Finite Group Databasebeta

← #14908873

Subgroups — #14908873

Order 2816.

548 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079188C211yesmaximal, characteristic
2C4×Q16×D11C211yesmaximal, characteristic, complemented
3#13070820C211yesmaximal, characteristic, complemented
4#13070803C211yesmaximal, characteristic
5#13070777C211yesmaximal, characteristic, complemented
6#13070679C211yesmaximal, characteristic, complemented
7#13070678C211yesmaximal, characteristic, complemented
8#13070551C211yesmaximal, characteristic, complemented
9#13070534C211yesmaximal, characteristic
10#13070486C211yesmaximal, characteristic, complemented
11#13070484C211yesmaximal, characteristic, complemented
12#13070483C211yesmaximal, characteristic, complemented
13#13070479C211yesmaximal, characteristic, complemented
14#13070418C211yesmaximal, characteristic, complemented
15C11×#2229C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17#10623222—21no—
18C4×Q8×D11—21no—
19C11×#499C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21Q16×Dic11C2211yescharacteristic
22C2×#66893C2211yescharacteristic
23C2×#66892C2211yescharacteristic
24#10622681—21no—
25C4×#4326—21no—
26C2×Dic88C2211yescharacteristic
27C2×#66864C2211yescharacteristic
28#10622500C2211yescharacteristic
29#10622496C2211yescharacteristic
30D11×#107C2211yescharacteristic
31#10622486C2211yescharacteristic
32#10622486C2211yescharacteristic
33#10622485C2211yescharacteristic
34#10622477—21no—
35#10622465—21no—
36D11×#103—21no—
37#10622403—21no—
38C4×Dic44C2211yescharacteristic
39#10622309C2211yescharacteristic
40C4×C8×D11C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×C4⋊C16C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#358C2211yescharacteristic
46#10622147C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48(C2×D11)⋊C16C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622140C2211yescharacteristic
51#10622140C2211yescharacteristic
52#10622130C2211yescharacteristic
53#10622130C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4⋊(C11⋊C16)C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×C11×Q16C2311yescharacteristic
61C11×#125—21no—
62C4×Q8×C11—21no—
63Q8×Dic11—21no—
64C2×#4326—21no—
65Q16×D11—22no—
66Q16×D11—22no—
67C2×Dic44C2311yescharacteristic
68C2×Dic44C2311yescharacteristic
69C2×D88C2311yescharacteristic
70C2×#4314—21no—
71C2×C8×D11D411yescharacteristic
72C2×C8×D11C2311yescharacteristic
73#66951—41no—
74#66950—21no—
75#66948—21no—
76#66947—41no—
77#66946—21no—
78#66946—41no—
79#66945—41no—
80C4⋊C4×D11—21no—
81C4⋊C4×D11—41no—
82#66940—21no—
83#66940—21no—
84#66940—41no—
85#66928—21no—
86C42×D11—41no—
87C42×D11D411yescharacteristic
88C4×Dic22—21no—
89C4×Dic22—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#106—21no—
96C11×#103—21no—
97C4×C8×C11C2311yescharacteristic
98#66899—21no—
99#66893—22no—
100#66892—22no—
101#66882C2311yescharacteristic
102#66880—21no—
103C8×Dic11D411yescharacteristic
104C8×Dic11C2311yescharacteristic
105C2×C11⋊C16C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107#66874—21no—
108#66874—21no—
109#66874—21no—
110#66873—21no—
111#66873—21no—
112#66871—21no—
113C4×C11⋊C8D411yescharacteristic
114Dic88—22no—
115#66864—22no—
116#33677—111nomaximal, Sylow
117C2×Q8×C11—21no—
118Q8×D11—24no—
119Q8×D11—42no—
120C2×D44—21no—
121C2×D44—41no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11D811yescharacteristic
126C2×C4×D11D811yescharacteristic
127C2×C4×D11C2×D411yescharacteristic
128C2×Dic22—21no—
