Finite Group Databasebeta

← #14732557

Subgroups — #14732557

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079760C211yesmaximal, characteristic, complemented
2#13078624C211yesmaximal, characteristic
3#13078421C211yesmaximal, characteristic, complemented
4#13067879C214yesmaximal, complemented
5#13067781C214yesmaximal, complemented
6#13067288C211yesmaximal, characteristic, complemented
7#13067041C211yesmaximal, characteristic
8#13067011C211yesmaximal, characteristic, complemented
9C2×D4×Q8×C11C211yesmaximal, characteristic
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
22#10623001C2211yescharacteristic
23#10622838—21no—
24#10622831—21no—
25#10622707—22no—
26#10622706C2212yescomplemented
27#10622692C2212yescomplemented
28#10622635—22no—
29#10622634C2212yescomplemented
30#10622633C2212yescomplemented
31#10622632C2212yes—
32C4×#4324—22no—
33#10622621C2212yes—
34#10622584—21no—
35#10622584—22no—
36#10622577—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—
53C11×C4⋊Q8—24no—
54C11×C4⋊Q8—24no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8D412yes—
58C11×C4⋊Q8C2312yes—
59C11×C22⋊Q8—24no—
60C11×C22⋊Q8—28no—
61C11×C22⋊Q8—24no—
62C11×C22⋊Q8—28no—
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11D412yes—
66C4×Q8×C11C2312yes—
67C4×D4×C11—24no—
68C4×D4×C11—24no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11D412yes—
72C4×D4×C11C2312yes—
73C2×C11×C4⋊C4—22no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D412yes—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×#4324—22no—
84#66979—21no—
85#66977—21no—
86#66977—21no—
87C2×#4318—21no—
88#66923—21no—
89#66922C2311yescharacteristic
90#66922C2311yescharacteristic
91C4×Dic22—21no—
92C4×Dic22—21no—
93#66899—22no—
94#66899—22no—
95#66896—22no—
96C22⋊(C11⋊C8)—21no—
97C22⋊(C11⋊C8)—21no—
98#66874—22no—
99#66874—24no—
100#66872—22no—
101#66872—22no—
102#66872—24no—
103#66871—22no—
104C4⋊(C11⋊C8)—21no—
105C4⋊(C11⋊C8)—21no—
106C4⋊(C11⋊C8)C2312yes—
107C4⋊(C11⋊C8)C2312yes—
108C4×C11⋊C8—21no—
109C4×C11⋊C8C2312yes—
110#18777—111nomaximal, Sylow
111C24×C11—21no—
112C2×Q8×C11—28no—
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—48no—
118C2×Q8×C11—48no—
119C2×Q8×C11—416no—
120C2×Q8×C11—48no—
121C2×Q8×C11—42no—
122C2×Q8×C11—42no—
123C2×Q8×C11SD1614yescomplemented
124C2×Q8×C11C2×D412yes—
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11C2×D412yes—
128C22×C4×C11—21no—
129C22×C4×C11—28no—
130C22×C4×C11—21no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—48no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C2×Dic22—21no—
142C2×Dic22—21no—
143C11×C4⋊C4—28no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—22no—
151C11×C4⋊C4C2×D412yes—
152C11×C4⋊C4C2×D412yes—
153C11×C4⋊C4C2×D414yes—
154C11×C22⋊C4—28no—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—22no—
157C42×C11—22no—
158C42×C11—22no—
159C42×C11C2×D411yescharacteristic
160C42×C11C2×D411yescharacteristic
161C42×C11C2×D411yescharacteristic
162C42×C11C2411yescharacteristic
163C22⋊Dic11—41no—
164#4324—44no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169Dic11⋊C4—41no—
170Dic11⋊C4—41no—
171C4×Dic11—41no—
172#4318—42no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C2×C11⋊C8—22no—
