Finite Group Databasebeta

← #14908841

Subgroups — #14908841

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079190C211yesmaximal, characteristic, complemented
2#135×Dic11C211yesmaximal, characteristic, complemented
3#13070808C211yesmaximal, characteristic, complemented
4#13070804C211yesmaximal, characteristic, complemented
5#13070756C211yesmaximal, characteristic, complemented
6#13070751C211yesmaximal, characteristic, complemented
7#13070654C211yesmaximal, characteristic, complemented
8#13070649C211yesmaximal, characteristic, complemented
9#13070539C211yesmaximal, characteristic, complemented
10#13070492C211yesmaximal, characteristic, complemented
11#13070489C211yesmaximal, characteristic, complemented
12#13070483C211yesmaximal, characteristic, complemented
13#13070481C211yesmaximal, characteristic, complemented
14#13070416C211yesmaximal, characteristic, complemented
15C11×#2186C211yesmaximal, characteristic, complemented
16C2×C11×#135C2211yescharacteristic
17#41×Dic11—21no—
18#10623127—21no—
19C2×C11×SD32C2211yescharacteristic
20C2×C11×D16C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622846—21no—
23Q16×Dic11C2211yescharacteristic
24Q16×Dic11C2211yescharacteristic
25C2×#66892C2211yescharacteristic
26SD16×Dic11—21no—
27SD16×Dic11—21no—
28#10622764C2211yescharacteristic
29D8×Dic11C2211yescharacteristic
30D8×Dic11C2211yescharacteristic
31D8×Dic11C2211yescharacteristic
32C2×#66890C2211yescharacteristic
33#10622728C2211yescharacteristic
34#10622719C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622651—21no—
37#10622487C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622373—21no—
40#10622369—21no—
41C11×#358C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×C22⋊C16C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622200C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51#10622143C2211yescharacteristic
52#10622142C2211yescharacteristic
53#10622140C2211yescharacteristic
54#10622140C2211yescharacteristic
55Dic11⋊C16C2211yescharacteristic
56Dic11⋊C16C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622127C2211yescharacteristic
59C2×C11×#41—21no—
60C2×#4341—41no—
61C11×#135—22no—
62C11×#135—22no—
63C2×C11×Q16C2311yescharacteristic
64C2×C11×SD16—21no—
65C2×C11×D8C2311yescharacteristic
66C2×C11×D8C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#121—21no—
69Q8×Dic11—21no—
70Q8×Dic11—21no—
71#66993—21no—
72#66992—41no—
73D4×Dic11—21no—
74D4×Dic11—21no—
75D4×Dic11—21no—
76D4×Dic11—41no—
77D4×Dic11—41no—
78C2×#4323—21no—
79#66983—21no—
80#66979—21no—
81#66979—41no—
82C2×C4×Dic11—41no—
83C2×C4×Dic11D411yescharacteristic
84C22×C11⋊C8D411yescharacteristic
85C2×D88C2311yescharacteristic
86#66946—21no—
87#66941—21no—
88#66938—41no—
89(C22⋊D11)⋊C4—41no—
90C11×SD32—22no—
91C11×D16—22no—
92C2×C11×C16C2311yescharacteristic
93C2×C11×C16C2311yescharacteristic
94C11×#107C2311yescharacteristic
95C11×#102—21no—
96#66899—21no—
97#66899—21no—
98#66896—21no—
99#66896—21no—
100#66896—21no—
101#66892—22no—
102#66890—22no—
103#66885—21no—
104#66882C2311yescharacteristic
105#66882C2311yescharacteristic
106#66882C2311yescharacteristic
107#66881—21no—
108C8×Dic11D411yescharacteristic
109C8×Dic11D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C8×Dic11C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113C2×C11⋊C16C2311yescharacteristic
114#66873—21no—
115#66871—21no—
116#33675—111nomaximal, Sylow
117C11×#41—24no—
118C11×#41—42no—
119C2×Q8×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—21no—
122C2×D4×C11—41no—
123C2×D4×C11—41no—
124C22×C4×C11—41no—
125C22×C4×C11C2×D411yescharacteristic
126C2×C22⋊D11—41no—
127C2×C22⋊D11—41no—
128C2×C22⋊D11—41no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11D811yescharacteristic
133C22×Dic11D811yescharacteristic
134#4341—84no—
135C2×D44—21no—
136C2×C4×D11—41no—
137C2×Dic22—41no—
