Finite Group Databasebeta

← #14909342

Subgroups — #14909342

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079192C211yesmaximal, characteristic, complemented
2#13079184C211yesmaximal, characteristic, complemented
3#13070900C211yesmaximal, characteristic, complemented
4#13070879C211yesmaximal, characteristic, complemented
5#13070856C211yesmaximal, characteristic, complemented
6#13070851C211yesmaximal, characteristic, complemented
7#13070730C211yesmaximal, characteristic, complemented
8#13070728C211yesmaximal, characteristic, complemented
9#13070718C211yesmaximal, characteristic, complemented
10#13070716C211yesmaximal, characteristic, complemented
11C4×#66864C211yesmaximal, characteristic, complemented
12C4×#66891C211yesmaximal, characteristic, complemented
13C4×#66890C211yesmaximal, characteristic, complemented
14C4×#66862C211yesmaximal, characteristic, complemented
15C4×C11×D16C211yesmaximal, characteristic, complemented
16#10623088—21no—
17#10623079—21no—
18C2×C11×D16C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21#10622770C2211yescharacteristic
22#10622770C2211yescharacteristic
23#10622768C2211yescharacteristic
24#10622764C2211yescharacteristic
25C2×#66891C2211yescharacteristic
26C2×#66890C2211yescharacteristic
27C4×#4324—21no—
28C4×#4323—21no—
29C2×#66864C2211yescharacteristic
30C2×#66862C2211yescharacteristic
31C2×#66862C2211yescharacteristic
32#10622500C2211yescharacteristic
33#10622496C2211yescharacteristic
34#10622491C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622391—21no—
37#10622388—21no—
38#10622381—21no—
39#10622373—21no—
40C4×Dic44C2211yescharacteristic
41C4×D88C2211yescharacteristic
42C4×C8×D11C2211yescharacteristic
43C11×#366C2211yescharacteristic
44C11×#357C2211yescharacteristic
45C11×#357C2211yescharacteristic
46C4×C11×C16C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622200C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622143C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622140C2211yescharacteristic
53#10622140C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622128C2211yescharacteristic
57#10622127C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×#4339—41no—
60C2×C11×D8C2311yescharacteristic
61C2×C11×D8C2311yescharacteristic
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64#66993—21no—
65#66991—21no—
66#66991—21no—
67#66989—21no—
68C2×#4324—21no—
69C2×#4323—21no—
70C4×C22⋊D11—41no—
71C4×C22⋊D11—41no—
72#66979—41no—
73C2×Dic44C2311yescharacteristic
74C2×D88C2311yescharacteristic
75C2×C8×D11D411yescharacteristic
76C2×C8×D11C2311yescharacteristic
77#66950—21no—
78#66948—21no—
79#66943—21no—
80#66941—21no—
81#66938—41no—
82#66937—41no—
83#66936—41no—
84#66932—41no—
85C4×D44—21no—
86C42×D11D411yescharacteristic
87C4×Dic22—21no—
88C11×D16—22no—
89C2×C11×C16C2311yescharacteristic
90C2×C11×C16C2311yescharacteristic
91C11×#107C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#102—21no—
94C11×#102—21no—
95C4×C8×C11C2311yescharacteristic
96#66896—21no—
97#66896—21no—
98#66891—22no—
99#66890—22no—
100#66885—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66880—21no—
104C8×Dic11D411yescharacteristic
105C8×Dic11C2311yescharacteristic
106C2×C11⋊C16C2311yescharacteristic
107C2×C11⋊C16C2311yescharacteristic
108#66874—21no—
109#66873—21no—
110#66872—21no—
111#66871—21no—
112C4×C11⋊C8D411yescharacteristic
113#66864—22no—
114#66862—22no—
115#66862—22no—
116#33737—111nomaximal, Sylow
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C22×C4×C11—41no—
120C22×C4×C11—41no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125#4339—84no—
126C2×D44—21no—
127C2×D44—41no—
128C2×C4×D11—41no—
129C2×C4×D11D811yescharacteristic
130C2×C4×D11D811yescharacteristic
131C2×C4×D11C2×D411yescharacteristic
132C2×Dic22—21no—
133C2×Dic22—41no—
134C11×D8—21no—
135C11×D8—21no—
136C11×D8—21no—
137C11×D8—21no—
138C2×C8×C11C2×D411yescharacteristic
139C2×C8×C11C2411yescharacteristic
