Finite Group Databasebeta

← #14911383

Subgroups — #14911383

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#13081019C211yesmaximal, characteristic, complemented
2#13070892C211yesmaximal, characteristic, complemented
3#13070807C211yesmaximal, characteristic, complemented
4#13070804C211yesmaximal, characteristic, complemented
5#13070796C211yesmaximal, characteristic, complemented
6#13070794C211yesmaximal, characteristic, complemented
7#13070773C211yesmaximal, characteristic, complemented
8#13070770C211yesmaximal, characteristic, complemented
9#13070717C211yesmaximal, characteristic, complemented
10#13070717C211yesmaximal, characteristic, complemented
11C4×#66890C211yesmaximal, characteristic, complemented
12#13070448C211yesmaximal, characteristic, complemented
13#13070405C211yesmaximal, characteristic, complemented
14#13070402C211yesmaximal, characteristic, complemented
15C11×#3339C211yesmaximal, characteristic, complemented
16C11×#553—21no—
17#10623096—21no—
18C11×#499C2211yescharacteristic
19C11×#482—21no—
20C11×#481—21no—
21C11×#478—21no—
22C11×#466C2211yescharacteristic
23C11×#466C2211yescharacteristic
24C4×C11×D8C2211yescharacteristic
25C8×D4×C11C2211yescharacteristic
26C11×#427C2211yescharacteristic
27C2×C11×#107C2211yescharacteristic
28C2×#66890C2211yescharacteristic
29#10622728C2211yescharacteristic
30#10622728C2211yescharacteristic
31#10622719C2211yescharacteristic
32C2×#66882C2211yescharacteristic
33C2×#66876C2211yescharacteristic
34C2×#66876C2211yescharacteristic
35#10622460—21no—
36#10622350—21no—
37#10622348—21no—
38C4×D88C2211yescharacteristic
39#10622296C2211yescharacteristic
40#10622200C2211yescharacteristic
41#10622200C2211yescharacteristic
42#10622200C2211yescharacteristic
43C22⋊(C11⋊C16)C2211yescharacteristic
44C22⋊(C11⋊C16)C2211yescharacteristic
45#10622129C2211yescharacteristic
46#10622129C2211yescharacteristic
47#10622129C2211yescharacteristic
48#10622128C2211yescharacteristic
49#10622128C2211yescharacteristic
50#10622128C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622127C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55#10622127C2211yescharacteristic
56#10622127C2211yescharacteristic
57C4⋊(C11⋊C16)C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×D8C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×#126—41no—
63C11×#125—21no—
64C11×#123—41no—
65C11×#121—21no—
66C11×#121—21no—
67C11×#121—41no—
68C4×D4×C11—21no—
69C4×D4×C11—41no—
70C4×D4×C11D411yescharacteristic
71C11×#117—21no—
72C2×C11×C4⋊C4—21no—
73#66992—41no—
74#66983—21no—
75#66983—21no—
76#66979—21no—
77C2×C4⋊Dic11—21no—
78C2×D88C2311yescharacteristic
79#66951—41no—
80#66936—41no—
81(C22⋊D11)⋊C4—41no—
82C4×D44—21no—
83#66923—21no—
84C11×#107—21no—
85C11×#107C2311yescharacteristic
86C11×#107C2311yescharacteristic
87C11×#107C2311yescharacteristic
88C11×#106—21no—
89C11×#106—21no—
90C11×C4⋊C8D411yescharacteristic
91C11×#102—21no—
92C11×#102—21no—
93C11×#102—21no—
94C11×C22⋊C8D411yescharacteristic
95C11×C22⋊C8D411yescharacteristic
96C4×C8×C11C2311yescharacteristic
97#66890—22no—
98#66885—21no—
99#66885—21no—
100#66885—21no—
101#66882—21no—
102#66882C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106#66881—21no—
107#66876—22no—
108#66876—22no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#33922—111nomaximal, Sylow
114C2×D4×C11—21no—
115C2×D4×C11—41no—
116C2×D4×C11—41no—
117C2×D4×C11D811yescharacteristic
118C22×C4×C11—41no—