176C2×D4×Q8D1111yescharacteristic
177#3229—111no—
178#3101—111no—
179#3078—111no—
180#1651—114no—
181#1637—114no—
182#1546—111no—
183#1486—111no—
184#1479—111no—
185C23×C11—24no—
186C23×C11—22no—
187C23×C11—42no—
188C23×C11—42no—
189C23×C11#12011yescharacteristic
190Q8×C11—22no—
191Q8×C11—24no—
192Q8×C11—416no—
193Q8×C11—42no—
194Q8×C11—42no—
195Q8×C11—44no—
196Q8×C11C2×SD1614yes—
197D4×C11—24no—
198D4×C11—22no—
199D4×C11#13714yes—
200C2×C4×C11—22no—
201C2×C4×C11—24no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—41no—
207C2×C4×C11—416no—
208C2×C4×C11—42no—
209C2×C4×C11—44no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—44no—
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11#12011yescharacteristic
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11C2×SD1612yes—
218C2×C4×C11AGL(1,ℤ/8)12yes—
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×Dic11—41no—
223C2×Dic11—41no—
224Dic22—42no—
225Dic22—42no—
226C11⋊C8—42no—
227C11⋊C8—42no—
228C11⋊C8—42no—
229C23×Q8—21no—
230D4×Q8—22no—
231D4×Q8—22no—
232D4×Q8—22no—
233D4×Q8C2×D1114yes—
234#533—111no—
235C2×C4⋊Q8—21no—
236C2×C4⋊Q8C2×D1111yescharacteristic
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—22no—
239C2×C4×Q8C2×D1111yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C2×D1111yescharacteristic
242#498—112no—
243#487—112no—
244#483—221no—
245#483—222no—
246#479—222no—
247#477—112no—
248#476—112no—
249#475—112no—
250#475—222no—
251#461—112no—
252#450—221no—
253C4×SD16—222no—
254#431—111no—
255#431—111no—
256#428—221no—
257#423—111no—
258#419—221no—
259#332—114no—
260Q8⋊C8—114no—
261D4⋊C8—114no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—24no—
265C22×C11—48no—
266C22×C11—42no—
267C22×C11—42no—
268C22×C11#45012yes—
269C22×C11C2×#12011yescharacteristic
270C4×C11—24no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—44no—
275C4×C11—42no—
276C4×C11—42no—
277C4×C11#45012yes—
278C4×C11C22×SD1611yescharacteristic
279C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
280C4×C11C2×#13712yes—
281Dic11—81no—
282Dic11—81no—
283C22×Q8—22no—
284C22×Q8—24no—
285C22×Q8—24no—
286C22×Q8—21no—
287C22×Q8—44no—
288C22×Q8—44no—
289C22×Q8C22⋊D1111yescharacteristic
290C22×D4C22⋊D1111yescharacteristic
291C23×C4—22no—
292C23×C4—21no—
293C2×SD16—222no—
294C2×M16—221no—
295C4⋊Q8—24no—
296C4⋊Q8—24no—
297C4⋊Q8—21no—
298C4⋊Q8—21no—
299C4⋊Q8—111no—
300C4⋊Q8—111no—
301C4⋊Q8C22⋊D1112yes—
302C4⋊Q8C22×D1112yes—
303#125—221no—
304C22⋊Q8—24no—
305C22⋊Q8—28no—
306C22⋊Q8—24no—
307C22⋊Q8—28no—
308C22⋊Q8—221no—
309C22⋊Q8—221no—
310C4×Q8—21no—
311C4×Q8—21no—
312C4×Q8—221no—
313C4×Q8—221no—
314C4×Q8C22⋊D1112yes—
315C4×Q8C22×D1112yes—
316C4×D4—24no—
317C4×D4—24no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4C22⋊D1112yes—
321C4×D4C22×D1112yes—
322#117—221no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4C22⋊D1111yescharacteristic
327C2×C4⋊C4C22⋊D1111yescharacteristic
328C2×C4⋊C4C22⋊D1112yes—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—21no—
331C2×C42—21no—
332C2×C42C22×D1111yescharacteristic
333#107—222no—
334#106—222no—
335#106—222no—
336#106—224no—
337C4⋊C8—112no—
338C4⋊C8—112no—
339C4⋊C8—221no—
340C4⋊C8—221no—
341#103—222no—
342#103—222no—
343#103—222no—
344#103—224no—