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C22⋊C4—41no—
143C11×C22⋊C4—41no—
144C42×C11C2×D411yescharacteristic
145C22⋊Dic11—41no—
146C22⋊Dic11—41no—
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149#4324—42no—
150#4323—42no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153(C2×D11)⋊C4—41no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—41no—
157C4⋊Dic11—41no—
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161C4×Dic11—41no—
162C4×Dic11D811yescharacteristic
163C4×Dic11D811yescharacteristic
164C4×Dic11C2×D411yescharacteristic
165C2×C11⋊C8C2×D411yescharacteristic
166C2×C11⋊C8C2×D411yescharacteristic
167Dic44—21no—
168Dic44—21no—
169D88—21no—
170D88—21no—
171C8×D11—21no—
172C8×D11—21no—
173C8×D11—22no—
174C11×C16—21no—
175C11×C16#4112yescomplemented
176C11⋊C16—21no—
177C11⋊C16#4112yescomplemented
178#3169—111no—
179#3168—111no—
180#2255—111no—
181#2250—111no—
182#2244—111no—
183#2243—111no—
184#2220—111no—
185#2220—111no—
186#2218—111no—
187#2218—111no—
188C4×SD32—111no—
189C4×SD32—111no—
190C4×D16—111no—
191C4×D16D1111yescharacteristic, complemented
192C4×M32—111no—
193C23×C11—41no—
194C23×C11—41no—
195C22×D11—41no—
196C22×D11C2×D811yescharacteristic
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—41no—
200D4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—82no—
204C2×C4×C11—82no—
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C2×D811yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C22⋊D11—82no—
209C22⋊D11—82no—
210C22⋊D11—82no—
211C22⋊D11—82no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11C2×D811yescharacteristic
216C2×Dic11C2×D811yescharacteristic
217C2×Dic11C2×D811yescharacteristic
218D44—41no—
219D44—41no—
220D44—82no—
221C4×D11—21no—
222C4×D11—21no—
223C4×D11—22no—
224C4×D11—41no—
225C4×D11—82no—
226Dic22—41no—
227Dic22—41no—
228Dic22—82no—
229C8×C11—21no—
230C8×C11C2×#4111yescharacteristic
231C8×C11C2×#4111yescharacteristic
232C11⋊C8—21no—
233C11⋊C8#13512yes—
234#532—221no—
235#529—221no—
236C2×SD32—111no—
237C2×SD32—111no—
238C2×D16—111no—
239C2×D16C2×D1111yescharacteristic
240C2×M32—111no—
241C2×M32—111no—
242#500—111no—
243#499—111no—
244#495—111no—
245#493—111no—
246#488—221no—
247#486—221no—
248#467—111no—
249#466—111no—
250#466—111no—
251#466—111no—
252#466—221no—
253#465—221no—
254C4×Q16—111no—
255C4×SD16—221no—
256C4×D8—111no—
257C4×D8—221no—
258C4×D8C2×D1111yescharacteristic
259C4×D8C2×D1111yescharacteristic
260C2×C4×C8—111no—
261#367—111no—
262#367—111no—
263#366—111no—
264#366C2×D1111yescharacteristic
265#358—111no—
266#358—111no—
267#357—111no—
268#357—111no—
269#357—111no—
270#357—111no—
271#357C2×D1111yescharacteristic
272#357C2×D1111yescharacteristic
273#346—111no—
274#346—111no—
275C4×C16—111no—
276C4×C16C2×D1111yescharacteristic
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—81no—
280C22×C11—81no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11C22×D811yescharacteristic
284C2×D11—21no—
285C2×D11—21no—
286C2×D11—21no—
287C2×D11—81no—
288C2×D11—81no—
289C2×D11—81no—
290C4×C11—21no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11#50912yes—
294C4×C11#53211yescharacteristic
295C4×C11C2×#13511yescharacteristic
296Dic11—21no—
297Dic11—21no—
298Dic11—21no—
299Dic11—81no—
300Dic11—81no—
301Dic11—81no—
302C2×#41—441no—
303C2×Q16—111no—
304C2×SD16—221no—
305C2×D8—111no—
306C2×D8—221no—
307C2×D8C22×D1111yescharacteristic
308C2×D8C22×D1111yescharacteristic
309C22×C8—111no—
310C22×C8—111no—
311C4⋊Q8—221no—
312#127—221no—
313#126—441no—
314#125—221no—
315#124—221no—
316#124—441no—
317#123—441no—
318C22⋊Q8—221no—
319#121—221no—
320#121—221no—
321#121—221no—
322#121—441no—
323C4×Q8—221no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—221no—
327C4×D4—441no—
328C4×D4—441no—
329#117—441no—
330C2×C42—111no—
331SD32—222no—
332SD32—222no—
333D16—22no—
334D16—222no—
335M32—222no—
336M32—222no—
337C2×C16—111no—
338C2×C16—111no—
