Finite Group Databasebeta

← #14649500

Subgroups — #14649500

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076900C211yesmaximal, characteristic
2C2×#10622279C211yesmaximal, characteristic
3#13068525C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic, complemented
5#13066496C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C2×C11×#328C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C2×C11×C22⋊Q8C2211yescharacteristic
10C2×#66999C412yescomplemented
11C22×(C2×D11)⋊C4—21no—
12C22×C4×Dic11—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14C2×C11×#95C2211yescharacteristic
15#10622825C2211yescharacteristic
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18C2×(C2×D11)⋊C8—22no—
19#10622602—22no—
20#10622600C412yescomplemented
21#10622568—21no—
22#10622559—21no—
23#10622279—22no—
24#10622279—22no—
25C11×#328—22no—
26#10622176—22no—
27C24×D11D411yescharacteristic
28C22×Q8×C11C2×C411yescharacteristic
29C23×C4×C11—21no—
30C23×C4×C11C2311yescharacteristic
31C23×Dic11—21no—
32C23×Dic11D411yescharacteristic
33C22×C4×D11—21no—
34C22×C4×D11—21no—
35C22×C4×D11—21no—
36C22×C4×D11—21no—
37C22×C4×D11—44no—
38C22×C4×D11C2×C412yes—
39C22×C4×D11D412yes—
40C22×C8×C11—21no—
41C11×C22⋊Q8—21no—
42C11×C22⋊Q8—21no—
43C11×C22⋊Q8—21no—
44C11×C22⋊Q8—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4C2×C411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C22⋊Dic11—21no—
49#66999—44no—
50C2×(C2×D11)⋊C4—24no—
51C2×(C2×D11)⋊C4—28no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—22no—
54C2×C4⋊Dic11C2×C412yes—
55C2×Dic11⋊C4—22no—
56C2×C4×Dic11—24no—
57C2×C4×Dic11—44no—
58C22×C11⋊C8—21no—
59C11×C22⋊C8—21no—
60C11×C22⋊C8—21no—
61C11×#95—21no—
62C11×#95D412yes—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—22no—
66C11⋊#95D412yes—
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69(C2×D11)⋊C8—44no—
70#9146—111nomaximal, Sylow
71C24×C11C2×D411yescharacteristic
72C23×D11—21no—
73C23×D11—21no—
74C23×D11—24no—
75C23×D11—21no—
76C23×D11—21no—
77C23×D11—21no—
78C23×D11—21no—
79C23×D11—42no—
80C23×D11C22⋊C412yes—
81C2×Q8×C11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—42no—
84C22×C4×C11—24no—
85C22×C4×C11—22no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—22no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11—21no—
104C22×Dic11—42no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107C22×Dic11C22⋊C412yes—
108C2×C4×D11—24no—
109C2×C4×D11—24no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—42no—
115C2×C4×D11—42no—
116C2×C4×D11—44no—
117C2×C4×D11—44no—
118C2×C4×D11—44no—
119C2×C4×D11—44no—
120C2×C8×C11—42no—
121C2×C8×C11—41no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130(C2×D11)⋊C4—216no—
131(C2×D11)⋊C4—44no—
132(C2×D11)⋊C4—44no—
133C4⋊Dic11—42no—
134Dic11⋊C4—44no—
135C4×Dic11—48no—
136C2×C11⋊C8—42no—
137C2×C11⋊C8—41no—
138#2848—111no—
139C2×C4×C22⋊C4—111no—
140#1779—111no—
141C2×#328—111no—
142C2×#328D1111yescharacteristic, complemented
143#1294—111no—
144#1294—111no—
145C23×C11—22no—
146C23×C11—22no—
147C23×C11C2×C22⋊C411yescharacteristic
148C23×C11#12011yescharacteristic
149C23×C11#12311yescharacteristic
150C23×C11#13511yescharacteristic
151C23×C11#13511yescharacteristic
152C23×C11#13711yescharacteristic
153C23×C11#13711yescharacteristic
154C22×D11—24no—
155C22×D11—24no—
156C22×D11—22no—
157C22×D11—22no—
158C22×D11—22no—
159C22×D11—22no—
160C22×D11—22no—
161C22×D11—22no—
162C22×D11—44no—
163C22×D11—44no—
164C22×D11—44no—
165C22×D11—44no—
166C22×D11—42no—
167C22×D11—42no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11#10414yes—
173Q8×C11—81no—
174Q8×C11—81no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—24no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—44no—
184C2×C4×C11—44no—
185C2×C4×C11—42no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11C4×D411yescharacteristic
191C2×C4×C11C4×D411yescharacteristic
192C2×C4×C11#12111yescharacteristic
193C2×C4×C11#12111yescharacteristic
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—24no—
199C2×Dic11—42no—
200C2×Dic11—44no—
201C2×Dic11—44no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11#9914yes—
207C4×D11—44no—
208C4×D11—44no—
209C4×D11—44no—
210C4×D11—44no—
211C8×C11—81no—
212C11⋊C8—81no—
213C24×C4—111no—
214C2×C22⋊Q8—112no—
215C2×C22⋊Q8C2×D1111yescharacteristic
216C22×C22⋊C4—221no—
217C22×C42—221no—
218C2×C22⋊C8—111no—
219C2×C22⋊C8—222no—
220C2×C22⋊C8C2×D1111yescharacteristic
221#385—221no—
222#385—222no—
223#380—111no—
224#380—112no—
225#379—221no—
226C4×C22⋊C4—222no—
227C4×C22⋊C4—222no—
228C2×#95—111no—
229C2×#95C2×D1111yescharacteristic
230#328—22no—
231#328—222no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—22no—
239C22×C11—22no—
240C22×C11#38611yescharacteristic
241C22×C11C2×#9912yes—
242C22×C11#41611yescharacteristic
243C22×C11#41911yescharacteristic
244C22×C11C2×#10412yes—
245C22×C11#45211yescharacteristic
246C22×C11#45211yescharacteristic
247C22×C11#48511yescharacteristic
