Finite Group Databasebeta

← #14770517

Subgroups — #14770517

Order 2816.

1108 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2C2×#10622441C212yesmaximal, complemented
3#13069413C212yesmaximal, complemented
4#13069412C212yesmaximal, complemented
5#13069408C212yesmaximal, complemented
6#13068599C212yesmaximal, complemented
7#13068381C212yesmaximal, complemented
8#13068378C211yesmaximal, characteristic, complemented
9C11×#1797C211yesmaximal, characteristic, complemented
10C22×C42×C11C2211yescharacteristic
11C2×#66983C411yescharacteristic
12C2×#66982C412yes—
13C2×C4×C22⋊D11C2212yes—
14C2×#66977C411yescharacteristic
15#10623010—28no—
16C2×#66929C412yes—
17C2×#66928C411yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×#66925C2212yes—
20C2×#66923C411yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C11×C4⋊C8C2212yes—
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2212yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×(C2×D11)⋊C8C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×(C2×D11)⋊C8C2212yes—
30C2×#66879C2212yes—
31C2×Dic11⋊C8C2212yes—
32C2×Dic11⋊C8C2212yes—
33C2×C8×Dic11C2212yes—
34C2×#66867C2212yes—
35#10622441—28no—
36C11×#336C2212yes—
37#10622162C2211yescharacteristic
38#10622162C2211yescharacteristic
39C23×C4×C11C2×C411yescharacteristic
40C23×C4×C11C2×C411yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11C2×C412yes—
43C22×D44C2×C411yescharacteristic
44C22×C4×D11C2312yes—
45C22×Dic22C2×C411yescharacteristic
46C22×C8×C11C2312yes—
47C22×C8×C11C2312yes—
48C2×C42×C11—24no—
49C2×C42×C11C2×C411yescharacteristic
50C2×C42×C11C2×C411yescharacteristic
51C2×C42×C11C2311yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11C2×C412yes—
54#66983—24no—
55#66982—28no—
56C4×C22⋊D11—24no—
57C4×C22⋊D11—24no—
58C2×(C2×D11)⋊C4C2×C412yes—
59C2×(C2×D11)⋊C4C2×C412yes—
60C2×(C2×D11)⋊C4C2×C412yes—
61C2×(C2×D11)⋊C4C2×C412yes—
62C2×C4⋊Dic11C2×C411yescharacteristic
63C2×C4⋊Dic11C2×C411yescharacteristic
64#66977—24no—
65C2×Dic11⋊C4C2×C412yes—
66C2×Dic11⋊C4C2×C412yes—
67C2×Dic11⋊C4C2×C412yes—
68C2×Dic11⋊C4C2×C412yes—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8C2312yes—
71C22×C11⋊C8C2312yes—
72#66929—28no—
73#66928—24no—
74C4×D44—24no—
75#66925—24no—
76#66925—24no—
77#66923—24no—
78C4×Dic22D418yes—
79C11×C4⋊C8—24no—
80C11×C22⋊C8—41no—
81C11×C22⋊C8—41no—
82C22⋊(C11⋊C8)—24no—
83(C2×D11)⋊C8—24no—
84(C2×D11)⋊C8—24no—
85(C2×D11)⋊C8—42no—
86(C2×D11)⋊C8—42no—
87#66879—24no—
88Dic11⋊C8—24no—
89Dic11⋊C8—24no—
90C8×Dic11—24no—
91#66867—24no—
92#22533—111nomaximal, Sylow
93C24×C11C22×C411yescharacteristic
94C23×D11C22×C412yes—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C2×C22⋊D11—24no—
112C2×C22⋊D11—24no—
113C2×C22⋊D11—42no—
114C22×Dic11C22×C412yes—
115C22×Dic11C22×C412yes—
116C22×Dic11C22×C412yes—
117C2×D44—22no—
118C2×D44—41no—
119C2×D44—41no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×Dic22—41no—
127C2×Dic22—41no—
128C2×Dic22C22⋊C414yes—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—22no—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C42×C11—22no—
136C42×C11—22no—
137C42×C11—22no—
138C42×C11C2×D414yes—
139C22⋊Dic11—24no—
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4—24no—
144C4⋊Dic11—22no—
145C4⋊Dic11C22⋊C414yes—
146Dic11⋊C4—24no—
147Dic11⋊C4—24no—
148Dic11⋊C4—24no—
149Dic11⋊C4C22⋊C418yes—
150C4×Dic11C2×D414yes—
