Finite Group Databasebeta

← #14723781

Subgroups — #14723781

Order 2816.

632 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078681C211yesmaximal, characteristic
2#13077572C211yesmaximal, characteristic
3#13077551C211yesmaximal, characteristic, complemented
4#13067490C212yesmaximal, complemented
5#13067476C212yesmaximal, complemented
6#13067420C212yesmaximal, complemented
7#13067413C212yesmaximal, complemented
8#13067404C211yesmaximal, characteristic, complemented
9#13067056C211yesmaximal, characteristic
10M16×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#1485C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C4×#4339C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C4×C11×M16C2211yescharacteristic
16#10622707C411yescharacteristic
17#10622703C411yescharacteristic
18#10622700C411yescharacteristic
19#10622696C411yescharacteristic
20#10622660C412yes—
21#10622658C412yes—
22C4×#4326C2212yes—
23C4×#4325C2212yes—
24#10622637—21no—
25#10622637C2212yes—
26Q8×C11⋊C8—21no—
27Q8×C11⋊C8C2212yes—
28#10622612—21no—
29#10622610—21no—
30#10622538C2211yescharacteristic
31#10622537C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622447C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622443C2211yescharacteristic
36#10622443C2211yescharacteristic
37(C22⋊D11)⋊C8—21no—
38(C22⋊D11)⋊C8—21no—
39#10622298—21no—
40C4×C8×D11—21no—
41C11×Q8⋊C8C2212yes—
42C11×Q8⋊C8C2212yes—
43#10622118C2212yes—
44#10622117C2212yes—
45#10622097C2212yes—
46#10622094C2212yes—
47#10622093C2212yes—
48C8×C11⋊C8C2212yes—
49C2×#4339C2×C411yescharacteristic
50C2×C11×M16—21no—
51C11×C4⋊Q8C2×C411yescharacteristic
52C11×C4⋊Q8C2×C411yescharacteristic
53C11×#125—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8C2×C412yes—
56C4×Q8×C11—21no—
57C4×Q8×C11C2312yes—
58C11×#117—21no—
59C2×C42×C11C2311yescharacteristic
60C2×#4326C2×C412yes—
61C2×#4325C2×C412yes—
62C4×C22⋊D11—21no—
63C4×C22⋊D11—21no—
64#66979C2×C411yescharacteristic
65C2×#4318—21no—
66C22×C11⋊C8D411yescharacteristic
67C22×C11⋊C8D411yescharacteristic
68C2×C8×D11—21no—
69C2×C8×D11—21no—
70C4×D44C2×C411yescharacteristic
71C4×D44C2311yescharacteristic
72#66925—21no—
73C42×D11—21no—
74C4×Dic22C2×C411yescharacteristic
75C4×Dic22C2311yescharacteristic
76C11×C4⋊C8C2311yescharacteristic
77C11×C4⋊C8C2311yescharacteristic
78C11×C22⋊C8—21no—
79C11×#97—21no—
80C4×C8×C11—21no—
81C4×C8×C11C2312yes—
82#66899C2×C412yes—
83#66899C2×C412yes—
84C22⋊(C11⋊C8)C2×C412yes—
85(C2×D11)⋊C8—21no—
86(C2×D11)⋊C8—21no—
87Dic11⋊C8—21no—
88Dic11⋊C8—21no—
89C8×Dic11—21no—
90C8×Dic11—21no—
91#66874C2×C412yes—
92#66873C2×C412yes—
93#66872C2×C412yes—
94#66871C2×C412yes—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—22no—
97C4⋊(C11⋊C8)—22no—
98C4⋊(C11⋊C8)C2×C411yescharacteristic
99C4⋊(C11⋊C8)C2×C411yescharacteristic
100C4⋊(C11⋊C8)C2312yes—
101#66867—22no—
102C4×C11⋊C8—22no—
103C4×C11⋊C8D411yescharacteristic
104C4×C11⋊C8D411yescharacteristic
105C4×C11⋊C8C2312yes—
106C4×C11⋊C8C2311yescharacteristic
107C4×C11⋊C8C2311yescharacteristic
108#17913—111nomaximal, Sylow
109C2×Q8×C11—21no—
110C2×Q8×C11C22×C412yes—
111C22×C4×C11C22×C411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C2×C22⋊D11—21no—
115#4339—22no—
116#4339—22no—
117C2×D44C22×C411yescharacteristic
118C2×C4×D11—21no—
119C2×C4×D11—21no—
120C2×C4×D11—21no—
121C2×Dic22C22×C411yescharacteristic
122C11×M16—24no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4C22×C412yes—
