Finite Group Databasebeta

← #14765283

Subgroups — #14765283

Order 2816.

796 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622343C211yesmaximal, characteristic
2C2×#10622612C211yesmaximal, characteristic, complemented
3#13071873C211yesmaximal, characteristic
4#13069338C212yesmaximal, complemented
5#13069230C212yesmaximal, complemented
6#13069183C212yesmaximal, complemented
7#13068911C211yesmaximal, characteristic
8#13068800C212yesmaximal, complemented
9#13068798C211yesmaximal, characteristic, complemented
10#13068395C211yesmaximal, characteristic, complemented
11C11×#1818C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13C2×C4×C22⋊D11C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C22×#4313C2211yescharacteristic
17C2×C11×C22⋊C8C2211yescharacteristic
18C2×C11×C22⋊C8C2211yescharacteristic
19C4×C22⋊Dic11C2211yescharacteristic
20C2×(C2×D11)⋊C8C2211yescharacteristic
21C2×(C2×D11)⋊C8C2212yes—
22C2×#66879C2211yescharacteristic
23C2×#66879C2212yes—
24C2×Dic11⋊C8C2211yescharacteristic
25C2×Dic11⋊C8C2212yes—
26#10622612—24no—
27#10622606C411yescharacteristic
28#10622605C411yescharacteristic
29#10622595C411yescharacteristic
30#10622593C411yescharacteristic
31#10622572C412yes—
32#10622565C412yes—
33C4×(C2×D11)⋊C4C2212yes—
34C4×Dic11⋊C4C2212yes—
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×C4⋊(C11⋊C8)C2212yes—
37#10622343—24no—
38C11×#336C2212yes—
39C11×#336C2212yes—
40#10622188C2212yes—
41#10622188C2212yes—
42#10622188C2212yes—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11C2×C411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C22×C8×C11C2311yescharacteristic
49C11×#117—22no—
50C11×#117—22no—
51C2×C11×C4⋊C4C2×C411yescharacteristic
52C2×C11×C4⋊C4C2×C411yescharacteristic
53C2×C11×C22⋊C4C2×C412yes—
54C2×C42×C11C2312yes—
55C2×C22⋊Dic11C2×C411yescharacteristic
56C2×C22⋊Dic11C2×C412yes—
57C4×C22⋊D11—22no—
58C4×C22⋊D11—22no—
59C2×(C2×D11)⋊C4C2×C411yescharacteristic
60C2×(C2×D11)⋊C4C2×C412yes—
61C2×(C2×D11)⋊C4C2×C412yes—
62C2×Dic11⋊C4C2×C411yescharacteristic
63C2×Dic11⋊C4C2×C412yes—
64C2×Dic11⋊C4C2×C412yes—
65C2×C4×Dic11C2311yescharacteristic
66C2×C4×Dic11C2312yes—
67C2×#4318—22no—
68C2×#4318—42no—
69C22×C11⋊C8—42no—
70C22×C11⋊C8D414yes—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C2×#4313—22no—
75C2×#4313—42no—
76C11×C22⋊C8—22no—
77C11×C22⋊C8—22no—
78C11⋊#95C2×C412yes—
79C11⋊#95C2×C412yes—
80C11⋊#95C2×C412yes—
81C11⋊#95C2×C412yes—
82C11⋊#95C2×C411yescharacteristic
83C11⋊#95C2×C411yescharacteristic
84(C2×D11)⋊C8—22no—
85(C2×D11)⋊C8—42no—
86#66879—22no—
87#66879—42no—
88Dic11⋊C8—22no—
89Dic11⋊C8—42no—
90C4⋊(C11⋊C8)—24no—
91C4⋊(C11⋊C8)—24no—
92#22070—111nomaximal, Sylow
93C24×C11C22×C411yescharacteristic
94C23×D11C22×C411yescharacteristic
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11#4112yes—
102C22×C4×C11C2411yescharacteristic
103C2×C22⋊D11—22no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C22×Dic11C22×C412yes—
107C22×Dic11C22×C411yescharacteristic
108C22×Dic11C22×C411yescharacteristic
109C22×Dic11C22×C411yescharacteristic
110C22×Dic11C22×C412yes—
111C2×C4×D11—21no—
112C2×C4×D11—21no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C8×C11—21no—
116C2×C8×C11—21no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—22no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C22⋊C4—24no—
