Finite Group Databasebeta

← #14909320

Subgroups — #14909320

Order 2816.

526 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#13079186C211yesmaximal, characteristic, complemented
2#13070892C211yesmaximal, characteristic, complemented
3#13070875C211yesmaximal, characteristic, complemented
4#13070850C211yesmaximal, characteristic, complemented
5#13070847C211yesmaximal, characteristic, complemented
6#13070714C211yesmaximal, characteristic, complemented
7#13070710C211yesmaximal, characteristic, complemented
8#13070705C211yesmaximal, characteristic, complemented
9#13070700C211yesmaximal, characteristic
10C4×#66893C211yesmaximal, characteristic, complemented
11C4×#66892C211yesmaximal, characteristic, complemented
12C4×#66891C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14C2×C4×C11⋊C16C211yesmaximal, characteristic, complemented
15C11×#3168C211yesmaximal, characteristic, complemented
16C11×#529—21no—
17#10623010—21no—
18C11×#499C2211yescharacteristic
19C11×#495C2211yescharacteristic
20C11×#488—21no—
21C11×#467C2211yescharacteristic
22C11×#466C2211yescharacteristic
23C11×#465—21no—
24C4×C11×Q16C2211yescharacteristic
25C4×C11×SD16—21no—
26C4×C11×D8C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32#10622729C2211yescharacteristic
33#10622728C2211yescharacteristic
34#10622727—21no—
35C22×C11⋊C16C2211yescharacteristic
36C22×C11⋊C16C2211yescharacteristic
37C4×Dic44C2211yescharacteristic
38#10622310—21no—
39#10622309C2211yescharacteristic
40C4×D88C2211yescharacteristic
41C4×#4314—21no—
42#10622296C2211yescharacteristic
43#10622202C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622129C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55C4×C11⋊C16C2211yescharacteristic
56C4×C11⋊C16C2211yescharacteristic
57C4×C11⋊C16C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×SD16—21no—
61C2×C11×D8C2311yescharacteristic
62C22×C8×C11D411yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C11×#126—41no—
65C11×#125—21no—
66C11×#124—21no—
67C11×#123—41no—
68C11×C22⋊Q8—21no—
69C11×#121—21no—
70C4×Q8×C11—21no—
71C4×D4×C11—21no—
72C4×D4×C11—41no—
73C11×#117—41no—
74C2×C42×C11D411yescharacteristic
75#66983—21no—
76#66982—41no—
77C4×C22⋊D11—41no—
78#66977—21no—
79C2×Dic44C2311yescharacteristic
80C2×D88C2311yescharacteristic
81C2×#4314—21no—
82#66929—41no—
83#66928—21no—
84C4×D44—21no—
85#66925—41no—
86#66923—21no—
87C4×Dic22—21no—
88C11×#107C2311yescharacteristic
89C11×#107C2311yescharacteristic
90C11×#106—21no—
91C11×#103—21no—
92C11×#103—21no—
93C11×#102—21no—
94C11×#102—21no—
95C4×C8×C11D411yescharacteristic
96C4×C8×C11D411yescharacteristic
97C4×C8×C11C2311yescharacteristic
98C4×C8×C11C2311yescharacteristic
99#66893—22no—
100#66892—22no—
101#66891—22no—
102#66890—22no—
103#66885—21no—
104#66885—21no—
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108#66880—21no—
109#66880—21no—
110C2×C11⋊C16—22no—
111C2×C11⋊C16—22no—
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#33735—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11—41no—
121C22×C4×C11D811yescharacteristic
122C22×C4×C11D811yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C2×C22⋊D11—41no—
125C2×D44—21no—
126C2×C4×D11—41no—
127C2×Dic22—21no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×SD16—42no—
131C11×D8—21no—
132C11×D8—21no—
133C2×C8×C11—22no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11C2×D411yescharacteristic