119C22×C4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C22×Dic11—41no—
125C2×D44—21no—
126C2×C4×D11—41no—
127C11×D8—21no—
128C11×D8—21no—
129C2×C8×C11—21no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11C2×D411yescharacteristic
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2411yescharacteristic
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4—41no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4D811yescharacteristic
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4D811yescharacteristic
149C11×C22⋊C4D811yescharacteristic
150C42×C11—41no—
151C42×C11C2×D411yescharacteristic
152C22⋊Dic11—41no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4—41no—
155(C2×D11)⋊C4—41no—
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—21no—
159C4⋊Dic11—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163D88—21no—
164D88—21no—
165C11⋊C16—21no—
166C11⋊C16—21no—
167C11⋊C16—21no—
168C11⋊C16#4112yes—
169#3339—111no—
170#3339D1111yescharacteristic, complemented
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#2159—111no—
184C23×C11—41no—
185C23×C11C2×D811yescharacteristic
186C23×C11C2×D811yescharacteristic
187C22×D11—41no—
188D4×C11—41no—
189D4×C11—41no—
190D4×C11—41no—
191D4×C11—82no—
192D4×C11—161no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—161no—
201C2×C4×C11—161no—
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11C2×D811yescharacteristic
204C2×C4×C11C2×D811yescharacteristic
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C22⋊D11—82no—
208C22⋊D11—161no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—161no—
213D44—41no—
214D44—41no—
215C4×D11—161no—
216C8×C11—21no—
217C8×C11—21no—
218C8×C11—21no—
219C8×C11C2×#4111yescharacteristic
220C8×C112−1+411yescharacteristic
221#553—21no—
222#553—221no—
223C2×D16—111no—
224C2×M32—111no—
225C2×M32—111no—
226#499—111no—
227#499C2×D1111yescharacteristic
228#482—21no—
229#482—221no—
230#481—21no—
231#481—221no—
232#478—21no—
233#478—221no—
234#466—111no—
235#466—111no—
236#466C2×D1111yescharacteristic
237#466C2×D1111yescharacteristic
238C4×D8—111no—
239C4×D8C2×D1111yescharacteristic
240C8×D4C2×D1111yescharacteristic
241#427—111no—
242#427C2×D1111yescharacteristic
243C2×#107—111no—
244C2×#107C2×D1111yescharacteristic
245#367—111no—
246#367—111no—
247#367—111no—
248#367—111no—
249#366—111no—
250#366—111no—
251#366—111no—
252#366—111no—
253#366—111no—
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×C11—21no—
268C22×C11—21no—
269C22×C11—21no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11C22×D811yescharacteristic
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11#54711yescharacteristic
285C4×C11#57811yescharacteristic
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289C2×D8—111no—
290C2×D8C22×D1111yescharacteristic
291C22×C8C22×D1111yescharacteristic
292C22×C8C22×D1111yescharacteristic
293#126—41no—
294#126—441no—
295#125—21no—
296#125—221no—
297#123—41no—
298#123—441no—
299#121—21no—
300#121—21no—
301#121—41no—
302#121—221no—
303#121—221no—
304#121—441no—
305C4×D4—21no—
306C4×D4—41no—
307C4×D4—221no—
308C4×D4—441no—
309C4×D4C22⋊D1111yescharacteristic
310#117—21no—
311#117—221no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—221no—
314D16—222no—
315M32—222no—
316M32—222no—
317C2×C16—111no—
318C2×C16—111no—
319C2×C16—111no—
320C2×C16—111no—
321#107—21no—
322#107—111no—
323#107—111no—
324#107—111no—
325#107—221no—
326#107C22×D1111yescharacteristic
327#107C22×D1111yescharacteristic
