Finite Group Databasebeta

← #14671268

Subgroups — #14671268

Order 2816.

818 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 818 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622850C211yesmaximal, characteristic, complemented
2C2×#10622174C212yesmaximal, complemented
3#13068534C211yesmaximal, characteristic, complemented
4#13066734C212yesmaximal, complemented
5C11×#2404C211yesmaximal, characteristic
6C22×C11×#41C2211yescharacteristic
7C2×C11×#120C411yescharacteristic, complemented
8C2×C11×#120C2211yescharacteristic
9C22×C11×C22⋊C4C411yescharacteristic, complemented
10C22×#4318—21no—
11C11×#393—21no—
12C11×#392—21no—
13C11×#386—21no—
14C11×#386—21no—
15C11×#386C411yescharacteristic, complemented
16C11×#386C2211yescharacteristic
17C11×#381C411yescharacteristic, complemented
18#10622850—24no—
19C2×#66900—21no—
20C2×#66898—21no—
21C2×#66898C2212yes—
22C2×#66897C2212yes—
23#10622824—21no—
24#10622174—24no—
25C25×C11C2×C411yescharacteristic
26C2×C11×#41—22no—
27C2×C11×#41—22no—
28C2×C11×#41—41no—
29C2×C11×#41—41no—
30C2×C11×#41—42no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11C2×C411yescharacteristic
35C22×D4×C11D411yescharacteristic
36C22×D4×C11C2311yescharacteristic
37C23×C4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11D411yescharacteristic
41C11×#120—22no—
42C11×#120—22no—
43C11×#120—42no—
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4—21no—
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—41no—
51C2×C11×C22⋊C4—41no—
52C2×C11×C22⋊C4C2×C411yescharacteristic
53C2×C11×C22⋊C4C2×C411yescharacteristic
54C2×C22⋊Dic11—22no—
55C2×#4318—24no—
56C2×#4318—22no—
57C2×#4318—42no—
58C2×#4318—41no—
59C22×C11⋊C8—41no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64#66900—24no—
65#66898—22no—
66#66898—22no—
67#66898—42no—
68#66897—22no—
69#66897D414yescomplemented
70C11⋊#95—41no—
71C11⋊#95—41no—
72#13083—111nomaximal, Sylow
73C24×C11—21no—
74C24×C11—22no—
75C24×C11—41no—
76C24×C11—42no—
77C24×C11—41no—
78C24×C11—81no—
79C24×C11C22⋊C411yescharacteristic
80C24×C11C22×C411yescharacteristic
81C24×C11C2×D411yescharacteristic
82C11×#41—44no—
83C11×#41—44no—
84C11×#41—44no—
85C11×#41—44no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—41no—
89C2×Q8×C11—41no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—42no—
99C2×D4×C11—42no—
100C2×D4×C11—42no—
101C2×D4×C11—42no—
102C2×D4×C11—81no—
103C2×D4×C11—81no—
104C2×D4×C11C2×D412yes—
105C2×D4×C11#4112yes—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—41no—
121C22×C4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—81no—
124C22×C4×C11C22⋊C411yescharacteristic
125C22×C4×C11C22⋊C411yescharacteristic
126C22×C4×C11C22⋊C411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×Dic11—42no—
129C11×C22⋊C4—22no—
130C11×C22⋊C4—42no—
131C11×C22⋊C4—42no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—81no—
138C11×C22⋊C4—81no—
139C22⋊Dic11—42no—
140C22⋊Dic11—42no—
141#4318—24no—
142#4318—44no—
143#4318—42no—
144C2×C11⋊C8—44no—
145C2×C11⋊C8—42no—
146C2×#413—111no—
147#2404D1111yescharacteristic
148C2×AΣL(1,𝔽16)—112no—
149#1782—111no—
150#1390—112no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—22no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—42no—
168C23×C11—42no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—82no—
173C23×C11—84no—
174C23×C11—84no—
175C23×C11—82no—
176C23×C11#9912yes—
177C23×C11C2×C22⋊C411yescharacteristic
178C23×C11C4×D412yes—
179C23×C11#12112yes—
180Q8×C11—42no—
181Q8×C11—42no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—44no—
185D4×C11—44no—
186D4×C11—84no—
187D4×C11—84no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—82no—
216C2×C4×C11#9911yescharacteristic
217C2×C4×C11#9911yescharacteristic
218C2×C4×C11#12011yescharacteristic
219C2×C4×C11#12311yescharacteristic
220C2×Dic11—82no—
221C2×Dic11—82no—
222C2×Dic11—82no—
223C11⋊C8—44no—
224C22×#41C2×D1111yescharacteristic
225C22×M16—221no—
226C2×#120Dic1111yescharacteristic, complemented
227C2×#120C2×D1111yescharacteristic
228C22×C22⋊C4Dic1111yescharacteristic, complemented
229#413—224no—
230C2×#101—221no—
231C2×#100—112no—
232C2×#99—112no—
233C2×#99—221no—
234#393—21no—
235#392—21no—
236#386—21no—
237#386—21no—
238#386Dic1111yescharacteristic, complemented
239#386C2×D1111yescharacteristic
240#381—221no—