125C42×C11—22no—
126C42×C11—22no—
127C22⋊Dic11—22no—
128C22⋊Dic11—42no—
129(C2×D11)⋊C4—22no—
130(C2×D11)⋊C4—42no—
131(C2×D11)⋊C4—42no—
132Dic11⋊C4—22no—
133Dic11⋊C4—42no—
134Dic11⋊C4—42no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—22no—
138C4×Dic11—22no—
139#4318—44no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—44no—
146C2×C11⋊C8C2×D412yes—
147C2×C11⋊C8C2×D412yes—
148#4313—44no—
149C2×#435—111no—
150C2×#424—111no—
151#2395—111no—
152#1940—112no—
153#1924—112no—
154#1917—112no—
155#1870—111no—
156#1851—111no—
157#1851—112no—
158#1818D1111yescharacteristic, complemented
159#1752—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11C4×D412yes—
165C23×C11C23×C411yescharacteristic
166C22×D11—21no—
167C22×D11—22no—
168C22×D11—21no—
169C22×D11—22no—
170C22×D11—21no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—24no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11C4×D412yes—
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11H(5,𝔽2)12yes—
185C2×C4×C112−1+412yes—
186C22⋊D11—44no—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—22no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—21no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—21no—
200C4×D11—41no—
201C4×D11—41no—
202C4×D11—42no—
203C8×C11—41no—
204C8×C11—41no—
205C8×C11—42no—
206C11⋊C8—22no—
207C11⋊C8—22no—
208C11⋊C8—42no—
209C22×M16—111no—
210C22×M16—111no—
211C23×C8—111no—
212C2×C4×D4—111no—
213C2×#117C2×D1111yescharacteristic
214#435—224no—
215#424—224no—
216C2×C4⋊C8—111no—
217C2×C4⋊C8—112no—
218C2×C4⋊C8—112no—
219C2×C4⋊C8—112no—
220C2×C22⋊C8—111no—
221C2×C22⋊C8—112no—
222C2×C22⋊C8C2×D1111yescharacteristic
223C2×C22⋊C8C2×D1111yescharacteristic
224C2×#97—111no—
225C2×#97—112no—
226#400—111no—
227#399—111no—
228#398—111no—
229#397—111no—
230#397—112no—
231#394—112no—
232C4×C4⋊C4—112no—
233C4×C22⋊C4—111no—
234C4×C22⋊C4—112no—
235#336—112no—
236#336—112no—
237#336—112no—
238#336C2×D1112yes—
239#336C2×D1112yes—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11C2×C4×D411yescharacteristic
246C22×C11#52012yes—
247C22×C11#56811yescharacteristic
248C22×C11#56811yescharacteristic
249C22×C11#56812yes—
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C2×D11—42no—
254C2×D11—42no—
255C4×C11—22no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11#53411yescharacteristic
259C4×C11#53611yescharacteristic
260C4×C11#53912yes—
261Dic11—41no—
262Dic11—41no—
263Dic11—41no—
264Dic11—42no—
265Dic11—42no—
266C22×D4—111no—
267C23×C4—111no—
268C23×C4C22×D1111yescharacteristic
269C2×M16—222no—
270C2×M16—222no—
271C2×M16—442no—
272C2×M16—442no—
273C22×C8—111no—
274C22×C8—111no—
275C22×C8—114no—
276C22×C8—112no—
277C22×C8—442no—
278C22×C8C22×D1111yescharacteristic
279C22×C8C22×D1111yescharacteristic
280C22×C8C22×D1112yes—
281C4×D4—222no—
282C4×D4—222no—
283#117—22no—
284#117—22no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4C4×D1111yescharacteristic
289C2×C4⋊C4C4×D1111yescharacteristic
290C2×C22⋊C4—111no—
291C2×C22⋊C4—111no—
292C2×C22⋊C4—112no—
293C2×C22⋊C4—112no—
294C2×C22⋊C4—112no—
295C2×C22⋊C4C4×D1112yes—
296C2×C42—111no—
297C2×C42—112no—
298C2×C42C22×D1112yes—
299C4⋊C8—224no—
300C4⋊C8—224no—
301C4⋊C8—222no—
302C4⋊C8—442no—
303C22⋊C8—22no—
304C22⋊C8—22no—
305C22⋊C8—222no—
