Finite Group Databasebeta

← #14908715

Subgroups — #14908715

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2#13070824C211yesmaximal, characteristic, complemented
3#13070807C211yesmaximal, characteristic, complemented
4#13070780C211yesmaximal, characteristic, complemented
5#13070773C211yesmaximal, characteristic, complemented
6#13070678C211yesmaximal, characteristic, complemented
7#13070671C211yesmaximal, characteristic, complemented
8#13070556C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic
10C4×#66893C211yesmaximal, characteristic, complemented
11C4×#66892C211yesmaximal, characteristic, complemented
12C4×#66891C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14#13070415C211yesmaximal, characteristic, complemented
15C4×C11×#135C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17C4×C11×#41—21no—
18#10623010—21no—
19C4×C11×Q16C2211yescharacteristic
20C4×C11×Q16C2211yescharacteristic
21C4×C11×SD16—21no—
22C4×C11×SD16—21no—
23C4×C11×D8C2211yescharacteristic
24C4×C11×D8C2211yescharacteristic
25C11×#427C2211yescharacteristic
26C11×#416—21no—
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66893C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30C2×#66891C2211yescharacteristic
31C2×#66890C2211yescharacteristic
32#10622729C2211yescharacteristic
33#10622728C2211yescharacteristic
34#10622727—21no—
35C4×Dic44C2211yescharacteristic
36#10622310—21no—
37#10622309C2211yescharacteristic
38C4×D88C2211yescharacteristic
39C4×#4314—21no—
40#10622296C2211yescharacteristic
41#10622202C2211yescharacteristic
42#10622202C2211yescharacteristic
43#10622200C2211yescharacteristic
44#10622200C2211yescharacteristic
45C22⋊(C11⋊C16)C2211yescharacteristic
46C22⋊(C11⋊C16)C2211yescharacteristic
47#10622130C2211yescharacteristic
48#10622130C2211yescharacteristic
49#10622129C2211yescharacteristic
50#10622129C2211yescharacteristic
51#10622128C2211yescharacteristic
52#10622128C2211yescharacteristic
53#10622127C2211yescharacteristic
54#10622127C2211yescharacteristic
55C4⋊(C11⋊C16)C2211yescharacteristic
56C4⋊(C11⋊C16)C2211yescharacteristic
57C4×C11⋊C16C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×C11×#41—21no—
60C11×#135—22no—
61C11×#135—22no—
62C2×C11×Q16C2311yescharacteristic
63C2×C11×SD16—21no—
64C2×C11×D8C2311yescharacteristic
65C22×C8×C11D411yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—21no—
68C4×Q8×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11—21no—
71C4×D4×C11—41no—
72C4×D4×C11—41no—
73C11×#117—21no—
74C11×#117—41no—
75C2×C42×C11—41no—
76C2×C42×C11D411yescharacteristic
77#66983—21no—
78#66982—41no—
79C4×C22⋊D11—41no—
80#66977—21no—
81C2×Dic44C2311yescharacteristic
82C2×D88C2311yescharacteristic
83C2×#4314—21no—
84#66929—41no—
85#66928—21no—
86C4×D44—21no—
87#66925—41no—
88#66923—21no—
89C4×Dic22—21no—
90C11×#107C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#106—21no—
93C11×#103—21no—
94C11×#103—21no—
95C11×#102—21no—
96C11×#102—21no—
97C4×C8×C11D411yescharacteristic
98C4×C8×C11D411yescharacteristic
99C4×C8×C11C2311yescharacteristic
100C4×C8×C11C2311yescharacteristic
101#66893—22no—
102#66892—22no—
103#66891—22no—
104#66890—22no—
105#66885—21no—
106#66885—21no—
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109#66881—21no—
110#66880—21no—
111#66880—21no—
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114C2×C11⋊C16C2311yescharacteristic
115C2×C11⋊C16C2311yescharacteristic
116#33662—111nomaximal, Sylow
117C11×#41—24no—
118C11×#41—42no—
119C2×Q8×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—41no—
122C22×C4×C11—41no—
123C22×C4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11D811yescharacteristic
126C22×C4×C11D811yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×D44—21no—
