Finite Group Databasebeta

← #14657093

Subgroups — #14657093

Order 2816.

570 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
1#13074432C211yesmaximal, characteristic
2#13068921C211yesmaximal, characteristic
3#13068808C211yesmaximal, characteristic
4C2×#10622090C211yesmaximal, characteristic
5C2×#10622107C211yesmaximal, characteristic
6#13066870C211yesmaximal, characteristic
7C11×#1294C211yesmaximal, characteristic
8C22×C4⋊Dic11C2211yescharacteristic
9C2×#66977C2211yescharacteristic
10C22×Dic11⋊C4C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17C2×#66880—21no—
18#10622596—21no—
19#10622596—21no—
20C2×#66872—21no—
21#10622563—21no—
22#10622556—21no—
23#10622272—21no—
24#10622269—21no—
25#10622189—21no—
26#10622167—21no—
27#10622107—22no—
28#10622090—22no—
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C23×Dic11D411yescharacteristic
34C22×Dic22D411yescharacteristic
35C22×C8×C11—21no—
36C2×C11×C4⋊C4D411yescharacteristic
37C2×C11×C4⋊C4D411yescharacteristic
38C2×C11×C22⋊C4—21no—
39C2×C22⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—42no—
45C2×C4⋊Dic11D411yescharacteristic
46#66977—21no—
47#66977—21no—
48#66977—21no—
49#66977—21no—
50C2×Dic11⋊C4—21no—
51C2×Dic11⋊C4—21no—
52C2×Dic11⋊C4—21no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C22×C11⋊C8—21no—
58C11×C22⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)D412yes—
73#66880—42no—
74#66872—42no—
75#10401—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C22×C4×C11—22no—
78C22×C4×C11—21no—
79C22×C4×C11—21no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11—41no—
83C22×C4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11#4111yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C22×C4×C11#4111yescharacteristic
94C22×Dic11—22no—
95C22×Dic11—21no—
96C22×Dic11—21no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—21no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11SD1612yes—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×Dic22—41no—
118C2×Dic22—41no—
119C2×C8×C11—41no—
120C2×C8×C11—41no—
121C2×C8×C11—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C22⋊C4—41no—
125C11×C22⋊C4—41no—
126C22⋊Dic11—41no—
127C22⋊Dic11—41no—
128C4⋊Dic11—22no—
129C4⋊Dic11—22no—
130C4⋊Dic11—21no—
131C4⋊Dic11—21no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134C4⋊Dic11—81no—
135C4⋊Dic11—81no—
136Dic11⋊C4—41no—
137Dic11⋊C4—41no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140Dic11⋊C4—41no—
141Dic11⋊C4—41no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145#2627—111no—
146#1872—111no—
147#1853—111no—
148C2×#328—111no—
149C2×#324—111no—
150#1441—111no—
151#1294D1111yescharacteristic
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11#12011yescharacteristic
157C23×C11#12111yescharacteristic
158C23×C11#12311yescharacteristic
159C23×C11C2×SD1611yescharacteristic
160C23×C11#13511yescharacteristic
161C23×C11#13711yescharacteristic
162C23×C11#13711yescharacteristic
163C2×C4×C11—21no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—81no—
181C2×C4×C11—81no—
182C2×C4×C11—81no—
183C2×C4×C11—81no—
184C2×C4×C11#12111yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12311yescharacteristic
187C2×C4×C11#12411yescharacteristic
188C2×Dic11—22no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—41no—
192C2×Dic11—41no—
193C2×Dic11—41no—
194C2×Dic11—41no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—42no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—81no—
209C2×Dic11—81no—
210C2×Dic11—81no—
211C2×Dic11—81no—
212C2×Dic11—81no—
213Dic22—42no—
214Dic22—81no—
215C8×C11—81no—
216C11⋊C8—42no—
217C2×C22⋊Q8—111no—
218C22×C4⋊C4—111no—
219C22×C4⋊C4—111no—
220C2×#106—221no—
221C2×#103—221no—
222C2×C22⋊C8—111no—
223C2×C22⋊C8C2×D1111yescharacteristic
224#400—221no—
225#398—221no—
226#398—221no—
227#395—221no—
228#385—221no—
229#381—221no—
230#380C2×D1111yescharacteristic
231C2×#95—221no—
232C2×#95—221no—
233C2×#95C2×D1111yescharacteristic
234#340—221no—
235#340—221no—
236#328—222no—
237#324—222no—
238C22×C11—21no—
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11#39411yescharacteristic
251C22×C11#44811yescharacteristic
252C22×C11#45211yescharacteristic
253C22×C11#45411yescharacteristic
254C22×C11#45611yescharacteristic
255C22×C11B(4,𝔽2)11yescharacteristic
