Finite Group Databasebeta

← #14765264

Subgroups — #14765264

Order 2816.

816 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×#10622724C211yesmaximal, characteristic
2#13071873C211yesmaximal, characteristic
3#13069331C212yesmaximal, complemented
4#13069221C212yesmaximal, complemented
5#13069177C212yesmaximal, complemented
6#13068913C211yesmaximal, characteristic
7#13068799C211yesmaximal, characteristic, complemented
8#13068797C212yesmaximal, complemented
9#13068687C211yesmaximal, characteristic, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C2×C11×#424C211yesmaximal, characteristic, complemented
12C22×C11×M16C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×C4×C22⋊D11C2211yescharacteristic
16C22×#4313C2211yescharacteristic
17C11×#424—24no—
18C2×C11×C4⋊C8C2212yes—
19C2×C11×C4⋊C8C2212yes—
20C4×C22⋊Dic11C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23#10622724—24no—
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×(C2×D11)⋊C8C2212yes—
26C2×#66879C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2212yes—
29C2×C8×Dic11C2212yes—
30#10622606C411yescharacteristic
31#10622605C411yescharacteristic
32#10622595C411yescharacteristic
33#10622593C411yescharacteristic
34#10622572C412yes—
35#10622565C412yes—
36C4×(C2×D11)⋊C4C2212yes—
37C4×Dic11⋊C4C2212yes—
38#10622188C2212yes—
39#10622188C2212yes—
40#10622188C2212yes—
41#10622162C2212yes—
42#10622162C2212yes—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11C2×C411yescharacteristic
45C22×C4×D11C2311yescharacteristic
46C2×C11×M16—22no—
47C2×C11×M16—42no—
48C22×C8×C11—42no—
49C22×C8×C11D414yes—
50C22×C8×C11C2312yes—
51C22×C8×C11C2311yescharacteristic
52C22×C8×C11C2311yescharacteristic
53C11×#117—22no—
54C11×#117—22no—
55C2×C11×C4⋊C4C2×C411yescharacteristic
56C2×C11×C4⋊C4C2×C411yescharacteristic
57C2×C11×C22⋊C4C2×C412yes—
58C2×C42×C11C2312yes—
59C2×C22⋊Dic11C2×C411yescharacteristic
60C2×C22⋊Dic11C2×C412yes—
61C4×C22⋊D11—22no—
62C4×C22⋊D11—22no—
63C2×(C2×D11)⋊C4C2×C412yes—
64C2×(C2×D11)⋊C4C2×C411yescharacteristic
65C2×(C2×D11)⋊C4C2×C412yes—
66C2×Dic11⋊C4C2×C412yes—
67C2×Dic11⋊C4C2×C411yescharacteristic
68C2×Dic11⋊C4C2×C412yes—
69C2×C4×Dic11C2311yescharacteristic
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74C2×#4313—22no—
75C2×#4313—42no—
76C11×C4⋊C8—24no—
77C11×C4⋊C8—24no—
78C11⋊#95C2×C412yes—
79C11⋊#95C2×C412yes—
80C11⋊#95C2×C412yes—
81C11⋊#95C2×C412yes—
82C11⋊#95C2×C411yescharacteristic
83C11⋊#95C2×C411yescharacteristic
84C22⋊(C11⋊C8)—22no—
85C22⋊(C11⋊C8)—22no—
86(C2×D11)⋊C8—22no—
87(C2×D11)⋊C8—42no—
88#66879—22no—
89Dic11⋊C8—22no—
90Dic11⋊C8—42no—
91C8×Dic11—42no—
92#22068—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—
115C11×M16—44no—
116C2×C8×C11—22no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11—22no—
121C2×C8×C11—44no—
122C2×C8×C11C2×D412yes—
123C2×C8×C11C2×D412yes—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C22⋊C4—24no—
127C42×C11—22no—
128C42×C11—22no—
129C22⋊Dic11—24no—
130C22⋊Dic11—22no—
131(C2×D11)⋊C4—24no—
132(C2×D11)⋊C4—22no—
133(C2×D11)⋊C4—42no—
134Dic11⋊C4—24no—
135Dic11⋊C4—22no—
136Dic11⋊C4—42no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139C4×Dic11—22no—
140C4×Dic11—22no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—21no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148#4313—44no—
149C2×#435—111no—
150C2×#424D1111yescharacteristic, complemented
151#2395—111no—
152#1939—112no—
153#1923—112no—
154#1917—112no—
155#1870—111no—
156#1851—112no—
157#1851—111no—
158#1818—111no—
159C8×C22⋊C4—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—22no—
169C22×D11—21no—
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—22no—
188C2×Dic11—22no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—21no—
197C2×Dic11—22no—
198C2×Dic11—21no—
199C2×Dic11#13114yes—
200C4×D11—41no—
201C4×D11—41no—
202C4×D11—42no—
203C8×C11—22no—
204C8×C11—22no—
205C8×C11—42no—
206C11⋊C8—41no—
207C11⋊C8—41no—
208C11⋊C8—42no—
209C22×M16—111no—
210C22×M16C2×D1111yescharacteristic
211C23×C8C2×D1111yescharacteristic
212C2×C4×D4—111no—
213C2×#117C2×D1111yescharacteristic
214#435—224no—
215#424—24no—
216C2×C4⋊C8—111no—
217C2×C4⋊C8—112no—
218C2×C4⋊C8C2×D1112yes—
219C2×C4⋊C8C2×D1112yes—
220C2×C22⋊C8—111no—
221C2×C22⋊C8—111no—
222C2×C22⋊C8—111no—
223C2×C22⋊C8—112no—
224C2×#97—111no—
