Finite Group Databasebeta

← #14807431

Subgroups — #14807431

Order 2816.

1094 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623049C211yesmaximal, characteristic, complemented
2C2×#10622673C211yesmaximal, characteristic, complemented
3C2×#10622669C211yesmaximal, characteristic, complemented
4#13069624C212yesmaximal, complemented
5#13069619C212yesmaximal
6#13069584C211yesmaximal, characteristic, complemented
7#13069417C211yesmaximal, characteristic, complemented
8#13068974C212yesmaximal, complemented
9#13068960C212yesmaximal, complemented
10#13068382C211yesmaximal, characteristic, complemented
11C11×#2620C211yesmaximal, characteristic
12C2×C11×#124C2211yescharacteristic
13C2×C11×C22⋊Q8C2211yescharacteristic
14C2×C11×#121C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×#4326C2212yes—
17C22×#4324C2212yes—
18C2×#66977C2212yes—
19#10623049—24no—
20#10623049—24no—
21C2×#66942—22no—
22C2×#66932—22no—
23C2×#66923C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22C2212yes—
26C11×#396—22no—
27C11×#394—22no—
28C11×#391C2211yescharacteristic
29C11×#390C2211yescharacteristic
30C11×#384C2211yescharacteristic
31C2×#66899C2212yes—
32C2×#66896C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622673—24no—
35#10622669—24no—
36C2×#66874C2212yes—
37C2×#66874C2212yes—
38C2×#66867C2211yescharacteristic
39C2×C4×C11⋊C8C2211yescharacteristic
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11—21no—
45C22×D4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C22×Dic22C2312yes—
48C11×#124—22no—
49C11×#124—22no—
50C11×C22⋊Q8—42no—
51C11×#121—42no—
52C11×#117—22no—
53C11×#117—22no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—22no—
63C2×C11×C22⋊C4D412yes—
64C2×C42×C11C2311yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C22⋊Dic11—22no—
67C2×#4326—24no—
68C2×#4326—24no—
69C2×#4326—42no—
70C2×#4324—24no—
71C2×#4324—24no—
72C2×#4324—42no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11C2312yes—
75#66977—24no—
76#66977—24no—
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—22no—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2312yes—
83#66942—216no—
84#66932—216no—
85#66923—22no—
86#66923D414yescomplemented
87#66922—22no—
88#66922D414yescomplemented
89C4×Dic22—24no—
90C4×Dic22—24no—
91C11×#95—22no—
92#66899—24no—
93#66896—24no—
94C22⋊(C11⋊C8)—24no—
95#66874—42no—
96#66874—42no—
97#66867—22no—
98C4×C11⋊C8—22no—
99#25612—111nomaximal, Sylow
100C24×C11—21no—
101C24×C11C2×D411yescharacteristic
102C2×Q8×C11—21no—
103C2×Q8×C11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×D4×C11—21no—
107C2×D4×C11—21no—
108C2×D4×C11—22no—
109C2×D4×C11—22no—
110C2×D4×C11—42no—
111C2×D4×C11—82no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—22no—
124C22×Dic11—22no—
125C2×Dic22—22no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22C2×D414yes—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—42no—
135C11×C4⋊C4—82no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—42no—
138C11×C22⋊C4—42no—
139C11×C22⋊C4—44no—
140C11×C22⋊C4—82no—
141C42×C11—21no—
142C42×C11—21no—
143C42×C11C2×D412yes—
144C42×C11C2×D412yes—
145C22⋊Dic11—28no—
146#4326—48no—
147#4324—48no—
148C4⋊Dic11—28no—
149C4⋊Dic11—22no—
150C4⋊Dic11C2×D414yes—
151Dic11⋊C4—28no—
152Dic11⋊C4—28no—
153Dic11⋊C4—28no—
154C4×Dic11—28no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8#4114yes—
161C2×#541—111no—
162C2×#497—111no—
163C2×#488—111no—
164#2620D1111yescharacteristic
165#2001—112no—
166#2000—112no—
167#1992—111no—
168#1956—111no—
169#1880—112no—
170#1878—112no—
171#1750—111no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—21no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—41no—
178C23×C11—41no—
179C23×C11—41no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11C22×D411yescharacteristic
183Q8×C11—42no—
184Q8×C11—42no—
185D4×C11—42no—
186D4×C11—42no—
187D4×C11—84no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11#12014yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C2×#4112yes—
209C2×C4×C11H(5,𝔽2)12yes—
210C2×Dic11—24no—
211C2×Dic11—24no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216Dic22—24no—
217Dic22—24no—
218Dic22—42no—
219Dic22—42no—
220C11⋊C8—24no—
221C11⋊C8—42no—
222C22×Q16—112no—
223C22×SD16—112no—
224#541—224no—
225#541—224no—
226C2×C4⋊Q8—111no—
227C2×#126—222no—
228C2×#125—111no—
229C2×#125—222no—
230C2×#124C2×D1111yescharacteristic
231C2×C22⋊Q8—112no—
232C2×C22⋊Q8C2×D1111yescharacteristic
233C2×#121C2×D1111yescharacteristic
234C2×C4×Q8—112no—
235C2×#117C2×D1111yescharacteristic
236#497—224no—
237#488—224no—
238C2×#103—112no—
239C2×#103—112no—
240C2×#103—112no—
241C2×#102—112no—
242C2×C22⋊C8—112no—
