Finite Group Databasebeta

← #14780323

Subgroups — #14780323

Order 2816.

944 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66927C211yesmaximal, characteristic
2#13068912C212yesmaximal, complemented
3#13068912C212yesmaximal, complemented
4#13068912C212yesmaximal, complemented
5#13068907C212yesmaximal, complemented
6#13068907C212yesmaximal, complemented
7#13068907C212yesmaximal, complemented
8#13068759C211yesmaximal, characteristic, complemented
9C11×#1839C211yesmaximal, characteristic, complemented
10C22×#4313C2212yes—
11C22×C8×D11C2212yes—
12C2×#66927C411yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×C4×D44C2212yes—
15C2×C4×D44C2212yes—
16C2×C4×D44C2211yescharacteristic
17C43×C11C2211yescharacteristic
18C2×(C2×D11)⋊C8C2212yes—
19C2×(C2×D11)⋊C8C2212yes—
20C2×(C2×D11)⋊C8C2212yes—
21C2×(C2×D11)⋊C8C2212yes—
22C2×(C2×D11)⋊C8C2212yes—
23C2×(C2×D11)⋊C8C2212yes—
24#10622552C412yes—
25#10622552C412yes—
26#10622552C411yescharacteristic
27#10622552C411yescharacteristic
28#10622548C411yescharacteristic
29C11×#336C2211yescharacteristic
30C11×#336C2212yes—
31C11×#336C2212yes—
32C11×#336C2211yescharacteristic
33#10622162C2211yescharacteristic
34#10622162C2212yes—
35#10622162C2212yes—
36#10622162C2211yescharacteristic
37C22×D44C2×C412yes—
38C22×D44C2×C412yes—
39C22×D44C2×C411yescharacteristic
40C22×D44C2×C411yescharacteristic
41C22×C4×D11C2312yes—
42C22×C4×D11C2312yes—
43C22×C8×C11C2312yes—
44C22×C8×C11C2312yes—
45C2×C42×C11C2×C411yescharacteristic
46C2×C42×C11C2×C411yescharacteristic
47C2×C42×C11C2×C411yescharacteristic
48C2×C42×C11C2×C411yescharacteristic
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×(C2×D11)⋊C4C2×C412yes—
53C2×(C2×D11)⋊C4C2×C412yes—
54C2×(C2×D11)⋊C4C2×C412yes—
55C2×(C2×D11)⋊C4C2×C412yes—
56C2×(C2×D11)⋊C4C2×C412yes—
57C2×(C2×D11)⋊C4C2×C412yes—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C2×C4⋊Dic11C2×C411yescharacteristic
60C2×C4⋊Dic11C2×C412yes—
61C2×C4⋊Dic11C2×C412yes—
62C22×C11⋊C8C2312yes—
63C22×C11⋊C8C2312yes—
64C2×#4313—42no—
65C2×#4313—42no—
66C2×#4313—42no—
67C2×C8×D11—42no—
68C2×C8×D11—42no—
69C2×C8×D11—42no—
70#66927—24no—
71C4×D44—41no—
72C4×D44—42no—
73C4×D44—42no—
74C4×D44—41no—
75C4×D44—41no—
76C4×D44—42no—
77C4×D44—42no—
78C4×D44—41no—
79(C2×D11)⋊C8—42no—
80(C2×D11)⋊C8—42no—
81(C2×D11)⋊C8—42no—
82(C2×D11)⋊C8—42no—
83(C2×D11)⋊C8—42no—
84(C2×D11)⋊C8—42no—
85#23356—111nomaximal, Sylow
86C23×D11C22×C412yes—
87C23×D11C22×C412yes—
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2411yescharacteristic
95C22×Dic11C22×C412yes—
96C22×Dic11C22×C412yes—
97C2×D44—24no—
98C2×D44—24no—
99C2×D44—22no—
100C2×D44—24no—
101C2×D44—24no—
102C2×D44—41no—
103C2×D44—42no—
104C2×D44—42no—
105C2×D44—41no—
106C2×D44—41no—
107C2×D44—41no—
108C2×D44M1614yescomplemented
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—22no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C42×C11—22no—
128C42×C11—22no—
129C42×C11—22no—
130C42×C11—21no—
131C42×C11—21no—
132C42×C11—22no—
133C42×C11—22no—
134C42×C11—41no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141C4⋊Dic11—41no—
142C4⋊Dic11—41no—
143C4⋊Dic11—42no—
144C4⋊Dic11—42no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151#4313—48no—
152C8×D11—48no—
