Finite Group Databasebeta

← #14756007

Subgroups — #14756007

Order 2816.

898 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622719C211yesmaximal, characteristic
2#13071240C211yesmaximal, characteristic
3#13070973C211yesmaximal, characteristic
4#13069207C212yesmaximal, complemented
5#13069200C212yesmaximal, complemented
6#13069193C212yesmaximal, complemented
7#13069186C212yesmaximal, complemented
8#13068335C211yesmaximal, characteristic
9#13068335C211yesmaximal, characteristic
10#13068312C211yesmaximal, characteristic
11C2×C11×#340C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19#10622823—22no—
20C4×C22⋊Dic11—22no—
21#10622719C418yescomplemented
22C2×#66882C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×#66881C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26#10622590—21no—
27#10622589—21no—
28C4⋊C4×Dic11—21no—
29C4⋊C4×Dic11—21no—
30C4⋊C4×Dic11C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622586C2212yes—
33#10622586C2212yes—
34C11×#340C2212yes—
35C11×#340C2212yes—
36#10622188C2212yes—
37#10622188C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11—21no—
44C23×C4×C11C2311yescharacteristic
45C22×C8×C11—22no—
46C22×C8×C11—22no—
47C22×C8×C11C2×C414yes—
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4Q814yes—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11D412yes—
61#66979—22no—
62#66979—22no—
63#66979—22no—
64#66979—22no—
65#66979C2×C414yes—
66#66979C2×C414yes—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2311yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11C2312yes—
80C2×#4318—22no—
81C2×#4318—22no—
82C2×#4318—22no—
83C22×C11⋊C8C2312yes—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66882C2×C414yescomplemented
89#66882C2×C414yescomplemented
90#66881C2×C414yescomplemented
91#66881C2×C414yescomplemented
92#21039—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C22×C4×C11—22no—
95C22×C4×C11—24no—
96C22×C4×C11—22no—
97C22×C4×C11—42no—
98C22×C4×C11—81no—
99C22×C4×C11—81no—
100C22×C4×C11—81no—
101C22×C4×C11—81no—
102C22×C4×C11C22×C412yes—
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×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11C2×D412yes—
115C22×Dic11C2×D412yes—
116C2×C8×C11—28no—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11C22×C412yes—
122C2×C8×C11C22×C412yes—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4C2×Q814yes—
129C22⋊Dic11—24no—
130C22⋊Dic11—24no—
131C22⋊Dic11—24no—
132C4⋊Dic11—22no—
133C4⋊Dic11—22no—
134C4⋊Dic11—21no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11C22×C412yes—
139C4⋊Dic11C22×C412yes—
140C4⋊Dic11C22×C412yes—
141C4⋊Dic11C22×C412yes—
142Dic11⋊C4—82no—
143Dic11⋊C4—82no—
144C4×Dic11—24no—
145C4×Dic11—24no—
146C4×Dic11—22no—
147C4×Dic11—22no—
148C4×Dic11—82no—
149C4×Dic11—82no—
150#4318—44no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×#427—111no—
155#2317—111no—
156#2274—111no—
157#1921—112no—
158#1920—112no—
159#1919—112no—
160#1918—112no—
161#1736—111no—
162#1736—111no—
163C2×#340D1111yescharacteristic
164#1729—111no—
165C23×C11—21no—
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11C4×D412yes—
170C23×C11C22⋊Q812yes—
171C23×C11#12312yes—
172C23×C11C22×D411yescharacteristic
173C2×C4×C11—24no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—84no—
180C2×C4×C11—84no—
181C2×C4×C11#11714yes—
182C2×C4×C11C4×D412yes—
183C2×C4×C11C4×Q814yes—
184C2×C4×C11C22⋊Q812yes—
185C2×C4×C11#12312yes—
186C2×C4×C11#12514yes—
187C2×C4×C11#12614yes—
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C22×Q811yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C8×C11—22no—
213C8×C11—22no—
214C11⋊C8—42no—
215C22×M16—111no—
216C23×C8C2×D1111yescharacteristic
217C2×#117—111no—
218C2×#117—111no—
219C2×#117—111no—
220C22×C4⋊C4C2×D1111yescharacteristic
221C22×C4⋊C4C2×D1111yescharacteristic
222#427—118no—
223C2×#107—111no—
224C2×#107—111no—
225C2×#106—111no—
226C2×#106—111no—
227#389—112no—
228#389—112no—
229#385—222no—
230#384—221no—
231#382—221no—
232C4×C4⋊C4—112no—
233C4×C4⋊C4—112no—
234C4×C4⋊C4—221no—
235C4×C4⋊C4—221no—
236C4×C22⋊C4—222no—
237#340—112no—
238#340—112no—
239#340—112no—
240#340—112no—
241#340C2×D1112yes—
242#340C2×D1112yes—
243#336—112no—
244#336—112no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11#38714yes—
252C22×C11C2×C4×D411yescharacteristic
253C22×C11C2×C22⋊Q811yescharacteristic
254C22×C11C2×#12311yescharacteristic
255C22×C11#57611yescharacteristic
256C22×C11#57711yescharacteristic
257C22×C11#57711yescharacteristic
258C22×C11#57811yescharacteristic
