Finite Group Databasebeta

← #14731017

Subgroups — #14731017

Order 2816.

938 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079757C211yesmaximal, characteristic, complemented
2C2×#10622694C211yesmaximal, characteristic, complemented
3#13078103C211yesmaximal, characteristic
4#13067837C214yesmaximal, complemented
5#13067823C214yesmaximal, complemented
6#13067297C211yesmaximal, characteristic, complemented
7#13067071C211yesmaximal, characteristic, complemented
8#13066998C211yesmaximal, characteristic
9C11×#3503C211yesmaximal, characteristic
10Q82×C11C2212yes—
11C11×#557—21no—
12C11×#554—22no—
13C11×#554C2212yes—
14D4×Q8×C11—22no—
15D4×Q8×C11—21no—
16C11×#544—22no—
17C11×#544—21no—
18C11×#533—21no—
19C11×#533C2211yescharacteristic
20C2×C11×C4⋊Q8—21no—
21C2×C11×C4⋊Q8C2211yescharacteristic
22C11×#520—21no—
23C4×C11×#41C2211yescharacteristic
24C2×#67004—21no—
25C2×#66922C2211yescharacteristic
26C2×#66899—22no—
27#10622694—22no—
28#10622694—21no—
29#10622694C2214yes—
30#10622692—21no—
31#10622656—22no—
32#10622644—21no—
33#10622644C2212yes—
34#10622633C2214yes—
35#10622632—21no—
36#10622632C2212yes—
37#10622617—21no—
38#10622538C2211yescharacteristic
39#10622537C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622184C2214yes—
42Q8⋊(C11⋊C8)C2214yes—
43Q8⋊(C11⋊C8)C2212yes—
44D4⋊(C11⋊C8)C2212yes—
45C2×C11×#41D411yescharacteristic
46C22×Q8×C11—22no—
47C22×Q8×C11D412yes—
48C22×Dic22—21no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—24no—
52C11×C4⋊Q8—22no—
53C11×C4⋊Q8—22no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8D411yescharacteristic
58C11×C4⋊Q8D411yescharacteristic
59C11×C4⋊Q8C2312yes—
60C11×#125—22no—
61C11×#125—24no—
62C11×#125—22no—
63C11×#125—21no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—24no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—24no—
69C11×C22⋊Q8—21no—
70C11×C22⋊Q8D412yes—
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11—22no—
74C4×Q8×C11—21no—
75C4×Q8×C11D411yescharacteristic
76C4×Q8×C11C2311yescharacteristic
77C4×Q8×C11C2312yes—
78C4×D4×C11—24no—
79C4×D4×C11—22no—
80C4×D4×C11—21no—
81C4×D4×C11—21no—
82C4×D4×C11D411yescharacteristic
83C4×D4×C11C2311yescharacteristic
84C11×#117—22no—
85C11×#117—21no—
86C11×#117—21no—
87C11×#117D411yescharacteristic
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—22no—
92C2×C42×C11—21no—
93C2×C42×C11C2311yescharacteristic
94#67004—44no—
95C2×#4326—22no—
96C2×#4324—22no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×#4318—21no—
100C22×C11⋊C8—21no—
101#66922—21no—
102#66922—21no—
103#66922—21no—
104#66922C2312yes—
105#66899—28no—
106#66899—24no—
107C22⋊(C11⋊C8)—21no—
108#66874—22no—
109#66874—22no—
110#66872—24no—
111C4⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)C2312yes—
113C4⋊(C11⋊C8)C2312yes—
114C4×C11⋊C8—21no—
115C4×C11⋊C8—21no—
116C4×C11⋊C8C2312yes—
117#18632—111nomaximal, Sylow
118C11×#41—22no—
119C11×#41SD1614yes—
120C2×Q8×C11—24no—
121C2×Q8×C11—22no—
122C2×Q8×C11—21no—
123C2×Q8×C11—44no—
124C2×Q8×C11—84no—
125C2×Q8×C11C2×D412yes—
126C2×Q8×C11C2×D411yescharacteristic
127C2×Q8×C11C2×D414yes—
128C2×D4×C11—21no—
129C2×D4×C11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×Dic11—41no—
139C2×Dic22—22no—
140C2×Dic22—41no—
141C2×Dic22—42no—
142C2×Dic22—42no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—24no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C2×D412yes—
159C11×C4⋊C4C2×D411yescharacteristic