153C4×#127—111no—
154#1870—112no—
155#1870—112no—
156#1870—112no—
157#1869—112no—
158#1869—112no—
159#1869—112no—
160#1839—111no—
161#1839D1111yescharacteristic, complemented
162C23×C11C23×C411yescharacteristic
163C22×D11—22no—
164C22×D11—22no—
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—22no—
176C22×D11C2×M1614yes—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
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×C11C2×M1612yes—
193C2×C4×C11#13112yes—
194C2×C4×C11#13112yes—
195C2×C4×C11H(5,𝔽2)11yescharacteristic
196C2×C4×C11H(5,𝔽2)11yescharacteristic
197C2×C4×C11H(5,𝔽2)12yes—
198C2×C4×C11H(5,𝔽2)12yes—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205D44—44no—
206D44—48no—
207D44—48no—
208D44—44no—
209C4×D11—42no—
210C4×D11—42no—
211C4×D11—42no—
212C4×D11—42no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—42no—
217C8×C11—42no—
218C8×C11—42no—
219C11⋊C8—42no—
220C11⋊C8—42no—
221C22×M16—112no—
222C23×C8—112no—
223C2×#127—111no—
224C2×C4×D4—111no—
225C2×C4×D4—112no—
226C2×C4×D4—112no—
227C2×C4×D4—111no—
228C2×C22⋊C8—112no—
229C2×C22⋊C8—112no—
230C2×C22⋊C8—112no—
231C2×C22⋊C8—112no—
232C2×C22⋊C8—112no—
233C2×C22⋊C8—112no—
234#390—112no—
235#390—112no—
236#390—111no—
237#390—111no—
238#384—111no—
239C43C2×D1111yescharacteristic
240#336—111no—
241#336—112no—
242#336—112no—
243#336—111no—
244#336C2×D1111yescharacteristic
245#336C2×D1112yes—
246#336C2×D1112yes—
247#336C2×D1111yescharacteristic
248C22×C11#51811yescharacteristic
249C22×C11#51811yescharacteristic
250C22×C11#51811yescharacteristic
251C22×C11C22×M1611yescharacteristic
252C22×C11C2×#13111yescharacteristic
253C22×C11C2×#13111yescharacteristic
254C22×C11#56811yescharacteristic
255C2×D11—24no—
256C2×D11—24no—
257C2×D11—24no—
258C2×D11—42no—
259C2×D11—42no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—22no—
272C4×C11—41no—
273C4×C11—41no—
274C4×C11—41no—
275C4×C11#56012yes—
276C4×C11#56012yes—
277Dic11—42no—
278Dic11—42no—
279C22×D4—111no—
280C22×D4—112no—
281C22×D4—112no—
282C22×D4—111no—
283C23×C4—112no—
284C23×C4—112no—
285C2×M16—442no—
286C2×M16—442no—
287C2×M16—442no—
288C22×C8—112no—
289C22×C8—112no—
290C22×C8—442no—
291C22×C8—442no—
292C22×C8—442no—
293C22×C8C22×D1112yes—
294C22×C8C22×D1112yes—
295#127—224no—
296C4×D4—441no—
297C4×D4—442no—
298C4×D4—442no—
299C4×D4—441no—
300C4×D4—441no—
301C4×D4—442no—
302C4×D4—442no—
303C4×D4—441no—
304C2×C4⋊C4—112no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—111no—
307C2×C4⋊C4—112no—
308C2×C22⋊C4—112no—
309C2×C22⋊C4—112no—
310C2×C22⋊C4—112no—
311C2×C22⋊C4—112no—
312C2×C22⋊C4—112no—
313C2×C22⋊C4—112no—
314C2×C42C4×D1111yescharacteristic
315C2×C42C4×D1111yescharacteristic
316C2×C42C4×D1111yescharacteristic
317C2×C42C4×D1111yescharacteristic
318C2×C42C22×D1111yescharacteristic
319C2×C42C22×D1111yescharacteristic
320C2×C42C22×D1111yescharacteristic
321C22⋊C8—442no—
322C22⋊C8—442no—
323C22⋊C8—442no—
324C22⋊C8—442no—
325C22⋊C8—442no—
326C22⋊C8—442no—
327C2×C11#238011yescharacteristic
328C2×C11#297311yescharacteristic
329C2×C11#297411yescharacteristic
330C2×C11#297411yescharacteristic
331C2×C11#297911yescharacteristic
332C2×C11#298111yescharacteristic
333C2×C11#298111yescharacteristic
334D11—44no—
335D11—82no—
