Finite Group Databasebeta

← #14732548

Subgroups — #14732548

Order 2816.

1192 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079737C211yesmaximal, characteristic, complemented
2#13078616C211yesmaximal, characteristic
3#13078088C211yesmaximal, characteristic, complemented
4#13067865C214yesmaximal, complemented
5#13067719C214yesmaximal, complemented
6#13067288C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic, complemented
8#13067011C211yesmaximal, characteristic, complemented
9C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
10C23×Q8×C11—21no—
11D4×Q8×C11—22no—
12D4×Q8×C11—22no—
13D4×Q8×C11—22no—
14D4×Q8×C11C2214yes—
15C2×C11×C4⋊Q8—21no—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—22no—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C2×#66995—21no—
23#10623008C2211yescharacteristic
24#10622830—21no—
25#10622701C2212yescomplemented
26#10622700—22no—
27#10622691C2212yescomplemented
28#10622644C2212yescomplemented
29#10622641—22no—
30#10622640C2212yescomplemented
31#10622628C2212yes—
32C4×#4323—22no—
33#10622620C2212yes—
34#10622580—21no—
35#10622580—22no—
36#10622579—21no—
37#10622538C2211yescharacteristic
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40#10622185C2214yescomplemented
41Q8⋊(C11⋊C8)C2214yescomplemented
42D4⋊(C11⋊C8)C2214yes—
43C22×Q8×C11—22no—
44C22×Q8×C11—24no—
45C22×Q8×C11—24no—
46C22×Q8×C11—21no—
47C22×Q8×C11—44no—
48C22×Q8×C11—44no—
49C22×Q8×C11D411yescharacteristic
50C22×D4×C11D411yescharacteristic
51C23×C4×C11—22no—
52C23×C4×C11—21no—
53C2×#4339—21no—
54C11×C4⋊Q8—24no—
55C11×C4⋊Q8—24no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8—21no—
58C11×C4⋊Q8D412yes—
59C11×C4⋊Q8C2312yes—
60C11×C22⋊Q8—24no—
61C11×C22⋊Q8—28no—
62C11×C22⋊Q8—24no—
63C11×C22⋊Q8—28no—
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66C4×Q8×C11D412yes—
67C4×Q8×C11C2312yes—
68C4×D4×C11—24no—
69C4×D4×C11—24no—
70C4×D4×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11D412yes—
73C4×D4×C11C2312yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D412yes—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×#4326—22no—
85#66995—44no—
86C2×#4325—22no—
87C2×#4323—22no—
88#66983—21no—
89#66983—21no—
90C2×#4318—21no—
91#66928—21no—
92#66927C2311yescharacteristic
93C4×D44—21no—
94C4×D44—21no—
95#66922C2311yescharacteristic
96#66896—22no—
97C22⋊(C11⋊C8)—21no—
98C22⋊(C11⋊C8)—21no—
99#66874—22no—
100#66873—22no—
101#66873—22no—
102#66873—24no—
103#66871—22no—
104#66871—24no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)C2312yes—
108C4⋊(C11⋊C8)C2312yes—
109C4×C11⋊C8—21no—
110C4×C11⋊C8C2312yes—
111#18776—111nomaximal, Sylow
112C24×C11—21no—
113C2×Q8×C11—28no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—48no—
119C2×Q8×C11—48no—
120C2×Q8×C11—416no—
121C2×Q8×C11—48no—
122C2×Q8×C11—42no—
123C2×Q8×C11—42no—
124C2×Q8×C11D814yescomplemented
125C2×Q8×C11C2×D412yes—
126C2×D4×C11—24no—
127C2×D4×C11—21no—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—21no—
130C22×C4×C11—28no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—48no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C2×C22⋊D11—41no—
143#4339—42no—
144#4339—42no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×C4×D11—41no—
149C2×Dic22—21no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D414yes—
160C11×C4⋊C4C2×D412yes—
161C11×C22⋊C4—28no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—22no—
164C42×C11—22no—
165C42×C11—22no—
166C42×C11C2×D411yescharacteristic
167C42×C11C2×D411yescharacteristic
168C42×C11C2×D411yescharacteristic
169C42×C11C2411yescharacteristic