160C11×C4⋊C4C2×D411yescharacteristic
161C11×C22⋊C4—24no—
162C11×C22⋊C4—22no—
163C11×C22⋊C4—21no—
164C11×C22⋊C4—21no—
165C11×C22⋊C4—21no—
166C42×C11—24no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—22no—
171C42×C11C2×D411yescharacteristic
172C42×C11C2×D411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2411yescharacteristic
175#4326—44no—
176#4324—44no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—41no—
180C4⋊Dic11—41no—
181#4318—42no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—42no—
186#3503D1111yescharacteristic
187#3229—111no—
188C2×#487—111no—
189#3039—111no—
190#1645—114no—
191#1643—114no—
192#1548—111no—
193#1493—111no—
194#1476—111no—
195C23×C11—21no—
196C23×C11#12011yescharacteristic
197Q8×C11—21no—
198Q8×C11—24no—
199Q8×C11—44no—
200Q8×C11—44no—
201Q8×C11—42no—
202Q8×C11—84no—
203Q8×C11C2×SD1612yes—
204D4×C11—24no—
205D4×C11—21no—
206D4×C11C2×SD1612yes—
207C2×C4×C11—21no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—82no—
219C2×C4×C11—84no—
220C2×C4×C11#12011yescharacteristic
221C2×C4×C11#12011yescharacteristic
222C2×C4×C11#12011yescharacteristic
223C2×C4×C11C2×SD1612yes—
224C2×C4×C11#13712yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×Dic11—42no—
229C2×Dic11—82no—
230Dic22—42no—
231Dic22—42no—
232Dic22—82no—
233C11⋊C8—42no—
234C11⋊C8—42no—
235C11⋊C8—42no—
236C2×#137—221no—
237Q82C2×D1112yes—
238#557—21no—
239#554—22no—
240#554C2×D1112yes—
241D4×Q8—22no—
242D4×Q8—21no—
243#544—22no—
244#544—21no—
245#533—21no—
246#533C2×D1111yescharacteristic
247C2×C4⋊Q8—21no—
248C2×C4⋊Q8—111no—
249C2×C4⋊Q8C2×D1111yescharacteristic
250#520—21no—
251C4×#41C2×D1111yescharacteristic
252#498—221no—
253#487—114no—
254#487—222no—
255#487—221no—
256#483—222no—
257#475—114no—
258#462—112no—
259#462—221no—
260#461—112no—
261#461—221no—
262#431—111no—
263#423—111no—
264#419—221no—
265C2×#103—222no—
266C2×C4×C8—111no—
267#333—114no—
268Q8⋊C8—114no—
269Q8⋊C8—112no—
270D4⋊C8—112no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—22no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11#44812yes—
277C22×C11C2×#12011yescharacteristic
278C4×C11—22no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—41no—
282C4×C11—42no—
283C4×C11—41no—
284C4×C11—44no—
285C4×C11—42no—
286C4×C11#44812yes—
287C4×C11#45512yes—
288C4×C11C22×SD1611yescharacteristic
289C4×C11C2×#13711yescharacteristic
290C4×C11#57812yes—
291Dic11—82no—
292C2×#41C22⋊D1111yescharacteristic
293C22×Q8—22no—
294C22×Q8—221no—
295C22×Q8C22⋊D1112yes—
296#137—444no—
297C2×Q16—222no—
298C2×SD16—222no—
299C2×M16—221no—
300C22×C8—221no—
301C4⋊Q8—22no—
302C4⋊Q8—22no—
303C4⋊Q8—24no—
304C4⋊Q8—22no—
305C4⋊Q8—22no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—112no—
309C4⋊Q8—221no—
310C4⋊Q8—221no—
311C4⋊Q8—221no—
312C4⋊Q8C22⋊D1112yes—
313C4⋊Q8C22⋊D1111yescharacteristic
314C4⋊Q8C22⋊D1111yescharacteristic
315C4⋊Q8C22×D1112yes—
316#125—22no—
317#125—24no—
318#125—22no—
319#125—21no—
320C22⋊Q8—22no—
321C22⋊Q8—24no—
322C22⋊Q8—24no—
323C22⋊Q8—22no—
324C22⋊Q8—24no—
325C22⋊Q8—21no—
326C22⋊Q8C22⋊D1112yes—
327C4×Q8—22no—
328C4×Q8—22no—
329C4×Q8—22no—
330C4×Q8—21no—
331C4×Q8C22⋊D1111yescharacteristic
332C4×Q8C22×D1111yescharacteristic
333C4×Q8C22×D1112yes—
334C4×D4—24no—
335C4×D4—22no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4C22⋊D1111yescharacteristic
339C4×D4C22×D1111yescharacteristic
340#117—22no—
341#117—21no—
342#117—21no—
