Finite Group Databasebeta

← #14783713

Subgroups — #14783713

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C211yesmaximal, characteristic
2#13071019C211yesmaximal, characteristic
3#13070189C212yesmaximal, complemented
4#13070187C212yesmaximal, complemented
5#13070182C212yesmaximal, complemented
6#13070177C212yesmaximal, complemented
7#13068337C211yesmaximal, characteristic
8#13068336C211yesmaximal, characteristic
9#13068335C211yesmaximal, characteristic
10#13068309C211yesmaximal, characteristic
11C11×#1736C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11—21no—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C2×C11⋊#95—21no—
21#10622598—21no—
22#10622598—21no—
23#10622598C2212yes—
24#10622598C2212yes—
25#10622590C2211yescharacteristic
26#10622590C2211yescharacteristic
27#10622589C2211yescharacteristic
28#10622589C2211yescharacteristic
29#10622555—21no—
30#10622555—21no—
31C4×Dic11⋊C4—21no—
32C4×Dic11⋊C4—21no—
33C11×#340C2212yes—
34C11×#340C2212yes—
35#10622189C2212yes—
36#10622189C2212yes—
37#10622188C2212yes—
38#10622188C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11—21no—
46C23×Dic11D411yescharacteristic
47C23×Dic11D411yescharacteristic
48C2×C11×M16—22no—
49C2×C11×M16—22no—
50C2×C11×M16—22no—
51C22×C8×C11C2312yes—
52C11×#117—22no—
53C11×#117—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4Q814yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C22⋊Dic11—21no—
63#66979—22no—
64#66979—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—44no—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318—22no—
88C22×C11⋊C8C2312yes—
89C11⋊#95—21no—
90C11⋊#95—21no—
91C11⋊#95—21no—
92C11⋊#95—21no—
93C11⋊#95—22no—
94C11⋊#95—22no—
95#23747—111nomaximal, Sylow
96C24×C11C2×D411yescharacteristic
97C22×C4×C11—24no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—42no—
102C22×C4×C11—42no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×Q812yes—
105C22×C4×C11#4112yes—
106C22×C4×C11#4112yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—22no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—42no—
121C22×Dic11—42no—
122C22×Dic11—42no—
123C22×Dic11C2×D411yescharacteristic
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C11×M16—44no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4C2×Q814yes—
138C11×C22⋊C4—42no—
139C42×C11—42no—
140C22⋊Dic11—42no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—44no—
148C4⋊Dic11—44no—
149C4⋊Dic11—42no—
150Dic11⋊C4—42no—
151Dic11⋊C4—42no—
152Dic11⋊C4—42no—
153Dic11⋊C4—42no—
154C4×Dic11—22no—
155C4×Dic11—22no—
156C4×Dic11—21no—
157C4×Dic11—21no—
158C4×Dic11—21no—
159C4×Dic11—21no—
160C4×Dic11—42no—
161#4318—44no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×#389—111no—
166#2285—111no—
167#2101—112no—
168#2101—112no—
169#2100—112no—
170#2099—112no—
171#1736—111no—
172#1736—111no—
173#1736—111no—
174#1736D1111yescharacteristic
175#1728—111no—
176C23×C11—21no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—21no—
180C23×C11C22⋊Q812yes—
181C23×C11#12312yes—
182C23×C11#12412yes—
183C23×C11C22×D411yescharacteristic
184C2×C4×C11—24no—
185C2×C4×C11—48no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11C22⋊Q812yes—
195C2×C4×C11#12312yes—
196C2×C4×C11#12412yes—
197C2×C4×C11#12514yes—
198C2×C4×C11#12514yes—
199C2×C4×C11#12614yes—
200C2×C4×C11#12614yes—
201C2×C4×C11C22×Q811yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—21no—
216C2×Dic11—21no—
217C2×Dic11—44no—
218C2×Dic11—44no—
219C2×Dic11—42no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—42no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11—42no—
228C2×Dic11—84no—
229C2×Dic11AGL(1,ℤ/8)12yes—
230C2×Dic11#13712yes—
231C8×C11—42no—
232C11⋊C8—42no—
233C22×M16—111no—
234C22×M16C2×D1111yescharacteristic
235C2×#117—111no—
236C2×#117C2×D1111yescharacteristic
237C22×C4⋊C4—111no—
238C22×C4⋊C4—221no—
239C22×C4⋊C4C2×D1111yescharacteristic
240C22×C42—111no—
241#389—112no—
242#389—112no—
243#389—221no—
244#389—221no—
245#384—111no—
246#384—111no—
247#382—111no—
248#382—111no—
249#380—221no—
250#380—221no—
251C4×C4⋊C4—221no—
252C4×C4⋊C4—221no—
253C2×#95—221no—
254#340—112no—
255#340—112no—
256#340—112no—
257#340—112no—
258#340—112no—
259#340—112no—
260#340C2×D1112yes—
261#340C2×D1112yes—
262#336—112no—
263#336—112no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—22no—
268C22×C11—22no—
269C22×C11—22no—
270C22×C11#40014yes—
271C22×C11C2×C22⋊Q811yescharacteristic
272C22×C11C2×#12311yescharacteristic
273C22×C11C2×#12411yescharacteristic
274C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
275C22×C11C2×#13711yescharacteristic
276C22×C11#57511yescharacteristic
277C22×C11#57511yescharacteristic