306C22⋊C8—442no—
307#97—222no—
308#97—442no—
309#95—112no—
310#95—111no—
311#95—112no—
312#95—111no—
313#95—112no—
314#95—112no—
315C2×C11—42no—
316C2×C11#232211yescharacteristic
317C2×C11#293011yescharacteristic
318C2×C11#293211yescharacteristic
319C2×C11#299512yes—
320C2×C11#299512yes—
321D11—81no—
322C24—111no—
323C24C2×C4×D1111yescharacteristic
324C2×D4—222no—
325C2×D4—441no—
326C2×D4—441no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—112no—
330C22×C4—111no—
331C22×C4—111no—
332C22×C4—112no—
333C22×C4—111no—
334C22×C4—221no—
335C22×C4—221no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4C2×C4×D1112yes—
339C22×C4C2×C4×D1112yes—
340C22×C4C2×C4×D1111yescharacteristic
341C22×C4D4×D1112yes—
342C22×C4#434112yes—
343C22×C4C23×D1111yescharacteristic
344M16—444no—
345M16—444no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—112no—
354C2×C8—112no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8—444no—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—222no—
364C4⋊C4—442no—
365C4⋊C4—442no—
366C22⋊C4—24no—
367C22⋊C4—222no—
368C22⋊C4—222no—
369C22⋊C4—442no—
370C22⋊C4—442no—
371C22⋊C4—442no—
372C42—22no—
373C42—22no—
374C42—221no—
375C42—221no—
376C42—222no—
377C42—222no—
378C11#2207011yescharacteristic, complemented, Sylow
379C23—22no—
380C23—21no—
381C23—21no—
382C23—22no—
383C23—221no—
384C23—221no—
385C23—222no—
386C23—221no—
387C23—222no—
388C23(C22⋊D11)⋊C412yes—
389C23C22×C4×D1111yescharacteristic
390D4—444no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—221no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—221no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—221no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—441no—
415C2×C4—441no—
416C2×C4—442no—
417C2×C4(C22⋊D11)⋊C412yes—
418C2×C4C2×D4×D1111yescharacteristic
419C2×C4C2×#434111yescharacteristic
420C2×C4#6704212yes—
421C2×C4#6704312yes—
422C8—41no—
423C8—41no—
424C8—42no—
425C8—222no—
426C8—222no—
427C8—442no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—42no—
432C22—42no—
433C22—442no—
434C22—442no—
435C22—441no—
436C22—441no—
437C22—441no—
438C22C2×(C22⋊D11)⋊C411yescharacteristic
439C22#1062305412yes—
440C22#1062328111yescharacteristic
441C22#1062328111yescharacteristic
442C22#1062328112yes—
443C4—22no—
444C4—42no—
445C4—42no—
446C4—442no—
447C4—442no—
448C4—441no—
449C4—441no—
450C4—441no—
451C4#1062317911yescharacteristic
452C4#1062318411yescharacteristic
453C4#1062319612yes—
454C2—42no—
455C2—881no—
456C2#1307128211yescharacteristic
457C2#1307732211yescharacteristic
458C2#1307733111yescharacteristic
459C2#1307778112yes—
460C2#1307778112yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1818C2
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1818D11
hypocenterC11#22070
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. C2×#10622612C2semidirect
4. #13069338C2semidirect
5. #13069230C2semidirect
6. #13069183C2semidirect
8. #13068800C2semidirect
9. #13068798C2semidirect
10. #13068395C2semidirect
11. C11×#1818C2semidirect
158. #1818D11semidirect
378. C11#22070semidirect

Maximal subgroups

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

subgroupindex
C2×#106223432
C2×#106226122
#130718732
#130693382
#130692302
#130691832
#130689112
#130688002
#130687982
#130683952
C11×#18182
#2207011