132C11×C22⋊C4—22no—
133C42×C11—22no—
134C42×C11C22×C411yescharacteristic
135C42×C11C2×D411yescharacteristic
136C42×C11#4111yescharacteristic
137C42×C11C2411yescharacteristic
138C22⋊Dic11—21no—
139#4326—24no—
140#4325—24no—
141(C2×D11)⋊C4—21no—
142(C2×D11)⋊C4—21no—
143C4⋊Dic11C22×C411yescharacteristic
144C4⋊Dic11C22×C411yescharacteristic
145Dic11⋊C4—21no—
146Dic11⋊C4—21no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150#4318—42no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—41no—
154C2×C11⋊C8C22×C412yes—
155C2×C11⋊C8C22×C412yes—
156C2×C11⋊C8C2×D411yescharacteristic
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159C2×C11⋊C8C2×D411yescharacteristic
160C8×D11—42no—
161C8×D11—42no—
162#3107—111no—
163C8×#41—111no—
164#2960—111no—
165#1587—112no—
166#1585—112no—
167C8×Q16—112no—
168C8×SD16—112no—
169#1574—111no—
170#1489—111no—
171#1485D1111yescharacteristic, complemented
172C8×M16—111no—
173C23×C11C4×D411yescharacteristic
174C22×D11—21no—
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—42no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11C4×D411yescharacteristic
187C2×C4×C11C4×D411yescharacteristic
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C22⋊D11—24no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195D44—21no—
196D44#13112yes—
197C4×D11—24no—
198C4×D11—41no—
199C4×D11—41no—
200C4×D11—42no—
201Dic22—21no—
202Dic22#13112yes—
203C8×C11—24no—
204C8×C11—41no—
205C8×C11—41no—
206C11⋊C8—22no—
207C11⋊C8—22no—
208C11⋊C8—21no—
209C11⋊C8—21no—
210C11⋊C8—21no—
211C11⋊C8—42no—
212C11⋊C8#13712yes—
213#533C2×D1111yescharacteristic
214C4×#41—111no—
215#485—112no—
216#475—111no—
217#474—111no—
218#462—111no—
219#461—111no—
220#452—112no—
221#446—112no—
222#446—221no—
223C8×Q8—112no—
224C8×Q8—111no—
225C8×Q8—111no—
226C8×Q8—221no—
227C4×Q16—112no—
228C4×SD16—112no—
229C8×D4—111no—
230C8×D4—111no—
231C8×D4—221no—
232C8×D4—221no—
233#431—111no—
234#431—221no—
235#431C2×D1111yescharacteristic
236#424—221no—
237#423—111no—
238#405—221no—
239C4×M16C2×D1111yescharacteristic
240C2×C4×C8—111no—
241C2×C4×C8—221no—
242#335—112no—
243#334—112no—
244Q8⋊C8—112no—
245Q8⋊C8C2×D1112yes—
246Q8⋊C8C2×D1112yes—
247D4⋊C8—112no—
248#322—112no—
249C82—112no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11C2×C4×D411yescharacteristic
254C2×D11—22no—
255C2×D11—41no—
256C2×D11—41no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11#44312yes—
263C4×C11C2×#13111yescharacteristic
264C4×C11C2×#13111yescharacteristic
265C4×C11C2×#13711yescharacteristic
266C4×C11#57511yescharacteristic
267Dic11—22no—
268Dic11—41no—
269Dic11—41no—
270C2×#41—111no—
271C2×Q16—112no—
272C2×SD16—112no—
273C2×M16—21no—
274C2×M16—221no—
275C22×C8—111no—
276C22×C8—111no—
277C22×C8—221no—
278C22×C8—221no—
279C4⋊Q8C4×D1111yescharacteristic
280C4⋊Q8C4×D1111yescharacteristic
281#125—21no—
282C22⋊Q8—21no—
283C22⋊Q8C4×D1112yes—
284C4×Q8—21no—
285C4×Q8—111no—
286C4×Q8—111no—
287C4×Q8C22×D1112yes—
288C4×D4—111no—
289C4×D4—111no—
290C4×D4—221no—
291C4×D4—221no—
292#117—21no—
293#117—111no—
294#117—221no—
295C2×C42—221no—
296C2×C42C22×D1111yescharacteristic
297#107—112no—
298#106—112no—
299C4⋊C8—111no—
300C4⋊C8—111no—
301C4⋊C8—112no—
302C4⋊C8—222no—
303C4⋊C8—222no—
304C4⋊C8—221no—
305C4⋊C8—221no—
306C4⋊C8—221no—
307C4⋊C8C22×D1111yescharacteristic
308C4⋊C8C22×D1111yescharacteristic
309#103—112no—
