no—
314C4×D4—221no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4C22⋊D1111yescharacteristic
322C2×C4⋊C4C22⋊D1111yescharacteristic
323C2×C4⋊C4C22⋊D1112yes—
324C2×C42—22no—
325C2×C42—21no—
326C2×C42—21no—
327C2×C42C22×D1111yescharacteristic
328#107—224no—
329#106—222no—
330C4⋊C8—112no—
331C4⋊C8—112no—
332C4⋊C8—221no—
333C4⋊C8—221no—
334#103—222no—
335#103—222no—
336#102—222no—
337#102—222no—
338#102—224no—
339C22⋊C8—221no—
340C22⋊C8—221no—
341C4×C8—112no—
342C4×C8—221no—
343C2×C11—22no—
344C2×C11C2×#44911yescharacteristic
345C2×C11#300411yescharacteristic
346C2×C11#302011yescharacteristic
347D11—161no—
348#41—442no—
349#41—442no—
350C2×Q8—24no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—42no—
358C2×Q8—42no—
359C2×Q8—221no—
360C2×Q8C2×C22⋊D1112yes—
361C2×Q8C2×C22⋊D1112yes—
362C2×D4—221no—
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—441no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—441no—
372C22×C4C2×C22⋊D1111yescharacteristic
373C22×C4C2×C22⋊D1111yescharacteristic
374C22×C4C2×C22⋊D1111yescharacteristic
375Q16—444no—
376SD16—444no—
377SD16—444no—
378M16—442no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—222no—
382C4⋊C4—28no—
383C4⋊C4—28no—
384C4⋊C4—28no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—221no—
395C4⋊C4—221no—
396C4⋊C4C2×C22⋊D1112yes—
397C4⋊C4C2×C22⋊D1112yes—
398C4⋊C4C2×C22⋊D1114yes—
399C22⋊C4—441no—
400C22⋊C4—441no—
401C42—28no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42—22no—
406C42C2×C22⋊D1111yescharacteristic
407C42C2×C22⋊D1111yescharacteristic
408C42C2×C22⋊D1111yescharacteristic
409C42C23×D1111yescharacteristic
410C11#1876011yescharacteristic, complemented, Sylow
411C23—441no—
412C23#6700611yescharacteristic
413Q8—24no—
414Q8—22no—
415Q8—22no—
416Q8—22no—
417Q8—42no—
418Q8—42no—
419Q8—42no—
420Q8—44no—
421Q8—441no—
422Q8—441no—
423Q8#6699514yescomplemented
424D4—442no—
425D4—442no—
426D4—441no—
427D4—441no—
428D4—882no—
429C2×C4—24no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—441no—
442C2×C4—882no—
443C2×C4#6700212yes—
444C2×C4#6700312yes—
445C2×C4#6700611yescharacteristic
446C2×C4#6700611yescharacteristic
447C2×C4#6700611yescharacteristic
448C2×C4C22×C22⋊D1111yescharacteristic
449C2×C4C22×C22⋊D1111yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—442no—
452C8—442no—
453C8—442no—
454C22—21no—
455C22—21no—
456C22—881no—
457C22—881no—
458C22—881no—
459C22#1062285112yes—
460C22C2×#6700611yescharacteristic
461C4—24no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—44no—
467C4—42no—
468C4—42no—
469C4—881no—
470C4#1062285112yes—
471C4C2×#6699512yes—
472C4C2×#6700211yescharacteristic
473C4C2×#6700311yescharacteristic
474C2—22no—
475C2—1761no—
476C2C2×#1062285111yescharacteristic
477C2#1307785011yescharacteristic
478C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#557C2
socleC22×C11C2×#120
prime radical#10623008C22
hypercenterC2×#557D11
hypocenterC11#18760
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13067858C2semidirect
5. #13067712C2semidirect
6. #13067288C2semidirect
7. #13067045C2semidirect
8. #13067011C2semidirect
9. C2×C11×#557C2semidirect
172. C2×#557D11semidirect
191. Q8×C11#137semidirect
410. C11#18760semidirect
423. Q8#66995semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130786472
#130780882
#130678582
#130677122
#130672882
#130670452
#130670112
C2×C11×#5572
#1876011