Finite Group Databasebeta

← #14737832

Subgroups — #14737832

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079175C211yesmaximal, characteristic
2#13078421C211yesmaximal, characteristic, complemented
3#13078088C211yesmaximal, characteristic
4#13068170C212yesmaximal, complemented
5#13068156C212yesmaximal, complemented
6#13068122C212yesmaximal, complemented
7#13068088C212yesmaximal, complemented
8#13067375C211yesmaximal, characteristic, complemented
9#13067304C211yesmaximal, characteristic, complemented
10#13067291C211yesmaximal, characteristic
11C2×C11×#446C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66995—21no—
14#10623008C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#446—21no—
17C11×#446—21no—
18C11×#446C2212yes—
19C11×#446C2212yes—
20C2×C11×C4⋊C8—21no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#97—21no—
23C2×C4×C8×C11C2211yescharacteristic
24#10622838—21no—
25#10622727—21no—
26#10622727—21no—
27#10622644C2212yes—
28#10622641—22no—
29#10622640C2212yes—
30#10622635—22no—
31#10622634C2212yes—
32#10622633C2212yes—
33#10622579—21no—
34#10622577—21no—
35#10622537C2211yescharacteristic
36#10622537C2211yescharacteristic
37#10622307C2211yescharacteristic
38#10622306C2211yescharacteristic
39C4×#4314—21no—
40C4×#4314—21no—
41#10622294C2211yescharacteristic
42#10622293C2211yescharacteristic
43#10622124C2212yes—
44#10622123C2212yes—
45#10622120C2212yes—
46#10622119C2212yes—
47#10622096C2212yes—
48#10622096C2212yes—
49C22×Q8×C11D411yescharacteristic
50C2×#4339—21no—
51C22×C8×C11—21no—
52C22×C8×C11D411yescharacteristic
53C22×C8×C11D411yescharacteristic
54C4×Q8×C11—21no—
55C4×Q8×C11—21no—
56C4×Q8×C11D412yes—
57C4×Q8×C11C2312yes—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4D411yescharacteristic
60C2×C42×C11—21no—
61C2×C42×C11C2311yescharacteristic
62C2×#4326—22no—
63#66995—44no—
64C2×#4325—22no—
65#66983—21no—
66#66983—21no—
67#66979—21no—
68#66977—21no—
69#66977—21no—
70C2×#4318—21no—
71C2×#4318—21no—
72C2×#4314—21no—
73C2×#4314—21no—
74#66928—21no—
75#66927C2311yescharacteristic
76C4×D44—21no—
77C4×D44—21no—
78#66923—21no—
79#66922C2311yescharacteristic
80#66922C2311yescharacteristic
81#66922C2311yescharacteristic
82C4×Dic22—21no—
83C4×Dic22—21no—
84C11×C4⋊C8—22no—
85C11×C4⋊C8—22no—
86C11×C4⋊C8—21no—
87C11×C4⋊C8C2312yes—
88C11×#97—22no—
89C11×#97—22no—
90C4×C8×C11D411yescharacteristic
91C4×C8×C11D411yescharacteristic
92C4×C8×C11C2311yescharacteristic
93C4×C8×C11C2311yescharacteristic
94#66899—22no—
95#66899—22no—
96#66885—21no—
97#66885—21no—
98#66881—21no—
99#66881—21no—
100#66880—21no—
101#66880—21no—
102#66874—22no—
103#66873—22no—
104#66872—22no—
105#66871—22no—
106C4⋊(C11⋊C8)—21no—
107C4⋊(C11⋊C8)—21no—
108C4⋊(C11⋊C8)C2312yes—
109C4⋊(C11⋊C8)C2312yes—
110#19285—111nomaximal, Sylow
111C2×Q8×C11—21no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11C2×D412yes—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11#4111yescharacteristic
120C2×C22⋊D11—41no—
121#4339—42no—
122#4339—42no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—21no—
126C2×C4×D11—41no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—41no—
133C2×C8×C11—42no—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C11×C4⋊C4—22no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4C2×D412yes—
142C42×C11—22no—
143C42×C11—22no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11#4111yescharacteristic
147C42×C11C2411yescharacteristic
148C22⋊Dic11—41no—
149#4326—44no—
150#4325—44no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162#4318—42no—
163#4318—42no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166#4314—42no—
167#4314—42no—
168#3167—111no—
169#3078—111no—
170#3037—111no—
171C2×#446D1111yescharacteristic, complemented
172#1700—112no—
173#1698—112no—
174#1692—112no—
175#1686—112no—
176#1567—111no—
177#1550—111no—
178#1547—111no—
179C23×C11#12111yescharacteristic
180C22×D11—41no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—42no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)12yes—
195C2×C4×C11#13712yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C22⋊D11—82no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203D44—41no—
204D44—41no—
205D44—41no—
206D44—41no—
207D44—81no—
208C4×D11—82no—
209Dic22—41no—
210Dic22—41no—
211Dic22—41no—
212Dic22—41no—
213Dic22—81no—
214C8×C11—21no—
215C8×C11—21no—
216C8×C11—21no—
217C8×C11—42no—
218C8×C11#13712yescomplemented
219C11⋊C8—42no—
220C11⋊C8—42no—
221C2×#137—221no—
222#533—111no—
223#532—111no—
224C2×C4×Q8C2×D1111yescharacteristic
225#498—111no—
226#492—111no—
227#487—111no—
228#486—111no—
229#479—222no—
230#477—112no—
231#475—112no—
232#465—221no—
233#465—221no—
234#464—222no—
235#462—112no—
236#460—112no—
237#446—21no—
238#446—21no—
239#446C2×D1112yes—
240#446C2×D1112yes—
241C4×SD16—221no—
242C4×SD16—221no—
243#428—221no—
244#423—111no—
245#423—111no—