278C4×C11—44no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11#40014yes—
282C4×C11C2×#12511yescharacteristic
283C4×C11C2×#12511yescharacteristic
284C4×C11C2×#12611yescharacteristic
285C4×C11C2×#12611yescharacteristic
286Dic11—22no—
287Dic11—22no—
288Dic11—41no—
289Dic11—41no—
290Dic11—82no—
291Dic11—81no—
292Dic11—81no—
293C23×C4—21no—
294C23×C4—111no—
295C23×C4—111no—
296C23×C4—221no—
297C23×C4C22×D1111yescharacteristic
298C2×M16—22no—
299C2×M16—22no—
300C2×M16—22no—
301C2×M16—222no—
302C2×M16—222no—
303C2×M16—222no—
304C22×C8—112no—
305C22×C8C22×D1112yes—
306#117—22no—
307#117—22no—
308#117—222no—
309#117—222no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—111no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—221no—
321C2×C4⋊C4—221no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—444no—
325C2×C4⋊C4Dic2214yes—
326C2×C4⋊C4C22×D1111yescharacteristic
327C2×C4⋊C4C22×D1111yescharacteristic
328C2×C4⋊C4C22×D1112yes—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—221no—
331C2×C42—21no—
332C2×C42—111no—
333C2×C42—111no—
334C2×C42—111no—
335C2×C42—111no—
336C2×C42—222no—
337C2×C42—222no—
338C2×C42—221no—
339#95—222no—
340#95—222no—
341#95—221no—
342#95—221no—
343#95—221no—
344#95—221no—
345C2×C11—24no—
346C2×C11C2×#40011yescharacteristic
347C2×C11#307711yescharacteristic
348C2×C11#307811yescharacteristic
349C2×C11#309411yescharacteristic
350C2×C11#309511yescharacteristic
351C2×C11#314111yescharacteristic
352C2×C11#314211yescharacteristic
353C24D4×D1111yescharacteristic
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—221no—
369C22×C4—221no—
370C22×C4—222no—
371C22×C4—441no—
372C22×C4—441no—
373C22×C4—442no—
374C22×C4—442no—
375C22×C4—442no—
376C22×C4C2×Dic2212yes—
377C22×C4#433912yes—
378C22×C4#433912yes—
379C22×C4D4×D1111yescharacteristic
380C22×C4#434112yes—
381C22×C4#434112yes—
382C22×C4#434312yes—
383C22×C4C23×D1111yescharacteristic
384M16—44no—
385M16—444no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—222no—
390C2×C8—222no—
391C2×C8—222no—
392C4⋊C4—24no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—222no—
399C4⋊C4—221no—
400C4⋊C4—221no—
401C4⋊C4—221no—
402C4⋊C4—221no—
403C4⋊C4—222no—
404C4⋊C4—444no—
405C4⋊C4—442no—
406C4⋊C4—442no—
407C4⋊C4—444no—
408C4⋊C4—442no—
409C4⋊C4—442no—
410C4⋊C4—442no—
411C4⋊C4C2×Dic2214yes—
412C22⋊C4—42no—
413C22⋊C4—442no—
414C42—42no—
415C42—222no—
416C42—222no—
417C42—221no—
418C42—221no—
419C42—221no—
420C42—221no—
421C42—442no—
422C11#2374711yescharacteristic, complemented, Sylow
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23#6693112yes—
428C23#6693812yes—
429C23#6694712yes—
430C23C2×D4×D1111yescharacteristic
431C2×C4—24no—
432C2×C4—48no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—112no—
442C2×C4—112no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—221no—
450C2×C4—221no—
451C2×C4—221no—
452C2×C4—221no—
453C2×C4—444no—
454C2×C4—444no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—441no—
462C2×C4—441no—
463C2×C4—442no—
464C2×C4—884no—
465C2×C4#6692314yes—
466C2×C4#6693112yes—
467C2×C4#6693214yes—
468C2×C4#6693812yes—
469C2×C4#6694314yes—
470C2×C4#6694712yes—
471C2×C4#6695114yes—
472C2×C4C22×Dic2211yescharacteristic
473C2×C4C2×#433911yescharacteristic
474C2×C4C2×#433911yescharacteristic
475C2×C4C2×#434111yescharacteristic
476C2×C4C2×#434111yescharacteristic
477C2×C4C2×#434311yescharacteristic
478C8—42no—
479C8—442no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22#1062227314yes—
487C22C2×#6693111yescharacteristic
488C22C2×#6693811yescharacteristic
489C22C2×#6694711yescharacteristic
490C22D11×AGL(1,ℤ/8)11yescharacteristic
491C22#1062330411yescharacteristic
492C22D11×#13711yescharacteristic
493C22#1062330811yescharacteristic
494C4—44no—
495C4—81no—
496C4—81no—
497C4—222no—
498C4—222no—
499C4—441no—
500C4—441no—
501C4—882no—
502C4—881no—
503C4—881no—
504C4#1062227314yes—
505C4C2×#6692311yescharacteristic
506C4C2×#6693211yescharacteristic
507C4C2×#6694311yescharacteristic
508C4C2×#6695111yescharacteristic
509C2—24no—
510C2C2×#1062227311yescharacteristic
511C2#1307841011yescharacteristic
512C2#1307841811yescharacteristic
513C2#1307855811yescharacteristic
514C2#1307856611yescharacteristic
515C2#1307900711yescharacteristic
516C2#1307901411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#1736D11
hypocenterC11#23747
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
3. #13070189C2semidirect
4. #13070187C2semidirect
5. #13070182C2semidirect
6. #13070177C2semidirect
422. C11#23747semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
#130710192
#130701892
#130701872
#130701822
#130701772
#130683372
#130683362
#130683352
#130683092
C11×#17362
#2374711