241#381Dic1111yescharacteristic, complemented
242AΣL(1,𝔽16)—224no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11—41no—
260C22×C11—42no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—84no—
266C22×C11—84no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11#38611yescharacteristic
270C22×C11C2×#9911yescharacteristic
271C22×C11C2×#9911yescharacteristic
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—41no—
277C4×C11—41no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11—81no—
281Dic11—162no—
282C25C2×Dic1111yescharacteristic
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—41no—
286C2×#41—41no—
287C2×#41—42no—
288C22×Q8C22⋊D1111yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2×Dic1111yescharacteristic
292C22×D4C22⋊D1111yescharacteristic
293C22×D4C22×D1111yescharacteristic
294C23×C4C2×Dic1111yescharacteristic
295C23×C4C2×Dic1111yescharacteristic
296C23×C4C22⋊D1111yescharacteristic
297C23×C4C22⋊D1111yescharacteristic
298C2×M16—224no—
299C2×M16—222no—
300C2×M16—442no—
301C2×M16—441no—
302C22×C8—441no—
303#120—22no—
304#120—22no—
305#120—42no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—41no—
313C2×C22⋊C4—41no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4C2×Dic1111yescharacteristic
316C2×C22⋊C4C2×Dic1111yescharacteristic
317#101—224no—
318#100—114no—
319#100—222no—
320#99—222no—
321#99—222no—
322#99—442no—
323#95—21no—
324#95—21no—
325#95—21no—
326#95—21no—
327#95—441no—
328#95—441no—
329C2×C11—21no—
330C2×C11—21no—
331C2×C11—42no—
332C2×C11—42no—
333C2×C11—42no—
334C2×C11—82no—
335C2×C11#189811yescharacteristic
336C2×C11#212011yescharacteristic
337C2×C11#212211yescharacteristic
338C24—21no—
339C24—22no—
340C24—41no—
341C24—42no—
342C24—41no—
343C24—81no—
344C24C22⋊Dic1111yescharacteristic
345C24C22×Dic1111yescharacteristic
346C24C2×C22⋊D1111yescharacteristic
347#41—44no—
348#41—44no—
349#41—44no—
350#41—44no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—81no—
368C2×D4—81no—
369C2×D4D4×D1112yes—
370C2×D4#434112yes—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—81no—
389C22×C4—442no—
390C22×C4C22⋊Dic1111yescharacteristic
391C22×C4C22⋊Dic1111yescharacteristic
392C22×C4C22⋊Dic1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394M16—224no—
395M16—444no—
396M16—442no—
397C2×C8—444no—
398C2×C8—442no—
399C22⋊C4—22no—
400C22⋊C4—42no—
401C22⋊C4—42no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—81no—
408C22⋊C4—81no—
409C22⋊C4—442no—
410C22⋊C4—442no—
411C11#1308311yescharacteristic, complemented, Sylow
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—82no—
434C23—84no—
435C23—84no—
436C23—82no—
437C23#6689812yes—
438C23D4×Dic1112yes—
439C23#6699212yes—
440C23C2×C22⋊Dic1111yescharacteristic
441Q8—42no—
442Q8—42no—
443D4—42no—
444D4—42no—
445D4—44no—
446D4—44no—
447D4—84no—
448D4—84no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—882no—
478C2×C4—882no—
479C2×C4—882no—
480C2×C4#6689811yescharacteristic
481C2×C4#6689811yescharacteristic
482C2×C4#6698811yescharacteristic
483C2×C4#6699011yescharacteristic
484C8—444no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—84no—
508C22—84no—
509C22—81no—
510C22—81no—
511C22C2×#6689811yescharacteristic
512C22C2×#6689811yescharacteristic
513C22#1062283311yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—41no—
519C4—41no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—1762no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—82no—
530C2#1306907011yescharacteristic
531C2#1307025711yescharacteristic
532C2#1307026611yescharacteristic
subgroupG/H
centerC22C2×#66898
commutatorC24×C11C22×C4
FrattiniC22×D4C22×D11
Fitting, prime radicalC11×#2404C2
socleC22×C11C2×#99
cosocleC22×D4×C11C23
hypercenter#2404D11
hypocenterC11#13083
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. C2×#10622850C2semidirect
2. C2×#10622174C2semidirect
3. #13068534C2semidirect
4. #13066734C2semidirect
7. C2×C11×#120C4semidirect
9. C22×C11×C22⋊C4C4semidirect
15. C11×#386C4semidirect
17. C11×#381C4semidirect
69. #66897D4semidirect
226. C2×#120Dic11semidirect
228. C22×C22⋊C4Dic11semidirect
238. #386Dic11semidirect
241. #381Dic11semidirect
411. C11#13083semidirect

Maximal subgroups

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

subgroupindex
C2×#106228502
C2×#106221742
#130685342
#130667342
C11×#24042
#1308311