170#4326—44no—
171#4325—44no—
172#4323—44no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177#4318—42no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—22no—
181C2×D4×Q8D1111yescharacteristic, complemented
182#3226—111no—
183#3100—111no—
184#3037—111no—
185#1649—114no—
186#1627—114no—
187#1546—111no—
188#1486—111no—
189#1479—111no—
190C23×C11—24no—
191C23×C11—22no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11#12011yescharacteristic
195C22×D11—41no—
196Q8×C11—22no—
197Q8×C11—24no—
198Q8×C11—416no—
199Q8×C11—42no—
200Q8×C11—42no—
201Q8×C11—44no—
202Q8×C11C2×D814yes—
203D4×C11—24no—
204D4×C11—22no—
205D4×C11#13714yescomplemented
206C2×C4×C11—22no—
207C2×C4×C11—24no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—41no—
213C2×C4×C11—416no—
214C2×C4×C11—42no—
215C2×C4×C11—44no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11C2×D812yes—
224C2×C4×C11AGL(1,ℤ/8)12yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C22⋊D11—82no—
229C2×Dic11—41no—
230D44—42no—
231D44—41no—
232D44—41no—
233D44—42no—
234C4×D11—82no—
235Dic22—41no—
236Dic22—41no—
237C11⋊C8—42no—
238C11⋊C8—42no—
239C11⋊C8—42no—
240C23×Q8—21no—
241C2×#137—221no—
242D4×Q8—22no—
243D4×Q8—22no—
244D4×Q8—22no—
245D4×Q8C2×D1114yes—
246#532—111no—
247C2×C4⋊Q8—21no—
248C2×C4⋊Q8C2×D1111yescharacteristic
249C2×C22⋊Q8—21no—
250C2×C22⋊Q8—22no—
251C2×C4×Q8C2×D1111yescharacteristic
252C2×C4×D4—21no—
253C2×C4×D4C2×D1111yescharacteristic
254#500—112no—
255#486—112no—
256#480—221no—
257#480—222no—
258#474—112no—
259#474—222no—
260#464—222no—
261#462—112no—
262#460—112no—
263#459—112no—
264#447—221no—
265C4×D8—222no—
266#431—111no—
267#431—111no—
268#423—111no—
269#417—221no—
270#332—114no—
271Q8⋊C8—114no—
272D4⋊C8—114no—
273C22×C11—21no—
274C22×C11—21no—
275C22×C11—24no—
276C22×C11—48no—
277C22×C11—42no—
278C22×C11—42no—
279C22×C11#44712yes—
280C22×C11C2×#12011yescharacteristic
281C2×D11—81no—
282C2×D11—81no—
283C2×D11—81no—
284C4×C11—24no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—44no—
289C4×C11—42no—
290C4×C11—42no—
291C4×C11#44712yes—
292C4×C11C22×D811yescharacteristic
293C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
294C4×C11C2×#13712yes—
295Dic11—81no—
296C2×#41—221no—
297C22×Q8—22no—
298C22×Q8—24no—
299C22×Q8—24no—
300C22×Q8—21no—
301C22×Q8—44no—
302C22×Q8—44no—
303C22×Q8C22⋊D1111yescharacteristic
304C22×D4C22⋊D1111yescharacteristic
305C23×C4—22no—
306C23×C4—21no—
307#137—444no—
308C2×Q16—222no—
309C2×SD16—222no—
310C2×D8—222no—
311C2×M16—221no—
312C4⋊Q8—24no—
313C4⋊Q8—24no—
314C4⋊Q8—21no—
315C4⋊Q8—21no—
316C4⋊Q8—111no—
317C4⋊Q8C22⋊D1112yes—
318C4⋊Q8C22×D1112yes—
319#127—111no—
320#124—221no—
321C22⋊Q8—24no—
322C22⋊Q8—28no—
323C22⋊Q8—24no—
324C22⋊Q8—28no—
325#121—221no—
326#121—221no—
327C4×Q8—21no—
328C4×Q8—21no—
329C4×Q8C22⋊D1112yes—
330C4×Q8C22×D1112yes—
331C4×D4—24no—
332C4×D4—24no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—221no—
336C4×D4—221no—
337C4×D4C22⋊D1112yes—
338C4×D4C22×D1112yes—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4C22⋊D1111yescharacteristic
343C2×C4⋊C4C22⋊D1111yescharacteristic
344C2×C4⋊C4C22⋊D1112yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C42—21no—
348C2×C42C22×D1111yescharacteristic
349#107—222no—
350#107—224no—
351C4⋊C8—112no—
352C4⋊C8—112no—
353C4⋊C8—221no—
354C4⋊C8—221no—
355#103—222no—
356#102—222no—
357#102—222no—
358#102—222no—
359#102—224no—
360C22⋊C8—221no—
361C22⋊C8—221no—
362C4×C8—112no—
363C4×C8—221no—
364C2×C11—22no—
365C2×C11—44no—
366C2×C11C2×#44711yescharacteristic
367C2×C11#300411yescharacteristic