129C2×Dic22—21no—
130C2×Dic22—41no—
131C11×Q16—21no—
132C11×Q16#4112yes—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2411yescharacteristic
135C11×C4⋊C4—21no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C42×C11—41no—
142C42×C11C2×D411yescharacteristic
143#4326—24no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—41no—
148(C2×D11)⋊C4—41no—
149C4⋊Dic11—21no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4—41no—
155Dic11⋊C4—41no—
156C4×Dic11—41no—
157C4×Dic11—41no—
158C4×Dic11—41no—
159C4×Dic11—41no—
160C4×Dic11D811yescharacteristic
161C4×Dic11D811yescharacteristic
162C4×Dic11C2×D411yescharacteristic
163C2×C11⋊C8C2×D411yescharacteristic
164C2×C11⋊C8C2×D411yescharacteristic
165Dic44—21no—
166Dic44—21no—
167Dic44—21no—
168Dic44#4112yes—
169D88—21no—
170D88—21no—
171#4314—42no—
172C8×D11—21no—
173C8×D11—21no—
174C8×D11—41no—
175C11×C16—21no—
176C11×C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3168—111no—
180C2×C4×Q16—111no—
181#2236—111no—
182#2233—111no—
183#2229—111no—
184#2229D1111yescharacteristic, complemented
185#2211—111no—
186#2211—111no—
187#2188—111no—
188#2185—111no—
189#2176—111no—
190#2176—111no—
191#2175—111no—
192#2175—111no—
193#2163—111no—
194C22×D11—41no—
195C22×D11C2×D811yescharacteristic
196Q8×C11—22no—
197Q8×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11C2×D811yescharacteristic
209C2×Dic11C2×D811yescharacteristic
210C2×Dic11C2×D811yescharacteristic
211D44—41no—
212D44—41no—
213D44—82no—
214C4×D11—22no—
215C4×D11—21no—
216C4×D11—21no—
217C4×D11—41no—
218C4×D11—44no—
219C4×D11—82no—
220C4×D11—82no—
221Dic22—22no—
222Dic22—44no—
223Dic22—41no—
224Dic22—41no—
225Dic22—41no—
226C8×C11—21no—
227C8×C11C2×#4111yescharacteristic
228C8×C11C2×#4111yescharacteristic
229C11⋊C8—21no—
230C11⋊C8—21no—
231C22×Q16—111no—
232#529—221no—
233C2×C4×Q8—221no—
234C2×Q32—111no—
235C2×Q32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238#499C2×D1111yescharacteristic
239#495—111no—
240#488—221no—
241#467—111no—
242#466—111no—
243#465—221no—
244C4×Q16—111no—
245C4×Q16—111no—
246C4×Q16—111no—
247C4×Q16—111no—
248C4×Q16—221no—
249C4×Q16—221no—
250C4×Q16C2×D1111yescharacteristic
251C4×SD16—221no—
252C4×D8—111no—
253C2×#107—111no—
254C2×#103—221no—
255C2×C4×C8—111no—
256#367—111no—
257#367C2×D1111yescharacteristic
258#366—111no—
259#366C2×D1111yescharacteristic
260C4⋊C16—111no—
261C4⋊C16C2×D1111yescharacteristic
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358C2×D1111yescharacteristic
267#358C2×D1111yescharacteristic
268#357—111no—
269#357—111no—
270C22⋊C16—111no—
271C22⋊C16—111no—
272#346—111no—
273#346—111no—
274C22×C11C22×D811yescharacteristic
275C2×D11—21no—
276C2×D11—21no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11#51012yes—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—42no—
284C4×C11—81no—
285C4×C11—81no—
286C4×C11—81no—
287C4×C11#52511yescharacteristic
288C4×C11#57511yescharacteristic
289Dic11—21no—
290Dic11—21no—
291Dic11—21no—
292Dic11—42no—
293Dic11—81no—
294Dic11—81no—
295C22×Q8—221no—
296C2×Q16—111no—
297C2×Q16—111no—
298C2×Q16—221no—
299C2×Q16—222no—
300C2×Q16—222no—
301C2×Q16C22×D1111yescharacteristic
302C2×SD16—221no—
303C2×D8—111no—
304C22×C8—111no—
305C22×C8—111no—
306#126—441no—
307#125—21no—
308#124—221no—
309#123—441no—
310C22⋊Q8—221no—
311#121—221no—
312C4×Q8—21no—
313C4×Q8—221no—
314C4×Q8—221no—
315C4×Q8—221no—
316C4×Q8—221no—
317C4×Q8—441no—
318C4×Q8—441no—
319C4×D4—221no—
320C4×D4—441no—
321#117—441no—
322C2×C4⋊C4—221no—