336C24—112no—
337C24—112no—
338C2×D4—114no—
339C2×D4—224no—
340C2×D4—224no—
341C2×D4—224no—
342C2×D4—222no—
343C2×D4—224no—
344C2×D4—441no—
345C2×D4—442no—
346C2×D4—442no—
347C2×D4—441no—
348C2×D4—441no—
349C2×D4—441no—
350C22×C4—112no—
351C22×C4—112no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4C2×C4×D1111yescharacteristic
365C22×C4C2×C4×D1111yescharacteristic
366C22×C4C2×C4×D1111yescharacteristic
367C22×C4C2×C4×D1111yescharacteristic
368C22×C4C2×C4×D1111yescharacteristic
369C22×C4C2×C4×D1111yescharacteristic
370C22×C4C23×D1111yescharacteristic
371M16—448no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—222no—
379C2×C8—222no—
380C2×C8—222no—
381C2×C8—222no—
382C2×C8—222no—
383C2×C8—222no—
384C2×C8—448no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—442no—
388C4⋊C4—442no—
389C22⋊C4—442no—
390C22⋊C4—442no—
391C22⋊C4—442no—
392C22⋊C4—442no—
393C22⋊C4—442no—
394C22⋊C4—442no—
395C42—22no—
396C42—22no—
397C42—22no—
398C42—21no—
399C42—21no—
400C42—22no—
401C42—22no—
402C42—41no—
403C11#2335611yescharacteristic, complemented, Sylow
404C23—114no—
405C23—222no—
406C23—222no—
407C23—222no—
408C23—222no—
409C23—222no—
410C23—222no—
411C23—222no—
412C23—222no—
413C23—222no—
414C23—222no—
415C23—222no—
416C23—222no—
417C23—222no—
418C23C22×C4×D1111yescharacteristic
419D4—444no—
420D4—448no—
421D4—448no—
422D4—444no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—222no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4#6695412yes—
453C2×C4M16×D1112yes—
454C2×C4#6696012yes—
455C2×C4#6704211yescharacteristic
456C2×C4#6704211yescharacteristic
457C2×C4#6704212yes—
458C2×C4#6704212yes—
459C8—42no—
460C8—42no—
461C8—442no—
462C8—442no—
463C22—224no—
464C22—224no—
465C22—224no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22—442no—
472C22—442no—
473C22—442no—
474C22—442no—
475C22—442no—
476C22—442no—
477C22#1062305211yescharacteristic
478C22#1062305211yescharacteristic
479C22#1062305211yescharacteristic
480C22C2×#6695411yescharacteristic
481C22C2×M16×D1111yescharacteristic
482C22C2×#6696011yescharacteristic
483C22#1062327611yescharacteristic
484C4—22no—
485C4—22no—
486C4—22no—
487C4—41no—
488C4—41no—
489C4—41no—
490C4—442no—
491C4—442no—
492C4#1062324212yes—
493C4#1062324212yes—
494C2—444no—
495C2—882no—
496C2#1307179211yescharacteristic
497C2#1307764411yescharacteristic
498C2#1307765011yescharacteristic
499C2#1307765311yescharacteristic
500C2#1307768211yescharacteristic
501C2#1307769111yescharacteristic
502C2#1307769411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1839C2
prime radicalC2×#66927C4
cosocleC22×C4×C11C24
hypercenter#1839D11
hypocenterC11#23356
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1839

Complements

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

NH ≅ G/Ntype
2. #13068912C2semidirect
3. #13068912C2semidirect
4. #13068912C2semidirect
5. #13068907C2semidirect
6. #13068907C2semidirect
7. #13068907C2semidirect
8. #13068759C2semidirect
9. C11×#1839C2semidirect
108. C2×D44M16semidirect
161. #1839D11semidirect
403. C11#23356semidirect

Maximal subgroups

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

subgroupindex
C4×#669272
#130689122
#130689072
#130687592
C11×#18392
#2335611