248C22×C11#48511yescharacteristic
249C2×D11—24no—
250C2×D11—24no—
251C2×D11—24no—
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—44no—
255C2×D11—44no—
256C2×D11—42no—
257C2×D11—42no—
258C2×D11—42no—
259C2×D11—42no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—44no—
265C4×C11—81no—
266C4×C11—81no—
267Dic11—24no—
268Dic11—44no—
269Dic11—82no—
270C25—111no—
271C22×Q8C4×D1111yescharacteristic
272C23×C4—21no—
273C23×C4—111no—
274C23×C4—112no—
275C23×C4—112no—
276C23×C4—221no—
277C23×C4—221no—
278C23×C4—221no—
279C23×C4—221no—
280C23×C4—221no—
281C23×C4—444no—
282C23×C4C22×D1111yescharacteristic
283C22×C8—21no—
284C22×C8—221no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8—444no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4C4×D1111yescharacteristic
294C2×C22⋊C4—21no—
295C2×C22⋊C4—224no—
296C2×C22⋊C4—228no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—221no—
300C2×C42—224no—
301C2×C42—444no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8—221no—
305C22⋊C8—221no—
306C22⋊C8—444no—
307#95—21no—
308#95—112no—
309#95—222no—
310#95—221no—
311#95—221no—
312#95C22⋊D1112yes—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11#150112yes—
318C2×C11#150812yes—
319C2×C11#187311yescharacteristic
320C2×C11#189611yescharacteristic
321C2×C11#189811yescharacteristic
322D11—44no—
323C24—112no—
324C24—224no—
325C24—221no—
326C24—221no—
327C24—221no—
328C24—221no—
329C24—221no—
330C24—221no—
331C24—442no—
332C24D4×D1111yescharacteristic
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—42no—
336C22×C4—24no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—112no—
345C22×C4—224no—
346C22×C4—224no—
347C22×C4—224no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—224no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—442no—
358C22×C4—442no—
359C22×C4—444no—
360C22×C4—444no—
361C22×C4—444no—
362C22×C4—444no—
363C22×C4—442no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4C2×C4×D1111yescharacteristic
367C22×C4#433911yescharacteristic
368C22×C4D4×D1111yescharacteristic
369C22×C4D4×D1111yescharacteristic
370C22×C4#434111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372C2×C8—42no—
373C2×C8—41no—
374C2×C8—442no—
375C2×C8—441no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—442no—
381C4⋊C4—444no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—2216no—
385C22⋊C4—444no—
386C22⋊C4—444no—
387C22⋊C4—441no—
388C22⋊C4—441no—
389C42—448no—
390C11#914611yescharacteristic, complemented, Sylow
391C23—22no—
392C23—22no—
393C23—114no—
394C23—224no—
395C23—224no—
396C23—222no—
397C23—222no—
398C23—222no—
399C23—222no—
400C23—222no—
401C23—222no—
402C23—444no—
403C23—444no—
404C23—444no—
405C23—444no—
406C23—442no—
407C23—442no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23C22⋊C4×D1111yescharacteristic
413C23#6693611yescharacteristic
414C23#6696811yescharacteristic
415C23#6696911yescharacteristic
416C23#6697111yescharacteristic
417C23#6697211yescharacteristic
418C23#6699011yescharacteristic
419Q8—81no—
420Q8—81no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—114no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—222no—
440C2×C4—222no—
441C2×C4—224no—
442C2×C4—444no—
443C2×C4—444no—
444C2×C4—444no—
445C2×C4—444no—
446C2×C4—442no—
447C2×C4—444no—
448C2×C4—444no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4(C22⋊D11)⋊C411yescharacteristic
454C2×C4#6693711yescharacteristic
455C2×C4C4×C22⋊D1111yescharacteristic
456C2×C4#6699111yescharacteristic
457C8—81no—
458C8—881no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—224no—
468C22—224no—
469C22—224no—
470C22—444no—
471C22—444no—
472C22—444no—
473C22—444no—
474C22—442no—
475C22—442no—
476C22—442no—
477C22—442no—
478C22D11×#9912yes—
479C22#1062241511yescharacteristic
480C22#1062241711yescharacteristic
481C22#1062242711yescharacteristic
482C22#1062242811yescharacteristic
483C22D11×#10412yes—
484C22#1062256911yescharacteristic
485C22#1062278611yescharacteristic
486C22#1062280011yescharacteristic
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—44no—
492C4—81no—
493C4—81no—
494C4—224no—
495C4—444no—
496C4—882no—
497C2—21no—
498C2—21no—
499C2—21no—
500C2—21no—
501C2—444no—
502C2#1306710612yes—
503C2#1306713412yes—
504C2#1306892511yescharacteristic
505C2#1306905611yescharacteristic
506C2#1306906611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#328C2
socleC23×C11C2×C22⋊C4
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenterC2×#328D11
hypocenterC11#9146
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
4. C2×#10622176C2semidirect
5. #13066496C2semidirect
6. #13066495C2semidirect
7. C2×C11×#328C2semidirect
10. C2×#66999C4semidirect
20. #10622600C4semidirect
142. C2×#328D11semidirect
390. C11#9146semidirect

Maximal subgroups

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

subgroupindex
#130769002
C2×#106222792
#130685252
C2×#106221762
#130664962
#130664952
C2×C11×#3282
#914611