Finite Group Databasebeta

← #14649390

Subgroups — #14649390

Order 2816.

600 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622318C211yesmaximal, characteristic, complemented
2#13076912C211yesmaximal, characteristic
3#13068379C211yesmaximal, characteristic, complemented
4C2×#10622178C211yesmaximal, characteristic, complemented
5#13066498C211yesmaximal, characteristic, complemented
6#13066498C211yesmaximal, characteristic, complemented
7C2×C11×#329C211yesmaximal, characteristic, complemented
8C2×C11×#124C2211yescharacteristic
9C2×#66999C411yescharacteristic
10C2×#66991C411yescharacteristic
11C2×C42×D11C2211yescharacteristic
12C2×C11×#97C2211yescharacteristic
13C2×C11×#97C2211yescharacteristic
14#10622843C411yescharacteristic
15#10622834C411yescharacteristic
16C2×(C2×D11)⋊C8—21no—
17C2×(C2×D11)⋊C8—21no—
18C2×Dic11⋊C8—21no—
19#10622569—21no—
20#10622569—21no—
21#10622557—21no—
22#10622557—21no—
23#10622549C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25C2×#66867C2211yescharacteristic
26#10622318—22no—
27#10622318—22no—
28C11×#329—22no—
29#10622188—21no—
30#10622178—22no—
31C22×Q8×C11C2×C411yescharacteristic
32C22×D4×C11C2×C411yescharacteristic
33C22×C22⋊D11—21no—
34C22×C4×D11C2×C411yescharacteristic
35C22×C4×D11D411yescharacteristic
36C22×C4×D11D411yescharacteristic
37C22×C8×C11—21no—
38C22×C8×C11—21no—
39C11×#124—21no—
40C11×#124—21no—
41C11×#124—21no—
42C11×#124—21no—
43C2×C11×C22⋊C4—21no—
44C2×C11×C22⋊C4—21no—
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49#66999—42no—
50#66991—42no—
51C2×(C2×D11)⋊C4—21no—
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×C4⋊Dic11C2×C411yescharacteristic
54C2×Dic11⋊C4—21no—
55C2×C4×Dic11C2×C411yescharacteristic
56C2×C4×Dic11D411yescharacteristic
57C2×C4×Dic11D411yescharacteristic
58C22×C11⋊C8—21no—
59C22×C11⋊C8—21no—
60C42×D11—21no—
61C42×D11—21no—
62C42×D11—21no—
63C42×D11—21no—
64C11×#97—21no—
65C11×#97—21no—
66C11×#97—21no—
67C11×#97D412yescomplemented
68C11⋊#95—21no—
69C11⋊#95—21no—
70C11⋊#95—21no—
71C11⋊#95—21no—
72(C2×D11)⋊C8—24no—
73(C2×D11)⋊C8—24no—
74Dic11⋊C8—24no—
75#66867—21no—
76#66867—21no—
77#66867—21no—
78#66867D412yescomplemented
79#9124—111nomaximal, Sylow
80C24×C11—21no—
81C23×D11C22⋊C411yescharacteristic
82C2×Q8×C11—21no—
83C2×Q8×C11—21no—
84C2×Q8×C11—41no—
85C2×Q8×C11—41no—
86C2×D4×C11—21no—
87C2×D4×C11—21no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C22×C4×C11—21no—
91C22×C4×C11C22×C411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—42no—
95C2×C22⋊D11—42no—
96C2×C22⋊D11—42no—
97C22×Dic11—21no—
98C22×Dic11—21no—
99C22×Dic11C22⋊C411yescharacteristic
100C22×Dic11C22⋊C411yescharacteristic
101C22×Dic11C22⋊C411yescharacteristic
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—21no—
105C2×C4×D11—21no—
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11—41no—
111C2×C4×D11—41no—
112C2×C4×D11—41no—
113C2×C4×D11—41no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—41no—
117C2×C8×C11—41no—
118C2×C8×C11—41no—
119C2×C8×C11—41no—
120C11×C22⋊C4—41no—
121C11×C22⋊C4—41no—
122C11×C22⋊C4—41no—
123C11×C22⋊C4—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11#4111yescharacteristic
128C22⋊Dic11—42no—
129C22⋊Dic11—42no—
130C22⋊Dic11—42no—
131(C2×D11)⋊C4—42no—
132C4⋊Dic11—41no—
133C4⋊Dic11—41no—
134Dic11⋊C4—42no—