138C11×Q16—21no—
139C11×Q16#4112yescomplemented
140C11×SD16—24no—
141C11×D8—21no—
142C11×D8—21no—
143C11×D8—21no—
144C11×D8#4112yescomplemented
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C11×C4⋊C4—21no—
150C11×C22⋊C4—41no—
151C22⋊Dic11—41no—
152C22⋊Dic11—41no—
153C22⋊Dic11—41no—
154C22⋊Dic11—41no—
155#4323—42no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158C4⋊Dic11—21no—
159C4⋊Dic11—21no—
160C4⋊Dic11—21no—
161C4⋊Dic11—41no—
162C4⋊Dic11—41no—
163Dic11⋊C4—41no—
164C4×Dic11—41no—
165C4×Dic11—41no—
166C4×Dic11—41no—
167C4×Dic11D811yescharacteristic
168C4×Dic11D811yescharacteristic
169C4×Dic11C2×D411yescharacteristic
170C4×Dic11C2×D411yescharacteristic
171C2×C11⋊C8—41no—
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174D88—21no—
175D88—21no—
176C11×C16—21no—
177C11×C16—21no—
178C11⋊C16—21no—
179C11⋊C16—21no—
180#3169—111no—
181C4×#135—111no—
182#2234—111no—
183#2234—111no—
184#2225—111no—
185#2224—111no—
186#2207—111no—
187#2206—111no—
188#2186—111no—
189#2186D1111yescharacteristic, complemented
190#2177—111no—
191#2177—111no—
192#2175—111no—
193#2175—111no—
194#2163—111no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11C2×D811yescharacteristic
198C22×D11—41no—
199Q8×C11—22no—
200Q8×C11—41no—
201D4×C11—22no—
202D4×C11—44no—
203D4×C11—41no—
204D4×C11—41no—
205D4×C11—41no—
206D4×C11—82no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—44no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—82no—
215C22⋊D11—82no—
216C22⋊D11—82no—
217C2×Dic11—22no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—82no—
223C2×Dic11—82no—
224C2×Dic11—82no—
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228C2×Dic11C2×D811yescharacteristic
229D44—41no—
230D44—41no—
231C4×D11—82no—
232Dic22—82no—
233C8×C11—21no—
234C8×C11C2×#4111yescharacteristic
235C8×C11C2×#4111yescharacteristic
236C11⋊C8—21no—
237C11⋊C8—21no—
238C2×#135C2×D1111yescharacteristic
239#532—221no—
240C4×#41—221no—
241C2×SD32—111no—
242C2×SD32C2×D1111yescharacteristic
243C2×D16—111no—
244C2×D16C2×D1111yescharacteristic
245#500—111no—
246#493—111no—
247#486—221no—
248#466—111no—
249#466—221no—
250#466C2×D1111yescharacteristic
251C4×Q16—111no—
252C4×Q16—111no—
253C4×SD16—221no—
254C4×SD16—221no—
255C4×D8—111no—
256C4×D8—111no—
257C4×D8—111no—
258C4×D8—111no—
259C4×D8—221no—
260#427—111no—
261#416—221no—
262C2×C4×C8—111no—
263#367—111no—
264#367—111no—
265#366—111no—
266#366—111no—
267C4⋊C16—111no—
268C4⋊C16—111no—
269#358—111no—
270#358C2×D1111yescharacteristic
271#357—111no—
272#357—111no—
273#357—111no—
274#357—111no—
275#357—111no—
276#357C2×D1111yescharacteristic
277C22⋊C16—111no—
278C22⋊C16C2×D1111yescharacteristic
279#346—111no—
280#346—111no—
281C22×C11—21no—
282C22×C11—21no—
283C22×C11—21no—
284C22×C11—42no—
285C22×C11—81no—
286C22×C11—81no—
287C22×C11—81no—
288C22×C11—81no—
289C22×C11—81no—
290C22×C11C22×D811yescharacteristic
291C2×D11—81no—
292C2×D11—81no—
293C2×D11—81no—
294C4×C11—21no—
295C4×C11—42no—
296C4×C11—81no—
297C4×C11#52511yescharacteristic
298C4×C11#57511yescharacteristic
299Dic11—21no—
300Dic11—21no—
301Dic11—21no—
302Dic11—81no—
303Dic11—81no—
304Dic11—81no—
305Dic11#50912yes—
306C2×#41—21no—
307C2×#41—441no—
308#135—22no—
309#135—22no—
310C2×Q16C22×D1111yescharacteristic
311C2×SD16—21no—
312C2×D8—111no—
313C2×D8—221no—
314C2×D8C22×D1111yescharacteristic
315C2×D8C22×D1111yescharacteristic
316C22×C8—111no—
317C22×C8C22×D1111yescharacteristic
318C4⋊Q8—221no—
319#127—221no—
320#124—441no—
321#121—21no—
322#121—221no—
323#121—441no—
324C4×Q8—221no—
325C4×Q8—221no—
326C4×D4—221no—
327C4×D4—221no—
328C4×D4—221no—
329C4×D4—221no—
330C4×D4—441no—
331C4×D4—441no—
332C4×D4—441no—
333#117—221no—
334#117—441no—
335C2×C42—111no—
336C2×C42—441no—
337SD32—22no—
338SD32—222no—
339D16—22no—
340D16—222no—
341C2×C16—111no—
342C2×C16—111no—
