Finite Group Databasebeta

← #14911385

Subgroups — #14911385

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081018C211yesmaximal, characteristic, complemented
2#13081014C211yesmaximal, characteristic, complemented
3#13070894C211yesmaximal, characteristic, complemented
4#13070809C211yesmaximal, characteristic, complemented
5#13070807C211yesmaximal, characteristic, complemented
6#13070798C211yesmaximal, characteristic, complemented
7#13070796C211yesmaximal, characteristic, complemented
8#13070776C211yesmaximal, characteristic, complemented
9#13070772C211yesmaximal, characteristic, complemented
10#13070720C211yesmaximal, characteristic, complemented
11#13070719C211yesmaximal, characteristic, complemented
12#13070462C211yesmaximal, characteristic, complemented
13#13070446C211yesmaximal, characteristic, complemented
14#13070401C211yesmaximal, characteristic, complemented
15C11×#2159C211yesmaximal, characteristic, complemented
16#10623061—21no—
17#10623045—21no—
18C2×C11×M32C2211yescharacteristic
19C11×#427C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21#10622728C2211yescharacteristic
22#10622728C2211yescharacteristic
23C8×C22⋊D11C2211yescharacteristic
24#10622616—21no—
25#10622581—21no—
26C2×D176C2211yescharacteristic
27C2×#66862C2211yescharacteristic
28#10622504—21no—
29#10622498—21no—
30#10622496C2211yescharacteristic
31#10622496C2211yescharacteristic
32#10622493C2211yescharacteristic
33D11×#107C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622491C2211yescharacteristic
36#10622485C2211yescharacteristic
37#10622485C2211yescharacteristic
38#10622484—21no—
39#10622476—21no—
40C11×#367C2211yescharacteristic
41C11×#367C2211yescharacteristic
42C11×#366C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622147C2211yescharacteristic
46#10622147C2211yescharacteristic
47(C2×D11)⋊C16C2211yescharacteristic
48#10622143C2211yescharacteristic
49Dic11⋊C16C2211yescharacteristic
50C16×Dic11C2211yescharacteristic
51#10622129C2211yescharacteristic
52#10622129C2211yescharacteristic
53#10622129C2211yescharacteristic
54#10622129C2211yescharacteristic
55#10622128C2211yescharacteristic
56#10622127C2211yescharacteristic
57#10622127C2211yescharacteristic
58#10622127C2211yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#117—21no—
61C2×C11×C4⋊C4—21no—
62#66983—21no—
63#66983—21no—
64#66983—41no—
65C4×C22⋊D11—41no—
66C4×C22⋊D11D411yescharacteristic
67C2×D88C2311yescharacteristic
68C2×D88C2311yescharacteristic
69C2×C8×D11C2311yescharacteristic
70#66951—41no—
71#66948—21no—
72#66948—21no—
73#66947—41no—
74#66946—21no—
75#66946—21no—
76#66945—21no—
77C4⋊C4×D11—21no—
78#66943—21no—
79#66943—21no—
80#66937—41no—
81#66936—41no—
82#66929—41no—
83C4×D44—41no—
84C11×M32—22no—
85C2×C11×C16C2311yescharacteristic
86C2×C11×C16C2311yescharacteristic
87C11×#107—21no—
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C22⋊(C11⋊C8)D411yescharacteristic
94#66885—21no—
95#66885—21no—
96(C2×D11)⋊C8D411yescharacteristic
97#66882C2311yescharacteristic
98#66882C2311yescharacteristic
99Dic11⋊C8D411yescharacteristic
100C8×Dic11C2311yescharacteristic
101C2×C11⋊C16C2311yescharacteristic
102C2×C11⋊C16C2311yescharacteristic
103#66873—21no—
104#66873—21no—
105#66873—21no—
106#66873—21no—
107#66872—21no—
108#66872—21no—
109#66872—21no—
110#66871—21no—
111D176—22no—
112#66862—22no—
113#33922—111nomaximal, Sylow
114C22×C4×C11—41no—
115C22×C4×C11C2×D411yescharacteristic
116C2×C22⋊D11—41no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11D811yescharacteristic
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—41no—
