Finite Group Databasebeta

← #14650353

Subgroups — #14650353

Order 2816.

564 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079369C211yesmaximal, characteristic
2#13069452C211yesmaximal, characteristic
3#13067188C211yesmaximal, characteristic, complemented
4C2×#10622089C211yesmaximal, characteristic
5#13066495C211yesmaximal, characteristic, complemented
6#13066464C211yesmaximal, characteristic, complemented
7C11×#2368C211yesmaximal, characteristic, complemented
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C11×#391—21no—
11C11×#387—21no—
12C11×#387—21no—
13C11×#385—21no—
14C4×C11×C4⋊C4—21no—
15C4×C11×C22⋊C4—21no—
16C4×C11×C22⋊C4C2211yescharacteristic
17C2×C11×#95C2211yescharacteristic
18#10622840—21no—
19#10622825C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2211yescharacteristic
22#10622661—22no—
23#10622659C412yescomplemented
24#10622656C412yescomplemented
25#10622581—21no—
26C2×#66870—21no—
27C2×#66870—21no—
28#10622176—22no—
29#10622089—21no—
30#10622089—21no—
31C22×Q8×C11D411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C22×D44C2×C411yescharacteristic
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8C2×C412yes—
39C11×C22⋊Q8D412yes—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—21no—
45C2×C11×C22⋊C4D411yescharacteristic
46C2×C11×C22⋊C4D411yescharacteristic
47C2×C42×C11—21no—
48C2×C42×C11—21no—
49C2×C42×C11—21no—
50C2×C22⋊Dic11—21no—
51C2×#4325—22no—
52#66983—21no—
53#66983—21no—
54#66983—21no—
55#66983—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11C2×C411yescharacteristic
59C22×C11⋊C8—21no—
60C22×C11⋊C8—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95—21no—
67C11×#95D411yescharacteristic
68C11×#95D411yescharacteristic
69#66899—22no—
70C11⋊#95—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)C2×C412yes—
75#66873—22no—
76#66872—22no—
77#66870—42no—
78#66870—42no—
79#9278—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C2×Q8×C11—21no—
83C2×Q8×C11—81no—
84C2×Q8×C11C22⋊C412yes—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—42no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—81no—
95C22×C4×C11—81no—
96C22×C4×C11C22×C411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C2×C22⋊D11—41no—
103C2×C22⋊D11—41no—
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—41no—
107C2×C22⋊D11—41no—
108C22×Dic11—21no—
109C22×Dic11—41no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—81no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—42no—
117C11×C4⋊C4—81no—
118C11×C4⋊C4C22⋊C412yes—
119C11×C22⋊C4—22no—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—21no—
122C11×C22⋊C4—21no—
123C11×C22⋊C4—21no—
124C11×C22⋊C4SD1612yescomplemented
125C42×C11—42no—
126C42×C11—81no—
127C42×C11—81no—
128C22⋊Dic11—41no—
129C22⋊Dic11—41no—
130#4325—82no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135C4⋊Dic11—81no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—41no—
138C2×C11⋊C8—81no—
139C2×C11⋊C8—81no—
140#3187—111no—
141#2368D1111yescharacteristic, complemented
142#1964—111no—
143#1520—111no—
144C2×#327—111no—
145#1294—111no—
146#1282—111no—
147C23×C11—41no—
148C23×C11—41no—
149C23×C11C4×D411yescharacteristic
150C23×C11#12011yescharacteristic