135C4×Dic11—21no—
136C4×Dic11—21no—
137C4×Dic11—21no—
138C4×Dic11—21no—
139C4×Dic11—21no—
140C4×Dic11—21no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147C2×#432—111no—
148#2850—111no—
149#1749—111no—
150C2×#329—111no—
151C2×#329D1111yescharacteristic, complemented
152#1295—111no—
153#1295—111no—
154C23×C11—41no—
155C23×C11—41no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11C2×C22⋊C411yescharacteristic
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11—21no—
168C22×D11#10012yes—
169Q8×C11—81no—
170Q8×C11—81no—
171D4×C11—81no—
172D4×C11—81no—
173C2×C4×C11—21no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11C4×D411yescharacteristic
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11#12311yescharacteristic
188C22⋊D11—84no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11#10412yes—
204C4×D11—42no—
205C4×D11—42no—
206C4×D11—42no—
207C4×D11—42no—
208C4×D11—42no—
209C4×D11—42no—
210C8×C11—42no—
211C8×C11—42no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C2×#124C2×D1111yescharacteristic
215C2×C22⋊Q8—111no—
216C2×#121—111no—
217C22×C42—111no—
218#432—222no—
219#432—222no—
220C2×C4⋊C8—221no—
221C2×C22⋊C8—221no—
222C2×C22⋊C8—221no—
223C2×#97—111no—
224C2×#97—111no—
225C2×#97C2×D1111yescharacteristic
226C2×#97C2×D1111yescharacteristic
227#391—111no—
228#390—111no—
229#388—221no—
230#388—221no—
231#386—221no—
232#386—221no—
233#382—111no—
234#336—221no—
235#329—22no—
236#329—222no—
237C22×C11—81no—
238C22×C11—81no—
239C22×C11—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11#38611yescharacteristic
245C22×C11C2×#10011yescharacteristic
246C22×C11#41311yescharacteristic
247C22×C11C2×#10411yescharacteristic
248C22×C11#42111yescharacteristic
249C22×C11#42111yescharacteristic
250C22×C11#42111yescharacteristic
251C2×D11—22no—
252C2×D11—22no—
253C2×D11—22no—
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—41no—
258C4×C11—21no—
259C4×C11—21no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—81no—
265Dic11—22no—
266Dic11—41no—
267Dic11—41no—
268Dic11—81no—
269Dic11—81no—
270C22×Q8C4×D1111yescharacteristic
271C22×D4—221no—
272C22×D4C4×D1111yescharacteristic
273C23×C4—111no—
274C23×C4—111no—
275C23×C4—111no—
276C22×C8—21no—
277C22×C8—21no—
278C22×C8—221no—
279C22×C8—221no—
280#124—21no—
281#124—21no—
282#124—21no—
283#124—21no—
284C22⋊Q8—442no—
285#121—442no—
286C2×C4⋊C4—111no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—221no—
289C2×C22⋊C4—21no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—221no—
292C2×C22⋊C4—221no—
293C2×C22⋊C4—221no—
294C2×C22⋊C4—221no—
295C2×C42—111no—
296C2×C42—111no—
297C2×C42—111no—
298C2×C42—221no—
299C2×C42—221no—
300C2×C42—221no—
301C2×C42—221no—
302C2×C42C22×D1111yescharacteristic
303C4⋊C8—224no—
304C22⋊C8—224no—
305C22⋊C8—224no—
306#97—21no—
307#97—21no—
308#97—21no—
309#97—112no—
310#97—221no—
311#97—221no—
312#97—221no—
313#97C22⋊D1112yescomplemented
314#95—221no—
315#95—221no—
316#95—221no—
317#95—221no—
318C2×C11—161no—
319C2×C11#152911yescharacteristic
320C2×C11#153011yescharacteristic
321C2×C11#153311yescharacteristic
322C2×C11#153511yescharacteristic
323C2×C11#187111yescharacteristic
324C2×C11#189711yescharacteristic
325C2×C11#190011yescharacteristic
326D11—42no—
327C24—21no—
328C24—111no—
329C2×Q8—21no—