122C2×D44—41no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C2×C4×D11C2×D411yescharacteristic
127C2×C8×C11—21no—
128C2×C8×C11—21no—
129C2×C8×C11C2×D411yescharacteristic
130C2×C8×C11C2411yescharacteristic
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—41no—
136C11×C22⋊C4—41no—
137C42×C11—41no—
138C22⋊Dic11D811yescharacteristic
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—41no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4D811yescharacteristic
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151Dic11⋊C4—41no—
152Dic11⋊C4—41no—
153Dic11⋊C4—41no—
154Dic11⋊C4D811yescharacteristic
155C4×Dic11—41no—
156C4×Dic11C2×D411yescharacteristic
157C2×C11⋊C8C2×D411yescharacteristic
158C2×C11⋊C8C2×D411yescharacteristic
159D88—21no—
160D88—21no—
161D88—21no—
162D88—21no—
163C8×D11—21no—
164C8×D11—21no—
165C11×C16—21no—
166C11×C16#4112yes—
167C11⋊C16—21no—
168C11⋊C16—21no—
169#3339—111no—
170#3339—111no—
171#2253—111no—
172#2234—111no—
173#2234—111no—
174#2232—111no—
175#2232—111no—
176#2228—111no—
177#2228—111no—
178#2218—111no—
179#2218—111no—
180C4×D16—111no—
181#2169—111no—
182#2159—111no—
183#2159D1111yescharacteristic, complemented
184C23×C11C2×D811yescharacteristic
185C22×D11—41no—
186C22×D11—41no—
187C22×D11C2×D811yescharacteristic
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—161no—
195C2×C4×C11C2×D811yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C22⋊D11—41no—
198C22⋊D11—82no—
199C22⋊D11—161no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11C2×D811yescharacteristic
203C2×Dic11C2×D811yescharacteristic
204C2×Dic11C2×D811yescharacteristic
205D44—41no—
206D44—41no—
207D44—41no—
208D44—41no—
209D44—82no—
210D44—161no—
211C4×D11—21no—
212C4×D11—21no—
213C4×D11—161no—
214C4×D11—161no—
215C4×D11—161no—
216C8×C11—21no—
217C8×C11C2×#4111yescharacteristic
218C8×C112−1+411yescharacteristic
219C11⋊C8—21no—
220C11⋊C8—21no—
221#553—221no—
222#553—221no—
223C2×D16—111no—
224C2×M32—111no—
225C2×M32C2×D1111yescharacteristic
226#499—111no—
227#499—111no—
228#482—221no—
229#482—221no—
230#481—221no—
231#481—221no—
232#478—221no—
233#478—221no—
234#466—111no—
235#466—111no—
236#466—111no—
237#466—111no—
238C4×D8—111no—
239C4×D8—111no—
240C8×D4—111no—
241#427—111no—
242#427C2×D1111yescharacteristic
243C2×#107—111no—
244C2×#107C2×D1111yescharacteristic
245#367—111no—
246#367—111no—
247#367C2×D1111yescharacteristic
248#367C2×D1111yescharacteristic
249#366—111no—
250#366—111no—
251#366—111no—
252#366C2×D1111yescharacteristic
253#366C2×D1111yescharacteristic
254C4⋊C16—111no—
255#357—111no—
256#357—111no—
257#357—111no—
258#357—111no—
259#357—111no—
260#357—111no—
261C22⋊C16—111no—
262C22⋊C16—111no—
263C4×C16—111no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11C22×D811yescharacteristic
268C2×D11—21no—
269C2×D11—21no—
270C2×D11—21no—
271C2×D11—81no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11—81no—
281C4×C11—81no—
282C4×C11#54711yescharacteristic
283C4×C11#57811yescharacteristic
284Dic11—21no—
285Dic11—21no—
286Dic11—21no—
287Dic11—81no—
288Dic11—81no—
289C2×D8—111no—
290C2×D8—111no—
291C22×C8—111no—
292C22×C8C22×D1111yescharacteristic
293#126—441no—
294#126—441no—
295#125—221no—
296#125—221no—
297#123—441no—
298#123—441no—
299#121—221no—
300#121—221no—
301#121—221no—
302#121—221no—
303#121—441no—
304#121—441no—
305C4×D4—111no—
306C4×D4—221no—
307C4×D4—221no—
308C4×D4—441no—
309C4×D4—441no—
310#117—21no—
311#117—221no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—221no—
314D16—222no—
315M32—22no—
316M32—222no—
317C2×C16—111no—