151C23×C11#12111yescharacteristic
152C23×C11C2×SD1611yescharacteristic
153C23×C11#13511yescharacteristic
154C23×C11AGL(1,ℤ/8)11yescharacteristic
155C23×C11#13711yescharacteristic
156C22×D11—41no—
157C22×D11—41no—
158C22×D11—41no—
159C22×D11—81no—
160C22×D11—81no—
161Q8×C11—42no—
162Q8×C11—81no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—41no—
168C2×C4×C11—41no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
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—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—82no—
188C2×C4×C11—82no—
189C2×C4×C11C2×C22⋊C411yescharacteristic
190C2×C4×C11C4×D411yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12311yescharacteristic
193C22⋊D11—81no—
194C22⋊D11—81no—
195C22⋊D11—81no—
196C22⋊D11—81no—
197C2×Dic11—41no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—81no—
201C2×Dic11—81no—
202C2×Dic11—81no—
203D44—42no—
204D44—81no—
205C11⋊C8—42no—
206C11⋊C8—81no—
207C2×C22⋊Q8C2×D1111yescharacteristic
208C2×#121—111no—
209#483—112no—
210#481—221no—
211#465—222no—
212#450—112no—
213#448—221no—
214C2×#99—221no—
215C2×#99—221no—
216C2×C22⋊C8—111no—
217C2×C22⋊C8—111no—
218#391—21no—
219#387—21no—
220#387—21no—
221#385—21no—
222#380—111no—
223C4×C4⋊C4—21no—
224C4×C22⋊C4—21no—
225C4×C22⋊C4C2×D1111yescharacteristic
226C2×#95C2×D1111yescharacteristic
227#328—222no—
228#327—221no—
229#327—221no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—41no—
237C22×C11—41no—
238C22×C11—41no—
239C22×C11—41no—
240C22×C11#38611yescharacteristic
241C22×C11C4×SD1611yescharacteristic
242C22×C11#44011yescharacteristic
243C22×C11#44811yescharacteristic
244C22×C11#44911yescharacteristic
245C22×C11#46011yescharacteristic
246C22×C11#46411yescharacteristic
247C2×D11—81no—
248C2×D11—81no—
249C2×D11—81no—
250C2×D11—161no—
251C2×D11—161no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—21no—
256C4×C11—42no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—81no—
261C4×C11—81no—
262Dic11—81no—
263Dic11—161no—
264C22×Q8C22⋊D1111yescharacteristic
265C22×D4—111no—
266C22×D4—221no—
267C23×C4—21no—
268C23×C4C22×D1111yescharacteristic
269C2×SD16—222no—
270C22×C8—221no—
271C22×C8—221no—
272C22⋊Q8—21no—
273C22⋊Q8—21no—
274C22⋊Q8C4×D1112yes—
275C22⋊Q8D4412yes—
276#121—221no—
277#121—221no—
278#121—221no—
279#121—221no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—111no—
284C2×C4⋊C4—221no—
285C2×C4⋊C4C22⋊D1111yescharacteristic
286C2×C22⋊C4—21no—
287C2×C22⋊C4—221no—
288C2×C22⋊C4—221no—
289C2×C22⋊C4C22⋊D1111yescharacteristic
290C2×C22⋊C4C22⋊D1111yescharacteristic
291C2×C42—21no—
292C2×C42—21no—
293C2×C42—21no—
294#106—222no—
295#103—222no—
296#102—222no—
297#99—442no—
298#99—442no—
299C22⋊C8—112no—
300C22⋊C8—221no—
301C22⋊C8—221no—
302C22⋊C8—221no—
303#95—21no—
304#95—21no—
305#95—21no—
306#95—21no—
307#95—21no—
308#95—21no—
309#95—221no—
310#95C22⋊D1111yescharacteristic
311#95C22⋊D1111yescharacteristic
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—21no—
315C2×C11—21no—
316C2×C11—21no—
317C2×C11—21no—
318C2×C11#188011yescharacteristic
319C2×C11#190611yescharacteristic
320C2×C11#191311yescharacteristic
321D11—161no—
322C24—221no—
323C24C2×C22⋊D1111yescharacteristic
324C2×Q8—21no—