130C2×C4×D11—41no—
131C2×Dic22—21no—
132C11×Q16—21no—
133C11×Q16#4112yes—
134C11×SD16—24no—
135C11×D8—21no—
136C11×D8#4112yes—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C2×C8×C11—41no—
140C2×C8×C11C2×D411yescharacteristic
141C2×C8×C11C2×D411yescharacteristic
142C2×C8×C11C2×D411yescharacteristic
143C2×C8×C11C2411yescharacteristic
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4—41no—
148C11×C22⋊C4—41no—
149C11×C22⋊C4—41no—
150C11×C22⋊C4—41no—
151C42×C11—41no—
152C42×C11—41no—
153C42×C11—41no—
154C42×C11D811yescharacteristic
155C42×C11D811yescharacteristic
156C42×C11C2×D411yescharacteristic
157C42×C11C2×D411yescharacteristic
158C22⋊Dic11—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163C4⋊Dic11—21no—
164C4⋊Dic11—21no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4—41no—
169C4×Dic11—41no—
170Dic44—21no—
171Dic44—21no—
172D88—21no—
173D88—21no—
174#4314—42no—
175C11⋊C16—21no—
176C11⋊C16—21no—
177C11⋊C16—21no—
178C11⋊C16—21no—
179#3168—111no—
180C4×#135D1111yescharacteristic, complemented
181#2237—111no—
182#2234—111no—
183#2229—111no—
184#2228—111no—
185#2211—111no—
186#2210—111no—
187#2189—111no—
188#2186—111no—
189C4×Q32—111no—
190C4×SD32—111no—
191C4×SD32—111no—
192C4×D16—111no—
193#2162—111no—
194C23×C11—41no—
195C23×C11C2×D811yescharacteristic
196C22×D11—41no—
197Q8×C11—22no—
198Q8×C11—41no—
199D4×C11—22no—
200D4×C11—44no—
201D4×C11—41no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—22no—
205C2×C4×C11—41no—
206C2×C4×C11—44no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—82no—
211C2×C4×C11—82no—
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C2×D811yescharacteristic
214C2×C4×C11C2×D811yescharacteristic
215C2×C4×C11C2×D811yescharacteristic
216C2×C4×C11C2×D811yescharacteristic
217C2×C4×C11C22×D411yescharacteristic
218C22⋊D11—82no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222D44—41no—
223D44—41no—
224C4×D11—82no—
225Dic22—41no—
226Dic22—41no—
227C8×C11—21no—
228C8×C11—21no—
229C8×C11—21no—
230C8×C11C2×#4111yescharacteristic
231C8×C11C2×#4111yescharacteristic
232C2×#135C2×D1111yescharacteristic
233#529—221no—
234C4×#41—21no—
235C2×Q32—111no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×D16—111no—
239#499—111no—
240#495—111no—
241#488—221no—
242#467—111no—
243#466—111no—
244#465—221no—
245C4×Q16—111no—
246C4×Q16C2×D1111yescharacteristic
247C4×Q16C2×D1111yescharacteristic
248C4×SD16—21no—
249C4×SD16—21no—
250C4×SD16—221no—
251C4×D8—111no—
252C4×D8C2×D1111yescharacteristic
253C4×D8C2×D1111yescharacteristic
254#427C2×D1111yescharacteristic
255#416—21no—
256C2×C4×C8C2×D1111yescharacteristic
257#367—111no—
258#367—111no—
259#366—111no—
260#366—111no—
261C4⋊C16—111no—
262C4⋊C16—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271C22⋊C16—111no—
272C22⋊C16—111no—
273C4×C16—111no—
274C4×C16—111no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—42no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11C22×D811yescharacteristic
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—42no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11#50812yes—
293C4×C11#52511yescharacteristic
294C4×C11#57511yescharacteristic
295Dic11—81no—
296Dic11—81no—
297Dic11—81no—
298C2×#41—21no—
299#135—22no—
300#135—22no—
301C2×Q16—111no—
302C2×Q16C22×D1111yescharacteristic
303C2×SD16—21no—
304C2×SD16—221no—
305C2×D8—111no—
306C2×D8C22×D1111yescharacteristic
307C22×C8C22⋊D1111yescharacteristic
308C22×C8C22×D1111yescharacteristic
309#126—441no—
310#125—221no—
311#124—221no—
312#123—441no—
313C22⋊Q8—221no—
314#121—221no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×Q8—221no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—41no—