246C2×C4⋊C8—21no—
247C2×C4⋊C8C2×D1111yescharacteristic
248#419—221no—
249#417—221no—
250C2×#97—21no—
251C2×C4×C8C2×D1111yescharacteristic
252#335—112no—
253#335—112no—
254#333—112no—
255#332—112no—
256#332—112no—
257#331—112no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11#46812yes—
261C22×C11C2×#12111yescharacteristic
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—21no—
268C4×C11—42no—
269C4×C11—42no—
270C4×C11#46812yes—
271C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C4×C11C2×#13711yescharacteristic
273C4×C11C2×#13711yescharacteristic
274C4×C11#57511yescharacteristic
275Dic11—81no—
276Dic11—81no—
277Dic11—81no—
278C2×#41—221no—
279C22×Q8D4411yescharacteristic
280#137—444no—
281C2×Q16—222no—
282C2×SD16—222no—
283C2×SD16—221no—
284C2×SD16—221no—
285C2×M16—221no—
286C2×M16—221no—
287C22×C8—21no—
288C22×C8C22⋊D1111yescharacteristic
289C22×C8C22⋊D1111yescharacteristic
290C4⋊Q8—111no—
291C4⋊Q8—111no—
292C4⋊Q8—111no—
293#127—111no—
294#125—221no—
295#124—221no—
296C22⋊Q8—221no—
297C22⋊Q8—221no—
298#121—221no—
299#121—221no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8—221no—
303C4×Q8—221no—
304C4×Q8D4412yes—
305C4×Q8C22×D1112yes—
306C4×D4—221no—
307C4×D4—221no—
308#117—221no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4D4411yescharacteristic
311C2×C42—21no—
312C2×C42C22×D1111yescharacteristic
313#107—222no—
314#106—221no—
315#106—221no—
316#106—222no—
317C4⋊C8—22no—
318C4⋊C8—22no—
319C4⋊C8—21no—
320C4⋊C8—112no—
321C4⋊C8—112no—
322C4⋊C8—221no—
323C4⋊C8—221no—
324C4⋊C8C22×D1112yes—
325#103—222no—
326#103—222no—
327#103—221no—
328#103—221no—
329#103—222no—
330#102—221no—
331#102—221no—
332#102—222no—
333#97—22no—
334#97—22no—
335C4×C8C22⋊D1111yescharacteristic
336C4×C8C22⋊D1111yescharacteristic
337C4×C8C22×D1111yescharacteristic
338C4×C8C22×D1111yescharacteristic
339C2×C11—22no—
340C2×C11#303711yescharacteristic
341C2×C11C2×#46811yescharacteristic
342C2×C11#306711yescharacteristic
343D11—161no—
344#41—442no—
345#41—442no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×Q8—221no—
352C2×Q8C2×D4412yes—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—441no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—441no—
360C22×C4C2×D4411yescharacteristic
361C22×C4#433911yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363Q16—444no—
364SD16—442no—
365SD16—444no—
366SD16—442no—
367M16—442no—
368M16—442no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—41no—
372C2×C8—42no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8C2×C22⋊D1111yescharacteristic
376C2×C8C2×C22⋊D1111yescharacteristic
377C2×C8C2×C22⋊D1111yescharacteristic
378C2×C8C2×C22⋊D1111yescharacteristic
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4C2×D4412yes—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C42—22no—
395C42—22no—
396C42—441no—
397C42C2×D4411yescharacteristic
398C42#433911yescharacteristic
399C42C2×C22⋊D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11#1928511yescharacteristic, complemented, Sylow
402C23—441no—
403C23#6698311yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—42no—
407Q8—441no—
408Q8—441no—
409Q8—441no—
410Q8—441no—
411Q8—881no—
412D4—441no—
413D4—441no—
414D4—441no—
415D4—441no—
416D4—881no—
417D4—882no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4—882no—
429C2×C4#6696112yes—
430C2×C4#6696212yes—
431C2×C4#6698311yescharacteristic
432C2×C4#6698311yescharacteristic
433C2×C4#6698311yescharacteristic
434C2×C4C22×D4411yescharacteristic
435C2×C4C2×#433911yescharacteristic
436C2×C4C22×C22⋊D1111yescharacteristic
437C8—21no—
438C8—21no—
439C8—21no—
440C8—42no—
441C8—442no—
442C8—442no—
443C8#6699512yescomplemented
444C22—21no—
445C22—21no—
446C22—881no—
447C22—881no—
448C22—881no—
449C22#1062274712yes—
450C22C2×#6698311yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—42no—
456C4—881no—
457C4—881no—
458C4—881no—
459C4#1062274712yes—
460C4C2×#6696111yescharacteristic
461C4C2×#6696211yescharacteristic
462C4C2×#6699511yescharacteristic
463C4#1062335311yescharacteristic
464C2—22no—
465C2—1761no—
466C2#1307808811yescharacteristic
467C2C2×#1062274711yescharacteristic
468C2#1307833611yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#446C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenterC2×#446D11
hypocenterC11#19285
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. #13078421C2semidirect
4. #13068170C2semidirect
5. #13068156C2semidirect
6. #13068122C2semidirect
7. #13068088C2semidirect
8. #13067375C2semidirect
9. #13067304C2semidirect
11. C2×C11×#446C2semidirect
171. C2×#446D11semidirect
218. C8×C11#137semidirect
401. C11#19285semidirect
443. C8#66995semidirect

Maximal subgroups

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

subgroupindex
#130791752
#130784212
#130780882
#130681702
#130681562
#130681222
#130680882
#130673752
#130673042
#130672912
C2×C11×#4462
#1928511