343C2×C16C22×D1111yescharacteristic
344C2×C16C22×D1111yescharacteristic
345#107—111no—
346#107—111no—
347#107—111no—
348#107—221no—
349#107C22×D1111yescharacteristic
350#106—221no—
351#103—221no—
352#103—221no—
353#102—21no—
354#102—221no—
355#102—221no—
356#102—221no—
357#102—221no—
358#102—221no—
359C4×C8—111no—
360C4×C8—111no—
361C4×C8—111no—
362C4×C8—111no—
363C2×C11—41no—
364C2×C11—82no—
365C2×C11—161no—
366C2×C11#310011yescharacteristic
367C2×C11C2×#50911yescharacteristic
368C2×C11#341411yescharacteristic
369D11—161no—
370#41—24no—
371#41—42no—
372#41—884no—
373C2×Q8—21no—
374C2×Q8—441no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—221no—
380C2×D4—441no—
381C2×D4—441no—
382C2×D4—441no—
383C22×C4—41no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4D4×D1111yescharacteristic
391Q16—21no—
392Q16#434112yescomplemented
393SD16—24no—
394D8—21no—
395D8—21no—
396D8—21no—
397D8—221no—
398D8—221no—
399D8—442no—
400D8#434112yescomplemented
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—111no—
404C2×C8—111no—
405C2×C8—441no—
406C2×C8D4×D1111yescharacteristic
407C2×C8C23×D1111yescharacteristic
408C4⋊C4—21no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C22⋊C4—41no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—441no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C42—111no—
423C42—111no—
424C42—111no—
425C42—111no—
426C42—441no—
427C42—441no—
428C42—441no—
429C16—21no—
430C16—21no—
431C16—221no—
432C16—221no—
433C11#3367511yescharacteristic, complemented, Sylow
434C23—41no—
435C23—41no—
436C23—441no—
437C23D8×D1111yescharacteristic
438Q8—22no—
439Q8—41no—
440Q8—882no—
441D4—22no—
442D4—44no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—82no—
447D4—441no—
448D4—441no—
449D4—882no—
450D4—882no—
451D4—882no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—44no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—111no—
458C2×C4—111no—
459C2×C4—111no—
460C2×C4—111no—
461C2×C4—222no—
462C2×C4—441no—
463C2×C4—441no—
464C2×C4—441no—
465C2×C4—441no—
466C2×C4—882no—
467C2×C4—882no—
468C2×C4—882no—
469C2×C4—882no—
470C2×C4D8×D1111yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C8—21no—
473C8—221no—
474C8—221no—
475C8C2×#434111yescharacteristic
476C8C2×#434111yescharacteristic
477C22—21no—
478C22—21no—
479C22—21no—
480C22—42no—
481C22—81no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—881no—
487C22—881no—
488C22—881no—
489C22C2×D8×D1111yescharacteristic
490C4—21no—
491C4—42no—
492C4—81no—
493C4—112no—
494C4—221no—
495C4—221no—
496C4—221no—
497C4—881no—
498C4—881no—
499C4—881no—
500C4#1062311711yescharacteristic
501C4#1062330411yescharacteristic
502C2—41no—
503C2—82no—
504C2—161no—
505C2—1761no—
506C2#1307861111yescharacteristic
507C2D11×#50911yescharacteristic
508C2#1308174911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2186C2
socleC22×C11C22×D8
hypercenter#2186D11
hypocenterC11#33675
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2186

Complements

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

NH ≅ G/Ntype
1. #13079190C2semidirect
2. #135×Dic11C2semidirect
3. #13070808C2semidirect
4. #13070804C2semidirect
5. #13070756C2semidirect
6. #13070751C2semidirect
7. #13070654C2semidirect
8. #13070649C2semidirect
9. #13070539C2semidirect
10. #13070492C2semidirect
11. #13070489C2semidirect
12. #13070483C2semidirect
13. #13070481C2semidirect
14. #13070416C2semidirect
15. C11×#2186C2semidirect
139. C11×Q16#41semidirect
144. C11×D8#41semidirect
189. #2186D11semidirect
392. Q16#4341semidirect
400. D8#4341semidirect
433. C11#33675semidirect

Maximal subgroups

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

subgroupindex
#130791902
#135×Dic112
#130708082
#130708042
#130707562
#130707512
#130706542
#130706492
#130705392
#130704922
#130704892
#130704832
#130704812
#130704162
C11×#21862
#3367511