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4—41no—
146C11×C22⋊C4—41no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11—41no—
152C42×C11D811yescharacteristic
153C42×C11D811yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2×D411yescharacteristic
156C22⋊Dic11—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161C4⋊Dic11—21no—
162C4⋊Dic11—21no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167C4×Dic11—41no—
168Dic44—21no—
169Dic44—21no—
170D88—21no—
171D88—21no—
172#4314—42no—
173C11⋊C16—21no—
174C11⋊C16—21no—
175C11⋊C16#4112yes—
176C11⋊C16#4112yes—
177#3168—111no—
178#3168D1111yescharacteristic, complemented
179#2253—111no—
180#2249—111no—
181#2242—111no—
182#2242—111no—
183#2217—111no—
184#2217—111no—
185#2216—111no—
186#2215—111no—
187C4×Q32—111no—
188C4×SD32—111no—
189C4×SD32—111no—
190C4×D16—111no—
191C2×C4×C16—111no—
192C23×C11—41no—
193C23×C11C2×D811yescharacteristic
194C22×D11—41no—
195Q8×C11—41no—
196Q8×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—82no—
200C2×C4×C11—22no—
201C2×C4×C11—21no—
202C2×C4×C11—21no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—82no—
208C2×C4×C11C2×D811yescharacteristic
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×D811yescharacteristic
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—82no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218D44—41no—
219D44—41no—
220C4×D11—82no—
221Dic22—41no—
222Dic22—41no—
223C8×C11—21no—
224C8×C11—21no—
225C8×C11#13512yes—
226C8×C11C2×#4111yescharacteristic
227C8×C11C2×#4111yescharacteristic
228#529—21no—
229#529—221no—
230C2×Q32—111no—
231C2×SD32—111no—
232C2×SD32—111no—
233C2×D16—111no—
234C22×C16—111no—
235C22×C16—111no—
236#499—111no—
237#499C2×D1111yescharacteristic
238#495—111no—
239#495C2×D1111yescharacteristic
240#488—21no—
241#488—221no—
242#467—111no—
243#467C2×D1111yescharacteristic
244#466—111no—
245#466C2×D1111yescharacteristic
246#465—21no—
247#465—221no—
248C4×Q16—111no—
249C4×Q16C2×D1111yescharacteristic
250C4×SD16—21no—
251C4×SD16—221no—
252C4×D8—111no—
253C4×D8C2×D1111yescharacteristic
254C2×C4×C8C2×D1111yescharacteristic
255#367—111no—
256#367—111no—
257#366—111no—
258#366—111no—
259#358—111no—
260#358—111no—
261#358—111no—
262#358—111no—
263#357—111no—
264#357—111no—
265#357—111no—
266#357—111no—
267C4×C16—111no—
268C4×C16—111no—
269C4×C16—111no—
270C4×C16—111no—
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—81no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11#50812yes—
277C22×C11C22×D811yescharacteristic
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—81no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11#50812yes—
289C4×C11#53211yescharacteristic
290C4×C11C2×#13511yescharacteristic
291Dic11—81no—
292Dic11—81no—
293Dic11—81no—
294C2×Q16—111no—
295C2×Q16C22×D1111yescharacteristic
296C2×SD16—21no—
297C2×SD16—221no—
298C2×D8—111no—
299C2×D8C22×D1111yescharacteristic
300C22×C8C22⋊D1111yescharacteristic
301C22×C8C22×D1111yescharacteristic
302#126—41no—
303#126—441no—
304#125—21no—
305#125—221no—
306#124—21no—
307#124—221no—
308#123—41no—
309#123—441no—
310C22⋊Q8—21no—
311C22⋊Q8—221no—
312#121—21no—
313#121—221no—
314C4×Q8—21no—
315C4×Q8—221no—
316C4×D4—21no—
317C4×D4—41no—
318C4×D4—221no—
319C4×D4—441no—
320#117—41no—
321#117—441no—
322C2×C42C22⋊D1111yescharacteristic
323Q32—222no—
324SD32—222no—
325SD32—222no—
326D16—222no—
327C2×C16—111no—
328C2×C16—111no—
329C2×C16—111no—
330C2×C16—111no—