310#103—112no—
311#103—112no—
312#102—112no—
313C22⋊C8—21no—
314C22⋊C8—112no—
315C22⋊C8—221no—
316C22⋊C8—221no—
317#97—21no—
318#97—222no—
319C4×C8—21no—
320C4×C8—111no—
321C4×C8—111no—
322C4×C8—111no—
323C4×C8—112no—
324C4×C8—111no—
325C4×C8—222no—
326C4×C8—221no—
327C4×C8—221no—
328C4×C8C22×D1112yes—
329C2×C11—41no—
330C2×C11#292911yescharacteristic
331C2×C11C4×#13711yescharacteristic
332C2×C11C2×#44311yescharacteristic
333D11—42no—
334#41—222no—
335#41—222no—
336C2×Q8—21no—
337C2×Q8—111no—
338C2×Q8C2×C4×D1112yes—
339C2×D4—111no—
340C2×D4—221no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4C2×C4×D1111yescharacteristic
345C22×C4D4×D1111yescharacteristic
346C22×C4#434111yescharacteristic
347Q16—224no—
348SD16—224no—
349M16—24no—
350M16—442no—
351C2×C8—22no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8—111no—
355C2×C8—112no—
356C2×C8—112no—
357C2×C8—111no—
358C2×C8—111no—
359C2×C8—111no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8—442no—
363C2×C8—442no—
364C2×C8—441no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—111no—
371C4⋊C4—111no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C4⋊C4C2×C4×D1112yes—
375C22⋊C4—22no—
376C22⋊C4—221no—
377C22⋊C4—221no—
378C22⋊C4—221no—
379C42—22no—
380C42—221no—
381C42—221no—
382C42—221no—
383C42C2×C4×D1111yescharacteristic
384C42D4×D1111yescharacteristic
385C42#434111yescharacteristic
386C42C23×D1111yescharacteristic
387C11#1791311yescharacteristic, complemented, Sylow
388C23—221no—
389C23(C22⋊D11)⋊C411yescharacteristic
390Q8—22no—
391Q8—22no—
392Q8—42no—
393Q8—112no—
394Q8—221no—
395D4—112no—
396D4—224no—
397D4—221no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—224no—
406C2×C4—221no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4—442no—
412C2×C4(C22⋊D11)⋊C411yescharacteristic
413C2×C4(C22⋊D11)⋊C411yescharacteristic
414C2×C4(C22⋊D11)⋊C411yescharacteristic
415C2×C4C22×C4×D1111yescharacteristic
416C2×C4C2×D4×D1111yescharacteristic
417C2×C4C2×#434111yescharacteristic
418C8—24no—
419C8—41no—
420C8—41no—
421C8—112no—
422C8—222no—
423C8—222no—
424C8—221no—
425C8—221no—
426C8—221no—
427C8—442no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—222no—
432C22—441no—
433C22—441no—
434C22C2×(C22⋊D11)⋊C411yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—42no—
439C4—42no—
440C4—222no—
441C4—441no—
442C4—441no—
443C4#1062243712yes—
444C4D11×#13111yescharacteristic
445C4D11×#13111yescharacteristic
446C4D11×#13711yescharacteristic
447C4#1062330811yescharacteristic
448C2—41no—
449C2—442no—
450C2#1307731311yescharacteristic
451C2#1307743111yescharacteristic
452C2C2×#1062243711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1485C2
socleC22×C11C2×C4×D4
prime radicalC2×#4339C2×C4
cosocleC42×C11C24
hypercenter#1485D11
hypocenterC11#17913
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1485

Complements

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

NH ≅ G/Ntype
3. #13077551C2semidirect
4. #13067490C2semidirect
5. #13067476C2semidirect
6. #13067420C2semidirect
7. #13067413C2semidirect
8. #13067404C2semidirect
10. M16×C11⋊C8C2semidirect
11. C11×#1485C2semidirect
171. #1485D11semidirect
387. C11#17913semidirect

Maximal subgroups

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

subgroupindex
#130786812
#130775722
#130775512
#130674902
#130674762
#130674202
#130674132
#130674042
#130670562
M16×C11⋊C82
C11×#14852
#1791311