Finite Group Databasebeta

← #14811852

Subgroups — #14811852

Order 2816.

786 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071563C211yesmaximal, characteristic
2#13070001C212yesmaximal
3#13069749C212yesmaximal
4#13069569C212yesmaximal, complemented
5#13069374C211yesmaximal, characteristic, complemented
6#13069335C211yesmaximal, characteristic, complemented
7#13069184C212yesmaximal, complemented
8#13068743C211yesmaximal, characteristic, complemented
9#13068613C211yesmaximal, characteristic
10C4×#66873C211yesmaximal, characteristic
11C11×#2551C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8—21no—
13C2×C11×C4⋊Q8C2212yes—
14C2×#66945—21no—
15C2×C4×D44C2211yescharacteristic
16C11×#395—22no—
17C11×#389—21no—
18C11×#389C2212yes—
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22#10622600—21no—
23C2×#66873C2211yescharacteristic
24C2×#66873C2211yescharacteristic
25C2×#66873C2212yes—
26C2×#66871C2212yes—
27#10622552C2212yes—
28#10622548C2211yescharacteristic
29C4×C4⋊Dic11C2212yes—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2212yes—
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622283—22no—
34#10622167C2211yescharacteristic
35#10622167C2212yes—
36#10622167C2212yes—
37#10622167C2212yes—
38#10622167C2211yescharacteristic
39#10622167C2212yes—
40#10622162C2212yes—
41C22×Q8×C11—22no—
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C11×C4⋊Q8—24no—
45C11×C4⋊Q8—42no—
46C11×C4⋊Q8—44no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2312yes—
58C2×C42×C11C2311yescharacteristic
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4×Dic11—22no—
67C22×C11⋊C8C2311yescharacteristic
68C22×C11⋊C8C2311yescharacteristic
69C22×C11⋊C8C2312yes—
70#66945—44no—
71C4×D44—22no—
72C4×D44Q814yescomplemented
73C11×#95—21no—
74C11×#95—22no—
75C11×#95D412yes—
76C11⋊#95—22no—
77#66873—22no—
78#66873—22no—
79#66873—42no—
80#66871—24no—
81C4⋊(C11⋊C8)—22no—
82C4⋊(C11⋊C8)—42no—
83C4×C11⋊C8—22no—
84#26020—111nomaximal, Sylow
85C23×D11—21no—
86C2×Q8×C11—44no—
87C2×Q8×C11—44no—
88C2×Q8×C11—82no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—21no—
98C22×Dic11—22no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×D44C2×Q812yes—
105C2×C4×D11—24no—
106C2×C4×D11—42no—
107C2×C4×D11—42no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—44no—
114C11×C4⋊C4—44no—
115C11×C4⋊C4—42no—
116C11×C4⋊C4—81no—
117C11×C4⋊C4D814yes—
118C11×C4⋊C4#4112yes—
119C11×C4⋊C4#4112yes—
120C42×C11—22no—
121C42×C11—22no—
122C42×C11—42no—
123C42×C11C2×Q812yes—
124C42×C11#4112yes—
125(C2×D11)⋊C4—24no—
126(C2×D11)⋊C4—44no—
127(C2×D11)⋊C4—82no—
128C4⋊Dic11—21no—
129C4⋊Dic11—22no—
130C4⋊Dic11—22no—
131C4⋊Dic11—42no—
132C4⋊Dic11—81no—
133C4⋊Dic11C2×Q812yes—
134C4×Dic11—44no—
135C2×C11⋊C8—21no—
136C2×C11⋊C8—21no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8—21no—
141C2×C11⋊C8—21no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—21no—
144#2551D1111yescharacteristic, complemented
145#2354—111no—
146#2067—112no—
147#2023—112no—
148#1988—112no—
149#1947—111no—
150#1939—111no—
151#1918—112no—
152#1834—111no—
153#1802—111no—
154C4×#102—111no—
155C23×C11C22×D411yescharacteristic