339C2×C16C22×D1111yescharacteristic
340C2×C16C22×D1111yescharacteristic
341#107—111no—
342#107—111no—
343#107—221no—
344#107C22×D1111yescharacteristic
345#107C22×D1111yescharacteristic
346#106—221no—
347#103—221no—
348#103—221no—
349#102—21no—
350#102—21no—
351#102—221no—
352#102—221no—
353#102—221no—
354#102—221no—
355C4×C8—111no—
356C4×C8—111no—
357C4×C8—111no—
358C4×C8C22×D1111yescharacteristic
359C2×C11—161no—
360C2×C11—161no—
361C2×C11#316911yescharacteristic
362C2×C11C2×#50911yescharacteristic
363C2×C11#341411yescharacteristic
364D11—41no—
365D11—161no—
366#41—884no—
367C2×Q8—221no—
368C2×Q8—441no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—221no—
372C2×D4—441no—
373C2×D4—441no—
374C2×D4—441no—
375C2×D4—441no—
376C2×D4—441no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—111no—
380C22×C4—111no—
381C22×C4—111no—
382C22×C4—441no—
383Q16—221no—
384Q16—221no—
385SD16—442no—
386D8—21no—
387D8—21no—
388D8—21no—
389D8—21no—
390D8—221no—
391D8—221no—
392D8—442no—
393C2×C8—111no—
394C2×C8—111no—
395C2×C8—222no—
396C2×C8—221no—
397C2×C8—221no—
398C2×C8D4×D1111yescharacteristic
399C2×C8C23×D1111yescharacteristic
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—221no—
403C4⋊C4—221no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4—441no—
407C4⋊C4—441no—
408C4⋊C4—441no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C22⋊C4—441no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C42—111no—
419C42—111no—
420C42—111no—
421C42—441no—
422C42D4×D1111yescharacteristic
423C16—21no—
424C16—112no—
425C16—221no—
426C16#433912yescomplemented
427C11#3373711yescharacteristic, complemented, Sylow
428C23—41no—
429C23—41no—
430C23—111no—
431C23—441no—
432Q8—441no—
433Q8—441no—
434Q8—882no—
435D4—41no—
436D4—41no—
437D4—41no—
438D4—41no—
439D4—441no—
440D4—441no—
441D4—882no—
442D4—882no—
443D4—882no—
444D4—882no—
445D4—882no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—82no—
449C2×C4—82no—
450C2×C4—111no—
451C2×C4—111no—
452C2×C4—111no—
453C2×C4—222no—
454C2×C4—221no—
455C2×C4—221no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—882no—
461C2×C4D8×D1111yescharacteristic
462C2×C4D8×D1111yescharacteristic
463C2×C4C2×D4×D1111yescharacteristic
464C8—21no—
465C8—112no—
466C8—221no—
467C8C2×#433911yescharacteristic
468C8#41×D1111yescharacteristic
469C22—81no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22—221no—
476C22—221no—
477C22—221no—
478C22—881no—
479C22—881no—
480C22—881no—
481C22C2×D8×D1111yescharacteristic
482C4—21no—
483C4—81no—
484C4—81no—
485C4—221no—
486C4—221no—
487C4—221no—
488C4—881no—
489C4—881no—
490C4—881no—
491C4#1062252412yes—
492C4#1062307911yescharacteristic
493C4D11×#13511yescharacteristic
494C2—161no—
495C2—161no—
496C2—441no—
497C2—1761no—
498C2#1307919211yescharacteristic
499C2C2×#1062252411yescharacteristic
500C2#1308174911yescharacteristic
subgroupG/H
centerC2×C4D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×D16C2
socleC22×C11C22×D8
hypercenterC4×D16D11
hypocenterC11#33737
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×D16

Complements

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

NH ≅ G/Ntype
1. #13079192C2semidirect
2. #13079184C2semidirect
3. #13070900C2semidirect
4. #13070879C2semidirect
5. #13070856C2semidirect
6. #13070851C2semidirect
7. #13070730C2semidirect
8. #13070728C2semidirect
9. #13070718C2semidirect
10. #13070716C2semidirect
11. C4×#66864C2semidirect
12. C4×#66891C2semidirect
13. C4×#66890C2semidirect
14. C4×#66862C2semidirect
15. C4×C11×D16C2semidirect
175. C11×C16#41semidirect
177. C11⋊C16#41semidirect
191. C4×D16D11semidirect
426. C16#4339semidirect
427. C11#33737semidirect

Maximal subgroups

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

subgroupindex
#130791922
#130791842
#130709002
#130708792
#130708562
#130708512
#130707302
#130707282
#130707182
#130707162
C4×#668642
C4×#668912
C4×#668902
C4×#668622
C4×C11×D162
#3373711