151C4×Dic11C2×D414yes—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8#4114yes—
158C2×#529—111no—
159C2×#446—112no—
160#1955—112no—
161#1955—112no—
162#1954—112no—
163#1798—112no—
164#1797D1111yescharacteristic, complemented
165#1750—112no—
166#1749—111no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11#13112yes—
174C23×C11C23×C411yescharacteristic
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
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×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—44no—
196C2×C4×C11—44no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11C2×C22⋊C412yes—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11C22×D412yes—
202C2×C4×C11C2×#4112yes—
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C22⋊D11—48no—
206C2×Dic11—22no—
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11C2×C22⋊C414yes—
214C2×Dic11C2×C22⋊C414yes—
215D44—44no—
216C4×D11—42no—
217C4×D11—42no—
218C4×D11—42no—
219C4×D11—42no—
220Dic22—44no—
221C8×C11—42no—
222C8×C11—42no—
223C11⋊C8—24no—
224C11⋊C8—42no—
225#529—228no—
226C2×#126—112no—
227C2×#125—111no—
228C2×#124—111no—
229C2×#123—112no—
230C2×C22⋊Q8—111no—
231C2×#121—111no—
232C2×C4×Q8—111no—
233C2×C4×D4—112no—
234C2×C4×D4—111no—
235C2×#117—112no—
236C22×C42C2×D1111yescharacteristic
237#446—228no—
238C2×C4⋊C8—112no—
239C2×C4⋊C8—112no—
240C2×C4⋊C8C2×D1112yes—
241C2×C22⋊C8—112no—
242C2×C22⋊C8—112no—
243C2×C22⋊C8—112no—
244C2×C22⋊C8—112no—
245C2×C22⋊C8—112no—
246C2×C22⋊C8C2×D1111yescharacteristic
247C2×C22⋊C8C2×D1111yescharacteristic
248C2×#97—112no—
249C2×#97—112no—
250C2×C4×C8—112no—
251#336—111no—
252#336—111no—
253#336C2×D1112yes—
254C22×C11—22no—
255C22×C11—22no—
256C22×C11—22no—
257C22×C11—41no—
258C22×C11—41no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11C22×C22⋊C411yescharacteristic
262C22×C11C4×#4111yescharacteristic
263C22×C11#52011yescharacteristic
264C22×C11C2×#13111yescharacteristic
265C22×C11#56811yescharacteristic
266C22×C11#56811yescharacteristic
267C22×C11#56811yescharacteristic
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—42no—
275C4×C11—22no—
276C4×C11—22no—
277C4×C11—41no—
278C4×C11—41no—
279C4×C11—41no—
280C4×C11#54812yes—
281C4×C11#55012yes—
282Dic11—24no—
283Dic11—24no—
284Dic11—42no—
285C22×Q8—111no—
286C22×D4—112no—
287C22×D4—111no—
288C23×C4—112no—
289C23×C4C4×D1111yescharacteristic
290C23×C4C4×D1111yescharacteristic
291C23×C4C22×D1111yescharacteristic
292C22×C8—112no—
293C22×C8—112no—
294C22×C8C22×D1112yes—
295C22×C8C22×D1112yes—
296#126—228no—
297#125—224no—
298#124—224no—
299#123—228no—
300C22⋊Q8—224no—
301#121—224no—
302C4×Q8—118no—
303C4×D4—224no—
304C4×D4—224no—
305C4×D4—224no—
306#117—224no—
307#117—224no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—112no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—112no—
314C2×C22⋊C4—112no—
315C2×C22⋊C4—112no—
316C2×C22⋊C4—112no—
317C2×C22⋊C4—112no—
318C2×C22⋊C4—112no—
319C2×C42—24no—
320C2×C42—112no—
321C2×C42C4×D1111yescharacteristic
322C2×C42C4×D1111yescharacteristic
323C2×C42C22×D1111yescharacteristic
324C2×C42C22×D1111yescharacteristic
325C4⋊C8—24no—
326C4⋊C8—224no—
327C4⋊C8—224no—
328C22⋊C8—41no—
329C22⋊C8—41no—
330C22⋊C8—224no—
331C22⋊C8—224no—
332C22⋊C8—224no—
333C22⋊C8—442no—
334C22⋊C8—442no—
335#97—224no—
336#97—224no—
337C4×C8—224no—
338C2×C11—42no—
339C2×C11#234111yescharacteristic
340C2×C11#287911yescharacteristic