156C22×D11—22no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—41no—
160C22×D11—41no—
161C22×D11—41no—
162C22×D11—41no—
163Q8×C11—88no—
164C2×C4×C11—22no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C22⋊Q812yes—
181C2×C4×C11C22⋊Q812yes—
182C2×C4×C11C2×D814yes—
183C2×C4×C11C2×D812yes—
184C2×C4×C11#13712yes—
185C2×C4×C11C22×Q811yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11H(5,𝔽2)11yescharacteristic
190C2×C4×C112−1+411yescharacteristic
191C2×Dic11—22no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197D44—22no—
198D44—22no—
199D44—41no—
200D44—41no—
201C4×D11—48no—
202C11⋊C8—41no—
203C11⋊C8—42no—
204C11⋊C8—41no—
205C2×C4⋊Q8—21no—
206C2×C4⋊Q8C2×D1112yes—
207C2×C4×D4—111no—
208C2×#117—221no—
209C2×#107—112no—
210C2×C4⋊C8—111no—
211C2×C4⋊C8—112no—
212C2×#102—111no—
213C2×#102—111no—
214C2×#102—112no—
215C2×C4×C8—111no—
216#395—22no—
217#390—112no—
218#389—21no—
219#389C2×D1112yes—
220#388—222no—
221#384—111no—
222#384C2×D1111yescharacteristic
223#380—221no—
224C4×C4⋊C4—112no—
225C4×C4⋊C4C2×D1111yescharacteristic
226C4×C4⋊C4C2×D1111yescharacteristic
227#340—112no—
228#340—112no—
229#340—112no—
230#340—111no—
231#340—112no—
232#340—111no—
233#336—112no—
234C22×C11C2×C22⋊Q811yescharacteristic
235C22×C11#54611yescharacteristic
236C22×C11#54811yescharacteristic
237C22×C11C22×D811yescharacteristic
238C22×C11C2×#13711yescharacteristic
239C22×C11#57711yescharacteristic
240C22×C11#57711yescharacteristic
241C2×D11—42no—
242C2×D11—42no—
243C2×D11—42no—
244C2×D11—81no—
245C2×D11—81no—
246C2×D11—81no—
247C2×D11—81no—
248C4×C11—22no—
249C4×C11—24no—
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—82no—
254C4×C11#47414yes—
255C4×C11#53311yescharacteristic
256C4×C11#54411yescharacteristic
257C4×C11#55511yescharacteristic
258C4×C11#55611yescharacteristic
259Dic11—42no—
260Dic11—82no—
261C22×Q8—22no—
262C22×D4—111no—
263C23×C4—221no—
264C22×C8—111no—
265C22×C8—112no—
266C22×C8—111no—
267C4⋊Q8—24no—
268C4⋊Q8—42no—
269C4⋊Q8—44no—
270C4×D4—114no—
271C4×D4—222no—
272#117—444no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—111no—
278C2×C4⋊C4—112no—
279C2×C4⋊C4—221no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4C22⋊D1111yescharacteristic
282C2×C4⋊C4C22⋊D1111yescharacteristic
283C2×C4⋊C4C22×D1112yes—
284C2×C4⋊C4C22×D1111yescharacteristic
285C2×C4⋊C4C22×D1111yescharacteristic
286C2×C22⋊C4—221no—
287C2×C22⋊C4—222no—
288C2×C22⋊C4—222no—
289C2×C42—21no—
290C2×C42—222no—
291C2×C42C22×D1112yes—
292C2×C42C22×D1111yescharacteristic
293#107—224no—
294C4⋊C8—222no—
295C4⋊C8—442no—
296#102—222no—
297#102—222no—
298#102—442no—
299C4×C8—222no—
300#95—21no—
301#95—22no—
302#95—222no—
303#95C22⋊D1112yes—
304C2×C11#243911yescharacteristic
305C2×C11C2×#47411yescharacteristic
306C2×C11#308411yescharacteristic
307C2×C11#329411yescharacteristic
308C2×C11#332911yescharacteristic
309C2×C11#335811yescharacteristic
310C2×C11#336911yescharacteristic
311D11—82no—
312C24—221no—
313C2×Q8—44no—
314C2×Q8—44no—
315C2×Q8—82no—
316C2×D4—112no—
317C2×D4—221no—
318C2×D4—221no—
319C2×D4—221no—
320C2×D4—221no—
321C2×D4—221no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—221no—
326C22×C4—224no—
327C22×C4—222no—
328C22×C4—442no—