243C2×#97—111no—
244C2×C4×C8—111no—
245#396—22no—
246#394—22no—
247#391C2×D1111yescharacteristic
248#390C2×D1111yescharacteristic
249#384C2×D1111yescharacteristic
250#340—112no—
251#340—112no—
252#336—112no—
253C22×C11—42no—
254C22×C11—41no—
255C22×C11—41no—
256C22×C11—41no—
257C22×C11—42no—
258C22×C11—82no—
259C22×C11—81no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—82no—
263C22×C11C2×#12011yescharacteristic
264C22×C11#53211yescharacteristic
265C22×C11#53511yescharacteristic
266C22×C11#57712yes—
267C22×C11#57812yes—
268C4×C11—24no—
269C4×C11—41no—
270C4×C11—42no—
271C4×C11—81no—
272C4×C11—81no—
273C4×C11—81no—
274C4×C11#54612yes—
275C4×C11#55012yes—
276Dic11—44no—
277Dic11—44no—
278C22×Q8—112no—
279C22×Q8C22×D1111yescharacteristic
280C22×D4—21no—
281C22×D4C22×D1111yescharacteristic
282C23×C4C22×D1111yescharacteristic
283C2×Q16—224no—
284C2×Q16—224no—
285C2×Q16—442no—
286C2×SD16—224no—
287C2×SD16—224no—
288C2×SD16—442no—
289C22×C8—112no—
290C22×C8—112no—
291C4⋊Q8—114no—
292C4⋊Q8—222no—
293#126—2216no—
294#125—114no—
295#125—2216no—
296#125—222no—
297#124—22no—
298#124—22no—
299C22⋊Q8—42no—
300C22⋊Q8—224no—
301C22⋊Q8—224no—
302#121—42no—
303C4×Q8—224no—
304C4×Q8—224no—
305#117—22no—
306#117—22no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4C22⋊D1112yes—
315C2×C4⋊C4C22×D1111yescharacteristic
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4C22⋊D1112yes—
323C2×C42—222no—
324C2×C42C22×D1111yescharacteristic
325C2×C42C22×D1111yescharacteristic
326#103—224no—
327#103—442no—
328#103—442no—
329#102—224no—
330C22⋊C8—224no—
331#97—222no—
332C4×C8—222no—
333#95—22no—
334C2×C11—81no—
335C2×C11—161no—
336C2×C11#243111yescharacteristic
337C2×C11#301312yes—
338C2×C11#317812yes—
339C2×C11#322211yescharacteristic
340C2×C11#322311yescharacteristic
341C24—21no—
342C24C2×C22⋊D1111yescharacteristic
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—114no—
348C2×Q8—222no—
349C2×Q8—222no—
350C2×Q8—222no—
351C2×Q8—222no—
352C2×Q8—222no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—42no—
358C2×D4—82no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4C2×C22⋊D1112yes—
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1112yes—
371C22×C4C23×D1111yescharacteristic
372Q16—448no—
373SD16—448no—
374C2×C8—114no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C2×C8—222no—
379C2×C8—222no—
380C4⋊C4—24no—
381C4⋊C4—22no—
382C4⋊C4—22no—
383C4⋊C4—42no—
384C4⋊C4—82no—
385C4⋊C4—114no—
386C4⋊C4—228no—
387C4⋊C4—228no—
388C4⋊C4—228no—
389C4⋊C4—228no—
390C4⋊C4—222no—
391C22⋊C4—24no—
392C22⋊C4—42no—
393C22⋊C4—42no—
394C22⋊C4—44no—
395C22⋊C4—82no—
396C22⋊C4—228no—
397C42—21no—
398C42—21no—
399C42—228no—
400C42D4×D1112yes—
401C42D4×D1112yes—
402C11#2561211yescharacteristic, complemented, Sylow
403C23—21no—
404C23—21no—
405C23—21no—
406C23—22no—
407C23—22no—
408C23—41no—
409C23—41no—
410C23—41no—
411C23—42no—
412C23—42no—
413C23C22×C22⋊D1111yescharacteristic
414Q8—42no—
415Q8—42no—
416Q8—224no—
417Q8—224no—
418Q8—442no—
419Q8—442no—
420D4—42no—
421D4—42no—
422D4—84no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4#6699014yes—
447C2×C4C2×D4×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C2×C4#6703712yes—
450C2×C4#41×D1112yes—
451C8—224no—
452C8—442no—
453C22—41no—
454C22—41no—
455C22—41no—
456C22—42no—
457C22—42no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—82no—
462C22—82no—
463C22C2×#6699011yescharacteristic
464C22#1062333611yescharacteristic
465C22#1062336311yescharacteristic
466C22#1062336712yes—
467C22#1062336912yes—
468C4—24no—
469C4—41no—
470C4—42no—
471C4—81no—
472C4—81no—
473C4—81no—
474C4—444no—
475C4—444no—
476C4#1062313012yes—
477C4#1062314312yes—
478C2—81no—
479C2—161no—
480C2#1307223611yescharacteristic
481C2#1307792812yes—
482C2#1307927812yes—
483C2#1307968811yescharacteristic
484C2#1307969911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2620C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2620D11
hypocenterC11#25612
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2620

Complements

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

NH ≅ G/Ntype
1. C2×#10623049C2semidirect
2. C2×#10622673C2semidirect
3. C2×#10622669C2semidirect
4. #13069624C2semidirect
6. #13069584C2semidirect
7. #13069417C2semidirect
8. #13068974C2semidirect
9. #13068960C2semidirect
10. #13068382C2semidirect
86. #66923D4semidirect
88. #66922D4semidirect
402. C11#25612semidirect

Maximal subgroups

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

subgroupindex
C2×#106230492
C2×#106226732
C2×#106226692
#130696242
#130696192
#130695842
#130694172
#130689742
#130689602
#130683822
C11×#26202
#2561211