321C4×D4—41no—
322C4×D4—221no—
323C4×D4—441no—
324#117—21no—
325#117—41no—
326#117—441no—
327C2×C42—41no—
328C2×C42C22⋊D1111yescharacteristic
329Q32—222no—
330SD32—222no—
331SD32—222no—
332D16—222no—
333C2×C16—111no—
334C2×C16—111no—
335C2×C16—111no—
336C2×C16—111no—
337#107—111no—
338#107—111no—
339#107C22×D1111yescharacteristic
340#107C22×D1111yescharacteristic
341#106—21no—
342#106—221no—
343#103—21no—
344#103—21no—
345#103—221no—
346#103—221no—
347#102—21no—
348#102—21no—
349#102—221no—
350#102—221no—
351C4×C8C22⋊D1111yescharacteristic
352C4×C8C22⋊D1111yescharacteristic
353C4×C8C22×D1111yescharacteristic
354C4×C8C22×D1111yescharacteristic
355C2×C11—41no—
356C2×C11—82no—
357C2×C11#310011yescharacteristic
358C2×C11C2×#50811yescharacteristic
359C2×C11#341411yescharacteristic
360D11—161no—
361#41—24no—
362#41—42no—
363C2×Q8—21no—
364C2×Q8—221no—
365C2×D4—21no—
366C2×D4—41no—
367C2×D4—221no—
368C2×D4—441no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—441no—
373C22×C4#432311yescharacteristic
374C22×C4#432311yescharacteristic
375C22×C4C2×C22⋊D1111yescharacteristic
376Q16—21no—
377Q16—221no—
378Q16—221no—
379Q16#433912yes—
380SD16—24no—
381SD16—442no—
382D8—21no—
383D8—221no—
384D8—221no—
385D8#433912yes—
386C2×C8—21no—
387C2×C8—21no—
388C2×C8—41no—
389C2×C8C2×C22⋊D1111yescharacteristic
390C2×C8C2×C22⋊D1111yescharacteristic
391C2×C8C2×C22⋊D1111yescharacteristic
392C2×C8C23×D1111yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—221no—
398C4⋊C4—221no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C22⋊C4—441no—
410C22⋊C4—441no—
411C42—41no—
412C42—41no—
413C42—41no—
414C42—441no—
415C42#432311yescharacteristic
416C42#432311yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C42C2×C22⋊D1111yescharacteristic
419C16—221no—
420C16—221no—
421C16—221no—
422C16—221no—
423C11#3366211yescharacteristic, complemented, Sylow
424C23—41no—
425C23—441no—
426C23C2×#432311yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—441no—
430Q8—441no—
431D4—22no—
432D4—44no—
433D4—41no—
434D4—441no—
435D4—441no—
436D4—882no—
437C2×C4—22no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—882no—
451C2×C4C2×#432311yescharacteristic
452C2×C4C2×#432311yescharacteristic
453C2×C4C2×#432311yescharacteristic
454C2×C4C2×#432311yescharacteristic
455C2×C4C2×#432311yescharacteristic
456C2×C4C22×C22⋊D1111yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×#433911yescharacteristic
461C8C2×#433911yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—881no—
469C22—881no—
470C22—881no—
471C22C22×#432311yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—42no—
477C4—81no—
478C4—81no—
479C4—881no—
480C4—881no—
481C4—881no—
482C4#1062280712yes—
483C4#1062332211yescharacteristic
484C4#1062335311yescharacteristic
485C2—41no—
486C2—82no—
487C2—1761no—
488C2#1307861611yescharacteristic
489C2C2×#1062280711yescharacteristic
490C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×#135C2
socleC22×C11C22×D8
prime radical#13070539C2
hypercenterC4×#135D11
hypocenterC11#33662
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13070824C2semidirect
3. #13070807C2semidirect
4. #13070780C2semidirect
5. #13070773C2semidirect
6. #13070678C2semidirect
7. #13070671C2semidirect
8. #13070556C2semidirect
10. C4×#66893C2semidirect
11. C4×#66892C2semidirect
12. C4×#66891C2semidirect
13. C4×#66890C2semidirect
14. #13070415C2semidirect
15. C4×C11×#135C2semidirect
180. C4×#135D11semidirect
423. C11#33662semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708242
#130708072
#130707802
#130707732
#130706782
#130706712
#130705562
#130705392
C4×#668932
C4×#668922
C4×#668912
C4×#668902
#130704152
C4×C11×#1352
#3366211