343#117C22⋊D1111yescharacteristic
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—221no—
350C2×C42—21no—
351C2×C42C22×D1111yescharacteristic
352#106—224no—
353C4⋊C8—112no—
354C4⋊C8—112no—
355C4⋊C8—221no—
356#103—228no—
357#103—224no—
358#103—222no—
359#103—222no—
360C22⋊C8—221no—
361C4×C8—112no—
362C4×C8—221no—
363C4×C8—221no—
364C2×C11—22no—
365C2×C11—42no—
366C2×C11C2×#44811yescharacteristic
367C2×C11#301111yescharacteristic
368C2×C11C2×#45511yescharacteristic
369#41—22no—
370#41#432514yes—
371C2×Q8—24no—
372C2×Q8—22no—
373C2×Q8—21no—
374C2×Q8—44no—
375C2×Q8—84no—
376C2×Q8—222no—
377C2×Q8—441no—
378C2×Q8—442no—
379C2×Q8—442no—
380C2×Q8C2×C22⋊D1112yes—
381C2×Q8C2×C22⋊D1111yescharacteristic
382C2×Q8C2×C22⋊D1114yes—
383C2×D4—21no—
384C2×D4C2×C22⋊D1111yescharacteristic
385C22×C4—21no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—441no—
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C2×C22⋊D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394Q16—444no—
395SD16—444no—
396M16—442no—
397C2×C8—222no—
398C2×C8—222no—
399C2×C8—222no—
400C2×C8—442no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—22no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—21no—
415C4⋊C4—22no—
416C4⋊C4—222no—
417C4⋊C4—222no—
418C4⋊C4—441no—
419C4⋊C4—441no—
420C4⋊C4C2×C22⋊D1111yescharacteristic
421C4⋊C4C2×C22⋊D1111yescharacteristic
422C4⋊C4C2×C22⋊D1112yes—
423C22⋊C4—24no—
424C22⋊C4—22no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—21no—
428C42—24no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42—22no—
433C42C2×C22⋊D1111yescharacteristic
434C42C2×C22⋊D1111yescharacteristic
435C42C2×C22⋊D1111yescharacteristic
436C42C23×D1111yescharacteristic
437C11#1863211yescharacteristic, complemented, Sylow
438C23—21no—
439C23#6700611yescharacteristic
440Q8—21no—
441Q8—24no—
442Q8—44no—
443Q8—44no—
444Q8—42no—
445Q8—84no—
446Q8—442no—
447Q8—442no—
448Q8—882no—
449Q8C2×#432512yes—
450D4—24no—
451D4—21no—
452D4C2×#432512yes—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—82no—
465C2×C4—84no—
466C2×C4—442no—
467C2×C4—882no—
468C2×C4C2×#432512yes—
469C2×C4#6699512yes—
470C2×C4#6700611yescharacteristic
471C2×C4#6700611yescharacteristic
472C2×C4#6700611yescharacteristic
473C2×C4C22×C22⋊D1111yescharacteristic
474C2×C4C22×C22⋊D1111yescharacteristic
475C2×C4C22×C22⋊D1111yescharacteristic
476C8—442no—
477C8—442no—
478C8—442no—
479C22—21no—
480C22—21no—
481C22—22no—
482C22—41no—
483C22—41no—
484C22#1062284012yes—
485C22C2×#6700611yescharacteristic
486C4—22no—
487C4—21no—
488C4—21no—
489C4—41no—
490C4—42no—
491C4—41no—
492C4—44no—
493C4—42no—
494C4—882no—
495C4#1062284012yes—
496C4#1062285512yes—
497C4C22×#432511yescharacteristic
498C4C2×#6699511yescharacteristic
499C4#1062336912yes—
500C2—22no—
501C2—42no—
502C2C2×#1062284011yescharacteristic
503C2#1307791111yescharacteristic
504C2C2×#1062285511yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radicalC2×C11×#41D4
hypercenter#3503D11
hypocenterC11#18632
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13079757C2semidirect
2. C2×#10622694C2semidirect
4. #13067837C2semidirect
5. #13067823C2semidirect
6. #13067297C2semidirect
7. #13067071C2semidirect
437. C11#18632semidirect

Maximal subgroups

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

subgroupindex
#130797572
C2×#106226942
#130781032
#130678372
#130678232
#130672972
#130670712
#130669982
C11×#35032
#1863211