328#107C22×D1111yescharacteristic
329#106—21no—
330#106—21no—
331#106—221no—
332#106—221no—
333C4⋊C8C22⋊D1111yescharacteristic
334#102—21no—
335#102—21no—
336#102—21no—
337#102—221no—
338#102—221no—
339#102—221no—
340C22⋊C8C22⋊D1111yescharacteristic
341C22⋊C8C22⋊D1111yescharacteristic
342C4×C8C22×D1111yescharacteristic
343C2×C11—41no—
344C2×C11—41no—
345C2×C11—161no—
346C2×C11#333411yescharacteristic
347C2×C11#341411yescharacteristic
348C2×C11#341511yescharacteristic
349D11—161no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—221no—
354C2×D4—441no—
355C2×D4—441no—
356C2×D4#432311yescharacteristic
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4C2×C22⋊D1111yescharacteristic
362C22×C4C2×C22⋊D1111yescharacteristic
363D8—21no—
364D8—21no—
365D8—221no—
366D8—221no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8C2×C22⋊D1111yescharacteristic
372C2×C8C2×C22⋊D1111yescharacteristic
373C2×C8C2×C22⋊D1111yescharacteristic
374C2×C8C23×D1111yescharacteristic
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—441no—
385C4⋊C4—441no—
386C4⋊C4—441no—
387C4⋊C4#432311yescharacteristic
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—441no—
393C22⋊C4—441no—
394C22⋊C4—441no—
395C22⋊C4—441no—
396C22⋊C4#432311yescharacteristic
397C22⋊C4#432311yescharacteristic
398C42—41no—
399C42—441no—
400C42C2×C22⋊D1111yescharacteristic
401C16—112no—
402C16—221no—
403C16—221no—
404C16—221no—
405C11#3392211yescharacteristic, complemented, Sylow
406C23—41no—
407C23—441no—
408C23C2×#432311yescharacteristic
409C23C2×#432311yescharacteristic
410D4—41no—
411D4—41no—
412D4—41no—
413D4—82no—
414D4—161no—
415D4—441no—
416D4—441no—
417D4—882no—
418D4—1761no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—161no—
427C2×C4—161no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—1761no—
432C2×C4—1761no—
433C2×C4C2×#432311yescharacteristic
434C2×C4C2×#432311yescharacteristic
435C2×C4C2×#432311yescharacteristic
436C2×C4C2×#432311yescharacteristic
437C2×C4C22×C22⋊D1111yescharacteristic
438C8—21no—
439C8—21no—
440C8—21no—
441C8#41×D1111yescharacteristic
442C8#6704311yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—881no—
453C22—881no—
454C22—881no—
455C22C22×#432311yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—881no—
464C4—881no—
465C4—881no—
466C4#1062335511yescharacteristic
467C4#1062336911yescharacteristic
468C2—41no—
469C2—41no—
470C2—161no—
471C2—1761no—
472C2#1308095911yescharacteristic
473C2#1308175011yescharacteristic
474C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3339C2
socleC22×C11C22×D8
hypercenter#3339D11
hypocenterC11#33922
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3339

Complements

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

NH ≅ G/Ntype
1. #13081019C2semidirect
2. #13070892C2semidirect
3. #13070807C2semidirect
4. #13070804C2semidirect
5. #13070796C2semidirect
6. #13070794C2semidirect
7. #13070773C2semidirect
8. #13070770C2semidirect
9. #13070717C2semidirect
10. #13070717C2semidirect
11. C4×#66890C2semidirect
12. #13070448C2semidirect
13. #13070405C2semidirect
14. #13070402C2semidirect
15. C11×#3339C2semidirect
170. #3339D11semidirect
405. C11#33922semidirect

Maximal subgroups

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

subgroupindex
#130810192
#130708922
#130708072
#130708042
#130707962
#130707942
#130707732
#130707702
#130707172
C4×#668902
#130704482
#130704052
#130704022
C11×#33392
#3392211