341C2×C11#288011yescharacteristic
342C2×C11#296711yescharacteristic
343C2×C11#296811yescharacteristic
344C2×C11#299211yescharacteristic
345C2×C11#299511yescharacteristic
346D11—82no—
347C24—112no—
348C24C2×C4×D1111yescharacteristic
349C2×Q8—114no—
350C2×Q8—441no—
351C2×Q8—441no—
352C2×D4—224no—
353C2×D4—224no—
354C2×D4—222no—
355C2×D4—441no—
356C2×D4—441no—
357C2×D4—442no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—22no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—112no—
369C22×C4—112no—
370C22×C4—112no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4C2×C4×D1111yescharacteristic
378C22×C4C2×C4×D1111yescharacteristic
379C22×C4C2×C4×D1111yescharacteristic
380C22×C4C2×C4×D1111yescharacteristic
381C22×C4C2×C4×D1111yescharacteristic
382C22×C4C23×D1111yescharacteristic
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—114no—
390C2×C8—222no—
391C2×C8—222no—
392C2×C8—222no—
393C2×C8—222no—
394C2×C8—222no—
395C4⋊C4—114no—
396C4⋊C4—118no—
397C4⋊C4—224no—
398C4⋊C4—224no—
399C4⋊C4—224no—
400C4⋊C4—222no—
401C22⋊C4—224no—
402C22⋊C4—224no—
403C22⋊C4—224no—
404C22⋊C4—224no—
405C22⋊C4—224no—
406C42—22no—
407C42—22no—
408C42—22no—
409C42—114no—
410C42—114no—
411C42D4×D1114yes—
412C11#2253311yescharacteristic, complemented, Sylow
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—222no—
420C23—222no—
421C23—222no—
422C23—222no—
423C23—222no—
424C23—222no—
425C23—222no—
426C23#6695412yes—
427C23C22×C4×D1111yescharacteristic
428Q8—444no—
429D4—444no—
430D4—448no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—114no—
449C2×C4—114no—
450C2×C4—222no—
451C2×C4—222no—
452C2×C4—222no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—222no—
456C2×C4—222no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4C22⋊C4×D1112yes—
462C2×C4C22⋊C4×D1112yes—
463C2×C4C2×D4×D1112yes—
464C2×C4#6703711yescharacteristic
465C2×C4#6704011yescharacteristic
466C2×C4#41×D1112yes—
467C8—42no—
468C8—42no—
469C8—224no—
470C8—442no—
471C22—22no—
472C22—22no—
473C22—22no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—442no—
479C22—442no—
480C22—442no—
481C22—442no—
482C22—442no—
483C22—442no—
484C22—442no—
485C22C2×C22⋊C4×D1111yescharacteristic
486C22#1062303511yescharacteristic
487C22#1062305311yescharacteristic
488C22C2×#6695411yescharacteristic
489C22#1062327611yescharacteristic
490C22#1062327611yescharacteristic
491C22#1062327611yescharacteristic
492C4—22no—
493C4—22no—
494C4—41no—
495C4—41no—
496C4—41no—
497C4—224no—
498C4—224no—
499C4—442no—
500C4#1062313012yes—
501C4#1062316412yes—
502C2—42no—
503C2—882no—
504C2#1307145311yescharacteristic
505C2#1307705911yescharacteristic
506C2#1307706211yescharacteristic
507C2#1307759611yescharacteristic
508C2#1307760511yescharacteristic
509C2#1307775211yescharacteristic
510C2#1307778311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1797C2
prime radicalC2×#66983C4
cosocleC22×C4×C11C24
hypercenter#1797D11
hypocenterC11#22533
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#10622441C2semidirect
3. #13069413C2semidirect
4. #13069412C2semidirect
5. #13069408C2semidirect
6. #13068599C2semidirect
7. #13068381C2semidirect
8. #13068378C2semidirect
9. C11×#1797C2semidirect
164. #1797D11semidirect
412. C11#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
C2×#106224412
#130694132
#130694122
#130694082
#130685992
#130683812
#130683782
C11×#17972
#2253311