225C2×C4×C8—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#336—112no—
239#336—112no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—42no—
244C22×C11—42no—
245C22×C11C2×C4×D411yescharacteristic
246C22×C11#52012yes—
247C22×C11C2×#13112yes—
248C22×C11#56811yescharacteristic
249C22×C11#56811yescharacteristic
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—24no—
262Dic11—41no—
263Dic11—41no—
264Dic11—41no—
265Dic11—42no—
266C22×D4—111no—
267C23×C4—111no—
268C23×C4C22×D1111yescharacteristic
269C2×M16—22no—
270C2×M16—42no—
271C2×M16—222no—
272C2×M16—442no—
273C22×C8—42no—
274C22×C8—111no—
275C22×C8—112no—
276C22×C8—111no—
277C22×C8C22⋊D1114yes—
278C22×C8C22×D1112yes—
279C22×C8C22×D1111yescharacteristic
280C22×C8C22×D1111yescharacteristic
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—112no—
292C2×C22⋊C4—111no—
293C2×C22⋊C4—112no—
294C2×C22⋊C4—112no—
295C2×C22⋊C4C4×D1112yes—
296C2×C42—111no—
297C2×C42—112no—
298C2×C42C22×D1112yes—
299C4⋊C8—24no—
300C4⋊C8—24no—
301C4⋊C8—222no—
302C4⋊C8—442no—
303C22⋊C8—222no—
304C22⋊C8—222no—
305C22⋊C8—222no—
306C22⋊C8—442no—
307#97—222no—
308C4×C8—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#293111yescharacteristic
319C2×C11#299212yes—
320C2×C11#299312yes—
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—112no—
331C22×C4—111no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—221no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—221no—
338C22×C4C2×C4×D1112yes—
339C22×C4C2×C4×D1112yes—
340C22×C4C2×C4×D1111yescharacteristic
341C22×C4#433912yes—
342C22×C4C2×C22⋊D1112yes—
343C22×C4C23×D1111yescharacteristic
344M16—44no—
345M16—444no—
346C2×C8—22no—
347C2×C8—22no—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—44no—
352C2×C8—222no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8—222no—
356C2×C8—222no—
357C2×C8—221no—
358C2×C8—221no—
359C2×C8C2×C22⋊D1112yes—
360C2×C8C2×C22⋊D1112yes—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—224no—
364C4⋊C4—222no—
365C4⋊C4—442no—
366C22⋊C4—24no—
367C22⋊C4—224no—
368C22⋊C4—224no—
369C22⋊C4—222no—
370C22⋊C4—222no—
371C22⋊C4—442no—
372C42—22no—
373C42—22no—
374C42—221no—
375C42—222no—
376C42—222no—
377C42—221no—
378C11#2206811yescharacteristic, complemented, Sylow
379C23—22no—
380C23—21no—
381C23—21no—
382C23—22no—
383C23—222no—
384C23—221no—
385C23—221no—
386C23—222no—
387C23—221no—
388C23C4×C22⋊D1112yes—
389C23C22×C4×D1111yescharacteristic
390D4—444no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—114no—
402C2×C4—222no—
403C2×C4—222no—
404C2×C4—222no—
405C2×C4—222no—
406C2×C4—222no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—221no—
414C2×C4—442no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4C4×C22⋊D1112yes—
418C2×C4C2×#433911yescharacteristic
419C2×C4#6703712yes—
420C2×C4#6704012yes—
421C2×C4C22×C22⋊D1111yescharacteristic
422C8—22no—
423C8—22no—
424C8—42no—
425C8—442no—
426C8—441no—
427C8—441no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—42no—
432C22—42no—
433C22—442no—
434C22—441no—
435C22—441no—
436C22—441no—
437C22—442no—
438C22#1062303512yes—
439C22D11×#13112yes—
440C22#1062328111yescharacteristic
441C22#1062328111yescharacteristic
442C22C2×C4×C22⋊D1111yescharacteristic
443C4—22no—
444C4—42no—
445C4—42no—
446C4—224no—
447C4—442no—
448C4—441no—
449C4—441no—
450C4—441no—
451C4#1062304612yes—
452C4#1062333511yescharacteristic
453C4#1062334711yescharacteristic
454C2—42no—
455C2—881no—
456C2#1307128511yescharacteristic
457C2#1307731711yescharacteristic
458C2#1307732611yescharacteristic
459C2#1307775312yes—
460C2#1307776312yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC2×C11×#424C2
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×#424D11
hypocenterC11#22068
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#424

Complements

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

NH ≅ G/Ntype
3. #13069331C2semidirect
4. #13069221C2semidirect
5. #13069177C2semidirect
7. #13068799C2semidirect
8. #13068797C2semidirect
9. #13068687C2semidirect
10. C8×C22⋊Dic11C2semidirect
11. C2×C11×#424C2semidirect
150. C2×#424D11semidirect
378. C11#22068semidirect

Maximal subgroups

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

subgroupindex
C2×#106227242
#130718732
#130693312
#130692212
#130691772
#130689132
#130687992
#130687972
#130686872
C8×C22⋊Dic112
C2×C11×#4242
#2206811