345#102—222no—
346C22⋊C8—221no—
347C22⋊C8—221no—
348C4×C8—112no—
349C4×C8—221no—
350C2×C11—22no—
351C2×C11—44no—
352C2×C11C2×#45011yescharacteristic
353C2×C11#300411yescharacteristic
354C2×C11#302011yescharacteristic
355C24—21no—
356C2×Q8—28no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—48no—
362C2×Q8—48no—
363C2×Q8—416no—
364C2×Q8—48no—
365C2×Q8—42no—
366C2×Q8—42no—
367C2×Q8—221no—
368C2×Q8—221no—
369C2×Q8#432414yescomplemented
370C2×Q8C2×C22⋊D1112yes—
371C2×D4—24no—
372C2×D4—21no—
373C2×D4C2×C22⋊D1112yes—
374C22×C4—21no—
375C22×C4—28no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—48no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4C2×C22⋊D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C22×C4C2×C22⋊D1111yescharacteristic
387SD16—444no—
388M16—442no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—222no—
392C4⋊C4—28no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4C2×C22⋊D1112yes—
407C4⋊C4C2×C22⋊D1114yes—
408C4⋊C4C2×C22⋊D1112yes—
409C22⋊C4—28no—
410C22⋊C4—22no—
411C22⋊C4—22no—
412C22⋊C4—441no—
413C42—22no—
414C42—22no—
415C42—441no—
416C42C2×C22⋊D1111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C42C23×D1111yescharacteristic
420C11#1877711yescharacteristic, complemented, Sylow
421C23—24no—
422C23—22no—
423C23—42no—
424C23—42no—
425C23#6700611yescharacteristic
426Q8—22no—
427Q8—24no—
428Q8—416no—
429Q8—42no—
430Q8—42no—
431Q8—44no—
432Q8—442no—
433Q8—442no—
434Q8C2×#432414yes—
435D4—24no—
436D4—22no—
437D4#6699514yes—
438C2×C4—24no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—416no—
446C2×C4—42no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4#6698512yes—
455C2×C4C2×#432412yes—
456C2×C4#6700611yescharacteristic
457C2×C4#6700611yescharacteristic
458C2×C4#6700611yescharacteristic
459C2×C4C22×C22⋊D1111yescharacteristic
460C2×C4C22×C22⋊D1111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—442no—
463C8—442no—
464C8—442no—
465C22—21no—
466C22—21no—
467C22—24no—
468C22—48no—
469C22—42no—
470C22—42no—
471C22#1062283112yes—
472C22C2×#6700611yescharacteristic
473C4—24no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—44no—
478C4—42no—
479C4—42no—
480C4—881no—
481C4—881no—
482C4#1062283112yes—
483C4C2×#6698511yescharacteristic
484C4C22×#432411yescharacteristic
485C4C2×#6699512yes—
486C2—22no—
487C2—44no—
488C2C2×#1062283111yescharacteristic
489C2#1307785011yescharacteristic
490C2#1307798011yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×D4×Q8×C11C2
socleC22×C11C2×#120
prime radicalC22×D4×C11D4
hypercenterC2×D4×Q8D11
hypocenterC11#18777
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. #13079760C2semidirect
3. #13078421C2semidirect
4. #13067879C2semidirect
5. #13067781C2semidirect
6. #13067288C2semidirect
8. #13067011C2semidirect
26. #10622706C22semidirect
27. #10622692C22semidirect
29. #10622634C22semidirect
30. #10622633C22semidirect
40. #10622185C22semidirect
41. Q8⋊(C11⋊C8)C22semidirect
123. C2×Q8×C11SD16semidirect
369. C2×Q8#4324semidirect
420. C11#18777semidirect

Maximal subgroups

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

subgroupindex
#130797602
#130786242
#130784212
#130678792
#130677812
#130672882
#130670412
#130670112
C2×D4×Q8×C112
#1877711