331C2×C16—222no—
332C2×C16—222no—
333#107—111no—
334#107—111no—
335#107C22×D1111yescharacteristic
336#107C22×D1111yescharacteristic
337#106—21no—
338#106—221no—
339#103—21no—
340#103—21no—
341#103—221no—
342#103—221no—
343#102—21no—
344#102—21no—
345#102—221no—
346#102—221no—
347C4×C8C22⋊D1111yescharacteristic
348C4×C8C22⋊D1111yescharacteristic
349C4×C8C22×D1111yescharacteristic
350C4×C8C22×D1111yescharacteristic
351C2×C11—22no—
352C2×C11—161no—
353C2×C11#316911yescharacteristic
354C2×C11C2×#50811yescharacteristic
355C2×C11C2×#50811yescharacteristic
356D11—161no—
357C2×Q8—21no—
358C2×Q8—221no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4—221no—
362C2×D4—441no—
363C22×C4—41no—
364C22×C4—441no—
365C22×C4#432311yescharacteristic
366C22×C4#432311yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368Q16—21no—
369Q16—21no—
370Q16—221no—
371Q16—221no—
372SD16—42no—
373SD16—442no—
374D8—21no—
375D8—21no—
376D8—221no—
377D8—221no—
378C2×C8—22no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×C22⋊D1111yescharacteristic
382C2×C8C2×C22⋊D1111yescharacteristic
383C2×C8C2×C22⋊D1111yescharacteristic
384C2×C8C23×D1111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C42—41no—
408C42—441no—
409C42#432311yescharacteristic
410C42#432311yescharacteristic
411C42C2×C22⋊D1111yescharacteristic
412C42C2×C22⋊D1111yescharacteristic
413C16—112no—
414C16—112no—
415C16—221no—
416C16—221no—
417C11#3373511yescharacteristic, complemented, Sylow
418C23—41no—
419C23—441no—
420C23C2×#432311yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—441no—
424Q8—441no—
425D4—41no—
426D4—41no—
427D4—82no—
428D4—441no—
429D4—441no—
430D4—882no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—82no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—441no—
442C2×C4—882no—
443C2×C4C2×#432311yescharacteristic
444C2×C4C2×#432311yescharacteristic
445C2×C4C2×#432311yescharacteristic
446C2×C4C2×#432311yescharacteristic
447C2×C4C2×#432311yescharacteristic
448C2×C4C22×C22⋊D1111yescharacteristic
449C8—21no—
450C8—21no—
451C8#6700312yes—
452C8#41×D1111yescharacteristic
453C8#41×D1111yescharacteristic
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—881no—
460C22—881no—
461C22—881no—
462C22#1062280712yes—
463C22C22×#432311yescharacteristic
464C4—21no—
465C4—21no—
466C4—21no—
467C4—21no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—881no—
472C4—881no—
473C4—881no—
474C4#1062280712yes—
475C4C2×#6700311yescharacteristic
476C4#1062336311yescharacteristic
477C2—22no—
478C2—161no—
479C2—1761no—
480C2#1307919111yescharacteristic
481C2C2×#1062280711yescharacteristic
482C2C2×#1062280711yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3168C2
socleC22×C11C22×D8
prime radical#13070700C2
hypercenter#3168D11
hypocenterC11#33735
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13070892C2semidirect
3. #13070875C2semidirect
4. #13070850C2semidirect
5. #13070847C2semidirect
6. #13070714C2semidirect
7. #13070710C2semidirect
8. #13070705C2semidirect
10. C4×#66893C2semidirect
11. C4×#66892C2semidirect
12. C4×#66891C2semidirect
13. C4×#66890C2semidirect
14. C2×C4×C11⋊C16C2semidirect
15. C11×#3168C2semidirect
178. #3168D11semidirect
417. C11#33735semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708922
#130708752
#130708502
#130708472
#130707142
#130707102
#130707052
#130707002
C4×#668932
C4×#668922
C4×#668912
C4×#668902
C2×C4×C11⋊C162
C11×#31682
#3373511