329C22×C4—442no—
330C22×C4C2×C22⋊D1112yes—
331C22×C4C2×C22⋊D1112yes—
332C22×C4C2×C22⋊D1111yescharacteristic
333C22×C4C2×C22⋊D1111yescharacteristic
334C22×C4C23×D1111yescharacteristic
335C2×C8—221no—
336C2×C8—222no—
337C2×C8—221no—
338C2×C8—221no—
339C2×C8—221no—
340C2×C8—221no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—221no—
344C4⋊C4—22no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—44no—
350C4⋊C4—44no—
351C4⋊C4—42no—
352C4⋊C4—81no—
353C4⋊C4—112no—
354C4⋊C4—221no—
355C4⋊C4—222no—
356C4⋊C4—222no—
357C4⋊C4—442no—
358C4⋊C4—881no—
359C4⋊C4#432314yes—
360C4⋊C4#434112yes—
361C4⋊C4#434312yes—
362C22⋊C4—224no—
363C22⋊C4—444no—
364C22⋊C4—882no—
365C42—22no—
366C42—22no—
367C42—42no—
368C42—444no—
369C42Q8×D1112yes—
370C42#434312yes—
371C11#2602011yescharacteristic, complemented, Sylow
372C23—222no—
373C23—441no—
374C23—441no—
375C23—441no—
376C23—441no—
377C23—441no—
378C23—441no—
379C23C22×C22⋊D1111yescharacteristic
380Q8—88no—
381D4—222no—
382D4—222no—
383D4—441no—
384D4—441no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—22no—
388C2×C4—21no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—222no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—448no—
405C2×C4—442no—
406C2×C4—442no—
407C2×C4—442no—
408C2×C4C2×#432314yes—
409C2×C4C2×#432312yes—
410C2×C4#6699512yes—
411C2×C4#6699912yes—
412C2×C4#6699912yes—
413C2×C4C2×#434111yescharacteristic
414C2×C4#6703711yescharacteristic
415C2×C4C2×Q8×D1111yescharacteristic
416C2×C4C2×#434311yescharacteristic
417C2×C4C2×#434311yescharacteristic
418C2×C4#6704011yescharacteristic
419C8—441no—
420C8—442no—
421C8—441no—
422C22—442no—
423C22—442no—
424C22—442no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22C22×#432311yescharacteristic
430C22#1062333711yescharacteristic
431C22C2×#6699511yescharacteristic
432C22C2×#6699911yescharacteristic
433C22#1062334811yescharacteristic
434C22#1062336711yescharacteristic
435C22#1062336811yescharacteristic
436C4—24no—
437C4—22no—
438C4—42no—
439C4—42no—
440C4—42no—
441C4—82no—
442C4—442no—
443C4—882no—
444C4#1062270014yes—
445C4#1062325911yescharacteristic
446C4#1062326011yescharacteristic
447C4#1062326311yescharacteristic
448C4#1062326511yescharacteristic
449C2—882no—
450C2#1307230311yescharacteristic
451C2C2×#1062270011yescharacteristic
452C2#1307847411yescharacteristic
453C2#1308042911yescharacteristic
454C2#1308091011yescharacteristic
455C2#1308125111yescharacteristic
456C2#1308135611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2551C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2551D11
hypocenterC11#26020
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2551

Complements

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

NH ≅ G/Ntype
4. #13069569C2semidirect
5. #13069374C2semidirect
6. #13069335C2semidirect
7. #13069184C2semidirect
8. #13068743C2semidirect
11. C11×#2551C2semidirect
72. C4×D44Q8semidirect
144. #2551D11semidirect
371. C11#26020semidirect

Maximal subgroups

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

subgroupindex
#130715632
#130700012
#130697492
#130695692
#130693742
#130693352
#130691842
#130687432
#130686132
C4×#668732
C11×#25512
#2602011