Finite Group Databasebeta

← #14795089

Subgroups — #14795089

Order 2816.

828 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622707C211yesmaximal, characteristic, complemented
2C2×#10622539C211yesmaximal, characteristic
3C4×#66977C211yesmaximal, characteristic
4#13070053C212yesmaximal
5#13069819C212yesmaximal
6#13069569C211yesmaximal, characteristic, complemented
7#13069372C211yesmaximal, characteristic, complemented
8#13069351C212yesmaximal, complemented
9#13069305C212yesmaximal, complemented
10#13068618C211yesmaximal, characteristic, complemented
11C11×#2857C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C11×C22⋊Q8—21no—
14C22×C42×C11C2211yescharacteristic
15C2×#66977C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C11×#391—21no—
18C11×#389—21no—
19C11×#389C2212yes—
20C11×#384C2211yescharacteristic
21C11×#380—21no—
22C11×#380C2212yes—
23#10622825C2211yescharacteristic
24#10622823—21no—
25C4×C22⋊Dic11—21no—
26C2×C22⋊(C11⋊C8)C2212yes—
27#10622707—24no—
28C2×#66874C2212yes—
29C2×#66874C2212yes—
30C2×#66872C2212yes—
31C2×#66871C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622546—21no—
34C4×Dic11⋊C4—21no—
35#10622542C2211yescharacteristic
36#10622541C2211yescharacteristic
37#10622539—24no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×#66867C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×Q8×C11—21no—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×Dic22C2311yescharacteristic
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8—22no—
52C11×C22⋊Q8—44no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C11×C22⋊C4—22no—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—21no—
67C2×C22⋊Dic11—21no—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71#66977—22no—
72#66977—22no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C22×C11⋊C8C2312yes—
79C22×C11⋊C8C2312yes—
80C4×Dic22—22no—
81C4×Dic22—22no—
82C11×#95—22no—
83C11×#95—22no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88C11⋊#95—21no—
89C22⋊(C11⋊C8)—24no—
90#66874—24no—
91#66874—24no—
92#66872—24no—
93#66871—24no—
94C4⋊(C11⋊C8)—22no—
95C4⋊(C11⋊C8)D414yes—
96#66867—24no—
97#24710—111nomaximal, Sylow
98C24×C11C2×D411yescharacteristic
99C2×Q8×C11—42no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C22×Dic11—21no—
126C2×Dic22—21no—
127C2×Dic22—21no—
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—21no—
131C2×Dic22#4112yes—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—42no—
137C11×C4⋊C4—44no—
138C11×C4⋊C4—42no—
139C11×C4⋊C4—42no—
140C11×C22⋊C4—44no—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11—21no—
144C42×C11—21no—
145C42×C11C2×D412yes—
146C42×C11#4112yes—
147C22⋊Dic11—24no—
148C22⋊Dic11—42no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—21no—
154C4⋊Dic11#4112yes—
155Dic11⋊C4—24no—
156Dic11⋊C4—42no—
157Dic11⋊C4—42no—
158C4×Dic11—42no—
159C4×Dic11—42no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8C2×D414yes—
166C2×#475—111no—
167C2×#432—111no—
168#2857D1111yescharacteristic
169C4×C22⋊Q8—111no—
170#2077—112no—
171#2036—112no—
172#1988—111no—
173#1947—111no—
174#1943—112no—
175#1935—112no—
176#1803—111no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11—21no—
182C23×C11—21no—
183C23×C11#13712yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—84no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—44no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11#12112yes—
210C2×C4×C11#12112yes—
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11#13712yes—
213C2×C4×C11C22×D411yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C112−1+411yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—41no—
228C2×Dic11—41no—
229C2×Dic11—41no—
230C2×Dic11—41no—
231Dic22—22no—
232Dic22—22no—
233Dic22—41no—
234Dic22—41no—
235C11⋊C8—24no—
236C11⋊C8—42no—
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—111no—
240C2×C4×Q8—111no—
241C22×C42C2×D1111yescharacteristic
242#475—224no—
243#432—224no—
244C2×#107—112no—
245C2×#106—112no—
246C2×C4⋊C8—111no—
247C2×C4⋊C8—111no—
248C2×#103—112no—
249C2×#103—112no—
250C2×C22⋊C8—112no—
251C2×#97—112no—
252#391—21no—
253#391—111no—
254#389—21no—
255#389—111no—
256#389C2×D1112yes—
257#387—221no—
258#385—221no—
259#384C2×D1111yescharacteristic
260#380—21no—
261#380—111no—
262#380C2×D1112yes—
263C4×C4⋊C4—111no—
264C4×C4⋊C4—221no—
265C4×C22⋊C4—221no—
266#340—112no—
267#340—112no—
268#340—112no—
269#340—112no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—22no—
273C22×C11—41no—
274C22×C11—41no—
275C22×C11—41no—
276C22×C11—41no—
277C22×C11C2×#12111yescharacteristic
278C22×C11#52511yescharacteristic
279C22×C11#53611yescharacteristic
280C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C11C2×#13711yescharacteristic
282C22×C11C2×#13711yescharacteristic
283C22×C11#57511yescharacteristic