325C2×Q8—81no—
326C2×Q8(C2×D11)⋊C412yes—
327C2×D4—221no—
328C2×D4—221no—
329C2×D4—441no—
330C2×D4—441no—
331C2×D4—441no—
332C2×D4—441no—
333C2×D4—441no—
334C2×D4—441no—
335C2×D4—881no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—42no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—81no—
346C22×C4—81no—
347C22×C4—221no—
348C22×C4—441no—
349C22×C4C2×C4×D1111yescharacteristic
350C22×C4C2×D4411yescharacteristic
351C22×C4#433911yescharacteristic
352C22×C4#433911yescharacteristic
353C22×C4C2×C22⋊D1111yescharacteristic
354C22×C4C2×C22⋊D1111yescharacteristic
355SD16—882no—
356C2×C8—222no—
357C2×C8—441no—
358C2×C8—881no—
359C2×C8—881no—
360C4⋊C4—22no—
361C4⋊C4—21no—
362C4⋊C4—22no—
363C4⋊C4—42no—
364C4⋊C4—81no—
365C4⋊C4—221no—
366C4⋊C4—221no—
367C4⋊C4—881no—
368C4⋊C4(C2×D11)⋊C412yes—
369C22⋊C4—22no—
370C22⋊C4—22no—
371C22⋊C4—21no—
372C22⋊C4—21no—
373C22⋊C4—21no—
374C22⋊C4—441no—
375C22⋊C4—441no—
376C22⋊C4—441no—
377C22⋊C4—441no—
378C22⋊C4#432512yescomplemented
379C42—42no—
380C42—81no—
381C42—81no—
382C11#927811yescharacteristic, complemented, Sylow
383C23—41no—
384C23—41no—
385C23—441no—
386C23—441no—
387C23—441no—
388C23—881no—
389C23—881no—
390C23C4×C22⋊D1111yescharacteristic
391C23#6698311yescharacteristic
392C23C2×#432511yescharacteristic
393C23#6699511yescharacteristic
394C23#6700211yescharacteristic
395C23#6700311yescharacteristic
396C23#6700611yescharacteristic
397Q8—42no—
398Q8—81no—
399D4—442no—
400D4—881no—
401D4—881no—
402D4—881no—
403D4—881no—
404D4—881no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—881no—
435C2×C4—881no—
436C2×C4—881no—
437C2×C4C2×(C2×D11)⋊C411yescharacteristic
438C2×C4C4×C22⋊D1111yescharacteristic
439C2×C4#6698211yescharacteristic
440C2×C4#6698311yescharacteristic
441C8—442no—
442C8—881no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—881no—
454C22—881no—
455C22—881no—
456C22—1761no—
457C22—1761no—
458C22C4×#432511yescharacteristic
459C22#1062263911yescharacteristic
460C22#1062264011yescharacteristic
461C22#1062264111yescharacteristic
462C22#1062282611yescharacteristic
463C22#1062284011yescharacteristic
464C22#1062285111yescharacteristic
465C4—21no—
466C4—21no—
467C4—21no—
468C4—21no—
469C4—42no—
470C4—42no—
471C4—42no—
472C4—42no—
473C4—81no—
474C4—81no—
475C4—881no—
476C4—1761no—
477C2—21no—
478C2—21no—
479C2—21no—
480C2—21no—
481C2—21no—
482C2—21no—
483C2—1761no—
484C2#1306897111yescharacteristic
485C2#1306911711yescharacteristic
486C2#1306915811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2368C2
socleC22×C11#386
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#2368D11
hypocenterC11#9278
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2368

Complements

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

NH ≅ G/Ntype
3. #13067188C2semidirect
5. #13066495C2semidirect
6. #13066464C2semidirect
7. C11×#2368C2semidirect
23. #10622659C4semidirect
24. #10622656C4semidirect
124. C11×C22⋊C4SD16semidirect
141. #2368D11semidirect
378. C22⋊C4#4325semidirect
382. C11#9278semidirect

Maximal subgroups

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

subgroupindex
#130793692
#130694522
#130671882
C2×#106220892
#130664952
#130664642
C11×#23682
#927811