259C4×C11—44no—
260C4×C11—82no—
261C4×C11#38714yes—
262C4×C11C2×#11711yescharacteristic
263C4×C11C2×C4×Q811yescharacteristic
264C4×C11C2×#12511yescharacteristic
265C4×C11C2×#12611yescharacteristic
266Dic11—42no—
267Dic11—42no—
268Dic11—42no—
269Dic11—42no—
270Dic11—42no—
271Dic11—42no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4C22×D1111yescharacteristic
275C2×M16—222no—
276C2×M16—222no—
277C2×M16—222no—
278C22×C8—22no—
279C22×C8—22no—
280C22×C8—112no—
281C22×C8C4×D1114yes—
282C22×C8C22×D1111yescharacteristic
283C22×C8C22×D1111yescharacteristic
284#117—114no—
285#117—114no—
286#117—222no—
287#117—222no—
288#117—222no—
289#117—222no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—111no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4Dic2214yes—
304C2×C4⋊C4C22×D1112yes—
305C2×C4⋊C4C22×D1112yes—
306C2×C22⋊C4—112no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—221no—
309C2×C42—112no—
310C2×C42—221no—
311C2×C42—221no—
312C2×C42—222no—
313C2×C42—222no—
314#107—114no—
315#107—114no—
316#106—114no—
317#106—114no—
318#95—222no—
319#95—222no—
320#95—222no—
321#95—222no—
322C2×C11—24no—
323C2×C11C2×#38711yescharacteristic
324C2×C11#295111yescharacteristic
325C2×C11#295211yescharacteristic
326C2×C11#308111yescharacteristic
327C2×C11#308211yescharacteristic
328C2×C11#309611yescharacteristic
329C2×C11#309711yescharacteristic
330C24D4×D1111yescharacteristic
331C22×C4—22no—
332C22×C4—24no—
333C22×C4—22no—
334C22×C4—42no—
335C22×C4—81no—
336C22×C4—81no—
337C22×C4—81no—
338C22×C4—81no—
339C22×C4—112no—
340C22×C4—112no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4C2×Dic2212yes—
346C22×C4C2×C4×D1112yes—
347C22×C4#433912yes—
348C22×C4D4×D1111yescharacteristic
349C22×C4#434112yes—
350C22×C4#434112yes—
351C22×C4#434312yes—
352C22×C4C23×D1111yescharacteristic
353M16—444no—
354C2×C8—28no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—222no—
362C2×C8C2×C4×D1112yes—
363C2×C8C2×C4×D1112yes—
364C4⋊C4—24no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—42no—
369C4⋊C4—112no—
370C4⋊C4—112no—
371C4⋊C4—112no—
372C4⋊C4—112no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—882no—
380C4⋊C4—882no—
381C4⋊C4C2×Dic2214yes—
382C22⋊C4—224no—
383C22⋊C4—224no—
384C22⋊C4—224no—
385C42—224no—
386C42—224no—
387C42—222no—
388C42—222no—
389C42—882no—
390C42—882no—
391C11#2103911yescharacteristic, complemented, Sylow
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23#6693112yes—
397C23#6693612yes—
398C23#6694612yes—
399C23C2×D4×D1111yescharacteristic
400C2×C4—24no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—84no—
407C2×C4—84no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4C4×Dic2214yes—
427C2×C4#6693014yes—
428C2×C4#6693112yes—
429C2×C4#6693612yes—
430C2×C4#6694314yes—
431C2×C4#6694612yes—
432C2×C4#6695114yes—
433C2×C4C22×Dic2211yescharacteristic
434C2×C4C22×C4×D1111yescharacteristic
435C2×C4C2×#433911yescharacteristic
436C2×C4C2×#434111yescharacteristic
437C2×C4C2×#434111yescharacteristic
438C2×C4C2×#434311yescharacteristic
439C8—22no—
440C8—22no—
441C8—442no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22#1062226714yes—
449C22C2×#6693111yescharacteristic
450C22C2×#6693611yescharacteristic
451C22C2×#6694611yescharacteristic
452C22#1062328811yescharacteristic
453C22#1062329311yescharacteristic
454C22#1062329311yescharacteristic
455C22#1062329711yescharacteristic
456C4—44no—
457C4—82no—
458C4—442no—
459C4—442no—
460C4—442no—
461C4—442no—
462C4—442no—
463C4—442no—
464C4#1062226714yes—
465C4C2×C4×Dic2211yescharacteristic
466C4C2×#6693011yescharacteristic
467C4C2×#6694311yescharacteristic
468C4C2×#6695111yescharacteristic
469C2—24no—
470C2C2×#1062226711yescharacteristic
471C2#1307749011yescharacteristic
472C2#1307749911yescharacteristic
473C2#1307844311yescharacteristic
474C2#1307845411yescharacteristic
475C2#1307857011yescharacteristic
476C2#1307858111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#340D11
hypocenterC11#21039
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
4. #13069207C2semidirect
5. #13069200C2semidirect
6. #13069193C2semidirect
7. #13069186C2semidirect
21. #10622719C4semidirect
88. #66882C2×C4semidirect
89. #66882C2×C4semidirect
90. #66881C2×C4semidirect
91. #66881C2×C4semidirect
391. C11#21039semidirect

Maximal subgroups

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

subgroupindex
C2×#106227192
#130712402
#130709732
#130692072
#130692002
#130691932
#130691862
#130683352
#130683122
C2×C11×#3402
#2103911