323C2×C4⋊C4—441no—
324C2×C42—111no—
325C2×C42—441no—
326Q32—222no—
327Q32—222no—
328SD32—222no—
329SD32—222no—
330C2×C16—111no—
331C2×C16—111no—
332C2×C16C22×D1111yescharacteristic
333C2×C16C22×D1111yescharacteristic
334#107—111no—
335#107—221no—
336#107C22×D1111yescharacteristic
337#107C22×D1111yescharacteristic
338#107C22×D1111yescharacteristic
339#106—21no—
340#103—21no—
341#103—221no—
342#103—221no—
343#103—221no—
344#103—221no—
345#103—221no—
346#102—221no—
347#102—221no—
348C4×C8—111no—
349C4×C8—111no—
350C4×C8—111no—
351C4×C8C22×D1111yescharacteristic
352C2×C11#310011yescharacteristic
353C2×C11C2×#51011yescharacteristic
354C2×C11#341411yescharacteristic
355D11—22no—
356D11—161no—
357C2×Q8—21no—
358C2×Q8—224no—
359C2×Q8—221no—
360C2×Q8—221no—
361C2×Q8—441no—
362C2×Q8—442no—
363C2×D4—221no—
364C2×D4—441no—
365C22×C4—111no—
366C22×C4—111no—
367C22×C4—111no—
368C22×C4—441no—
369C22×C4—441no—
370C22×C4—441no—
371Q16—21no—
372Q16—112no—
373Q16—224no—
374Q16—221no—
375Q16—221no—
376Q16—221no—
377Q16#434312yes—
378SD16—442no—
379D8—221no—
380D8—221no—
381C2×C8—111no—
382C2×C8—111no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8—441no—
386C2×C8D4×D1111yescharacteristic
387C2×C8C23×D1111yescharacteristic
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—221no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C4⋊C4—441no—
398C4⋊C4—441no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C42—41no—
407C42—111no—
408C42—111no—
409C42—111no—
410C42—441no—
411C42—441no—
412C42—441no—
413C42—441no—
414C42D4×D1111yescharacteristic
415C16—21no—
416C16—21no—
417C16—221no—
418C16—221no—
419C11#3367711yescharacteristic, complemented, Sylow
420C23—111no—
421C23—441no—
422Q8—22no—
423Q8—41no—
424Q8—222no—
425Q8—444no—
426Q8—441no—
427Q8—441no—
428Q8—441no—
429D4—441no—
430D4—441no—
431D4—882no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—111no—
437C2×C4—111no—
438C2×C4—111no—
439C2×C4—222no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—441no—
443C2×C4—444no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—441no—
447C2×C4—882no—
448C2×C4—882no—
449C2×C4D8×D1111yescharacteristic
450C2×C4D8×D1111yescharacteristic
451C2×C4C2×D4×D1111yescharacteristic
452C8—21no—
453C8—221no—
454C8—221no—
455C8C2×#434311yescharacteristic
456C8#41×D1111yescharacteristic
457C22—112no—
458C22—221no—
459C22—221no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4—221no—
471C4—221no—
472C4—221no—
473C4—442no—
474C4—881no—
475C4—881no—
476C4#1062315811yescharacteristic
477C4#1062330811yescharacteristic
478C2—222no—
479C2—1761no—
480C2#1307861811yescharacteristic
481C2D11×#51011yescharacteristic
482C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2229C2
socleC22×C11C22×D8
prime radical#10622496C22
hypercenter#2229D11
hypocenterC11#33677
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
2. C4×Q16×D11C2semidirect
3. #13070820C2semidirect
5. #13070777C2semidirect
6. #13070679C2semidirect
7. #13070678C2semidirect
8. #13070551C2semidirect
10. #13070486C2semidirect
11. #13070484C2semidirect
12. #13070483C2semidirect
13. #13070479C2semidirect
14. #13070418C2semidirect
15. C11×#2229C2semidirect
184. #2229D11semidirect
419. C11#33677semidirect

Maximal subgroups

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

subgroupindex
#130791882
C4×Q16×D112
#130708202
#130708032
#130707772
#130706792
#130706782
#130705512
#130705342
#130704862
#130704842
#130704832
#130704792
#130704182
C11×#22292
#3367711