318C2×C16—111no—
319C2×C16C22×D1111yescharacteristic
320C2×C16C22×D1111yescharacteristic
321#107—21no—
322#107—111no—
323#107—111no—
324#107—221no—
325#107C22×D1111yescharacteristic
326#107C22×D1111yescharacteristic
327#107C22×D1111yescharacteristic
328#107C22×D1111yescharacteristic
329#106—21no—
330#106—221no—
331#106—221no—
332#106—221no—
333C4⋊C8—111no—
334#102—221no—
335#102—221no—
336#102—221no—
337#102—221no—
338#102—221no—
339#102—221no—
340C22⋊C8—111no—
341C22⋊C8—111no—
342C4×C8—111no—
343C2×C11—41no—
344C2×C11#333411yescharacteristic
345C2×C11#341411yescharacteristic
346C2×C11#341511yescharacteristic
347D11—41no—
348D11—161no—
349D11—161no—
350C2×D4—111no—
351C2×D4—221no—
352C2×D4—221no—
353C2×D4—441no—
354C2×D4—441no—
355C2×D4—441no—
356C2×D4—441no—
357C22×C4—41no—
358C22×C4—111no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4D4×D1111yescharacteristic
363D8—221no—
364D8—221no—
365D8—221no—
366D8—221no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—111no—
370C2×C8—111no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8D4×D1111yescharacteristic
374C2×C8C23×D1111yescharacteristic
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—111no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—441no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4—441no—
388C22⋊C4—41no—
389C22⋊C4—111no—
390C22⋊C4—111no—
391C22⋊C4—441no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4—441no—
397C22⋊C4—441no—
398C42—41no—
399C42—111no—
400C42—441no—
401C16—21no—
402C16—221no—
403C16—221no—
404C16#433912yes—
405C11#3392211yescharacteristic, complemented, Sylow
406C23—111no—
407C23—441no—
408C23—441no—
409C23D8×D1111yescharacteristic
410D4—441no—
411D4—441no—
412D4—441no—
413D4—441no—
414D4—441no—
415D4—882no—
416D4—882no—
417D4—1761no—
418D4—1761no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—111no—
426C2×C4—111no—
427C2×C4—111no—
428C2×C4—161no—
429C2×C4—221no—
430C2×C4—221no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—1761no—
434C2×C4—1761no—
435C2×C4—1761no—
436C2×C4D8×D1111yescharacteristic
437C2×C4C2×D4×D1111yescharacteristic
438C8—21no—
439C8—221no—
440C8—221no—
441C8C2×#433911yescharacteristic
442C8#6704011yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—221no—
447C22—221no—
448C22—221no—
449C22—881no—
450C22—881no—
451C22—881no—
452C22—881no—
453C22—881no—
454C22—881no—
455C22C2×D8×D1111yescharacteristic
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—221no—
462C4—221no—
463C4—221no—
464C4—881no—
465C4—881no—
466C4#1062303811yescharacteristic
467C4#1062329711yescharacteristic
468C2—41no—
469C2—441no—
470C2—1761no—
471C2—1761no—
472C2#1308096111yescharacteristic
473C2#1308175111yescharacteristic
474C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
hypercenter#2159D11
hypocenterC11#33922
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
1. #13081018C2semidirect
2. #13081014C2semidirect
3. #13070894C2semidirect
4. #13070809C2semidirect
5. #13070807C2semidirect
6. #13070798C2semidirect
7. #13070796C2semidirect
8. #13070776C2semidirect
9. #13070772C2semidirect
10. #13070720C2semidirect
11. #13070719C2semidirect
12. #13070462C2semidirect
13. #13070446C2semidirect
14. #13070401C2semidirect
15. C11×#2159C2semidirect
183. #2159D11semidirect
405. C11#33922semidirect

Maximal subgroups

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

subgroupindex
#130810182
#130810142
#130708942
#130708092
#130708072
#130707982
#130707962
#130707762
#130707722
#130707202
#130707192
#130704622
#130704462
#130704012
C11×#21592
#3392211