284C4×C11—22no—
285C4×C11—41no—
286C4×C11—41no—
287C4×C11—41no—
288C4×C11—82no—
289C4×C11—82no—
290C4×C11#46814yes—
291C4×C11#54711yescharacteristic
292C4×C11#54811yescharacteristic
293C4×C11#55211yescharacteristic
294C4×C11#55611yescharacteristic
295Dic11—42no—
296Dic11—42no—
297Dic11—81no—
298Dic11—81no—
299C22×Q8—21no—
300C22×Q8—111no—
301C23×C4C22⋊D1111yescharacteristic
302C23×C4C22⋊D1111yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C22×C8—112no—
305C22×C8—112no—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C22⋊Q8—44no—
309C22⋊Q8—222no—
310C22⋊Q8—222no—
311C4×Q8—222no—
312C4×Q8—222no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—111no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4C22×D1112yes—
324C2×C4⋊C4C22×D1112yes—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C42—22no—
329C2×C42—22no—
330C2×C42—221no—
331C2×C42—221no—
332C2×C42C22⋊D1111yescharacteristic
333C2×C42C22⋊D1111yescharacteristic
334C2×C42C22×D1111yescharacteristic
335C2×C42C22×D1111yescharacteristic
336#107—224no—
337#106—224no—
338C4⋊C8—114no—
339C4⋊C8—222no—
340#103—224no—
341#103—224no—
342C22⋊C8—224no—
343#97—224no—
344#95—22no—
345#95—22no—
346#95—221no—
347#95—221no—
348#95—221no—
349#95—221no—
350#95—221no—
351C2×C11—42no—
352C2×C11#241511yescharacteristic
353C2×C11C2×#46811yescharacteristic
354C2×C11#305611yescharacteristic
355C2×C11#311311yescharacteristic
356C2×C11#311511yescharacteristic
357C2×C11#323711yescharacteristic
358C2×C11#323911yescharacteristic
359C24C2×C22⋊D1111yescharacteristic
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—42no—
363C2×Q8—112no—
364C2×Q8—221no—
365C2×Q8—221no—
366C2×Q8—221no—
367C2×Q8—221no—
368C2×Q8—221no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—41no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1111yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—114no—
394C2×C8—222no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—222no—
398C2×C8—222no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—44no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—112no—
408C4⋊C4—224no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—221no—
413C4⋊C4—221no—
414C4⋊C4—442no—
415C4⋊C4—442no—
416C22⋊C4—44no—
417C22⋊C4—224no—
418C22⋊C4—442no—
419C42—22no—
420C42—22no—
421C42—21no—
422C42—21no—
423C42—442no—
424C42—442no—
425C42D4×D1112yes—
426C42#434112yes—
427C11#2471011yescharacteristic, complemented, Sylow
428C23—21no—
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23#6699512yes—
435C23C22×C22⋊D1111yescharacteristic
436Q8—84no—
437Q8—222no—
438Q8—222no—
439Q8—441no—
440Q8—441no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—44no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—44no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—222no—
465C2×C4—222no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4—441no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—441no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4#6698512yes—
477C2×C4#6699212yes—
478C2×C4#6699212yes—
479C2×C4#6700412yes—
480C2×C4C2×D4×D1111yescharacteristic
481C2×C4C2×#434111yescharacteristic
482C2×C4#6704011yescharacteristic
483C2×C4#6704011yescharacteristic
484C2×C4#41×D1111yescharacteristic
485C2×C4#41×D1111yescharacteristic
486C8—224no—
487C8—442no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22C2×#6698511yescharacteristic
496C22C2×#6699211yescharacteristic
497C22C2×#6699511yescharacteristic
498C22#1062334711yescharacteristic
499C22#1062335311yescharacteristic
500C22C2×#6700411yescharacteristic
501C22#1062335911yescharacteristic
502C4—22no—
503C4—41no—
504C4—41no—
505C4—41no—
506C4—82no—
507C4—82no—
508C4—442no—
509C4—442no—
510C4—881no—
511C4—881no—
512C4#1062265514yes—
513C4#1062316211yescharacteristic
514C4#1062316411yescharacteristic
515C4#1062317011yescharacteristic
516C4#1062317211yescharacteristic
517C2—42no—
518C2#1307204611yescharacteristic
519C2C2×#1062265511yescharacteristic
520C2#1307824211yescharacteristic
521C2#1307874211yescharacteristic
522C2#1307876111yescharacteristic
523C2#1307983011yescharacteristic
524C2#1307984611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2857C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2857D11
hypocenterC11#24710
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2857

Complements

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

NH ≅ G/Ntype
1. C2×#10622707C2semidirect
6. #13069569C2semidirect
7. #13069372C2semidirect
8. #13069351C2semidirect
9. #13069305C2semidirect
10. #13068618C2semidirect
427. C11#24710semidirect

Maximal subgroups

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

subgroupindex
C2×#106227072
C2×#106225392
C4×#669772
#130700532
#130698192
#130695692
#130693722
#130693512
#130693052
#130686182
C11×#28572
#2471011