330C2×Q8—21no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—41no—
336C2×D4—41no—
337C2×D4—442no—
338C2×D4—442no—
339C2×D4—442no—
340C22×C4—21no—
341C22×C4—111no—
342C22×C4—111no—
343C22×C4—111no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—221no—
347C22×C4—221no—
348C22×C4—221no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4C2×C4×D1111yescharacteristic
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—41no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—441no—
370C2×C8—441no—
371C2×C8—441no—
372C2×C8—441no—
373C4⋊C4—441no—
374C4⋊C4—441no—
375C4⋊C4—442no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—442no—
381C22⋊C4—442no—
382C22⋊C4—442no—
383C22⋊C4—442no—
384C42—221no—
385C42—221no—
386C42—221no—
387C42—221no—
388C42—221no—
389C42—221no—
390C42#433911yescharacteristic
391C42D4×D1111yescharacteristic
392C42#434111yescharacteristic
393C42C2×C22⋊D1111yescharacteristic
394C11#912411yescharacteristic, complemented, Sylow
395C23—41no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—41no—
402C23—112no—
403C23—221no—
404C23—221no—
405C23—221no—
406C23—221no—
407C23—221no—
408C23—221no—
409C23C22⋊C4×D1111yescharacteristic
410Q8—81no—
411Q8—81no—
412D4—81no—
413D4—81no—
414D4—884no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—112no—
425C2×C4—221no—
426C2×C4—221no—
427C2×C4—221no—
428C2×C4—221no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—221no—
432C2×C4—221no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4(C22⋊D11)⋊C411yescharacteristic
446C2×C4#6693611yescharacteristic
447C2×C4#6693711yescharacteristic
448C2×C4C4×C22⋊D1111yescharacteristic
449C2×C4#6699011yescharacteristic
450C2×C4#6699111yescharacteristic
451C8—42no—
452C8—42no—
453C8—442no—
454C8—442no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22—81no—
462C22—222no—
463C22—222no—
464C22—222no—
465C22—441no—
466C22—441no—
467C22—441no—
468C22—441no—
469C22D11×#10011yescharacteristic
470C22#1062235811yescharacteristic
471C22D11×#10411yescharacteristic
472C22#1062243411yescharacteristic
473C22#1062243411yescharacteristic
474C22#1062243411yescharacteristic
475C22#1062256911yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—21no—
482C4—81no—
483C4—222no—
484C4—441no—
485C4—441no—
486C4—881no—
487C4—881no—
488C2—161no—
489C2—442no—
490C2#1306722011yescharacteristic
491C2#1306722511yescharacteristic
492C2#1306723811yescharacteristic
493C2#1306724411yescharacteristic
494C2#1306891511yescharacteristic
495C2#1306906111yescharacteristic
496C2#1306907611yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC2×C11×#329C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66991C4
cosocleC2×C42×C11C23
hypercenterC2×#329D11
hypocenterC11#9124
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#329

Complements

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

NH ≅ G/Ntype
1. C2×#10622318C2semidirect
3. #13068379C2semidirect
4. C2×#10622178C2semidirect
5. #13066498C2semidirect
6. #13066498C2semidirect
7. C2×C11×#329C2semidirect
67. C11×#97D4semidirect
78. #66867D4semidirect
151. C2×#329D11semidirect
313. #97C22⋊D11semidirect
394. C11#9124semidirect

Maximal subgroups

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

subgroupindex
C2×#106223182
#130769122
#130683792
C2×#106221782
#130664982
C2×C11×#3292
#912411