368C2×C11#302011yescharacteristic
369D11—161no—
370C24—21no—
371#41—442no—
372#41—442no—
373C2×Q8—28no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—22no—
377C2×Q8—22no—
378C2×Q8—48no—
379C2×Q8—48no—
380C2×Q8—416no—
381C2×Q8—48no—
382C2×Q8—42no—
383C2×Q8—42no—
384C2×Q8—221no—
385C2×Q8#432314yescomplemented
386C2×Q8C2×C22⋊D1112yes—
387C2×D4—24no—
388C2×D4—21no—
389C2×D4—221no—
390C2×D4—221no—
391C2×D4—221no—
392C2×D4—441no—
393C2×D4C2×C22⋊D1112yes—
394C22×C4—21no—
395C22×C4—28no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—48no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—441no—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407C22×C4C2×C22⋊D1111yescharacteristic
408Q16—444no—
409SD16—444no—
410D8—444no—
411M16—442no—
412C2×C8—222no—
413C2×C8—222no—
414C2×C8—222no—
415C4⋊C4—28no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C4⋊C4C2×C22⋊D1112yes—
426C4⋊C4C2×C22⋊D1112yes—
427C4⋊C4C2×C22⋊D1114yes—
428C22⋊C4—28no—
429C22⋊C4—22no—
430C22⋊C4—22no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C42—22no—
434C42—22no—
435C42C2×C22⋊D1111yescharacteristic
436C42C2×C22⋊D1111yescharacteristic
437C42C2×C22⋊D1111yescharacteristic
438C42C23×D1111yescharacteristic
439C11#1877611yescharacteristic, complemented, Sylow
440C23—24no—
441C23—22no—
442C23—42no—
443C23—42no—
444C23—441no—
445C23#6700611yescharacteristic
446Q8—22no—
447Q8—24no—
448Q8—416no—
449Q8—42no—
450Q8—42no—
451Q8—44no—
452Q8—441no—
453Q8—441no—
454Q8C2×#432314yes—
455D4—24no—
456D4—22no—
457D4—442no—
458D4—441no—
459D4—441no—
460D4—442no—
461D4—882no—
462D4#6699514yescomplemented
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—41no—
470C2×C4—416no—
471C2×C4—42no—
472C2×C4—44no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4—441no—
478C2×C4—882no—
479C2×C4C2×#432312yes—
480C2×C4#6698512yes—
481C2×C4#6700611yescharacteristic
482C2×C4#6700611yescharacteristic
483C2×C4#6700611yescharacteristic
484C2×C4C22×C22⋊D1111yescharacteristic
485C2×C4C22×C22⋊D1111yescharacteristic
486C2×C4C22×C22⋊D1111yescharacteristic
487C8—442no—
488C8—442no—
489C8—442no—
490C22—21no—
491C22—21no—
492C22—24no—
493C22—48no—
494C22—42no—
495C22—42no—
496C22—881no—
497C22—881no—
498C22—881no—
499C22#1062283012yes—
500C22C2×#6700611yescharacteristic
501C4—24no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—44no—
506C4—42no—
507C4—42no—
508C4—881no—
509C4#1062283012yes—
510C4C22×#432311yescharacteristic
511C4C2×#6698511yescharacteristic
512C4C2×#6699512yes—
513C2—22no—
514C2—44no—
515C2—1761no—
516C2C2×#1062283011yescharacteristic
517C2#1307785011yescharacteristic
518C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D4×Q8×C11C2
socleC22×C11C2×#120
prime radical#13078616C2
hypercenterC2×D4×Q8D11
hypocenterC11#18776
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #13079737C2semidirect
3. #13078088C2semidirect
4. #13067865C2semidirect
5. #13067719C2semidirect
6. #13067288C2semidirect
7. #13067041C2semidirect
8. #13067011C2semidirect
9. C2×D4×Q8×C11C2semidirect
25. #10622701C22semidirect
27. #10622691C22semidirect
28. #10622644C22semidirect
30. #10622640C22semidirect
40. #10622185C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
124. C2×Q8×C11D8semidirect
181. C2×D4×Q8D11semidirect
205. D4×C11#137semidirect
385. C2×Q8#4323semidirect
439. C11#18776semidirect
462. D4#66995semidirect

Maximal subgroups

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

subgroupindex
#130797372
#130786162
#130780882
#130678652
#130677192
#130672882
#130670412
#130670112
C2×D4×Q8×C112
#1877611