256C22×C11#45811yescharacteristic
257C22×C11#46511yescharacteristic
258C22×C11#47011yescharacteristic
259C22×C11#48311yescharacteristic
260C22×C11#48511yescharacteristic
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—82no—
266C4×C11—81no—
267C4×C11—81no—
268Dic11—42no—
269Dic11—82no—
270Dic11—81no—
271Dic11—81no—
272Dic11—81no—
273C22×Q8—111no—
274C23×C4—21no—
275C23×C4—111no—
276C23×C4—111no—
277C23×C4—221no—
278C23×C4C22×D1111yescharacteristic
279C22×C8—21no—
280C22×C8—221no—
281C22⋊Q8—221no—
282C22⋊Q8—221no—
283C22⋊Q8—221no—
284C22⋊Q8—221no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—221no—
291C2×C4⋊C4—221no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4—442no—
298C2×C4⋊C4D4411yescharacteristic
299C2×C4⋊C4D4411yescharacteristic
300C2×C22⋊C4—21no—
301C2×C22⋊C4—221no—
302#106—442no—
303#103—442no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—112no—
307C22⋊C8—221no—
308#95—21no—
309#95—21no—
310#95—21no—
311#95—221no—
312#95—221no—
313#95—221no—
314#95—221no—
315#95—221no—
316#95—221no—
317#95—442no—
318#95—442no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11#159911yescharacteristic
324C2×C11#160311yescharacteristic
325C2×C11#161111yescharacteristic
326C2×C11#161511yescharacteristic
327C2×C11#203511yescharacteristic
328C2×C11#203811yescharacteristic
329C2×C11#204411yescharacteristic
330C24D4×D1111yescharacteristic
331C2×Q8—221no—
332C2×Q8—221no—
333C2×Q8—441no—
334C2×Q8—441no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—112no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—222no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4C2×D4411yescharacteristic
368C22×C4#433911yescharacteristic
369C22×C4#433911yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4D4×D1111yescharacteristic
372C22×C4#434311yescharacteristic
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—222no—
377C2×C8—441no—
378C2×C8—441no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—222no—
382C4⋊C4—222no—
383C4⋊C4—221no—
384C4⋊C4—221no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C4⋊C4—441no—
389C4⋊C4—441no—
390C4⋊C4—441no—
391C4⋊C4—441no—
392C4⋊C4—441no—
393C4⋊C4—881no—
394C4⋊C4—881no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—441no—
398C22⋊C4—441no—
399C11#1040111yescharacteristic, complemented, Sylow
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23#6693511yescharacteristic
405C23#6693711yescharacteristic
406C23#6694711yescharacteristic
407C23#6696511yescharacteristic
408C23SD16×D1111yescharacteristic
409C23#6696811yescharacteristic
410C23#6697111yescharacteristic
411Q8—442no—
412Q8—881no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—81no—
433C2×C4—81no—
434C2×C4—222no—
435C2×C4—222no—
436C2×C4—222no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—442no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—881no—
455C2×C4—881no—
456C2×C4—881no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4#6692811yescharacteristic
460C2×C4#6693711yescharacteristic
461C2×C4#6694711yescharacteristic
462C2×C4#6694811yescharacteristic
463C8—81no—
464C8—442no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22#1062228511yescharacteristic
478C22#1062235411yescharacteristic
479C22#1062235511yescharacteristic
480C22#1062239111yescharacteristic
481C22#1062239611yescharacteristic
482C22#1062241911yescharacteristic
483C22#1062242911yescharacteristic
484C22#1062243911yescharacteristic
485C22#1062244011yescharacteristic
486C22#1062247511yescharacteristic
487C22#1062250111yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—82no—
493C4—81no—
494C4—81no—
495C4—442no—
496C4—881no—
497C4—882no—
498C4—881no—
499C4—881no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2#1306755711yescharacteristic
505C2#1306758011yescharacteristic
506C2#1306762511yescharacteristic
507C2#1306764811yescharacteristic
508C2#1306981511yescharacteristic
509C2#1306983611yescharacteristic
510C2#1306986811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1294D11
hypocenterC11#10401
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
399. C11#10401semidirect

Maximal subgroups

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

subgroupindex
#130744322
#130689212
#130688082
C2×#106220902
C2×#106221072
#130668702
C11×#12942
#1040111